Subgroups — C₂₃×#61172 #19208798

Order 5888.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3488	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3317	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3316	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#556	C₂²	1	2	yes	complemented
32	C₂₃×#554	C₂²	1	2	yes	complemented
33	C₂₃×#552	—	2	2	no	—
34	C₂₃×#552	C₂²	1	2	yes	complemented
35	C₂₃×#552	C₂²	1	2	yes	complemented
36	C₂₃×#551	—	2	2	no	—
37	C₂₃×#550	C₂²	1	2	yes	—
38	C₂₃×#548	C₂²	1	2	yes	—
39	C₂₃×#546	—	2	2	no	—
40	C₂₃×#546	C₂²	1	2	yes	—
41	D₄²×C₂₃	—	2	2	no	—
42	D₄²×C₂₃	C₂²	1	2	yes	—
43	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#541	—	2	1	no	—
46	C₂₃×#537	—	2	1	no	—
47	C₂₃×#537	C₂²	1	1	yes	characteristic
48	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#535	—	2	1	no	—
50	C₂₃×#535	C₂²	1	1	yes	characteristic
51	C₂₃×#533	—	2	1	no	—
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#525	—	2	1	no	—
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂₃×#121	—	2	1	no	—
57	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#490	C₂²	1	2	yes	complemented
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#486	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#483	C₂²	1	2	yes	complemented
68	C₂₃×#482	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	complemented
70	C₂₃×#482	C₂²	1	2	yes	complemented
71	C₂₃×#481	C₂²	1	2	yes	complemented
72	C₂₃×#481	C₂²	1	2	yes	complemented
73	C₂₃×#480	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#478	C₂²	1	2	yes	complemented
76	C₂₃×#476	C₂²	1	2	yes	complemented
77	C₂₃×#475	C₂²	1	2	yes	complemented
78	C₂₃×#470	C₂²	1	2	yes	complemented
79	C₂₃×#468	C₂²	1	2	yes	complemented
80	C₂₃×#467	C₂²	1	2	yes	complemented
81	C₂₃×#465	C₂²	1	2	yes	complemented
82	C₂₃×#465	C₂²	1	2	yes	complemented
83	C₂₃×#465	C₂²	1	2	yes	complemented
84	C₂₃×#465	C₂²	1	2	yes	complemented
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#464	C₂²	1	2	yes	complemented
87	C₂₃×#464	C₂²	1	2	yes	complemented
88	C₂₃×#460	C₂²	1	2	yes	complemented
89	C₂₃×#460	C₂²	1	2	yes	complemented
90	C₂₃×#452	C₂²	1	2	yes	complemented
91	C₂₃×#452	C₂²	1	2	yes	complemented
92	C₂₃×#452	C₂²	1	2	yes	complemented
93	C₂₃×#452	C₂²	1	2	yes	complemented
94	C₂₃×#451	C₂²	1	2	yes	complemented
95	C₂₃×#450	C₂²	1	2	yes	complemented
96	C₂₃×#450	C₂²	1	2	yes	complemented
97	C₂₃×#450	C₂²	1	2	yes	complemented
98	C₂₃×#441	C₂²	1	2	yes	complemented
99	C₂₃×#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
102	C₂₃×#435	C₂²	1	2	yes	complemented
103	C₂₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
105	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#418	C₂²	1	2	yes	complemented
113	C₂₃×#417	C₂²	1	1	yes	characteristic
114	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#417	C₂²	1	2	yes	complemented
116	C₂₃×#416	C₂²	1	1	yes	characteristic
117	C₂₃×#416	C₂²	1	1	yes	characteristic
118	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#416	C₂²	1	2	yes	complemented
121	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×H(5,𝔽₂)	—	2	4	no	—
136	C₂₃×H(5,𝔽₂)	—	4	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	1	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	4	no	—
141	C₂×#41×C₂₃	—	4	2	no	—
142	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₂₃	C₂³	1	2	yes	—
144	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×D₄×C₂₃	—	2	1	no	—
151	C₂²×D₄×C₂₃	—	2	1	no	—
152	C₂²×D₄×C₂₃	—	2	1	no	—
153	C₂²×D₄×C₂₃	—	2	2	no	—
154	C₂²×D₄×C₂₃	—	2	2	no	—
155	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₂₃	—	2	1	no	—
159	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#137	—	2	4	no	—
161	C₂₃×#137	—	4	2	no	—
162	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₃	—	4	2	no	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
169	C₂₃×#131	—	4	2	no	—
170	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₂₃	—	4	2	no	—
174	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
181	C₂₃×C₄⋊Q₈	—	2	1	no	—
182	C₂₃×C₄⋊Q₈	—	2	1	no	—
183	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₂₃×#127	—	2	2	no	—
185	C₂₃×#127	C₂³	1	2	yes	—
186	C₂₃×#126	—	2	2	no	—
187	C₂₃×#126	—	2	2	no	—
188	C₂₃×#126	—	2	2	no	—
189	C₂₃×#126	—	2	2	no	—
190	C₂₃×#125	—	2	2	no	—
191	C₂₃×#125	—	2	2	no	—
192	C₂₃×#125	—	2	2	no	—
193	C₂₃×#125	—	2	1	no	—
194	C₂₃×#125	C₂³	1	2	yes	—
195	C₂₃×#124	—	2	2	no	—
196	C₂₃×#124	—	2	1	no	—
197	C₂₃×#124	—	2	2	no	—
198	C₂₃×#124	C₂³	1	2	yes	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	D₄	1	2	yes	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	1	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	1	no	—
223	C₂₃×#121	—	2	1	no	—
224	C₂₃×#121	—	2	1	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	—	2	2	no	—
227	C₂₃×#121	—	2	2	no	—
228	C₂₃×#121	—	2	2	no	—
229	C₂₃×#121	D₄	1	1	yes	characteristic
230	C₂₃×#121	D₄	1	1	yes	characteristic
231	C₂₃×#121	C₂³	1	2	yes	—
232	C₂₃×#121	C₂³	1	2	yes	—
233	C₂₃×#121	C₂³	1	2	yes	—
234	C₂₃×#120	—	2	2	no	—
235	C₂₃×#120	—	2	2	no	—
236	C₂₃×#120	—	2	2	no	—
237	C₂₃×#120	—	2	2	no	—
238	C₂₃×#120	D₄	1	2	yes	—
239	C₄×Q₈×C₂₃	—	2	1	no	—
240	C₄×Q₈×C₂₃	—	2	2	no	—
241	C₄×Q₈×C₂₃	—	2	1	no	—
242	C₄×Q₈×C₂₃	—	2	1	no	—
243	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	2	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	—	2	2	no	—
251	C₄×D₄×C₂₃	—	2	2	no	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₂₃×#117	—	2	1	no	—
256	C₂₃×#117	—	2	1	no	—
257	C₂₃×#117	—	2	1	no	—
258	C₂₃×#117	—	2	2	no	—
259	C₂₃×#117	—	2	2	no	—
260	C₂₃×#117	—	2	2	no	—
261	C₂₃×#117	C₂³	1	1	yes	characteristic
262	C₂₃×#117	C₂³	1	2	yes	—
263	C₂₃×#117	C₂³	1	1	yes	characteristic
264	C₂₃×#117	C₂³	1	1	yes	characteristic
265	C₂₃×#117	C₂³	1	1	yes	characteristic
266	C₂₃×#117	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
276	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
277	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
278	C₂×C₄²×C₂₃	—	2	1	no	—
279	C₂₃×#107	C₂³	1	2	yes	—
280	C₂₃×#107	C₂³	1	2	yes	—
281	C₂₃×#106	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×#106	C₂³	1	2	yes	—
285	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	1	yes	characteristic
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	1	yes	characteristic
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	1	yes	characteristic
305	C₂₃×#102	C₂³	1	1	yes	characteristic
306	C₂₃×#102	C₂³	1	1	yes	characteristic
307	C₂₃×#102	C₂³	1	1	yes	characteristic
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×#102	C₂³	1	2	yes	—
310	C₂₃×#102	C₂³	1	2	yes	—
311	C₂₃×#102	C₂³	1	2	yes	—
312	C₂₃×#102	C₂³	1	2	yes	—
313	C₂₃×#102	C₂³	1	2	yes	—
314	C₂₃×#102	C₂³	1	2	yes	—
315	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₂₃×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₂₃	C₂³	1	2	yes	—
321	C₂⁴×C₂₃	—	2	1	no	—
322	C₂⁴×C₂₃	—	2	2	no	—
323	C₂⁴×C₂₃	—	2	1	no	—
324	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
325	#41×C₂₃	—	2	2	no	—
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	2	no	—
328	#41×C₂₃	—	2	2	no	—
329	#41×C₂₃	—	2	4	no	—
330	#41×C₂₃	—	2	2	no	—
331	#41×C₂₃	—	2	2	no	—
332	#41×C₂₃	—	2	2	no	—
333	#41×C₂₃	—	4	4	no	—
334	#41×C₂₃	—	4	1	no	—
335	#41×C₂₃	—	4	1	no	—
336	#41×C₂₃	—	4	2	no	—
337	#41×C₂₃	—	4	4	no	—
338	#41×C₂₃	—	4	4	no	—
339	#41×C₂₃	#41	1	4	yes	—
340	C₂×Q₈×C₂₃	—	2	1	no	—
341	C₂×Q₈×C₂₃	—	2	1	no	—
342	C₂×Q₈×C₂₃	—	2	2	no	—
343	C₂×Q₈×C₂₃	—	2	2	no	—
344	C₂×Q₈×C₂₃	—	2	2	no	—
345	C₂×Q₈×C₂₃	—	2	2	no	—
346	C₂×Q₈×C₂₃	—	4	1	no	—
347	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
350	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₂₃	—	2	1	no	—
352	C₂×D₄×C₂₃	—	2	2	no	—
353	C₂×D₄×C₂₃	—	2	4	no	—
354	C₂×D₄×C₂₃	—	2	2	no	—
355	C₂×D₄×C₂₃	—	2	1	no	—
356	C₂×D₄×C₂₃	—	2	1	no	—
357	C₂×D₄×C₂₃	—	2	2	no	—
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	2	no	—
360	C₂×D₄×C₂₃	—	2	2	no	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	2	no	—
366	C₂×D₄×C₂₃	—	2	2	no	—
367	C₂×D₄×C₂₃	—	2	2	no	—
368	C₂×D₄×C₂₃	—	4	1	no	—
369	C₂×D₄×C₂₃	—	4	2	no	—
370	C₂×D₄×C₂₃	—	4	4	no	—
371	C₂×D₄×C₂₃	—	4	8	no	—
372	C₂×D₄×C₂₃	—	4	4	no	—
373	C₂×D₄×C₂₃	—	8	4	no	—
374	C₂×D₄×C₂₃	—	8	2	no	—
375	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
377	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
379	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
380	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	2	no	—
384	C₂²×C₄×C₂₃	—	2	2	no	—
385	C₂²×C₄×C₂₃	—	2	1	no	—
386	C₂²×C₄×C₂₃	—	2	1	no	—
387	C₂²×C₄×C₂₃	—	2	1	no	—
388	C₂²×C₄×C₂₃	—	2	1	no	—
389	C₂²×C₄×C₂₃	—	2	1	no	—
390	C₂²×C₄×C₂₃	—	2	1	no	—
391	C₂²×C₄×C₂₃	—	2	2	no	—
392	C₂²×C₄×C₂₃	—	2	1	no	—
393	C₂²×C₄×C₂₃	—	2	1	no	—
394	C₂²×C₄×C₂₃	—	2	2	no	—
395	C₂²×C₄×C₂₃	—	2	1	no	—
396	C₂²×C₄×C₂₃	—	2	2	no	—
397	C₂²×C₄×C₂₃	—	4	4	no	—
398	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	Q₁₆×C₂₃	—	2	4	no	—
406	Q₁₆×C₂₃	—	4	2	no	—
407	SD₁₆×C₂₃	—	2	4	no	—
408	SD₁₆×C₂₃	—	4	2	no	—
409	SD₁₆×C₂₃	—	4	2	no	—
410	SD₁₆×C₂₃	—	4	2	no	—
411	M₁₆×C₂₃	—	2	2	no	—
412	M₁₆×C₂₃	—	2	2	no	—
413	M₁₆×C₂₃	—	4	2	no	—
414	C₂×C₈×C₂₃	—	2	2	no	—
415	C₂×C₈×C₂₃	—	2	2	no	—
416	C₂×C₈×C₂₃	—	4	1	no	—
417	C₂×C₈×C₂₃	—	4	1	no	—
418	C₂×C₈×C₂₃	—	4	1	no	—
419	C₂×C₈×C₂₃	—	4	1	no	—
420	C₂×C₈×C₂₃	—	4	2	no	—
421	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
424	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
425	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	—	2	2	no	—
435	C₄⋊C₄×C₂₃	—	2	2	no	—
436	C₄⋊C₄×C₂₃	—	2	2	no	—
437	C₄⋊C₄×C₂₃	—	2	2	no	—
438	C₄⋊C₄×C₂₃	—	2	2	no	—
439	C₄⋊C₄×C₂₃	—	2	2	no	—
440	C₄⋊C₄×C₂₃	—	2	2	no	—
441	C₄⋊C₄×C₂₃	—	2	2	no	—
442	C₄⋊C₄×C₂₃	—	2	2	no	—
443	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
446	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
447	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
453	C₂²⋊C₄×C₂₃	—	2	1	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	2	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	2	no	—
462	C₂²⋊C₄×C₂₃	—	2	2	no	—
463	C₂²⋊C₄×C₂₃	—	2	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	—	2	2	no	—
466	C₂²⋊C₄×C₂₃	—	2	2	no	—
467	C₂²⋊C₄×C₂₃	—	2	2	no	—
468	C₂²⋊C₄×C₂₃	—	2	2	no	—
469	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
472	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
473	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
474	C₄²×C₂₃	—	2	1	no	—
475	C₄²×C₂₃	—	2	1	no	—
476	C₄²×C₂₃	—	2	1	no	—
477	C₄²×C₂₃	—	2	1	no	—
478	C₄²×C₂₃	—	2	2	no	—
479	C₄²×C₂₃	—	2	2	no	—
480	C₄²×C₂₃	—	2	2	no	—
481	C₄²×C₂₃	—	2	2	no	—
482	C₄²×C₂₃	C₂⁴	1	2	yes	—
483	#61172	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂³×C₂₃	—	2	2	no	—
485	C₂³×C₂₃	—	2	2	no	—
486	C₂³×C₂₃	—	2	1	no	—
487	C₂³×C₂₃	—	2	2	no	—
488	C₂³×C₂₃	—	2	1	no	—
489	C₂³×C₂₃	—	4	1	no	—
490	C₂³×C₂₃	—	4	2	no	—
491	C₂³×C₂₃	—	4	4	no	—
492	C₂³×C₂₃	—	4	2	no	—
493	C₂³×C₂₃	—	4	2	no	—
494	C₂³×C₂₃	—	8	1	no	—
495	C₂³×C₂₃	—	8	1	no	—
496	C₂³×C₂₃	—	8	2	no	—
497	C₂³×C₂₃	—	8	1	no	—
498	C₂³×C₂₃	—	8	2	no	—
499	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
500	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
501	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
502	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
503	Q₈×C₂₃	—	2	2	no	—
504	Q₈×C₂₃	—	2	1	no	—
505	Q₈×C₂₃	—	2	2	no	—
506	Q₈×C₂₃	—	2	1	no	—
507	Q₈×C₂₃	—	2	2	no	—
508	Q₈×C₂₃	—	2	1	no	—
509	Q₈×C₂₃	—	4	2	no	—
510	Q₈×C₂₃	—	4	2	no	—
511	Q₈×C₂₃	—	8	2	no	—
512	Q₈×C₂₃	C₂×#41	1	2	yes	—
513	D₄×C₂₃	—	2	4	no	—
514	D₄×C₂₃	—	2	4	no	—
515	D₄×C₂₃	—	2	4	no	—
516	D₄×C₂₃	—	2	2	no	—
517	D₄×C₂₃	—	2	2	no	—
518	D₄×C₂₃	—	2	1	no	—
519	D₄×C₂₃	—	2	1	no	—
520	D₄×C₂₃	—	2	2	no	—
521	D₄×C₂₃	—	2	1	no	—
522	D₄×C₂₃	—	4	2	no	—
523	D₄×C₂₃	—	4	4	no	—
524	D₄×C₂₃	—	4	2	no	—
525	D₄×C₂₃	—	4	4	no	—
526	D₄×C₂₃	—	4	2	no	—
527	D₄×C₂₃	—	4	2	no	—
528	D₄×C₂₃	—	4	2	no	—
529	D₄×C₂₃	—	4	4	no	—
530	D₄×C₂₃	—	4	2	no	—
531	D₄×C₂₃	—	8	2	no	—
532	D₄×C₂₃	—	8	2	no	—
533	D₄×C₂₃	—	8	2	no	—
534	D₄×C₂₃	—	8	2	no	—
535	D₄×C₂₃	C₂×#41	1	2	yes	—
536	C₂×C₄×C₂₃	—	2	2	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	2	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	4	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	2	no	—
544	C₂×C₄×C₂₃	—	2	1	no	—
545	C₂×C₄×C₂₃	—	2	1	no	—
546	C₂×C₄×C₂₃	—	2	2	no	—
547	C₂×C₄×C₂₃	—	2	1	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	1	no	—
550	C₂×C₄×C₂₃	—	2	2	no	—
551	C₂×C₄×C₂₃	—	2	1	no	—
552	C₂×C₄×C₂₃	—	2	2	no	—
553	C₂×C₄×C₂₃	—	2	2	no	—
554	C₂×C₄×C₂₃	—	2	1	no	—
555	C₂×C₄×C₂₃	—	4	2	no	—
556	C₂×C₄×C₂₃	—	4	4	no	—
557	C₂×C₄×C₂₃	—	4	2	no	—
558	C₂×C₄×C₂₃	—	4	2	no	—
559	C₂×C₄×C₂₃	—	4	2	no	—
560	C₂×C₄×C₂₃	—	4	2	no	—
561	C₂×C₄×C₂₃	—	4	2	no	—
562	C₂×C₄×C₂₃	—	8	2	no	—
563	C₂×C₄×C₂₃	—	8	2	no	—
564	C₂×C₄×C₂₃	—	8	1	no	—
565	C₂×C₄×C₂₃	—	8	1	no	—
566	C₂×C₄×C₂₃	—	8	1	no	—
567	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
568	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
574	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
575	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
576	C₈×C₂₃	—	2	2	no	—
577	C₈×C₂₃	—	2	1	no	—
578	C₈×C₂₃	—	2	1	no	—
579	C₈×C₂₃	—	2	1	no	—
580	C₈×C₂₃	—	2	1	no	—
581	C₈×C₂₃	—	2	2	no	—
582	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3488	C₂×C₂₃	1	1	yes	characteristic
584	#3317	C₂×C₂₃	1	2	yes	complemented
585	#3316	C₂×C₂₃	1	2	yes	complemented
586	#3311	C₂×C₂₃	1	2	yes	complemented
587	#3310	C₂×C₂₃	1	2	yes	complemented
588	#3304	C₂×C₂₃	1	2	yes	complemented
589	#3300	C₂×C₂₃	1	2	yes	complemented
590	#3296	C₂×C₂₃	1	2	yes	complemented
591	#3295	C₂×C₂₃	1	2	yes	complemented
592	#3136	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3099	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3084	C₂×C₂₃	1	1	yes	characteristic, complemented
596	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
597	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3043	C₂×C₂₃	1	1	yes	characteristic, complemented
599	#3009	C₂×C₂₃	1	1	yes	characteristic, complemented
600	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
601	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
602	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
603	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
604	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	2	1	no	—
607	C₂²×C₂₃	—	2	1	no	—
608	C₂²×C₂₃	—	2	1	no	—
609	C₂²×C₂₃	—	2	2	no	—
610	C₂²×C₂₃	—	2	1	no	—
611	C₂²×C₂₃	—	2	1	no	—
612	C₂²×C₂₃	—	2	2	no	—
613	C₂²×C₂₃	—	2	2	no	—
614	C₂²×C₂₃	—	2	2	no	—
615	C₂²×C₂₃	—	2	1	no	—
616	C₂²×C₂₃	—	4	4	no	—
617	C₂²×C₂₃	—	4	1	no	—
618	C₂²×C₂₃	—	4	1	no	—
619	C₂²×C₂₃	—	4	1	no	—
620	C₂²×C₂₃	—	4	2	no	—
621	C₂²×C₂₃	—	4	1	no	—
622	C₂²×C₂₃	—	4	2	no	—
623	C₂²×C₂₃	—	4	2	no	—
624	C₂²×C₂₃	—	4	1	no	—
625	C₂²×C₂₃	—	8	4	no	—
626	C₂²×C₂₃	—	16	2	no	—
627	C₂²×C₂₃	—	16	4	no	—
628	C₂²×C₂₃	#546	1	2	yes	—
629	C₂²×C₂₃	#577	1	2	yes	—
630	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
631	C₄×C₂₃	—	2	2	no	—
632	C₄×C₂₃	—	2	1	no	—
633	C₄×C₂₃	—	2	1	no	—
634	C₄×C₂₃	—	2	2	no	—
635	C₄×C₂₃	—	2	2	no	—
636	C₄×C₂₃	—	2	2	no	—
637	C₄×C₂₃	—	4	1	no	—
638	C₄×C₂₃	—	4	2	no	—
639	C₄×C₂₃	—	4	1	no	—
640	C₄×C₂₃	—	4	1	no	—
641	C₄×C₂₃	—	4	2	no	—
642	C₄×C₂₃	—	4	1	no	—
643	C₄×C₂₃	—	4	1	no	—
644	C₄×C₂₃	—	4	2	no	—
645	C₄×C₂₃	#546	1	2	yes	—
646	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
647	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
649	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
650	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
651	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#556	C₂²×C₂₃	1	2	yes	complemented
656	#554	C₂²×C₂₃	1	2	yes	complemented
657	#552	—	2	2	no	—
658	#552	C₂²×C₂₃	1	2	yes	complemented
659	#552	C₂²×C₂₃	1	2	yes	complemented
660	#551	—	2	2	no	—
661	#550	C₂²×C₂₃	1	2	yes	—
662	#548	C₂²×C₂₃	1	2	yes	—
663	#546	—	2	2	no	—
664	#546	C₂²×C₂₃	1	2	yes	—
665	D₄²	—	2	2	no	—
666	D₄²	C₂²×C₂₃	1	2	yes	—
667	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	#542	—	2	1	no	—
669	#541	—	2	1	no	—
670	#537	—	2	1	no	—
671	#537	C₂²×C₂₃	1	1	yes	characteristic
672	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	#535	—	2	1	no	—
674	#535	C₂²×C₂₃	1	1	yes	characteristic
675	#533	—	2	1	no	—
676	#529	—	2	1	no	—
677	#525	—	2	1	no	—
678	#525	C₂²×C₂₃	1	1	yes	characteristic
679	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	C₂×#121	—	2	1	no	—
681	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
682	#520	C₂²×C₂₃	1	1	yes	characteristic
683	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	#490	C₂²×C₂₃	1	2	yes	complemented
687	#489	C₂²×C₂₃	1	2	yes	complemented
688	#488	C₂²×C₂₃	1	2	yes	complemented
689	#486	C₂²×C₂₃	1	2	yes	complemented
690	#485	C₂²×C₂₃	1	2	yes	complemented
691	#483	C₂²×C₂₃	1	2	yes	complemented
692	#482	C₂²×C₂₃	1	2	yes	complemented
693	#482	C₂²×C₂₃	1	2	yes	complemented
694	#482	C₂²×C₂₃	1	2	yes	complemented
695	#481	C₂²×C₂₃	1	2	yes	complemented
696	#481	C₂²×C₂₃	1	2	yes	complemented
697	#480	C₂²×C₂₃	1	2	yes	complemented
698	#479	C₂²×C₂₃	1	2	yes	complemented
699	#478	C₂²×C₂₃	1	2	yes	complemented
700	#476	C₂²×C₂₃	1	2	yes	complemented
701	#475	C₂²×C₂₃	1	2	yes	complemented
702	#470	C₂²×C₂₃	1	2	yes	complemented
703	#468	C₂²×C₂₃	1	2	yes	complemented
704	#467	C₂²×C₂₃	1	2	yes	complemented
705	#465	C₂²×C₂₃	1	2	yes	complemented
706	#465	C₂²×C₂₃	1	2	yes	complemented
707	#465	C₂²×C₂₃	1	2	yes	complemented
708	#465	C₂²×C₂₃	1	2	yes	complemented
709	#465	C₂²×C₂₃	1	2	yes	complemented
710	#464	C₂²×C₂₃	1	2	yes	complemented
711	#464	C₂²×C₂₃	1	2	yes	complemented
712	#460	C₂²×C₂₃	1	2	yes	complemented
713	#460	C₂²×C₂₃	1	2	yes	complemented
714	#452	C₂²×C₂₃	1	2	yes	complemented
715	#452	C₂²×C₂₃	1	2	yes	complemented
716	#452	C₂²×C₂₃	1	2	yes	complemented
717	#452	C₂²×C₂₃	1	2	yes	complemented
718	#451	C₂²×C₂₃	1	2	yes	complemented
719	#450	C₂²×C₂₃	1	2	yes	complemented
720	#450	C₂²×C₂₃	1	2	yes	complemented
721	#450	C₂²×C₂₃	1	2	yes	complemented
722	#441	C₂²×C₂₃	1	2	yes	complemented
723	#440	C₂²×C₂₃	1	2	yes	complemented
724	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
725	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
726	#435	C₂²×C₂₃	1	2	yes	complemented
727	#435	C₂²×C₂₃	1	2	yes	complemented
728	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
729	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
730	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
732	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
733	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
734	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
735	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
736	#418	C₂²×C₂₃	1	2	yes	complemented
737	#417	C₂²×C₂₃	1	1	yes	characteristic
738	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
739	#417	C₂²×C₂₃	1	2	yes	complemented
740	#416	C₂²×C₂₃	1	1	yes	characteristic
741	#416	C₂²×C₂₃	1	1	yes	characteristic
742	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
743	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
744	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
746	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
747	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
748	#416	C₂²×C₂₃	1	2	yes	complemented
749	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
750	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
751	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
752	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
753	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
754	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
755	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
756	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
757	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
758	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
759	C₂×C₂₃	—	2	2	no	—
760	C₂×C₂₃	—	2	2	no	—
761	C₂×C₂₃	—	4	1	no	—
762	C₂×C₂₃	—	4	2	no	—
763	C₂×C₂₃	—	4	2	no	—
764	C₂×C₂₃	—	8	1	no	—
765	C₂×C₂₃	—	8	2	no	—
766	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
767	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
768	C₂×C₂₃	#3584	1	1	yes	characteristic
769	H(5,𝔽₂)	—	2	4	no	—
770	H(5,𝔽₂)	—	4	2	no	—
771	C₂×#41	—	2	1	no	—
772	C₂×#41	—	2	1	no	—
773	C₂×#41	—	2	1	no	—
774	C₂×#41	—	2	4	no	—
775	C₂×#41	—	4	2	no	—
776	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
777	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
778	C₂×#41	C₂³×C₂₃	1	2	yes	—
779	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
780	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
781	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
782	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
784	C₂²×D₄	—	2	1	no	—
785	C₂²×D₄	—	2	1	no	—
786	C₂²×D₄	—	2	1	no	—
787	C₂²×D₄	—	2	2	no	—
788	C₂²×D₄	—	2	2	no	—
789	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
790	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
791	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
792	C₂³×C₄	—	2	1	no	—
793	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
794	#137	—	2	4	no	—
795	#137	—	4	2	no	—
796	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
797	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
798	C₂×SD₁₆	—	4	2	no	—
799	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
800	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
801	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
802	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
803	#131	—	4	2	no	—
804	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
805	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
806	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
807	C₂²×C₈	—	4	2	no	—
808	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
809	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
810	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
811	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
812	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
813	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
814	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
815	C₄⋊Q₈	—	2	1	no	—
816	C₄⋊Q₈	—	2	1	no	—
817	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
818	#127	—	2	2	no	—
819	#127	C₂³×C₂₃	1	2	yes	—
820	#126	—	2	2	no	—
821	#126	—	2	2	no	—
822	#126	—	2	2	no	—
823	#126	—	2	2	no	—
824	#125	—	2	1	no	—
825	#125	—	2	2	no	—
826	#125	—	2	2	no	—
827	#125	—	2	2	no	—
828	#125	C₂³×C₂₃	1	2	yes	—
829	#124	—	2	1	no	—
830	#124	—	2	2	no	—
831	#124	—	2	2	no	—
832	#124	C₂³×C₂₃	1	2	yes	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	D₄×C₂₃	1	2	yes	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	2	no	—
845	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
846	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
848	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
849	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
850	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
851	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
852	#121	—	2	1	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	2	1	no	—
858	#121	—	2	1	no	—
859	#121	—	2	2	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	D₄×C₂₃	1	1	yes	characteristic
864	#121	D₄×C₂₃	1	1	yes	characteristic
865	#121	C₂³×C₂₃	1	2	yes	—
866	#121	C₂³×C₂₃	1	2	yes	—
867	#121	C₂³×C₂₃	1	2	yes	—
868	#120	—	2	2	no	—
869	#120	—	2	2	no	—
870	#120	—	2	2	no	—
871	#120	—	2	2	no	—
872	#120	D₄×C₂₃	1	2	yes	—
873	C₄×Q₈	—	2	1	no	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	2	no	—
877	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
878	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
879	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	—	2	2	no	—
884	C₄×D₄	—	2	2	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	C₂³×C₂₃	1	2	yes	—
887	C₄×D₄	C₂³×C₂₃	1	2	yes	—
888	C₄×D₄	C₂³×C₂₃	1	2	yes	—
889	#117	—	2	1	no	—
890	#117	—	2	1	no	—
891	#117	—	2	1	no	—
892	#117	—	2	2	no	—
893	#117	—	2	2	no	—
894	#117	—	2	2	no	—
895	#117	C₂³×C₂₃	1	1	yes	characteristic
896	#117	C₂³×C₂₃	1	1	yes	characteristic
897	#117	C₂³×C₂₃	1	1	yes	characteristic
898	#117	C₂³×C₂₃	1	1	yes	characteristic
899	#117	C₂³×C₂₃	1	2	yes	—
900	#117	C₂³×C₂₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	—	2	1	no	—
902	C₂×C₄⋊C₄	—	2	1	no	—
903	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
908	C₂×C₂²⋊C₄	—	2	1	no	—
909	C₂×C₂²⋊C₄	—	2	1	no	—
910	C₂×C₂²⋊C₄	—	2	1	no	—
911	C₂×C₂²⋊C₄	—	2	2	no	—
912	C₂×C₄²	—	2	1	no	—
913	#107	C₂³×C₂₃	1	2	yes	—
914	#107	C₂³×C₂₃	1	2	yes	—
915	#106	C₂³×C₂₃	1	2	yes	—
916	#106	C₂³×C₂₃	1	2	yes	—
917	#106	C₂³×C₂₃	1	2	yes	—
918	#106	C₂³×C₂₃	1	2	yes	—
919	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
920	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
921	#103	C₂³×C₂₃	1	1	yes	characteristic
922	#103	C₂³×C₂₃	1	1	yes	characteristic
923	#103	C₂³×C₂₃	1	1	yes	characteristic
924	#103	C₂³×C₂₃	1	1	yes	characteristic
925	#103	C₂³×C₂₃	1	1	yes	characteristic
926	#103	C₂³×C₂₃	1	1	yes	characteristic
927	#103	C₂³×C₂₃	1	1	yes	characteristic
928	#103	C₂³×C₂₃	1	1	yes	characteristic
929	#103	C₂³×C₂₃	1	2	yes	—
930	#103	C₂³×C₂₃	1	2	yes	—
931	#103	C₂³×C₂₃	1	2	yes	—
932	#103	C₂³×C₂₃	1	2	yes	—
933	#102	C₂³×C₂₃	1	1	yes	characteristic
934	#102	C₂³×C₂₃	1	2	yes	—
935	#102	C₂³×C₂₃	1	1	yes	characteristic
936	#102	C₂³×C₂₃	1	1	yes	characteristic
937	#102	C₂³×C₂₃	1	1	yes	characteristic
938	#102	C₂³×C₂₃	1	1	yes	characteristic
939	#102	C₂³×C₂₃	1	1	yes	characteristic
940	#102	C₂³×C₂₃	1	1	yes	characteristic
941	#102	C₂³×C₂₃	1	1	yes	characteristic
942	#102	C₂³×C₂₃	1	2	yes	—
943	#102	C₂³×C₂₃	1	2	yes	—
944	#102	C₂³×C₂₃	1	2	yes	—
945	#102	C₂³×C₂₃	1	2	yes	—
946	#102	C₂³×C₂₃	1	2	yes	—
947	#102	C₂³×C₂₃	1	2	yes	—
948	#102	C₂³×C₂₃	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
951	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
953	#97	C₂³×C₂₃	1	2	yes	—
954	C₄×C₈	C₂³×C₂₃	1	2	yes	—
955	C₂₃	#61172	1	1	yes	characteristic, direct product factor, Sylow
956	C₂⁴	—	2	1	no	—
957	C₂⁴	—	2	2	no	—
958	C₂⁴	—	2	1	no	—
959	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	4	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	2	2	no	—
968	#41	—	4	4	no	—
969	#41	—	4	1	no	—
970	#41	—	4	1	no	—
971	#41	—	4	2	no	—
972	#41	—	4	4	no	—
973	#41	—	4	4	no	—
974	#41	#41×C₂₃	1	4	yes	—
975	C₂×Q₈	—	2	1	no	—
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	2	no	—
979	C₂×Q₈	—	2	2	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	4	1	no	—
982	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
983	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
985	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	4	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	1	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	4	1	no	—
1004	C₂×D₄	—	4	2	no	—
1005	C₂×D₄	—	4	4	no	—
1006	C₂×D₄	—	4	8	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	8	4	no	—
1009	C₂×D₄	—	8	2	no	—
1010	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1011	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1012	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1013	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
1014	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1015	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	4	4	no	—
1033	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1037	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1038	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1040	Q₁₆	—	2	4	no	—
1041	Q₁₆	—	4	2	no	—
1042	SD₁₆	—	2	4	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	M₁₆	—	2	2	no	—
1047	M₁₆	—	2	2	no	—
1048	M₁₆	—	4	2	no	—
1049	C₂×C₈	—	2	2	no	—
1050	C₂×C₈	—	2	2	no	—
1051	C₂×C₈	—	4	1	no	—
1052	C₂×C₈	—	4	1	no	—
1053	C₂×C₈	—	4	1	no	—
1054	C₂×C₈	—	4	1	no	—
1055	C₂×C₈	—	4	2	no	—
1056	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1057	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1058	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1059	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1060	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1061	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1081	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1082	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1083	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1085	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1086	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1105	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1106	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1107	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1108	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	2	no	—
1114	C₄²	—	2	2	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	C₂⁴×C₂₃	1	2	yes	—
1118	C₂³	—	2	2	no	—
1119	C₂³	—	2	1	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	2	2	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	4	1	no	—
1124	C₂³	—	4	2	no	—
1125	C₂³	—	4	4	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	4	2	no	—
1128	C₂³	—	8	1	no	—
1129	C₂³	—	8	1	no	—
1130	C₂³	—	8	2	no	—
1131	C₂³	—	8	1	no	—
1132	C₂³	—	8	2	no	—
1133	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1134	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1135	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1136	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	2	no	—
1142	Q₈	—	2	1	no	—
1143	Q₈	—	4	2	no	—
1144	Q₈	—	4	2	no	—
1145	Q₈	—	8	2	no	—
1146	Q₈	C₂×#41×C₂₃	1	2	yes	—
1147	D₄	—	2	4	no	—
1148	D₄	—	2	4	no	—
1149	D₄	—	2	4	no	—
1150	D₄	—	2	2	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	2	no	—
1154	D₄	—	2	1	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	4	no	—
1158	D₄	—	4	2	no	—
1159	D₄	—	4	4	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	4	no	—
1163	D₄	—	4	2	no	—
1164	D₄	—	4	2	no	—
1165	D₄	—	8	2	no	—
1166	D₄	—	8	2	no	—
1167	D₄	—	8	2	no	—
1168	D₄	—	8	2	no	—
1169	D₄	C₂×#41×C₂₃	1	2	yes	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	4	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	2	no	—
1196	C₂×C₄	—	8	2	no	—
1197	C₂×C₄	—	8	1	no	—
1198	C₂×C₄	—	8	2	no	—
1199	C₂×C₄	—	8	1	no	—
1200	C₂×C₄	—	8	1	no	—
1201	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1204	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1205	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1207	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1208	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1209	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1210	C₈	—	2	2	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	1	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	1	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	1	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	8	4	no	—
1237	C₂²	—	16	2	no	—
1238	C₂²	—	16	4	no	—
1239	C₂²	C₂₃×#546	1	2	yes	—
1240	C₂²	C₂₃×#577	1	2	yes	—
1241	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	2	no	—
1247	C₄	—	2	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	2	no	—
1255	C₄	—	4	1	no	—
1256	C₄	C₂₃×#546	1	2	yes	—
1257	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1258	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1259	C₂	—	2	2	no	—
1260	C₂	—	2	2	no	—
1261	C₂	—	4	1	no	—
1262	C₂	—	4	2	no	—
1263	C₂	—	4	2	no	—
1264	C₂	—	8	1	no	—
1265	C₂	—	8	2	no	—
1266	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1267	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1268	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3495	C₂	semidirect
3. C₂₃×#3317	C₂	semidirect
4. C₂₃×#3316	C₂	semidirect
5. C₂₃×#3311	C₂	semidirect
6. C₂₃×#3310	C₂	semidirect
7. C₂₃×#3304	C₂	semidirect
8. C₂₃×#3300	C₂	semidirect
9. C₂₃×#3296	C₂	semidirect
10. C₂₃×#3295	C₂	semidirect
11. C₂₃×#3136	C₂	semidirect
12. C₂₃×#3099	C₂	semidirect
13. C₂₃×#3094	C₂	semidirect
14. C₂₃×#3084	C₂	semidirect
15. C₂₃×#3063	C₂	semidirect
16. C₂×C₂₃×#465	C₂	semidirect
17. C₂₃×#3043	C₂	semidirect
18. C₂₃×#3009	C₂	semidirect
19. C₂₃×#3007	C₂	semidirect
20. C₂₃×#2947	C₂	semidirect
21. C₂₃×#2929	C₂	semidirect
22. C₂₃×#2897	C₂	semidirect
23. C₂×C₂₃×#416	C₂	semidirect
27. C₂×C₂₃×#137	C₂²	semidirect
28. C₂²×SD₁₆×C₂₃	C₂²	semidirect
29. C₂×C₂₃×#131	C₂²	semidirect
30. C₂³×C₈×C₂₃	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
32. C₂₃×#554	C₂²	semidirect
34. C₂₃×#552	C₂²	semidirect
35. C₂₃×#552	C₂²	semidirect
43. C₂₃×#544	C₂²	semidirect
48. C₂₃×#536	C₂²	semidirect
55. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
59. C₂₃×#520	C₂²	semidirect
60. C₂₃×#519	C₂²	semidirect
61. C₂×C₂₃×#117	C₂²	semidirect
62. C₂₃×#490	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
65. C₂₃×#486	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#483	C₂²	semidirect
68. C₂₃×#482	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#482	C₂²	semidirect
71. C₂₃×#481	C₂²	semidirect
72. C₂₃×#481	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#476	C₂²	semidirect
77. C₂₃×#475	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#468	C₂²	semidirect
80. C₂₃×#467	C₂²	semidirect
81. C₂₃×#465	C₂²	semidirect
82. C₂₃×#465	C₂²	semidirect
83. C₂₃×#465	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
87. C₂₃×#464	C₂²	semidirect
88. C₂₃×#460	C₂²	semidirect
89. C₂₃×#460	C₂²	semidirect
90. C₂₃×#452	C₂²	semidirect
91. C₂₃×#452	C₂²	semidirect
92. C₂₃×#452	C₂²	semidirect
93. C₂₃×#452	C₂²	semidirect
94. C₂₃×#451	C₂²	semidirect
95. C₂₃×#450	C₂²	semidirect
96. C₂₃×#450	C₂²	semidirect
97. C₂₃×#450	C₂²	semidirect
98. C₂₃×#441	C₂²	semidirect
99. C₂₃×#440	C₂²	semidirect
100. C₄×Q₁₆×C₂₃	C₂²	semidirect
101. C₄×SD₁₆×C₂₃	C₂²	semidirect
102. C₂₃×#435	C₂²	semidirect
103. C₂₃×#435	C₂²	semidirect
104. C₈×D₄×C₂₃	C₂²	semidirect
105. C₈×D₄×C₂₃	C₂²	semidirect
106. C₂₃×#428	C₂²	semidirect
107. C₂₃×#428	C₂²	semidirect
108. C₂×C₂₃×#106	C₂²	semidirect
109. C₂₃×#424	C₂²	semidirect
110. C₂₃×#418	C₂²	semidirect
111. C₂₃×#418	C₂²	semidirect
112. C₂₃×#418	C₂²	semidirect
114. C₂₃×#417	C₂²	semidirect
115. C₂₃×#417	C₂²	semidirect
118. C₂₃×#416	C₂²	semidirect
119. C₂₃×#416	C₂²	semidirect
120. C₂₃×#416	C₂²	semidirect
121. C₂₃×#416	C₂²	semidirect
122. C₂₃×#416	C₂²	semidirect
123. C₂₃×#416	C₂²	semidirect
124. C₂₃×#416	C₂²	semidirect
125. C₂×C₂₃×#103	C₂²	semidirect
126. C₂×C₂₃×#103	C₂²	semidirect
127. C₂×C₂₃×#103	C₂²	semidirect
128. C₂×C₂₃×#102	C₂²	semidirect
129. C₂×C₂₃×#102	C₂²	semidirect
130. C₂×C₂₃×#102	C₂²	semidirect
131. C₂×C₂₃×#102	C₂²	semidirect
132. C₂₃×#408	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂₃×#405	C₂²	semidirect
483. #61172	C₂₃	direct (N × H)
582. #3495	C₂×C₂₃	semidirect
584. #3317	C₂×C₂₃	semidirect
585. #3316	C₂×C₂₃	semidirect
586. #3311	C₂×C₂₃	semidirect
587. #3310	C₂×C₂₃	semidirect
588. #3304	C₂×C₂₃	semidirect
589. #3300	C₂×C₂₃	semidirect
590. #3296	C₂×C₂₃	semidirect
591. #3295	C₂×C₂₃	semidirect
592. #3136	C₂×C₂₃	semidirect
593. #3099	C₂×C₂₃	semidirect
594. #3094	C₂×C₂₃	semidirect
595. #3084	C₂×C₂₃	semidirect
596. #3063	C₂×C₂₃	semidirect
597. C₂×#465	C₂×C₂₃	semidirect
598. #3043	C₂×C₂₃	semidirect
599. #3009	C₂×C₂₃	semidirect
600. #3007	C₂×C₂₃	semidirect
601. #2947	C₂×C₂₃	semidirect
602. #2929	C₂×C₂₃	semidirect
603. #2897	C₂×C₂₃	semidirect
604. C₂×#416	C₂×C₂₃	semidirect
651. C₂×#137	C₂²×C₂₃	semidirect
652. C₂²×SD₁₆	C₂²×C₂₃	semidirect
653. C₂×#131	C₂²×C₂₃	semidirect
654. C₂³×C₈	C₂²×C₂₃	semidirect
655. #556	C₂²×C₂₃	semidirect
656. #554	C₂²×C₂₃	semidirect
658. #552	C₂²×C₂₃	semidirect
659. #552	C₂²×C₂₃	semidirect
667. #544	C₂²×C₂₃	semidirect
672. #536	C₂²×C₂₃	semidirect
679. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
683. #520	C₂²×C₂₃	semidirect
684. #519	C₂²×C₂₃	semidirect
685. C₂×#117	C₂²×C₂₃	semidirect
686. #490	C₂²×C₂₃	semidirect
687. #489	C₂²×C₂₃	semidirect
688. #488	C₂²×C₂₃	semidirect
689. #486	C₂²×C₂₃	semidirect
690. #485	C₂²×C₂₃	semidirect
691. #483	C₂²×C₂₃	semidirect
692. #482	C₂²×C₂₃	semidirect
693. #482	C₂²×C₂₃	semidirect
694. #482	C₂²×C₂₃	semidirect
695. #481	C₂²×C₂₃	semidirect
696. #481	C₂²×C₂₃	semidirect
697. #480	C₂²×C₂₃	semidirect
698. #479	C₂²×C₂₃	semidirect
699. #478	C₂²×C₂₃	semidirect
700. #476	C₂²×C₂₃	semidirect
701. #475	C₂²×C₂₃	semidirect
702. #470	C₂²×C₂₃	semidirect
703. #468	C₂²×C₂₃	semidirect
704. #467	C₂²×C₂₃	semidirect
705. #465	C₂²×C₂₃	semidirect
706. #465	C₂²×C₂₃	semidirect
707. #465	C₂²×C₂₃	semidirect
708. #465	C₂²×C₂₃	semidirect
709. #465	C₂²×C₂₃	semidirect
710. #464	C₂²×C₂₃	semidirect
711. #464	C₂²×C₂₃	semidirect
712. #460	C₂²×C₂₃	semidirect
713. #460	C₂²×C₂₃	semidirect
714. #452	C₂²×C₂₃	semidirect
715. #452	C₂²×C₂₃	semidirect
716. #452	C₂²×C₂₃	semidirect
717. #452	C₂²×C₂₃	semidirect
718. #451	C₂²×C₂₃	semidirect
719. #450	C₂²×C₂₃	semidirect
720. #450	C₂²×C₂₃	semidirect
721. #450	C₂²×C₂₃	semidirect
722. #441	C₂²×C₂₃	semidirect
723. #440	C₂²×C₂₃	semidirect
724. C₄×Q₁₆	C₂²×C₂₃	semidirect
725. C₄×SD₁₆	C₂²×C₂₃	semidirect
726. #435	C₂²×C₂₃	semidirect
727. #435	C₂²×C₂₃	semidirect
728. C₈×D₄	C₂²×C₂₃	semidirect
729. C₈×D₄	C₂²×C₂₃	semidirect
730. #428	C₂²×C₂₃	semidirect
731. #428	C₂²×C₂₃	semidirect
732. C₂×#106	C₂²×C₂₃	semidirect
733. #424	C₂²×C₂₃	semidirect
734. #418	C₂²×C₂₃	semidirect
735. #418	C₂²×C₂₃	semidirect
736. #418	C₂²×C₂₃	semidirect
738. #417	C₂²×C₂₃	semidirect
739. #417	C₂²×C₂₃	semidirect
742. #416	C₂²×C₂₃	semidirect
743. #416	C₂²×C₂₃	semidirect
744. #416	C₂²×C₂₃	semidirect
745. #416	C₂²×C₂₃	semidirect
746. #416	C₂²×C₂₃	semidirect
747. #416	C₂²×C₂₃	semidirect
748. #416	C₂²×C₂₃	semidirect
749. C₂×#103	C₂²×C₂₃	semidirect
750. C₂×#103	C₂²×C₂₃	semidirect
751. C₂×#103	C₂²×C₂₃	semidirect
752. C₂×#102	C₂²×C₂₃	semidirect
753. C₂×#102	C₂²×C₂₃	semidirect
754. C₂×#102	C₂²×C₂₃	semidirect
755. C₂×#102	C₂²×C₂₃	semidirect
756. #408	C₂²×C₂₃	semidirect
757. #407	C₂²×C₂₃	semidirect
758. #405	C₂²×C₂₃	semidirect
955. C₂₃	#61172	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3495	2
C₂₃×#3488	2
C₂₃×#3317	2
C₂₃×#3316	2
C₂₃×#3311	2
C₂₃×#3310	2
C₂₃×#3304	2
C₂₃×#3300	2
C₂₃×#3296	2
C₂₃×#3295	2
C₂₃×#3136	2
C₂₃×#3099	2
C₂₃×#3094	2
C₂₃×#3084	2
C₂₃×#3063	2
C₂×C₂₃×#465	2
C₂₃×#3043	2
C₂₃×#3009	2
C₂₃×#3007	2
C₂₃×#2947	2
C₂₃×#2929	2
C₂₃×#2897	2
C₂×C₂₃×#416	2
#61172	23

Subgroups — C23×#61172 #19208798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61172 #19208798