Subgroups — C₂₃×#61177 #19208803

Order 5888.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3331	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3330	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3322	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3306	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#417	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, complemented
27	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#554	—	2	1	no	—
32	C₂₃×#554	C₂²	1	2	yes	complemented
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#553	C₂²	1	2	yes	complemented
35	C₂₃×#552	—	2	1	no	—
36	C₂₃×#552	C₂²	1	2	yes	complemented
37	C₂₃×#547	—	2	1	no	—
38	C₂₃×#547	—	2	1	no	—
39	C₂₃×#547	—	2	1	no	—
40	C₂₃×#547	C₂²	1	2	yes	—
41	C₂₃×#547	C₂²	1	2	yes	—
42	C₂₃×#547	C₂²	1	2	yes	complemented
43	C₂₃×#546	—	2	1	no	—
44	C₂₃×#546	—	2	1	no	—
45	C₂₃×#546	C₂²	1	2	yes	—
46	C₂₃×#546	C₂²	1	2	yes	—
47	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#539	—	2	2	no	—
49	C₂₃×#537	C₂²	1	1	yes	characteristic
50	C₂₃×#536	C₂²	1	1	yes	characteristic
51	C₂₃×#536	C₂²	1	1	yes	characteristic
52	C₂₃×#534	—	2	2	no	—
53	C₂₃×#525	—	2	2	no	—
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂₃×#525	C₂²	1	1	yes	characteristic
56	C₂₃×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂₃×#123	—	2	2	no	—
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#518	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#491	C₂²	1	2	yes	complemented
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	2	yes	complemented
66	C₂₃×#485	C₂²	1	2	yes	complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#484	C₂²	1	2	yes	complemented
69	C₂₃×#484	C₂²	1	2	yes	complemented
70	C₂₃×#483	C₂²	1	2	yes	complemented
71	C₂₃×#483	C₂²	1	2	yes	complemented
72	C₂₃×#481	C₂²	1	2	yes	complemented
73	C₂₃×#480	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#478	C₂²	1	2	yes	complemented
76	C₂₃×#476	C₂²	1	2	yes	complemented
77	C₂₃×#474	C₂²	1	2	yes	complemented
78	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#470	C₂²	1	2	yes	complemented
81	C₂₃×#469	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#469	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#468	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#468	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#468	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#468	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#468	C₂²	1	2	yes	complemented
88	C₂₃×#467	C₂²	1	2	yes	complemented
89	C₂₃×#465	C₂²	1	2	yes	complemented
90	C₂₃×#464	C₂²	1	2	yes	complemented
91	C₂₃×#463	C₂²	1	2	yes	complemented
92	C₂₃×#462	C₂²	1	2	yes	complemented
93	C₂₃×#461	C₂²	1	2	yes	complemented
94	C₂₃×#452	C₂²	1	2	yes	complemented
95	C₂₃×#452	C₂²	1	2	yes	complemented
96	C₂₃×#452	C₂²	1	2	yes	complemented
97	C₂₃×#450	C₂²	1	2	yes	complemented
98	C₂₃×#449	C₂²	1	2	yes	complemented
99	C₂₃×#449	C₂²	1	2	yes	complemented
100	C₂₃×#449	C₂²	1	2	yes	complemented
101	C₂₃×#447	C₂²	1	2	yes	complemented
102	C₂₃×#442	C₂²	1	2	yes	complemented
103	C₂₃×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
106	C₂₃×#436	C₂²	1	2	yes	complemented
107	C₂₃×#436	C₂²	1	2	yes	complemented
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₂₃×#435	C₂²	1	2	yes	complemented
110	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#418	C₂²	1	1	yes	characteristic
116	C₂₃×#418	C₂²	1	2	yes	complemented
117	C₂₃×#417	C₂²	1	1	yes	characteristic
118	C₂₃×#417	C₂²	1	1	yes	characteristic
119	C₂₃×#417	C₂²	1	2	yes	complemented
120	C₂₃×#417	C₂²	1	2	yes	complemented
121	C₂₃×#417	C₂²	1	2	yes	complemented
122	C₂₃×#417	C₂²	1	2	yes	complemented
123	C₂₃×#417	C₂²	1	2	yes	complemented
124	C₂₃×#416	C₂²	1	1	yes	characteristic
125	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
126	C₂₃×#416	C₂²	1	2	yes	complemented
127	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
132	C₂₃×#408	C₂²	1	1	yes	characteristic
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	2	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	2	4	no	—
142	C₂×#41×C₂₃	—	4	2	no	—
143	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×#41×C₂₃	C₂³	1	2	yes	—
146	C₂×#41×C₂₃	C₂³	1	2	yes	—
147	C₂×#41×C₂₃	C₂³	1	2	yes	—
148	C₂×#41×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	2	no	—
152	C₂²×D₄×C₂₃	—	2	1	no	—
153	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
154	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₂₃	—	2	1	no	—
156	C₂³×C₄×C₂₃	—	2	1	no	—
157	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂₃×#137	—	4	2	no	—
159	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
160	C₂₃×#135	—	4	2	no	—
161	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂×D₈×C₂₃	C₂³	1	2	yes	—
168	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#131	—	4	2	no	—
170	C₂×M₁₆×C₂₃	—	4	2	no	—
171	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
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×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₂₃×#126	—	2	2	no	—
186	C₂₃×#126	—	2	2	no	—
187	C₂₃×#125	—	2	1	no	—
188	C₂₃×#125	—	2	2	no	—
189	C₂₃×#125	—	2	2	no	—
190	C₂₃×#125	C₂³	1	2	yes	—
191	C₂₃×#124	—	2	1	no	—
192	C₂₃×#124	C₂³	1	2	yes	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	1	no	—
196	C₂₃×#123	—	2	1	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
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	—	2	2	no	—
204	C₂₃×#123	—	2	2	no	—
205	C₂₃×#123	—	2	2	no	—
206	C₂₃×#123	—	2	2	no	—
207	C₂₃×#123	D₄	1	2	yes	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	1	no	—
210	C₂₃×C₂²⋊Q₈	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	2	no	—
212	C₂₃×C₂²⋊Q₈	—	2	2	no	—
213	C₂₃×C₂²⋊Q₈	—	2	2	no	—
214	C₂₃×C₂²⋊Q₈	—	2	2	no	—
215	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
216	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
230	C₂₃×#121	—	2	2	no	—
231	C₂₃×#121	D₄	1	1	yes	characteristic
232	C₂₃×#121	D₄	1	1	yes	characteristic
233	C₂₃×#121	C₂³	1	1	yes	characteristic
234	C₂₃×#121	C₂³	1	2	yes	—
235	C₂₃×#121	C₂³	1	1	yes	characteristic
236	C₂₃×#121	C₂³	1	1	yes	characteristic
237	C₂₃×#121	C₂³	1	1	yes	characteristic
238	C₂₃×#120	—	2	1	no	—
239	C₂₃×#120	—	2	1	no	—
240	C₂₃×#120	—	2	2	no	—
241	C₂₃×#120	—	2	2	no	—
242	C₂₃×#120	D₄	1	2	yes	—
243	C₄×Q₈×C₂₃	—	2	1	no	—
244	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
245	C₄×D₄×C₂₃	—	2	1	no	—
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	1	no	—
250	C₄×D₄×C₂₃	—	2	1	no	—
251	C₄×D₄×C₂₃	—	2	1	no	—
252	C₄×D₄×C₂₃	—	2	1	no	—
253	C₄×D₄×C₂₃	—	2	1	no	—
254	C₄×D₄×C₂₃	—	2	2	no	—
255	C₄×D₄×C₂₃	—	2	2	no	—
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₄×D₄×C₂₃	C₂³	1	2	yes	—
258	C₄×D₄×C₂₃	C₂³	1	2	yes	—
259	C₄×D₄×C₂₃	C₂³	1	2	yes	—
260	C₄×D₄×C₂₃	C₂³	1	2	yes	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	2	no	—
263	C₂₃×#117	C₂³	1	2	yes	—
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	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
279	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
280	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
281	C₂₃×#107	C₂³	1	1	yes	characteristic
282	C₂₃×#107	C₂³	1	1	yes	characteristic
283	C₂₃×#107	C₂³	1	2	yes	—
284	C₂₃×#107	C₂³	1	2	yes	—
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	1	yes	characteristic
287	C₂₃×#106	C₂³	1	2	yes	—
288	C₂₃×#106	C₂³	1	2	yes	—
289	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	1	yes	characteristic
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	1	yes	characteristic
299	C₂₃×#103	C₂³	1	1	yes	characteristic
300	C₂₃×#103	C₂³	1	2	yes	—
301	C₂₃×#103	C₂³	1	2	yes	—
302	C₂₃×#103	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
311	C₂₃×#102	C₂³	1	2	yes	—
312	C₂₃×#102	C₂³	1	1	yes	characteristic
313	C₂₃×#102	C₂³	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	2	2	no	—
326	#41×C₂₃	—	2	4	no	—
327	#41×C₂₃	—	2	4	no	—
328	#41×C₂₃	—	2	4	no	—
329	#41×C₂₃	—	2	2	no	—
330	#41×C₂₃	—	2	2	no	—
331	#41×C₂₃	—	2	2	no	—
332	#41×C₂₃	—	2	2	no	—
333	#41×C₂₃	—	4	2	no	—
334	#41×C₂₃	—	4	2	no	—
335	#41×C₂₃	—	4	2	no	—
336	#41×C₂₃	—	4	4	no	—
337	#41×C₂₃	—	4	4	no	—
338	#41×C₂₃	—	4	4	no	—
339	#41×C₂₃	—	8	4	no	—
340	C₂×Q₈×C₂₃	—	2	1	no	—
341	C₂×Q₈×C₂₃	—	2	2	no	—
342	C₂×Q₈×C₂₃	—	2	2	no	—
343	C₂×Q₈×C₂₃	—	2	2	no	—
344	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
345	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
346	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₂₃	—	2	4	no	—
349	C₂×D₄×C₂₃	—	2	1	no	—
350	C₂×D₄×C₂₃	—	2	1	no	—
351	C₂×D₄×C₂₃	—	2	1	no	—
352	C₂×D₄×C₂₃	—	2	2	no	—
353	C₂×D₄×C₂₃	—	2	2	no	—
354	C₂×D₄×C₂₃	—	2	1	no	—
355	C₂×D₄×C₂₃	—	2	2	no	—
356	C₂×D₄×C₂₃	—	2	1	no	—
357	C₂×D₄×C₂₃	—	2	1	no	—
358	C₂×D₄×C₂₃	—	2	2	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	2	no	—
361	C₂×D₄×C₂₃	—	2	2	no	—
362	C₂×D₄×C₂₃	—	4	2	no	—
363	C₂×D₄×C₂₃	—	4	4	no	—
364	C₂×D₄×C₂₃	—	4	8	no	—
365	C₂×D₄×C₂₃	—	4	4	no	—
366	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₂₃	#41	1	4	yes	complemented
371	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₂₃	—	2	2	no	—
375	C₂²×C₄×C₂₃	—	2	2	no	—
376	C₂²×C₄×C₂₃	—	2	2	no	—
377	C₂²×C₄×C₂₃	—	2	1	no	—
378	C₂²×C₄×C₂₃	—	2	1	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	2	no	—
382	C₂²×C₄×C₂₃	—	2	2	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	2	no	—
388	C₂²×C₄×C₂₃	—	2	2	no	—
389	C₂²×C₄×C₂₃	—	2	2	no	—
390	C₂²×C₄×C₂₃	—	4	4	no	—
391	C₂²×C₄×C₂₃	—	8	2	no	—
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₂₃	—	4	1	no	—
400	Q₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	2	4	no	—
402	SD₁₆×C₂₃	—	4	1	no	—
403	SD₁₆×C₂₃	—	4	1	no	—
404	SD₁₆×C₂₃	—	4	2	no	—
405	D₈×C₂₃	—	2	4	no	—
406	D₈×C₂₃	—	4	1	no	—
407	M₁₆×C₂₃	—	2	2	no	—
408	M₁₆×C₂₃	—	2	2	no	—
409	M₁₆×C₂₃	—	4	1	no	—
410	M₁₆×C₂₃	—	4	1	no	—
411	M₁₆×C₂₃	—	4	1	no	—
412	M₁₆×C₂₃	—	4	1	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	2	no	—
417	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
420	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	2	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	2	no	—
431	C₄⋊C₄×C₂₃	—	2	2	no	—
432	C₄⋊C₄×C₂₃	—	2	2	no	—
433	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
438	C₄⋊C₄×C₂₃	—	2	2	no	—
439	C₄⋊C₄×C₂₃	—	2	2	no	—
440	C₄⋊C₄×C₂₃	—	2	1	no	—
441	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
443	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
444	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₂²⋊C₄×C₂₃	—	2	1	no	—
452	C₂²⋊C₄×C₂₃	—	2	2	no	—
453	C₂²⋊C₄×C₂₃	—	2	2	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	2	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	1	no	—
462	C₂²⋊C₄×C₂₃	—	2	1	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	—	2	1	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
475	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
476	C₄²×C₂₃	—	2	2	no	—
477	C₄²×C₂₃	—	2	2	no	—
478	C₄²×C₂₃	—	2	1	no	—
479	C₄²×C₂₃	—	2	1	no	—
480	C₄²×C₂₃	C₂⁴	1	2	yes	—
481	#61177	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₂³×C₂₃	—	2	2	no	—
483	C₂³×C₂₃	—	2	2	no	—
484	C₂³×C₂₃	—	2	4	no	—
485	C₂³×C₂₃	—	2	1	no	—
486	C₂³×C₂₃	—	2	1	no	—
487	C₂³×C₂₃	—	4	1	no	—
488	C₂³×C₂₃	—	4	1	no	—
489	C₂³×C₂₃	—	4	4	no	—
490	C₂³×C₂₃	—	8	1	no	—
491	C₂³×C₂₃	—	8	1	no	—
492	C₂³×C₂₃	—	8	2	no	—
493	C₂³×C₂₃	—	8	2	no	—
494	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
495	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
496	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
497	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
498	Q₈×C₂₃	—	2	2	no	—
499	Q₈×C₂₃	—	2	1	no	—
500	Q₈×C₂₃	—	2	2	no	—
501	Q₈×C₂₃	—	2	1	no	—
502	Q₈×C₂₃	—	2	1	no	—
503	Q₈×C₂₃	—	2	2	no	—
504	Q₈×C₂₃	—	2	1	no	—
505	Q₈×C₂₃	—	4	2	no	—
506	Q₈×C₂₃	—	8	2	no	—
507	D₄×C₂₃	—	2	4	no	—
508	D₄×C₂₃	—	2	4	no	—
509	D₄×C₂₃	—	2	2	no	—
510	D₄×C₂₃	—	2	1	no	—
511	D₄×C₂₃	—	2	1	no	—
512	D₄×C₂₃	—	2	2	no	—
513	D₄×C₂₃	—	2	1	no	—
514	D₄×C₂₃	—	2	1	no	—
515	D₄×C₂₃	—	4	2	no	—
516	D₄×C₂₃	—	4	2	no	—
517	D₄×C₂₃	—	4	4	no	—
518	D₄×C₂₃	—	4	4	no	—
519	D₄×C₂₃	—	4	4	no	—
520	D₄×C₂₃	—	4	4	no	—
521	D₄×C₂₃	—	4	2	no	—
522	D₄×C₂₃	—	4	2	no	—
523	D₄×C₂₃	—	4	2	no	—
524	D₄×C₂₃	—	4	2	no	—
525	D₄×C₂₃	—	8	1	no	—
526	D₄×C₂₃	—	8	1	no	—
527	D₄×C₂₃	—	8	2	no	—
528	D₄×C₂₃	C₂×#41	1	4	yes	—
529	C₂×C₄×C₂₃	—	2	2	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	2	no	—
532	C₂×C₄×C₂₃	—	2	1	no	—
533	C₂×C₄×C₂₃	—	2	1	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	2	no	—
536	C₂×C₄×C₂₃	—	2	1	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	1	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	2	no	—
545	C₂×C₄×C₂₃	—	2	2	no	—
546	C₂×C₄×C₂₃	—	2	1	no	—
547	C₂×C₄×C₂₃	—	4	4	no	—
548	C₂×C₄×C₂₃	—	4	4	no	—
549	C₂×C₄×C₂₃	—	4	4	no	—
550	C₂×C₄×C₂₃	—	4	4	no	—
551	C₂×C₄×C₂₃	—	4	2	no	—
552	C₂×C₄×C₂₃	—	4	2	no	—
553	C₂×C₄×C₂₃	—	4	2	no	—
554	C₂×C₄×C₂₃	—	8	2	no	—
555	C₂×C₄×C₂₃	—	8	2	no	—
556	C₂×C₄×C₂₃	—	8	2	no	—
557	C₂×C₄×C₂₃	—	8	1	no	—
558	C₂×C₄×C₂₃	—	8	2	no	—
559	C₂×C₄×C₂₃	—	8	1	no	—
560	C₂×C₄×C₂₃	—	8	2	no	—
561	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
562	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
564	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
568	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
569	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
570	C₈×C₂₃	—	2	2	no	—
571	C₈×C₂₃	—	2	1	no	—
572	C₈×C₂₃	—	2	1	no	—
573	C₈×C₂₃	—	2	1	no	—
574	C₈×C₂₃	—	2	1	no	—
575	C₈×C₂₃	—	2	2	no	—
576	#3492	C₂×C₂₃	1	1	yes	characteristic, complemented
577	#3485	C₂×C₂₃	1	1	yes	characteristic, complemented
578	#3331	C₂×C₂₃	1	2	yes	complemented
579	#3330	C₂×C₂₃	1	2	yes	complemented
580	#3323	C₂×C₂₃	1	2	yes	complemented
581	#3322	C₂×C₂₃	1	2	yes	complemented
582	#3315	C₂×C₂₃	1	2	yes	complemented
583	#3314	C₂×C₂₃	1	2	yes	complemented
584	#3307	C₂×C₂₃	1	2	yes	complemented
585	#3306	C₂×C₂₃	1	2	yes	complemented
586	#3137	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3092	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3081	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
591	#3054	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#3046	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3012	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3005	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#2946	C₂×C₂₃	1	1	yes	characteristic, complemented
596	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
598	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
599	C₂²×C₂₃	—	2	1	no	—
600	C₂²×C₂₃	—	2	1	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	1	no	—
603	C₂²×C₂₃	—	2	2	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	2	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	4	no	—
611	C₂²×C₂₃	—	4	4	no	—
612	C₂²×C₂₃	—	4	2	no	—
613	C₂²×C₂₃	—	4	2	no	—
614	C₂²×C₂₃	—	4	1	no	—
615	C₂²×C₂₃	—	4	1	no	—
616	C₂²×C₂₃	—	4	1	no	—
617	C₂²×C₂₃	—	4	1	no	—
618	C₂²×C₂₃	—	4	1	no	—
619	C₂²×C₂₃	—	4	1	no	—
620	C₂²×C₂₃	—	8	4	no	—
621	C₂²×C₂₃	—	16	4	no	—
622	C₂²×C₂₃	#546	1	2	yes	—
623	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
624	C₄×C₂₃	—	2	2	no	—
625	C₄×C₂₃	—	2	2	no	—
626	C₄×C₂₃	—	2	1	no	—
627	C₄×C₂₃	—	2	1	no	—
628	C₄×C₂₃	—	2	2	no	—
629	C₄×C₂₃	—	4	2	no	—
630	C₄×C₂₃	—	4	2	no	—
631	C₄×C₂₃	—	4	1	no	—
632	C₄×C₂₃	—	4	1	no	—
633	C₄×C₂₃	—	4	1	no	—
634	C₄×C₂₃	—	4	1	no	—
635	C₄×C₂₃	—	4	1	no	—
636	C₄×C₂₃	—	4	2	no	—
637	C₄×C₂₃	—	4	1	no	—
638	C₄×C₂₃	#546	1	2	yes	—
639	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
640	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
642	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
643	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
645	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
646	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
647	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#554	—	2	1	no	—
649	#554	C₂²×C₂₃	1	2	yes	complemented
650	#553	—	2	1	no	—
651	#553	C₂²×C₂₃	1	2	yes	complemented
652	#552	—	2	1	no	—
653	#552	C₂²×C₂₃	1	2	yes	complemented
654	#547	—	2	1	no	—
655	#547	—	2	1	no	—
656	#547	—	2	1	no	—
657	#547	C₂²×C₂₃	1	2	yes	—
658	#547	C₂²×C₂₃	1	2	yes	—
659	#547	C₂²×C₂₃	1	2	yes	complemented
660	#546	—	2	1	no	—
661	#546	—	2	1	no	—
662	#546	C₂²×C₂₃	1	2	yes	—
663	#546	C₂²×C₂₃	1	2	yes	—
664	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
665	#539	—	2	2	no	—
666	#537	C₂²×C₂₃	1	1	yes	characteristic
667	#536	C₂²×C₂₃	1	1	yes	characteristic
668	#536	C₂²×C₂₃	1	1	yes	characteristic
669	#534	—	2	2	no	—
670	#525	—	2	2	no	—
671	#525	C₂²×C₂₃	1	1	yes	characteristic
672	#525	C₂²×C₂₃	1	1	yes	characteristic
673	#525	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	C₂×#123	—	2	2	no	—
675	#520	C₂²×C₂₃	1	1	yes	characteristic
676	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#518	C₂²×C₂₃	1	1	yes	characteristic
678	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#491	C₂²×C₂₃	1	2	yes	complemented
680	#489	C₂²×C₂₃	1	2	yes	complemented
681	#488	C₂²×C₂₃	1	2	yes	complemented
682	#487	C₂²×C₂₃	1	2	yes	complemented
683	#485	C₂²×C₂₃	1	2	yes	complemented
684	#485	C₂²×C₂₃	1	2	yes	complemented
685	#484	C₂²×C₂₃	1	2	yes	complemented
686	#484	C₂²×C₂₃	1	2	yes	complemented
687	#483	C₂²×C₂₃	1	2	yes	complemented
688	#483	C₂²×C₂₃	1	2	yes	complemented
689	#481	C₂²×C₂₃	1	2	yes	complemented
690	#480	C₂²×C₂₃	1	2	yes	complemented
691	#478	C₂²×C₂₃	1	2	yes	complemented
692	#478	C₂²×C₂₃	1	2	yes	complemented
693	#476	C₂²×C₂₃	1	2	yes	complemented
694	#474	C₂²×C₂₃	1	2	yes	complemented
695	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	#470	C₂²×C₂₃	1	2	yes	complemented
697	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	#469	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#469	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	#468	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#468	C₂²×C₂₃	1	2	yes	complemented
702	#468	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	#468	C₂²×C₂₃	1	1	yes	characteristic, complemented
704	#468	C₂²×C₂₃	1	1	yes	characteristic, complemented
705	#467	C₂²×C₂₃	1	2	yes	complemented
706	#465	C₂²×C₂₃	1	2	yes	complemented
707	#464	C₂²×C₂₃	1	2	yes	complemented
708	#463	C₂²×C₂₃	1	2	yes	complemented
709	#462	C₂²×C₂₃	1	2	yes	complemented
710	#461	C₂²×C₂₃	1	2	yes	complemented
711	#452	C₂²×C₂₃	1	2	yes	complemented
712	#452	C₂²×C₂₃	1	2	yes	complemented
713	#452	C₂²×C₂₃	1	2	yes	complemented
714	#450	C₂²×C₂₃	1	2	yes	complemented
715	#449	C₂²×C₂₃	1	2	yes	complemented
716	#449	C₂²×C₂₃	1	2	yes	complemented
717	#449	C₂²×C₂₃	1	2	yes	complemented
718	#447	C₂²×C₂₃	1	2	yes	complemented
719	#442	C₂²×C₂₃	1	2	yes	complemented
720	#440	C₂²×C₂₃	1	2	yes	complemented
721	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
722	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
723	#436	C₂²×C₂₃	1	2	yes	complemented
724	#436	C₂²×C₂₃	1	2	yes	complemented
725	#435	C₂²×C₂₃	1	2	yes	complemented
726	#435	C₂²×C₂₃	1	2	yes	complemented
727	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
728	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
729	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
730	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
731	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
732	#418	C₂²×C₂₃	1	1	yes	characteristic
733	#418	C₂²×C₂₃	1	2	yes	complemented
734	#417	C₂²×C₂₃	1	1	yes	characteristic
735	#417	C₂²×C₂₃	1	1	yes	characteristic
736	#417	C₂²×C₂₃	1	2	yes	complemented
737	#417	C₂²×C₂₃	1	2	yes	complemented
738	#417	C₂²×C₂₃	1	2	yes	complemented
739	#417	C₂²×C₂₃	1	2	yes	complemented
740	#417	C₂²×C₂₃	1	2	yes	complemented
741	#416	C₂²×C₂₃	1	1	yes	characteristic
742	#416	C₂²×C₂₃	1	2	yes	complemented
743	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
744	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
746	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
747	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
748	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
749	#408	C₂²×C₂₃	1	1	yes	characteristic
750	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
751	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
752	C₂×C₂₃	—	2	2	no	—
753	C₂×C₂₃	—	4	1	no	—
754	C₂×C₂₃	—	4	1	no	—
755	C₂×C₂₃	—	4	2	no	—
756	C₂×C₂₃	—	4	4	no	—
757	C₂×C₂₃	—	8	1	no	—
758	C₂×C₂₃	—	8	1	no	—
759	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
760	C₂×C₂₃	#3585	1	1	yes	characteristic
761	C₂×C₂₃	#3586	1	1	yes	characteristic
762	H(5,𝔽₂)	—	2	4	no	—
763	H(5,𝔽₂)	—	4	2	no	—
764	C₂×#41	—	2	1	no	—
765	C₂×#41	—	2	2	no	—
766	C₂×#41	—	2	1	no	—
767	C₂×#41	—	2	1	no	—
768	C₂×#41	—	2	4	no	—
769	C₂×#41	—	4	2	no	—
770	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
771	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×#41	C₂³×C₂₃	1	2	yes	—
773	C₂×#41	C₂³×C₂₃	1	2	yes	—
774	C₂×#41	C₂³×C₂₃	1	2	yes	—
775	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
776	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₂²×D₄	—	2	1	no	—
778	C₂²×D₄	—	2	2	no	—
779	C₂²×D₄	—	2	1	no	—
780	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
781	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
782	C₂³×C₄	—	2	1	no	—
783	C₂³×C₄	—	2	1	no	—
784	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
785	#137	—	4	2	no	—
786	AGL(1,ℤ/8)	—	2	4	no	—
787	#135	—	4	2	no	—
788	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
792	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
793	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
794	C₂×D₈	C₂³×C₂₃	1	2	yes	—
795	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
796	#131	—	4	2	no	—
797	C₂×M₁₆	—	4	2	no	—
798	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
799	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
800	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
801	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
802	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
803	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
804	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
805	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
806	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
807	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
808	C₄⋊Q₈	—	2	1	no	—
809	C₄⋊Q₈	—	2	1	no	—
810	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
811	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
812	#126	—	2	2	no	—
813	#126	—	2	2	no	—
814	#125	—	2	2	no	—
815	#125	—	2	2	no	—
816	#125	—	2	1	no	—
817	#125	C₂³×C₂₃	1	2	yes	—
818	#124	—	2	1	no	—
819	#124	C₂³×C₂₃	1	2	yes	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	1	no	—
823	#123	—	2	1	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	2	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	D₄×C₂₃	1	2	yes	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	2	no	—
839	C₂²⋊Q₈	—	2	2	no	—
840	C₂²⋊Q₈	—	2	2	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
843	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
844	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
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	#121	—	2	2	no	—
852	#121	—	2	2	no	—
853	#121	—	2	2	no	—
854	#121	—	2	2	no	—
855	#121	—	2	1	no	—
856	#121	—	2	2	no	—
857	#121	—	2	2	no	—
858	#121	D₄×C₂₃	1	1	yes	characteristic
859	#121	D₄×C₂₃	1	1	yes	characteristic
860	#121	C₂³×C₂₃	1	1	yes	characteristic
861	#121	C₂³×C₂₃	1	1	yes	characteristic
862	#121	C₂³×C₂₃	1	1	yes	characteristic
863	#121	C₂³×C₂₃	1	1	yes	characteristic
864	#121	C₂³×C₂₃	1	2	yes	—
865	#120	—	2	1	no	—
866	#120	—	2	1	no	—
867	#120	—	2	2	no	—
868	#120	—	2	2	no	—
869	#120	D₄×C₂₃	1	2	yes	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	2	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	2	1	no	—
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	C₂³×C₂₃	1	2	yes	—
884	C₄×D₄	C₂³×C₂₃	1	2	yes	—
885	C₄×D₄	C₂³×C₂₃	1	2	yes	—
886	C₄×D₄	C₂³×C₂₃	1	2	yes	—
887	C₄×D₄	C₂³×C₂₃	1	2	yes	—
888	#117	—	2	1	no	—
889	#117	—	2	2	no	—
890	#117	C₂³×C₂₃	1	1	yes	characteristic
891	#117	C₂³×C₂₃	1	1	yes	characteristic
892	#117	C₂³×C₂₃	1	2	yes	—
893	#117	C₂³×C₂₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	—	2	1	no	—
895	C₂×C₄⋊C₄	—	2	1	no	—
896	C₂×C₄⋊C₄	—	2	1	no	—
897	C₂×C₄⋊C₄	—	2	1	no	—
898	C₂×C₄⋊C₄	—	2	2	no	—
899	C₂×C₄⋊C₄	—	2	2	no	—
900	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
903	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
904	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
905	C₂×C₂²⋊C₄	—	2	2	no	—
906	C₂×C₂²⋊C₄	—	2	2	no	—
907	C₂×C₂²⋊C₄	—	2	2	no	—
908	#107	C₂³×C₂₃	1	1	yes	characteristic
909	#107	C₂³×C₂₃	1	1	yes	characteristic
910	#107	C₂³×C₂₃	1	2	yes	—
911	#107	C₂³×C₂₃	1	2	yes	—
912	#106	C₂³×C₂₃	1	1	yes	characteristic
913	#106	C₂³×C₂₃	1	1	yes	characteristic
914	#106	C₂³×C₂₃	1	2	yes	—
915	#106	C₂³×C₂₃	1	2	yes	—
916	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
917	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
918	#103	C₂³×C₂₃	1	2	yes	—
919	#103	C₂³×C₂₃	1	2	yes	—
920	#103	C₂³×C₂₃	1	2	yes	—
921	#103	C₂³×C₂₃	1	2	yes	—
922	#103	C₂³×C₂₃	1	1	yes	characteristic
923	#103	C₂³×C₂₃	1	1	yes	characteristic
924	#103	C₂³×C₂₃	1	2	yes	—
925	#103	C₂³×C₂₃	1	1	yes	characteristic
926	#103	C₂³×C₂₃	1	1	yes	characteristic
927	#103	C₂³×C₂₃	1	2	yes	—
928	#103	C₂³×C₂₃	1	2	yes	—
929	#103	C₂³×C₂₃	1	2	yes	—
930	#102	C₂³×C₂₃	1	2	yes	—
931	#102	C₂³×C₂₃	1	2	yes	—
932	#102	C₂³×C₂₃	1	2	yes	—
933	#102	C₂³×C₂₃	1	2	yes	—
934	#102	C₂³×C₂₃	1	1	yes	characteristic
935	#102	C₂³×C₂₃	1	2	yes	—
936	#102	C₂³×C₂₃	1	2	yes	—
937	#102	C₂³×C₂₃	1	1	yes	characteristic
938	#102	C₂³×C₂₃	1	2	yes	—
939	#102	C₂³×C₂₃	1	1	yes	characteristic
940	#102	C₂³×C₂₃	1	1	yes	characteristic
941	#102	C₂³×C₂₃	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
946	#97	C₂³×C₂₃	1	2	yes	—
947	C₄×C₈	C₂³×C₂₃	1	2	yes	—
948	C₂₃	#61177	1	1	yes	characteristic, direct product factor, Sylow
949	C₂⁴	—	2	1	no	—
950	C₂⁴	—	2	2	no	—
951	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
952	#41	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	4	no	—
955	#41	—	2	4	no	—
956	#41	—	2	4	no	—
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	4	2	no	—
962	#41	—	4	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	4	no	—
965	#41	—	4	4	no	—
966	#41	—	4	4	no	—
967	#41	—	8	4	no	—
968	C₂×Q₈	—	2	1	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	2	2	no	—
971	C₂×Q₈	—	2	2	no	—
972	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
974	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₂×D₄	—	2	4	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	4	2	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	—	4	8	no	—
993	C₂×D₄	—	4	4	no	—
994	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
995	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
996	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
997	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
998	C₂×D₄	#41×C₂₃	1	4	yes	complemented
999	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	1	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	2	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	4	4	no	—
1019	C₂²×C₄	—	8	2	no	—
1020	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1026	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1027	Q₁₆	—	4	1	no	—
1028	Q₁₆	—	4	2	no	—
1029	SD₁₆	—	2	4	no	—
1030	SD₁₆	—	4	1	no	—
1031	SD₁₆	—	4	1	no	—
1032	SD₁₆	—	4	2	no	—
1033	D₈	—	2	4	no	—
1034	D₈	—	4	1	no	—
1035	M₁₆	—	2	2	no	—
1036	M₁₆	—	2	2	no	—
1037	M₁₆	—	4	1	no	—
1038	M₁₆	—	4	1	no	—
1039	M₁₆	—	4	1	no	—
1040	M₁₆	—	4	1	no	—
1041	M₁₆	—	4	2	no	—
1042	C₂×C₈	—	2	2	no	—
1043	C₂×C₈	—	2	2	no	—
1044	C₂×C₈	—	4	2	no	—
1045	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1046	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1047	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1048	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1049	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1050	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	2	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1071	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1072	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1073	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1074	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1075	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1076	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1077	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	2	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	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1100	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1101	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1102	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1103	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1104	C₄²	—	2	2	no	—
1105	C₄²	—	2	2	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	C₂⁴×C₂₃	1	2	yes	—
1109	C₂³	—	2	2	no	—
1110	C₂³	—	2	2	no	—
1111	C₂³	—	2	4	no	—
1112	C₂³	—	2	1	no	—
1113	C₂³	—	2	1	no	—
1114	C₂³	—	4	1	no	—
1115	C₂³	—	4	1	no	—
1116	C₂³	—	4	4	no	—
1117	C₂³	—	8	1	no	—
1118	C₂³	—	8	1	no	—
1119	C₂³	—	8	2	no	—
1120	C₂³	—	8	2	no	—
1121	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1122	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1123	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1124	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1125	Q₈	—	2	2	no	—
1126	Q₈	—	2	1	no	—
1127	Q₈	—	2	2	no	—
1128	Q₈	—	2	1	no	—
1129	Q₈	—	2	1	no	—
1130	Q₈	—	2	2	no	—
1131	Q₈	—	2	1	no	—
1132	Q₈	—	4	2	no	—
1133	Q₈	—	8	2	no	—
1134	D₄	—	2	4	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	2	1	no	—
1137	D₄	—	2	2	no	—
1138	D₄	—	2	1	no	—
1139	D₄	—	2	1	no	—
1140	D₄	—	2	4	no	—
1141	D₄	—	2	2	no	—
1142	D₄	—	4	2	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	4	4	no	—
1145	D₄	—	4	4	no	—
1146	D₄	—	4	4	no	—
1147	D₄	—	4	4	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	1	no	—
1154	D₄	—	8	1	no	—
1155	D₄	C₂×#41×C₂₃	1	4	yes	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	2	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	4	4	no	—
1175	C₂×C₄	—	4	4	no	—
1176	C₂×C₄	—	4	4	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	2	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	—	8	2	no	—
1186	C₂×C₄	—	8	1	no	—
1187	C₂×C₄	—	8	2	no	—
1188	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1189	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1190	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1191	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1194	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1195	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1196	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1197	C₈	—	2	2	no	—
1198	C₈	—	2	1	no	—
1199	C₈	—	2	1	no	—
1200	C₈	—	2	1	no	—
1201	C₈	—	2	1	no	—
1202	C₈	—	2	2	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	4	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	4	4	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	8	4	no	—
1225	C₂²	—	16	4	no	—
1226	C₂²	C₂₃×#546	1	2	yes	—
1227	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	2	no	—
1231	C₄	—	2	2	no	—
1232	C₄	—	2	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	2	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	2	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	C₂₃×#546	1	2	yes	—
1243	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1244	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1245	C₂	—	2	2	no	—
1246	C₂	—	4	1	no	—
1247	C₂	—	4	1	no	—
1248	C₂	—	4	2	no	—
1249	C₂	—	4	4	no	—
1250	C₂	—	8	1	no	—
1251	C₂	—	8	1	no	—
1252	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1253	C₂	C₂₃×#3585	1	1	yes	characteristic
1254	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
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×#3492	C₂	semidirect
2. C₂₃×#3485	C₂	semidirect
3. C₂₃×#3331	C₂	semidirect
4. C₂₃×#3330	C₂	semidirect
5. C₂₃×#3323	C₂	semidirect
6. C₂₃×#3322	C₂	semidirect
7. C₂₃×#3315	C₂	semidirect
8. C₂₃×#3314	C₂	semidirect
9. C₂₃×#3307	C₂	semidirect
10. C₂₃×#3306	C₂	semidirect
11. C₂₃×#3137	C₂	semidirect
12. C₂₃×#3097	C₂	semidirect
13. C₂₃×#3092	C₂	semidirect
14. C₂₃×#3081	C₂	semidirect
15. C₂₃×#3063	C₂	semidirect
16. C₂₃×#3054	C₂	semidirect
17. C₂₃×#3046	C₂	semidirect
18. C₂₃×#3012	C₂	semidirect
19. C₂₃×#3005	C₂	semidirect
20. C₂₃×#2946	C₂	semidirect
21. C₂₃×#2930	C₂	semidirect
22. C₂₃×#2897	C₂	semidirect
23. C₂×C₂₃×#417	C₂	semidirect
26. C₂×C₂₃×#137	C₂²	semidirect
30. C₂²×M₁₆×C₂₃	C₂²	semidirect
32. C₂₃×#554	C₂²	semidirect
34. C₂₃×#553	C₂²	semidirect
36. C₂₃×#552	C₂²	semidirect
42. C₂₃×#547	C₂²	semidirect
47. C₂₃×#544	C₂²	semidirect
56. C₂₃×#525	C₂²	semidirect
59. C₂₃×#520	C₂²	semidirect
61. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
62. C₂₃×#491	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#485	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#484	C₂²	semidirect
69. C₂₃×#484	C₂²	semidirect
70. C₂₃×#483	C₂²	semidirect
71. C₂₃×#483	C₂²	semidirect
72. C₂₃×#481	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#476	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#470	C₂²	semidirect
80. C₂₃×#470	C₂²	semidirect
81. C₂₃×#469	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
83. C₂₃×#468	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#468	C₂²	semidirect
88. C₂₃×#467	C₂²	semidirect
89. C₂₃×#465	C₂²	semidirect
90. C₂₃×#464	C₂²	semidirect
91. C₂₃×#463	C₂²	semidirect
92. C₂₃×#462	C₂²	semidirect
93. C₂₃×#461	C₂²	semidirect
94. C₂₃×#452	C₂²	semidirect
95. C₂₃×#452	C₂²	semidirect
96. C₂₃×#452	C₂²	semidirect
97. C₂₃×#450	C₂²	semidirect
98. C₂₃×#449	C₂²	semidirect
99. C₂₃×#449	C₂²	semidirect
100. C₂₃×#449	C₂²	semidirect
101. C₂₃×#447	C₂²	semidirect
102. C₂₃×#442	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₄×SD₁₆×C₂₃	C₂²	semidirect
105. C₄×D₈×C₂₃	C₂²	semidirect
106. C₂₃×#436	C₂²	semidirect
107. C₂₃×#436	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₂₃×#435	C₂²	semidirect
110. C₂₃×#428	C₂²	semidirect
111. C₂₃×#428	C₂²	semidirect
112. C₂₃×#427	C₂²	semidirect
113. C₂₃×#424	C₂²	semidirect
114. C₂₃×#419	C₂²	semidirect
116. C₂₃×#418	C₂²	semidirect
119. C₂₃×#417	C₂²	semidirect
120. C₂₃×#417	C₂²	semidirect
121. C₂₃×#417	C₂²	semidirect
122. C₂₃×#417	C₂²	semidirect
123. C₂₃×#417	C₂²	semidirect
125. C₂₃×#416	C₂²	semidirect
126. C₂₃×#416	C₂²	semidirect
127. C₂×C₂₃×#103	C₂²	semidirect
128. C₂×C₂₃×#103	C₂²	semidirect
131. C₂×C₂₃×#102	C₂²	semidirect
133. C₂₃×#407	C₂²	semidirect
134. C₂₃×#405	C₂²	semidirect
370. C₂×D₄×C₂₃	#41	semidirect
481. #61177	C₂₃	direct (N × H)
576. #3492	C₂×C₂₃	semidirect
577. #3485	C₂×C₂₃	semidirect
578. #3331	C₂×C₂₃	semidirect
579. #3330	C₂×C₂₃	semidirect
580. #3323	C₂×C₂₃	semidirect
581. #3322	C₂×C₂₃	semidirect
582. #3315	C₂×C₂₃	semidirect
583. #3314	C₂×C₂₃	semidirect
584. #3307	C₂×C₂₃	semidirect
585. #3306	C₂×C₂₃	semidirect
586. #3137	C₂×C₂₃	semidirect
587. #3097	C₂×C₂₃	semidirect
588. #3092	C₂×C₂₃	semidirect
589. #3081	C₂×C₂₃	semidirect
590. #3063	C₂×C₂₃	semidirect
591. #3054	C₂×C₂₃	semidirect
592. #3046	C₂×C₂₃	semidirect
593. #3012	C₂×C₂₃	semidirect
594. #3005	C₂×C₂₃	semidirect
595. #2946	C₂×C₂₃	semidirect
596. #2930	C₂×C₂₃	semidirect
597. #2897	C₂×C₂₃	semidirect
598. C₂×#417	C₂×C₂₃	semidirect
643. C₂×#137	C₂²×C₂₃	semidirect
647. C₂²×M₁₆	C₂²×C₂₃	semidirect
649. #554	C₂²×C₂₃	semidirect
651. #553	C₂²×C₂₃	semidirect
653. #552	C₂²×C₂₃	semidirect
659. #547	C₂²×C₂₃	semidirect
664. #544	C₂²×C₂₃	semidirect
673. #525	C₂²×C₂₃	semidirect
676. #520	C₂²×C₂₃	semidirect
678. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
679. #491	C₂²×C₂₃	semidirect
680. #489	C₂²×C₂₃	semidirect
681. #488	C₂²×C₂₃	semidirect
682. #487	C₂²×C₂₃	semidirect
683. #485	C₂²×C₂₃	semidirect
684. #485	C₂²×C₂₃	semidirect
685. #484	C₂²×C₂₃	semidirect
686. #484	C₂²×C₂₃	semidirect
687. #483	C₂²×C₂₃	semidirect
688. #483	C₂²×C₂₃	semidirect
689. #481	C₂²×C₂₃	semidirect
690. #480	C₂²×C₂₃	semidirect
691. #478	C₂²×C₂₃	semidirect
692. #478	C₂²×C₂₃	semidirect
693. #476	C₂²×C₂₃	semidirect
694. #474	C₂²×C₂₃	semidirect
695. #470	C₂²×C₂₃	semidirect
696. #470	C₂²×C₂₃	semidirect
697. #470	C₂²×C₂₃	semidirect
698. #469	C₂²×C₂₃	semidirect
699. #469	C₂²×C₂₃	semidirect
700. #468	C₂²×C₂₃	semidirect
701. #468	C₂²×C₂₃	semidirect
702. #468	C₂²×C₂₃	semidirect
703. #468	C₂²×C₂₃	semidirect
704. #468	C₂²×C₂₃	semidirect
705. #467	C₂²×C₂₃	semidirect
706. #465	C₂²×C₂₃	semidirect
707. #464	C₂²×C₂₃	semidirect
708. #463	C₂²×C₂₃	semidirect
709. #462	C₂²×C₂₃	semidirect
710. #461	C₂²×C₂₃	semidirect
711. #452	C₂²×C₂₃	semidirect
712. #452	C₂²×C₂₃	semidirect
713. #452	C₂²×C₂₃	semidirect
714. #450	C₂²×C₂₃	semidirect
715. #449	C₂²×C₂₃	semidirect
716. #449	C₂²×C₂₃	semidirect
717. #449	C₂²×C₂₃	semidirect
718. #447	C₂²×C₂₃	semidirect
719. #442	C₂²×C₂₃	semidirect
720. #440	C₂²×C₂₃	semidirect
721. C₄×SD₁₆	C₂²×C₂₃	semidirect
722. C₄×D₈	C₂²×C₂₃	semidirect
723. #436	C₂²×C₂₃	semidirect
724. #436	C₂²×C₂₃	semidirect
725. #435	C₂²×C₂₃	semidirect
726. #435	C₂²×C₂₃	semidirect
727. #428	C₂²×C₂₃	semidirect
728. #428	C₂²×C₂₃	semidirect
729. #427	C₂²×C₂₃	semidirect
730. #424	C₂²×C₂₃	semidirect
731. #419	C₂²×C₂₃	semidirect
733. #418	C₂²×C₂₃	semidirect
736. #417	C₂²×C₂₃	semidirect
737. #417	C₂²×C₂₃	semidirect
738. #417	C₂²×C₂₃	semidirect
739. #417	C₂²×C₂₃	semidirect
740. #417	C₂²×C₂₃	semidirect
742. #416	C₂²×C₂₃	semidirect
743. #416	C₂²×C₂₃	semidirect
744. C₂×#103	C₂²×C₂₃	semidirect
745. C₂×#103	C₂²×C₂₃	semidirect
748. C₂×#102	C₂²×C₂₃	semidirect
750. #407	C₂²×C₂₃	semidirect
751. #405	C₂²×C₂₃	semidirect
948. C₂₃	#61177	direct (N × H)
998. C₂×D₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3492	2
C₂₃×#3485	2
C₂₃×#3331	2
C₂₃×#3330	2
C₂₃×#3323	2
C₂₃×#3322	2
C₂₃×#3315	2
C₂₃×#3314	2
C₂₃×#3307	2
C₂₃×#3306	2
C₂₃×#3137	2
C₂₃×#3097	2
C₂₃×#3092	2
C₂₃×#3081	2
C₂₃×#3063	2
C₂₃×#3054	2
C₂₃×#3046	2
C₂₃×#3012	2
C₂₃×#3005	2
C₂₃×#2946	2
C₂₃×#2930	2
C₂₃×#2897	2
C₂×C₂₃×#417	2
#61177	23

Subgroups — C23×#61177 #19208803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61177 #19208803