Subgroups — C₂₃×#61173 #19208799

Order 5888.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1240 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×#3489	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3302	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3011	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×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	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
28	C₂²×Q₁₆×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
31	C₂₃×#556	C₂²	1	2	yes	complemented
32	C₂₃×#554	C₂²	1	2	yes	—
33	C₂₃×#552	—	2	2	no	—
34	C₂₃×#552	C₂²	1	2	yes	—
35	C₂₃×#552	C₂²	1	2	yes	complemented
36	C₂₃×#551	—	2	2	no	—
37	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
38	C₂₃×#548	C₂²	1	2	yes	—
39	C₂₃×#547	—	2	2	no	—
40	C₂₃×#547	C₂²	1	2	yes	—
41	C₂₃×#546	—	2	2	no	—
42	C₂₃×#546	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	—	2	1	no	—
49	C₂₃×#536	C₂²	1	1	yes	characteristic
50	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
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	—	2	1	no	—
56	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×C₂²⋊Q₈	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
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×#485	C₂²	1	2	yes	complemented
69	C₂₃×#484	C₂²	1	2	yes	—
70	C₂₃×#484	C₂²	1	2	yes	complemented
71	C₂₃×#483	C₂²	1	2	yes	—
72	C₂₃×#482	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×#477	C₂²	1	2	yes	complemented
77	C₂₃×#474	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	—
81	C₂₃×#467	C₂²	1	2	yes	—
82	C₂₃×#467	C₂²	1	2	yes	complemented
83	C₂₃×#467	C₂²	1	2	yes	complemented
84	C₂₃×#467	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×#462	C₂²	1	2	yes	complemented
89	C₂₃×#462	C₂²	1	2	yes	complemented
90	C₂₃×#452	C₂²	1	2	yes	—
91	C₂₃×#452	C₂²	1	2	yes	—
92	C₂₃×#452	C₂²	1	2	yes	complemented
93	C₂₃×#452	C₂²	1	2	yes	complemented
94	C₂₃×#451	C₂²	1	2	yes	—
95	C₂₃×#451	C₂²	1	2	yes	complemented
96	C₂₃×#451	C₂²	1	2	yes	complemented
97	C₂₃×#450	C₂²	1	2	yes	—
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	—
103	C₂₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₂₃	C₂²	1	2	yes	—
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×#107	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#419	C₂²	1	2	yes	complemented
113	C₂₃×#417	C₂²	1	1	yes	characteristic
114	C₂₃×#417	C₂²	1	1	yes	characteristic
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
119	C₂₃×#416	C₂²	1	1	yes	characteristic
120	C₂₃×#416	C₂²	1	1	yes	characteristic
121	C₂₃×#416	C₂²	1	1	yes	characteristic
122	C₂₃×#416	C₂²	1	1	yes	characteristic
123	C₂₃×#416	C₂²	1	1	yes	characteristic
124	C₂₃×#416	C₂²	1	2	yes	complemented
125	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
126	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
127	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
129	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
131	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#407	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×2₋¹⁺⁴	—	2	4	no	—
136	C₂₃×2₋¹⁺⁴	—	4	2	no	—
137	C₂×#41×C₂₃	—	2	2	no	—
138	C₂×#41×C₂₃	—	2	1	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	1	yes	characteristic
147	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₂₃	—	2	1	no	—
150	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
153	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₂₃	—	2	1	no	—
155	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₂₃	—	2	1	no	—
157	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂₃×#137	—	2	4	no	—
159	C₂₃×#137	—	4	2	no	—
160	C₂×Q₁₆×C₂₃	—	4	2	no	—
161	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
162	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂₃×#131	—	4	2	no	—
168	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
171	C₂²×C₈×C₂₃	—	4	2	no	—
172	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
179	C₂₃×C₄⋊Q₈	—	2	1	no	—
180	C₂₃×C₄⋊Q₈	—	2	2	no	—
181	C₂₃×C₄⋊Q₈	—	2	1	no	—
182	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₂₃×#126	—	2	2	no	—
185	C₂₃×#126	—	2	2	no	—
186	C₂₃×#126	—	2	2	no	—
187	C₂₃×#126	—	2	2	no	—
188	C₂₃×#125	—	2	2	no	—
189	C₂₃×#125	—	2	2	no	—
190	C₂₃×#125	—	2	2	no	—
191	C₂₃×#125	—	2	1	no	—
192	C₂₃×#125	C₂³	1	2	yes	—
193	C₂₃×#124	—	2	2	no	—
194	C₂₃×#124	—	2	1	no	—
195	C₂₃×#124	—	2	2	no	—
196	C₂₃×#124	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	1	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	—	2	1	no	—
212	C₂₃×C₂²⋊Q₈	—	2	1	no	—
213	C₂₃×C₂²⋊Q₈	—	2	2	no	—
214	C₂₃×C₂²⋊Q₈	—	2	2	no	—
215	C₂₃×C₂²⋊Q₈	—	2	2	no	—
216	C₂₃×C₂²⋊Q₈	—	2	2	no	—
217	C₂₃×C₂²⋊Q₈	—	2	2	no	—
218	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₂₃×#121	—	2	2	no	—
228	C₂₃×#121	—	2	2	no	—
229	C₂₃×#121	—	2	2	no	—
230	C₂₃×#121	—	2	1	no	—
231	C₂₃×#121	—	2	2	no	—
232	C₂₃×#121	D₄	1	1	yes	characteristic
233	C₂₃×#121	D₄	1	1	yes	characteristic
234	C₂₃×#121	C₂³	1	2	yes	—
235	C₂₃×#120	—	2	2	no	—
236	C₂₃×#120	D₄	1	2	yes	—
237	C₄×Q₈×C₂₃	—	2	1	no	—
238	C₄×Q₈×C₂₃	—	2	2	no	—
239	C₄×Q₈×C₂₃	—	2	1	no	—
240	C₄×Q₈×C₂₃	—	2	1	no	—
241	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	2	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	C₂³	1	2	yes	—
251	C₄×D₄×C₂₃	C₂³	1	2	yes	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	—	2	1	no	—
255	C₂₃×#117	—	2	1	no	—
256	C₂₃×#117	—	2	2	no	—
257	C₂₃×#117	—	2	2	no	—
258	C₂₃×#117	—	2	2	no	—
259	C₂₃×#117	C₂³	1	2	yes	—
260	C₂₃×#117	C₂³	1	1	yes	characteristic
261	C₂₃×#117	C₂³	1	1	yes	characteristic
262	C₂₃×#117	C₂³	1	1	yes	characteristic
263	C₂₃×#117	C₂³	1	1	yes	characteristic
264	C₂₃×#117	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
266	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
267	C₂×C₄⋊C₄×C₂₃	—	2	2	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×#107	C₂³	1	2	yes	—
282	C₂₃×#107	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×#103	C₂³	1	2	yes	—
300	C₂₃×#103	C₂³	1	2	yes	—
301	C₂₃×#103	C₂³	1	2	yes	—
302	C₂₃×#103	C₂³	1	2	yes	—
303	C₂₃×#103	C₂³	1	2	yes	—
304	C₂₃×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
309	C₂₃×#102	C₂³	1	1	yes	characteristic
310	C₂₃×#102	C₂³	1	1	yes	characteristic
311	C₂₃×#102	C₂³	1	1	yes	characteristic
312	C₂₃×#102	C₂³	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
323	#41×C₂₃	—	2	2	no	—
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	2	2	no	—
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	2	no	—
328	#41×C₂₃	—	2	4	no	—
329	#41×C₂₃	—	2	2	no	—
330	#41×C₂₃	—	2	2	no	—
331	#41×C₂₃	—	4	4	no	—
332	#41×C₂₃	—	4	1	no	—
333	#41×C₂₃	—	4	1	no	—
334	#41×C₂₃	—	4	2	no	—
335	#41×C₂₃	—	4	4	no	—
336	#41×C₂₃	—	4	4	no	—
337	#41×C₂₃	—	4	8	no	—
338	#41×C₂₃	#41	1	4	yes	—
339	C₂×Q₈×C₂₃	—	2	1	no	—
340	C₂×Q₈×C₂₃	—	2	1	no	—
341	C₂×Q₈×C₂₃	—	2	2	no	—
342	C₂×Q₈×C₂₃	—	2	1	no	—
343	C₂×Q₈×C₂₃	—	2	2	no	—
344	C₂×Q₈×C₂₃	—	2	2	no	—
345	C₂×Q₈×C₂₃	—	2	4	no	—
346	C₂×Q₈×C₂₃	—	2	2	no	—
347	C₂×Q₈×C₂₃	—	2	2	no	—
348	C₂×Q₈×C₂₃	—	2	2	no	—
349	C₂×Q₈×C₂₃	—	2	2	no	—
350	C₂×Q₈×C₂₃	—	4	1	no	—
351	C₂×Q₈×C₂₃	—	4	2	no	—
352	C₂×Q₈×C₂₃	—	4	4	no	—
353	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	2	no	—
365	C₂×D₄×C₂₃	—	2	1	no	—
366	C₂×D₄×C₂₃	—	4	1	no	—
367	C₂×D₄×C₂₃	—	4	4	no	—
368	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₂₃	—	2	1	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	1	no	—
380	C₂²×C₄×C₂₃	—	2	2	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	1	no	—
385	C₂²×C₄×C₂₃	—	2	2	no	—
386	C₂²×C₄×C₂₃	—	2	2	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	2	no	—
391	C₂²×C₄×C₂₃	—	4	4	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	2	yes	—
397	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₂₃	—	2	4	no	—
400	Q₁₆×C₂₃	—	4	2	no	—
401	Q₁₆×C₂₃	—	4	2	no	—
402	Q₁₆×C₂₃	—	4	2	no	—
403	SD₁₆×C₂₃	—	2	4	no	—
404	SD₁₆×C₂₃	—	4	2	no	—
405	M₁₆×C₂₃	—	2	2	no	—
406	M₁₆×C₂₃	—	2	2	no	—
407	M₁₆×C₂₃	—	4	2	no	—
408	C₂×C₈×C₂₃	—	2	2	no	—
409	C₂×C₈×C₂₃	—	2	2	no	—
410	C₂×C₈×C₂₃	—	4	1	no	—
411	C₂×C₈×C₂₃	—	4	1	no	—
412	C₂×C₈×C₂₃	—	4	1	no	—
413	C₂×C₈×C₂₃	—	4	1	no	—
414	C₂×C₈×C₂₃	—	4	2	no	—
415	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
421	C₄⋊C₄×C₂₃	—	2	2	no	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	2	no	—
424	C₄⋊C₄×C₂₃	—	2	2	no	—
425	C₄⋊C₄×C₂₃	—	2	2	no	—
426	C₄⋊C₄×C₂₃	—	2	2	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	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	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	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
443	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
445	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
451	C₂²⋊C₄×C₂₃	—	2	2	no	—
452	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	2	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	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	C₄²×C₂₃	—	2	1	no	—
473	C₄²×C₂₃	—	2	1	no	—
474	C₄²×C₂₃	—	2	1	no	—
475	C₄²×C₂₃	—	2	1	no	—
476	C₄²×C₂₃	—	2	2	no	—
477	C₄²×C₂₃	—	2	2	no	—
478	C₄²×C₂₃	—	2	2	no	—
479	C₄²×C₂₃	—	2	2	no	—
480	C₄²×C₂₃	C₂⁴	1	2	yes	—
481	#61173	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	1	no	—
485	C₂³×C₂₃	—	2	1	no	—
486	C₂³×C₂₃	—	4	1	no	—
487	C₂³×C₂₃	—	4	2	no	—
488	C₂³×C₂₃	—	4	2	no	—
489	C₂³×C₂₃	—	8	1	no	—
490	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
491	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
492	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
493	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
494	Q₈×C₂₃	—	2	2	no	—
495	Q₈×C₂₃	—	2	1	no	—
496	Q₈×C₂₃	—	2	2	no	—
497	Q₈×C₂₃	—	2	2	no	—
498	Q₈×C₂₃	—	2	1	no	—
499	Q₈×C₂₃	—	2	2	no	—
500	Q₈×C₂₃	—	2	2	no	—
501	Q₈×C₂₃	—	2	1	no	—
502	Q₈×C₂₃	—	4	4	no	—
503	Q₈×C₂₃	—	4	2	no	—
504	Q₈×C₂₃	—	4	2	no	—
505	Q₈×C₂₃	—	4	2	no	—
506	Q₈×C₂₃	—	8	2	no	—
507	Q₈×C₂₃	C₂×#41	1	2	yes	—
508	D₄×C₂₃	—	2	4	no	—
509	D₄×C₂₃	—	2	4	no	—
510	D₄×C₂₃	—	2	4	no	—
511	D₄×C₂₃	—	2	2	no	—
512	D₄×C₂₃	—	2	1	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	2	no	—
518	D₄×C₂₃	—	4	2	no	—
519	D₄×C₂₃	—	4	4	no	—
520	D₄×C₂₃	—	4	2	no	—
521	D₄×C₂₃	—	8	2	no	—
522	D₄×C₂₃	C₂×#41	1	2	yes	—
523	C₂×C₄×C₂₃	—	2	2	no	—
524	C₂×C₄×C₂₃	—	2	1	no	—
525	C₂×C₄×C₂₃	—	2	2	no	—
526	C₂×C₄×C₂₃	—	2	2	no	—
527	C₂×C₄×C₂₃	—	2	4	no	—
528	C₂×C₄×C₂₃	—	2	1	no	—
529	C₂×C₄×C₂₃	—	2	1	no	—
530	C₂×C₄×C₂₃	—	2	2	no	—
531	C₂×C₄×C₂₃	—	2	1	no	—
532	C₂×C₄×C₂₃	—	2	1	no	—
533	C₂×C₄×C₂₃	—	2	2	no	—
534	C₂×C₄×C₂₃	—	2	1	no	—
535	C₂×C₄×C₂₃	—	2	1	no	—
536	C₂×C₄×C₂₃	—	2	1	no	—
537	C₂×C₄×C₂₃	—	2	2	no	—
538	C₂×C₄×C₂₃	—	2	1	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	2	2	no	—
542	C₂×C₄×C₂₃	—	2	1	no	—
543	C₂×C₄×C₂₃	—	4	2	no	—
544	C₂×C₄×C₂₃	—	4	2	no	—
545	C₂×C₄×C₂₃	—	4	2	no	—
546	C₂×C₄×C₂₃	—	4	4	no	—
547	C₂×C₄×C₂₃	—	4	4	no	—
548	C₂×C₄×C₂₃	—	4	2	no	—
549	C₂×C₄×C₂₃	—	4	2	no	—
550	C₂×C₄×C₂₃	—	4	2	no	—
551	C₂×C₄×C₂₃	—	4	2	no	—
552	C₂×C₄×C₂₃	—	8	2	no	—
553	C₂×C₄×C₂₃	—	8	2	no	—
554	C₂×C₄×C₂₃	—	8	1	no	—
555	C₂×C₄×C₂₃	—	8	1	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
558	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
564	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
565	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
566	C₈×C₂₃	—	2	2	no	—
567	C₈×C₂₃	—	2	1	no	—
568	C₈×C₂₃	—	2	1	no	—
569	C₈×C₂₃	—	2	1	no	—
570	C₈×C₂₃	—	2	1	no	—
571	C₈×C₂₃	—	2	2	no	—
572	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
573	#3489	C₂×C₂₃	1	1	yes	characteristic
574	#3315	C₂×C₂₃	1	2	yes	complemented
575	#3314	C₂×C₂₃	1	2	yes	complemented
576	#3313	C₂×C₂₃	1	2	yes	complemented
577	#3312	C₂×C₂₃	1	2	yes	complemented
578	#3302	C₂×C₂₃	1	2	yes	complemented
579	#3300	C₂×C₂₃	1	2	yes	complemented
580	#3299	C₂×C₂₃	1	2	yes	complemented
581	#3296	C₂×C₂₃	1	2	yes	complemented
582	#3137	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3098	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
585	#3083	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
587	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3044	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3011	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
591	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
594	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
595	C₂²×C₂₃	—	2	1	no	—
596	C₂²×C₂₃	—	2	1	no	—
597	C₂²×C₂₃	—	2	1	no	—
598	C₂²×C₂₃	—	2	1	no	—
599	C₂²×C₂₃	—	2	2	no	—
600	C₂²×C₂₃	—	2	1	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	2	no	—
603	C₂²×C₂₃	—	2	2	no	—
604	C₂²×C₂₃	—	2	2	no	—
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	4	4	no	—
607	C₂²×C₂₃	—	4	1	no	—
608	C₂²×C₂₃	—	4	1	no	—
609	C₂²×C₂₃	—	4	1	no	—
610	C₂²×C₂₃	—	4	1	no	—
611	C₂²×C₂₃	—	4	1	no	—
612	C₂²×C₂₃	—	8	4	no	—
613	C₂²×C₂₃	#546	1	2	yes	—
614	C₂²×C₂₃	#578	1	2	yes	—
615	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
616	C₄×C₂₃	—	2	2	no	—
617	C₄×C₂₃	—	2	1	no	—
618	C₄×C₂₃	—	2	1	no	—
619	C₄×C₂₃	—	2	2	no	—
620	C₄×C₂₃	—	2	2	no	—
621	C₄×C₂₃	—	2	2	no	—
622	C₄×C₂₃	—	4	1	no	—
623	C₄×C₂₃	—	4	2	no	—
624	C₄×C₂₃	—	4	2	no	—
625	C₄×C₂₃	—	4	1	no	—
626	C₄×C₂₃	—	4	1	no	—
627	C₄×C₂₃	—	4	2	no	—
628	C₄×C₂₃	—	4	2	no	—
629	C₄×C₂₃	—	4	1	no	—
630	C₄×C₂₃	—	4	1	no	—
631	C₄×C₂₃	#546	1	2	yes	—
632	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
633	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
634	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
635	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
636	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
637	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
638	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
639	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
641	#556	C₂²×C₂₃	1	2	yes	complemented
642	#554	C₂²×C₂₃	1	2	yes	—
643	#552	—	2	2	no	—
644	#552	C₂²×C₂₃	1	2	yes	—
645	#552	C₂²×C₂₃	1	2	yes	complemented
646	#551	—	2	2	no	—
647	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
648	#548	C₂²×C₂₃	1	2	yes	—
649	#547	—	2	2	no	—
650	#547	C₂²×C₂₃	1	2	yes	—
651	#546	—	2	2	no	—
652	#546	C₂²×C₂₃	1	2	yes	—
653	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#542	—	2	1	no	—
655	#541	—	2	1	no	—
656	#537	—	2	1	no	—
657	#537	C₂²×C₂₃	1	1	yes	characteristic
658	#536	—	2	1	no	—
659	#536	C₂²×C₂₃	1	1	yes	characteristic
660	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#533	—	2	1	no	—
662	#529	—	2	1	no	—
663	#525	—	2	1	no	—
664	#525	C₂²×C₂₃	1	1	yes	characteristic
665	C₂×C₂²⋊Q₈	—	2	1	no	—
666	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
667	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
668	#520	C₂²×C₂₃	1	1	yes	characteristic
669	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
672	#491	C₂²×C₂₃	1	2	yes	complemented
673	#489	C₂²×C₂₃	1	2	yes	complemented
674	#488	C₂²×C₂₃	1	2	yes	complemented
675	#487	C₂²×C₂₃	1	2	yes	complemented
676	#485	C₂²×C₂₃	1	2	yes	complemented
677	#485	C₂²×C₂₃	1	2	yes	complemented
678	#485	C₂²×C₂₃	1	2	yes	complemented
679	#484	C₂²×C₂₃	1	2	yes	—
680	#484	C₂²×C₂₃	1	2	yes	complemented
681	#483	C₂²×C₂₃	1	2	yes	—
682	#482	C₂²×C₂₃	1	2	yes	complemented
683	#480	C₂²×C₂₃	1	2	yes	complemented
684	#479	C₂²×C₂₃	1	2	yes	complemented
685	#478	C₂²×C₂₃	1	2	yes	complemented
686	#477	C₂²×C₂₃	1	2	yes	complemented
687	#474	C₂²×C₂₃	1	2	yes	complemented
688	#470	C₂²×C₂₃	1	2	yes	complemented
689	#468	C₂²×C₂₃	1	2	yes	complemented
690	#467	C₂²×C₂₃	1	2	yes	—
691	#467	C₂²×C₂₃	1	2	yes	—
692	#467	C₂²×C₂₃	1	2	yes	complemented
693	#467	C₂²×C₂₃	1	2	yes	complemented
694	#467	C₂²×C₂₃	1	2	yes	complemented
695	#465	C₂²×C₂₃	1	2	yes	complemented
696	#464	C₂²×C₂₃	1	2	yes	complemented
697	#464	C₂²×C₂₃	1	2	yes	complemented
698	#462	C₂²×C₂₃	1	2	yes	complemented
699	#462	C₂²×C₂₃	1	2	yes	complemented
700	#452	C₂²×C₂₃	1	2	yes	—
701	#452	C₂²×C₂₃	1	2	yes	—
702	#452	C₂²×C₂₃	1	2	yes	complemented
703	#452	C₂²×C₂₃	1	2	yes	complemented
704	#451	C₂²×C₂₃	1	2	yes	—
705	#451	C₂²×C₂₃	1	2	yes	complemented
706	#451	C₂²×C₂₃	1	2	yes	complemented
707	#450	C₂²×C₂₃	1	2	yes	—
708	#441	C₂²×C₂₃	1	2	yes	complemented
709	#440	C₂²×C₂₃	1	2	yes	complemented
710	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
711	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
712	#435	C₂²×C₂₃	1	2	yes	—
713	#435	C₂²×C₂₃	1	2	yes	complemented
714	C₈×D₄	C₂²×C₂₃	1	2	yes	—
715	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
716	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
717	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
718	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
720	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
721	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
722	#419	C₂²×C₂₃	1	2	yes	complemented
723	#417	C₂²×C₂₃	1	1	yes	characteristic
724	#417	C₂²×C₂₃	1	1	yes	characteristic
725	#417	C₂²×C₂₃	1	2	yes	complemented
726	#416	C₂²×C₂₃	1	1	yes	characteristic
727	#416	C₂²×C₂₃	1	1	yes	characteristic
728	#416	C₂²×C₂₃	1	1	yes	characteristic
729	#416	C₂²×C₂₃	1	1	yes	characteristic
730	#416	C₂²×C₂₃	1	1	yes	characteristic
731	#416	C₂²×C₂₃	1	1	yes	characteristic
732	#416	C₂²×C₂₃	1	1	yes	characteristic
733	#416	C₂²×C₂₃	1	1	yes	characteristic
734	#416	C₂²×C₂₃	1	2	yes	complemented
735	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
736	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
737	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
738	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
739	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
740	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
741	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
742	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
743	#407	C₂²×C₂₃	1	1	yes	characteristic
744	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	C₂×C₂₃	—	2	2	no	—
746	C₂×C₂₃	—	2	2	no	—
747	C₂×C₂₃	—	4	2	no	—
748	C₂×C₂₃	—	4	1	no	—
749	C₂×C₂₃	—	4	2	no	—
750	C₂×C₂₃	—	8	1	no	—
751	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
752	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
753	C₂×C₂₃	#3584	1	1	yes	characteristic
754	2₋¹⁺⁴	—	2	4	no	—
755	2₋¹⁺⁴	—	4	2	no	—
756	C₂×#41	—	2	1	no	—
757	C₂×#41	—	2	2	no	—
758	C₂×#41	—	2	1	no	—
759	C₂×#41	—	2	1	no	—
760	C₂×#41	—	2	4	no	—
761	C₂×#41	—	4	2	no	—
762	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
763	C₂×#41	C₂³×C₂₃	1	2	yes	—
764	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
765	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
766	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
767	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
768	C₂²×Q₈	—	2	1	no	—
769	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
771	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
772	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
773	C₂²×D₄	—	2	1	no	—
774	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
775	C₂³×C₄	—	2	1	no	—
776	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
777	#137	—	2	4	no	—
778	#137	—	4	2	no	—
779	C₂×Q₁₆	—	4	2	no	—
780	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
781	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
782	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
786	#131	—	4	2	no	—
787	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
788	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
790	C₂²×C₈	—	4	2	no	—
791	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
792	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
794	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
795	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
798	C₄⋊Q₈	—	2	1	no	—
799	C₄⋊Q₈	—	2	1	no	—
800	C₄⋊Q₈	—	2	2	no	—
801	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
802	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#126	—	2	2	no	—
807	#125	—	2	1	no	—
808	#125	—	2	2	no	—
809	#125	—	2	2	no	—
810	#125	—	2	2	no	—
811	#125	C₂³×C₂₃	1	2	yes	—
812	#124	—	2	1	no	—
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	C₂³×C₂₃	1	2	yes	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	D₄×C₂₃	1	2	yes	—
824	C₂²⋊Q₈	—	2	1	no	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	—	2	1	no	—
832	C₂²⋊Q₈	—	2	2	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	—	2	2	no	—
837	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
838	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
839	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
840	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
841	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
842	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
846	#121	—	2	1	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	D₄×C₂₃	1	1	yes	characteristic
852	#121	D₄×C₂₃	1	1	yes	characteristic
853	#121	C₂³×C₂₃	1	2	yes	—
854	#120	—	2	2	no	—
855	#120	D₄×C₂₃	1	2	yes	—
856	C₄×Q₈	—	2	1	no	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	—	2	2	no	—
860	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
861	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
862	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	C₂³×C₂₃	1	2	yes	—
870	C₄×D₄	C₂³×C₂₃	1	2	yes	—
871	C₄×D₄	C₂³×C₂₃	1	2	yes	—
872	#117	—	2	1	no	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	—	2	2	no	—
876	#117	—	2	2	no	—
877	#117	—	2	2	no	—
878	#117	C₂³×C₂₃	1	1	yes	characteristic
879	#117	C₂³×C₂₃	1	1	yes	characteristic
880	#117	C₂³×C₂₃	1	1	yes	characteristic
881	#117	C₂³×C₂₃	1	1	yes	characteristic
882	#117	C₂³×C₂₃	1	2	yes	—
883	#117	C₂³×C₂₃	1	1	yes	characteristic
884	C₂×C₄⋊C₄	—	2	1	no	—
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	—	2	1	no	—
887	C₂×C₄⋊C₄	—	2	2	no	—
888	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
893	C₂×C₂²⋊C₄	—	2	1	no	—
894	C₂×C₂²⋊C₄	—	2	1	no	—
895	C₂×C₂²⋊C₄	—	2	1	no	—
896	C₂×C₂²⋊C₄	—	2	2	no	—
897	C₂×C₄²	—	2	1	no	—
898	#107	C₂³×C₂₃	1	2	yes	—
899	#107	C₂³×C₂₃	1	2	yes	—
900	#107	C₂³×C₂₃	1	2	yes	—
901	#107	C₂³×C₂₃	1	2	yes	—
902	#106	C₂³×C₂₃	1	2	yes	—
903	#106	C₂³×C₂₃	1	2	yes	—
904	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
905	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
906	#103	C₂³×C₂₃	1	1	yes	characteristic
907	#103	C₂³×C₂₃	1	1	yes	characteristic
908	#103	C₂³×C₂₃	1	1	yes	characteristic
909	#103	C₂³×C₂₃	1	1	yes	characteristic
910	#103	C₂³×C₂₃	1	1	yes	characteristic
911	#103	C₂³×C₂₃	1	1	yes	characteristic
912	#103	C₂³×C₂₃	1	1	yes	characteristic
913	#103	C₂³×C₂₃	1	1	yes	characteristic
914	#103	C₂³×C₂₃	1	2	yes	—
915	#103	C₂³×C₂₃	1	2	yes	—
916	#103	C₂³×C₂₃	1	2	yes	—
917	#103	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	2	yes	—
923	#103	C₂³×C₂₃	1	2	yes	—
924	#102	C₂³×C₂₃	1	1	yes	characteristic
925	#102	C₂³×C₂₃	1	1	yes	characteristic
926	#102	C₂³×C₂₃	1	1	yes	characteristic
927	#102	C₂³×C₂₃	1	1	yes	characteristic
928	#102	C₂³×C₂₃	1	1	yes	characteristic
929	#102	C₂³×C₂₃	1	1	yes	characteristic
930	#102	C₂³×C₂₃	1	1	yes	characteristic
931	#102	C₂³×C₂₃	1	1	yes	characteristic
932	#102	C₂³×C₂₃	1	2	yes	—
933	#102	C₂³×C₂₃	1	2	yes	—
934	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
938	#97	C₂³×C₂₃	1	2	yes	—
939	C₄×C₈	C₂³×C₂₃	1	2	yes	—
940	C₂₃	#61173	1	1	yes	characteristic, direct product factor, Sylow
941	C₂⁴	—	2	1	no	—
942	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	4	4	no	—
952	#41	—	4	1	no	—
953	#41	—	4	1	no	—
954	#41	—	4	2	no	—
955	#41	—	4	4	no	—
956	#41	—	4	4	no	—
957	#41	—	4	8	no	—
958	#41	#41×C₂₃	1	4	yes	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	4	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	4	1	no	—
971	C₂×Q₈	—	4	2	no	—
972	C₂×Q₈	—	4	4	no	—
973	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
975	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
977	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	4	1	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
991	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
992	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
993	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	4	4	no	—
1012	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1019	Q₁₆	—	2	4	no	—
1020	Q₁₆	—	4	2	no	—
1021	Q₁₆	—	4	2	no	—
1022	Q₁₆	—	4	2	no	—
1023	SD₁₆	—	2	4	no	—
1024	SD₁₆	—	4	2	no	—
1025	M₁₆	—	2	2	no	—
1026	M₁₆	—	2	2	no	—
1027	M₁₆	—	4	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	4	1	no	—
1031	C₂×C₈	—	4	1	no	—
1032	C₂×C₈	—	4	1	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	2	no	—
1035	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1038	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	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	C₂×D₄×C₂₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1063	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1088	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	C₂⁴×C₂₃	1	2	yes	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	4	1	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	8	1	no	—
1109	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1110	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1111	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1113	Q₈	—	2	1	no	—
1114	Q₈	—	2	2	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	1	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	4	4	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	4	2	no	—
1125	Q₈	—	8	2	no	—
1126	Q₈	C₂×#41×C₂₃	1	2	yes	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	C₂×#41×C₂₃	1	2	yes	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	4	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	4	2	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	—	8	1	no	—
1176	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1180	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1182	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1183	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1184	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	2	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	4	4	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	8	4	no	—
1209	C₂²	C₂₃×#546	1	2	yes	—
1210	C₂²	C₂₃×#578	1	2	yes	—
1211	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	1	no	—
1227	C₄	C₂₃×#546	1	2	yes	—
1228	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1229	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1230	C₂	—	2	2	no	—
1231	C₂	—	2	2	no	—
1232	C₂	—	4	1	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1237	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1238	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×#3489	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×#3315	C₂	semidirect
4. C₂₃×#3314	C₂	semidirect
5. C₂₃×#3313	C₂	semidirect
6. C₂₃×#3312	C₂	semidirect
7. C₂₃×#3302	C₂	semidirect
8. C₂₃×#3300	C₂	semidirect
9. C₂₃×#3299	C₂	semidirect
10. C₂₃×#3296	C₂	semidirect
11. C₂₃×#3137	C₂	semidirect
12. C₂₃×#3098	C₂	semidirect
13. C₂₃×#3095	C₂	semidirect
14. C₂₃×#3083	C₂	semidirect
15. C₂₃×#3063	C₂	semidirect
16. C₂×C₂₃×#467	C₂	semidirect
17. C₂₃×#3044	C₂	semidirect
18. C₂₃×#3011	C₂	semidirect
19. C₂₃×#3007	C₂	semidirect
20. C₂₃×#2947	C₂	semidirect
21. C₂₃×#2929	C₂	semidirect
22. C₂₃×#2898	C₂	semidirect
23. C₂×C₂₃×#416	C₂	semidirect
28. C₂²×Q₁₆×C₂₃	C₂²	semidirect
29. C₂×C₂₃×#131	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
35. C₂₃×#552	C₂²	semidirect
43. C₂₃×#544	C₂²	semidirect
50. C₂₃×#536	C₂²	semidirect
59. C₂₃×#520	C₂²	semidirect
60. C₂₃×#519	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×#485	C₂²	semidirect
70. C₂₃×#484	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#480	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#474	C₂²	semidirect
78. C₂₃×#470	C₂²	semidirect
79. C₂₃×#468	C₂²	semidirect
82. C₂₃×#467	C₂²	semidirect
83. C₂₃×#467	C₂²	semidirect
84. C₂₃×#467	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
87. C₂₃×#464	C₂²	semidirect
88. C₂₃×#462	C₂²	semidirect
89. C₂₃×#462	C₂²	semidirect
92. C₂₃×#452	C₂²	semidirect
93. C₂₃×#452	C₂²	semidirect
95. C₂₃×#451	C₂²	semidirect
96. C₂₃×#451	C₂²	semidirect
98. C₂₃×#441	C₂²	semidirect
99. C₂₃×#440	C₂²	semidirect
100. C₄×Q₁₆×C₂₃	C₂²	semidirect
101. C₄×SD₁₆×C₂₃	C₂²	semidirect
103. C₂₃×#435	C₂²	semidirect
105. C₈×D₄×C₂₃	C₂²	semidirect
106. C₂₃×#428	C₂²	semidirect
107. C₂₃×#428	C₂²	semidirect
108. C₂×C₂₃×#107	C₂²	semidirect
109. C₂₃×#424	C₂²	semidirect
110. C₂₃×#419	C₂²	semidirect
111. C₂₃×#419	C₂²	semidirect
112. C₂₃×#419	C₂²	semidirect
115. C₂₃×#417	C₂²	semidirect
124. C₂₃×#416	C₂²	semidirect
127. C₂×C₂₃×#103	C₂²	semidirect
128. C₂×C₂₃×#103	C₂²	semidirect
129. C₂×C₂₃×#103	C₂²	semidirect
132. C₂₃×#408	C₂²	semidirect
134. C₂₃×#405	C₂²	semidirect
481. #61173	C₂₃	direct (N × H)
572. #3495	C₂×C₂₃	semidirect
574. #3315	C₂×C₂₃	semidirect
575. #3314	C₂×C₂₃	semidirect
576. #3313	C₂×C₂₃	semidirect
577. #3312	C₂×C₂₃	semidirect
578. #3302	C₂×C₂₃	semidirect
579. #3300	C₂×C₂₃	semidirect
580. #3299	C₂×C₂₃	semidirect
581. #3296	C₂×C₂₃	semidirect
582. #3137	C₂×C₂₃	semidirect
583. #3098	C₂×C₂₃	semidirect
584. #3095	C₂×C₂₃	semidirect
585. #3083	C₂×C₂₃	semidirect
586. #3063	C₂×C₂₃	semidirect
587. C₂×#467	C₂×C₂₃	semidirect
588. #3044	C₂×C₂₃	semidirect
589. #3011	C₂×C₂₃	semidirect
590. #3007	C₂×C₂₃	semidirect
591. #2947	C₂×C₂₃	semidirect
592. #2929	C₂×C₂₃	semidirect
593. #2898	C₂×C₂₃	semidirect
594. C₂×#416	C₂×C₂₃	semidirect
638. C₂²×Q₁₆	C₂²×C₂₃	semidirect
639. C₂×#131	C₂²×C₂₃	semidirect
641. #556	C₂²×C₂₃	semidirect
645. #552	C₂²×C₂₃	semidirect
653. #544	C₂²×C₂₃	semidirect
660. #536	C₂²×C₂₃	semidirect
669. #520	C₂²×C₂₃	semidirect
670. #519	C₂²×C₂₃	semidirect
672. #491	C₂²×C₂₃	semidirect
673. #489	C₂²×C₂₃	semidirect
674. #488	C₂²×C₂₃	semidirect
675. #487	C₂²×C₂₃	semidirect
676. #485	C₂²×C₂₃	semidirect
677. #485	C₂²×C₂₃	semidirect
678. #485	C₂²×C₂₃	semidirect
680. #484	C₂²×C₂₃	semidirect
682. #482	C₂²×C₂₃	semidirect
683. #480	C₂²×C₂₃	semidirect
684. #479	C₂²×C₂₃	semidirect
685. #478	C₂²×C₂₃	semidirect
686. #477	C₂²×C₂₃	semidirect
687. #474	C₂²×C₂₃	semidirect
688. #470	C₂²×C₂₃	semidirect
689. #468	C₂²×C₂₃	semidirect
692. #467	C₂²×C₂₃	semidirect
693. #467	C₂²×C₂₃	semidirect
694. #467	C₂²×C₂₃	semidirect
695. #465	C₂²×C₂₃	semidirect
696. #464	C₂²×C₂₃	semidirect
697. #464	C₂²×C₂₃	semidirect
698. #462	C₂²×C₂₃	semidirect
699. #462	C₂²×C₂₃	semidirect
702. #452	C₂²×C₂₃	semidirect
703. #452	C₂²×C₂₃	semidirect
705. #451	C₂²×C₂₃	semidirect
706. #451	C₂²×C₂₃	semidirect
708. #441	C₂²×C₂₃	semidirect
709. #440	C₂²×C₂₃	semidirect
710. C₄×Q₁₆	C₂²×C₂₃	semidirect
711. C₄×SD₁₆	C₂²×C₂₃	semidirect
713. #435	C₂²×C₂₃	semidirect
715. C₈×D₄	C₂²×C₂₃	semidirect
716. #428	C₂²×C₂₃	semidirect
717. #428	C₂²×C₂₃	semidirect
718. C₂×#107	C₂²×C₂₃	semidirect
719. #424	C₂²×C₂₃	semidirect
720. #419	C₂²×C₂₃	semidirect
721. #419	C₂²×C₂₃	semidirect
722. #419	C₂²×C₂₃	semidirect
725. #417	C₂²×C₂₃	semidirect
734. #416	C₂²×C₂₃	semidirect
737. C₂×#103	C₂²×C₂₃	semidirect
738. C₂×#103	C₂²×C₂₃	semidirect
739. C₂×#103	C₂²×C₂₃	semidirect
742. #408	C₂²×C₂₃	semidirect
744. #405	C₂²×C₂₃	semidirect
940. C₂₃	#61173	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×#3489	2
C₂₃×#3315	2
C₂₃×#3314	2
C₂₃×#3313	2
C₂₃×#3312	2
C₂₃×#3302	2
C₂₃×#3300	2
C₂₃×#3299	2
C₂₃×#3296	2
C₂₃×#3137	2
C₂₃×#3098	2
C₂₃×#3095	2
C₂₃×#3083	2
C₂₃×#3063	2
C₂×C₂₃×#467	2
C₂₃×#3044	2
C₂₃×#3011	2
C₂₃×#3007	2
C₂₃×#2947	2
C₂₃×#2929	2
C₂₃×#2898	2
C₂×C₂₃×#416	2
#61173	23

Subgroups — C23×#61173 #19208799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61173 #19208799