Subgroups — C₂₃×#60598 #19208224

Order 5888.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3127	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3126	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3120	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3119	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3111	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
29	C₂₃×#553	—	2	2	no	—
30	C₂₃×#553	—	2	2	no	—
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#552	—	2	1	no	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#541	C₂²	1	2	yes	—
36	C₂₃×#540	C₂²	1	2	yes	—
37	C₂₃×#537	C₂²	1	1	yes	characteristic
38	C₂₃×#537	C₂²	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂₃×#529	C₂²	1	2	yes	—
41	C₂₃×#529	C₂²	1	2	yes	—
42	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
43	C₂₃×#520	—	2	2	no	—
44	C₂₃×#520	—	2	1	no	—
45	C₂₃×#520	C₂²	1	1	yes	characteristic
46	C₂₃×#520	C₂²	1	2	yes	—
47	C₂₃×#520	C₂²	1	1	yes	characteristic
48	C₂₃×#520	C₂²	1	1	yes	characteristic
49	C₂₃×#520	C₂²	1	1	yes	characteristic
50	C₂₃×#519	—	2	1	no	—
51	C₂₃×#519	C₂²	1	1	yes	characteristic
52	C₂₃×#519	C₂²	1	2	yes	—
53	C₄×#41×C₂₃	—	2	2	no	—
54	C₄×#41×C₂₃	—	2	1	no	—
55	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
56	C₄×#41×C₂₃	C₂²	1	2	yes	—
57	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
59	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
61	C₂₃×#485	C₂²	1	2	yes	—
62	C₂₃×#485	C₂²	1	2	yes	—
63	C₂₃×#484	C₂²	1	2	yes	—
64	C₂₃×#483	C₂²	1	2	yes	—
65	C₂₃×#482	C₂²	1	2	yes	—
66	C₂₃×#482	C₂²	1	2	yes	—
67	C₂₃×#481	C₂²	1	2	yes	—
68	C₂₃×#480	C₂²	1	2	yes	—
69	C₂₃×#479	C₂²	1	2	yes	—
70	C₂₃×#479	C₂²	1	2	yes	—
71	C₂₃×#479	C₂²	1	2	yes	—
72	C₂₃×#479	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	—
74	C₂₃×#479	C₂²	1	2	yes	—
75	C₂₃×#478	C₂²	1	2	yes	—
76	C₂₃×#478	C₂²	1	2	yes	—
77	C₂₃×#464	C₂²	1	1	yes	characteristic
78	C₂₃×#464	C₂²	1	1	yes	characteristic
79	C₂₃×#464	C₂²	1	2	yes	—
80	C₂₃×#464	C₂²	1	2	yes	—
81	C₂₃×#463	C₂²	1	1	yes	characteristic
82	C₂₃×#463	C₂²	1	1	yes	characteristic
83	C₂₃×#462	C₂²	1	1	yes	characteristic
84	C₂₃×#462	C₂²	1	2	yes	—
85	C₂₃×#461	C₂²	1	1	yes	characteristic
86	C₂₃×#460	C₂²	1	1	yes	characteristic
87	C₂₃×#460	C₂²	1	2	yes	—
88	C₂₃×#459	C₂²	1	1	yes	characteristic
89	C₂₃×#452	C₂²	1	2	yes	—
90	C₂₃×#452	C₂²	1	2	yes	—
91	C₂₃×#451	C₂²	1	2	yes	—
92	C₂₃×#451	C₂²	1	2	yes	—
93	C₂₃×#449	C₂²	1	2	yes	—
94	C₂₃×#449	C₂²	1	2	yes	—
95	C₂₃×#448	C₂²	1	2	yes	—
96	C₂₃×#448	C₂²	1	2	yes	—
97	C₂₃×#442	C₂²	1	2	yes	—
98	C₂₃×#441	C₂²	1	2	yes	—
99	C₂₃×#441	C₂²	1	2	yes	—
100	C₂₃×#441	C₂²	1	2	yes	—
101	C₂₃×#440	C₂²	1	2	yes	—
102	C₂₃×#440	C₂²	1	2	yes	—
103	C₂₃×#440	C₂²	1	2	yes	—
104	C₂₃×#440	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
106	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
110	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
112	C₄×D₈×C₂₃	C₂²	1	2	yes	—
113	C₂₃×#433	C₂²	1	2	yes	—
114	C₂₃×#433	C₂²	1	2	yes	—
115	C₂₃×#432	C₂²	1	2	yes	—
116	C₂₃×#431	C₂²	1	2	yes	—
117	C₂₃×#428	C₂²	1	1	yes	characteristic
118	C₂₃×#428	C₂²	1	1	yes	characteristic
119	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
120	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
121	C₂₃×#423	C₂²	1	1	yes	characteristic
122	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	C₂₃×#417	C₂²	1	1	yes	characteristic
124	C₂₃×#417	C₂²	1	1	yes	characteristic
125	C₂₃×#417	C₂²	1	1	yes	characteristic
126	C₂₃×#417	C₂²	1	1	yes	characteristic
127	C₂₃×#416	C₂²	1	1	yes	characteristic
128	C₂₃×#416	C₂²	1	1	yes	characteristic
129	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
131	C₂₃×#408	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂₃×#405	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic
135	C₂₃×2₋¹⁺⁴	—	2	4	no	—
136	C₂₃×2₋¹⁺⁴	—	2	4	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	2	no	—
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	2	yes	—
142	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₂₃	—	2	1	no	—
145	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
147	C₂₃×#137	—	2	4	no	—
148	C₂₃×#137	—	2	4	no	—
149	C₂₃×#135	—	2	4	no	—
150	C₂₃×#135	—	2	4	no	—
151	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₂₃×#127	C₂³	1	1	yes	characteristic
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#125	—	2	2	no	—
174	C₂₃×#125	—	2	2	no	—
175	C₂₃×#125	—	2	1	no	—
176	C₂₃×#125	—	2	1	no	—
177	C₂₃×#125	C₂³	1	2	yes	—
178	C₂₃×#125	C₂³	1	2	yes	—
179	C₂₃×#124	C₂³	1	1	yes	characteristic
180	C₂₃×#124	C₂³	1	1	yes	characteristic
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	1	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₂₃×#121	—	2	1	no	—
190	C₂₃×#121	—	2	1	no	—
191	C₂₃×#121	—	2	2	no	—
192	C₂₃×#121	—	2	2	no	—
193	C₂₃×#121	—	2	1	no	—
194	C₂₃×#121	—	2	1	no	—
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	C₂³	1	2	yes	—
198	C₂₃×#121	C₂³	1	2	yes	—
199	C₄×Q₈×C₂₃	—	2	1	no	—
200	C₄×Q₈×C₂₃	—	2	1	no	—
201	C₄×Q₈×C₂₃	—	2	2	no	—
202	C₄×Q₈×C₂₃	—	2	1	no	—
203	C₄×Q₈×C₂₃	—	2	2	no	—
204	C₄×Q₈×C₂₃	—	2	2	no	—
205	C₄×Q₈×C₂₃	—	2	1	no	—
206	C₄×Q₈×C₂₃	—	2	2	no	—
207	C₄×Q₈×C₂₃	—	2	1	no	—
208	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
209	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
210	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	2	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	D₄	1	2	yes	—
235	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₂₃	D₄	1	2	yes	—
237	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
243	C₂₃×#117	—	2	1	no	—
244	C₂₃×#117	—	2	1	no	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	2	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	—	2	2	no	—
249	C₂₃×#117	—	2	2	no	—
250	C₂₃×#117	—	2	2	no	—
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	2	no	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	C₂³	1	1	yes	characteristic
255	C₂₃×#117	C₂³	1	2	yes	—
256	C₂₃×#117	C₂³	1	1	yes	characteristic
257	C₂₃×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
262	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
270	C₂×C₄²×C₂₃	—	2	1	no	—
271	C₂×C₄²×C₂₃	—	2	2	no	—
272	C₂×C₄²×C₂₃	—	2	2	no	—
273	C₂×C₄²×C₂₃	—	2	1	no	—
274	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
276	C₂₃×#107	C₂³	1	2	yes	—
277	C₂₃×#107	C₂³	1	2	yes	—
278	C₂₃×#107	C₂³	1	2	yes	—
279	C₂₃×#107	C₂³	1	2	yes	—
280	C₂₃×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
289	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₂₃×#103	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	1	yes	characteristic
295	C₂₃×#103	C₂³	1	1	yes	characteristic
296	C₂₃×#103	C₂³	1	1	yes	characteristic
297	C₂₃×#103	C₂³	1	1	yes	characteristic
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×#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	2	yes	—
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×#102	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₃×#97	C₂³	1	2	yes	—
315	C₂₃×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₂₃	C₂³	1	2	yes	—
317	C₄×C₈×C₂₃	C₂³	1	2	yes	—
318	#41×C₂₃	—	2	16	no	—
319	#41×C₂₃	—	2	8	no	—
320	#41×C₂₃	—	2	4	no	—
321	#41×C₂₃	—	2	4	no	—
322	#41×C₂₃	—	2	2	no	—
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	2	no	—
329	#41×C₂₃	#41	1	4	yes	—
330	C₂×Q₈×C₂₃	—	2	8	no	—
331	C₂×Q₈×C₂₃	—	2	4	no	—
332	C₂×Q₈×C₂₃	—	2	4	no	—
333	C₂×Q₈×C₂₃	—	2	2	no	—
334	C₂×Q₈×C₂₃	—	2	1	no	—
335	C₂×Q₈×C₂₃	—	2	2	no	—
336	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₂×Q₈×C₂₃	#41	1	4	yes	—
338	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
342	C₂×D₄×C₂₃	—	2	2	no	—
343	C₂×D₄×C₂₃	—	2	1	no	—
344	C₂×D₄×C₂₃	—	2	1	no	—
345	C₂×D₄×C₂₃	—	2	1	no	—
346	C₂×D₄×C₂₃	—	2	2	no	—
347	C₂×D₄×C₂₃	—	2	2	no	—
348	C₂×D₄×C₂₃	—	2	1	no	—
349	C₂×D₄×C₂₃	—	2	1	no	—
350	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	1	no	—
357	C₂²×C₄×C₂₃	—	2	2	no	—
358	C₂²×C₄×C₂₃	—	2	1	no	—
359	C₂²×C₄×C₂₃	—	2	2	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	1	no	—
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	1	no	—
365	C₂²×C₄×C₂₃	—	2	1	no	—
366	C₂²×C₄×C₂₃	—	2	2	no	—
367	C₂²×C₄×C₂₃	—	2	1	no	—
368	C₂²×C₄×C₂₃	—	2	2	no	—
369	C₂²×C₄×C₂₃	—	2	2	no	—
370	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
376	Q₁₆×C₂₃	—	2	2	no	—
377	Q₁₆×C₂₃	—	2	2	no	—
378	Q₁₆×C₂₃	—	2	4	no	—
379	Q₁₆×C₂₃	—	2	4	no	—
380	SD₁₆×C₂₃	—	2	2	no	—
381	SD₁₆×C₂₃	—	2	2	no	—
382	SD₁₆×C₂₃	—	2	4	no	—
383	SD₁₆×C₂₃	—	2	4	no	—
384	SD₁₆×C₂₃	—	2	2	no	—
385	SD₁₆×C₂₃	—	2	2	no	—
386	D₈×C₂₃	—	2	2	no	—
387	D₈×C₂₃	—	2	2	no	—
388	M₁₆×C₂₃	—	2	2	no	—
389	M₁₆×C₂₃	—	2	2	no	—
390	C₂×C₈×C₂₃	—	2	2	no	—
391	C₂×C₈×C₂₃	—	2	2	no	—
392	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
394	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	2	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	1	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	1	no	—
405	C₄⋊C₄×C₂₃	—	2	1	no	—
406	C₄⋊C₄×C₂₃	—	2	1	no	—
407	C₄⋊C₄×C₂₃	—	2	2	no	—
408	C₄⋊C₄×C₂₃	—	2	2	no	—
409	C₄⋊C₄×C₂₃	—	2	2	no	—
410	C₄⋊C₄×C₂₃	—	2	2	no	—
411	C₄⋊C₄×C₂₃	—	2	2	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	2	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	1	no	—
418	C₄⋊C₄×C₂₃	—	2	1	no	—
419	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	1	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	1	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	1	no	—
435	C₂²⋊C₄×C₂₃	—	2	1	no	—
436	C₂²⋊C₄×C₂₃	—	2	1	no	—
437	C₂²⋊C₄×C₂₃	—	2	2	no	—
438	C₂²⋊C₄×C₂₃	—	2	2	no	—
439	C₂²⋊C₄×C₂₃	—	2	2	no	—
440	C₂²⋊C₄×C₂₃	—	2	2	no	—
441	C₂²⋊C₄×C₂₃	—	2	1	no	—
442	C₂²⋊C₄×C₂₃	—	2	1	no	—
443	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	—	2	1	no	—
448	C₄²×C₂₃	—	2	2	no	—
449	C₄²×C₂₃	—	2	1	no	—
450	C₄²×C₂₃	—	2	2	no	—
451	C₄²×C₂₃	—	2	2	no	—
452	C₄²×C₂₃	—	2	2	no	—
453	C₄²×C₂₃	—	2	2	no	—
454	C₄²×C₂₃	—	2	1	no	—
455	C₄²×C₂₃	—	2	2	no	—
456	C₄²×C₂₃	—	2	2	no	—
457	C₄²×C₂₃	C₂×D₄	1	2	yes	—
458	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₂₃	C₂×D₄	1	2	yes	—
460	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
461	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
462	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
463	C₄²×C₂₃	C₂⁴	1	2	yes	—
464	#60598	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
465	C₂³×C₂₃	—	2	1	no	—
466	C₂³×C₂₃	—	2	1	no	—
467	C₂³×C₂₃	—	2	1	no	—
468	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
469	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₂₃	—	2	8	no	—
471	Q₈×C₂₃	—	2	2	no	—
472	Q₈×C₂₃	—	2	4	no	—
473	Q₈×C₂₃	—	2	1	no	—
474	Q₈×C₂₃	—	2	2	no	—
475	Q₈×C₂₃	—	2	1	no	—
476	Q₈×C₂₃	—	2	1	no	—
477	Q₈×C₂₃	—	2	1	no	—
478	Q₈×C₂₃	—	2	1	no	—
479	Q₈×C₂₃	C₂×#41	1	2	yes	—
480	Q₈×C₂₃	C₂×#41	1	4	yes	—
481	D₄×C₂₃	—	2	8	no	—
482	D₄×C₂₃	—	2	4	no	—
483	D₄×C₂₃	—	2	4	no	—
484	D₄×C₂₃	—	2	2	no	—
485	D₄×C₂₃	—	2	1	no	—
486	D₄×C₂₃	—	2	1	no	—
487	D₄×C₂₃	—	2	1	no	—
488	D₄×C₂₃	—	2	1	no	—
489	D₄×C₂₃	—	2	1	no	—
490	D₄×C₂₃	—	4	2	no	—
491	D₄×C₂₃	—	4	2	no	—
492	D₄×C₂₃	—	8	1	no	—
493	D₄×C₂₃	—	8	1	no	—
494	D₄×C₂₃	—	8	2	no	—
495	D₄×C₂₃	—	8	2	no	—
496	D₄×C₂₃	C₂×#41	1	2	yes	—
497	C₂×C₄×C₂₃	—	2	8	no	—
498	C₂×C₄×C₂₃	—	2	8	no	—
499	C₂×C₄×C₂₃	—	2	4	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	1	no	—
502	C₂×C₄×C₂₃	—	2	4	no	—
503	C₂×C₄×C₂₃	—	2	2	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	2	no	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	1	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	2	no	—
512	C₂×C₄×C₂₃	—	4	2	no	—
513	C₂×C₄×C₂₃	—	4	1	no	—
514	C₂×C₄×C₂₃	—	4	2	no	—
515	C₂×C₄×C₂₃	—	4	1	no	—
516	C₂×C₄×C₂₃	—	4	2	no	—
517	C₂×C₄×C₂₃	—	4	2	no	—
518	C₂×C₄×C₂₃	—	4	2	no	—
519	C₂×C₄×C₂₃	—	8	2	no	—
520	C₂×C₄×C₂₃	—	8	2	no	—
521	C₂×C₄×C₂₃	—	8	1	no	—
522	C₂×C₄×C₂₃	—	8	2	no	—
523	C₂×C₄×C₂₃	—	8	1	no	—
524	C₂×C₄×C₂₃	—	8	2	no	—
525	C₂×C₄×C₂₃	—	8	1	no	—
526	C₂×C₄×C₂₃	—	8	1	no	—
527	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
536	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
537	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
538	C₈×C₂₃	—	2	1	no	—
539	C₈×C₂₃	—	2	1	no	—
540	C₈×C₂₃	—	2	1	no	—
541	C₈×C₂₃	—	2	1	no	—
542	C₈×C₂₃	—	2	2	no	—
543	C₈×C₂₃	—	2	2	no	—
544	#3512	C₂×C₂₃	1	1	yes	characteristic, complemented
545	C₄×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3127	C₂×C₂₃	1	2	yes	complemented
547	#3126	C₂×C₂₃	1	2	yes	complemented
548	#3120	C₂×C₂₃	1	2	yes	complemented
549	#3119	C₂×C₂₃	1	2	yes	complemented
550	#3117	C₂×C₂₃	1	2	yes	complemented
551	#3111	C₂×C₂₃	1	2	yes	complemented
552	#3108	C₂×C₂₃	1	2	yes	complemented
553	#3102	C₂×C₂₃	1	2	yes	complemented
554	#3099	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#3098	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3080	C₂×C₂₃	1	1	yes	characteristic, complemented
557	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#3037	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
561	#3013	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#2952	C₂×C₂₃	1	1	yes	characteristic, complemented
563	#2951	C₂×C₂₃	1	1	yes	characteristic, complemented
564	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
565	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
566	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
567	C₂²×C₂₃	—	2	1	no	—
568	C₂²×C₂₃	—	2	1	no	—
569	C₂²×C₂₃	—	2	2	no	—
570	C₂²×C₂₃	—	2	2	no	—
571	C₂²×C₂₃	—	2	2	no	—
572	C₂²×C₂₃	—	2	2	no	—
573	C₂²×C₂₃	—	4	1	no	—
574	C₂²×C₂₃	—	4	1	no	—
575	C₂²×C₂₃	—	4	1	no	—
576	C₂²×C₂₃	—	4	1	no	—
577	C₂²×C₂₃	—	4	1	no	—
578	C₂²×C₂₃	—	4	1	no	—
579	C₂²×C₂₃	—	4	1	no	—
580	C₂²×C₂₃	—	4	1	no	—
581	C₂²×C₂₃	#525	1	2	yes	—
582	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
583	C₄×C₂₃	—	2	1	no	—
584	C₄×C₂₃	—	2	2	no	—
585	C₄×C₂₃	—	2	1	no	—
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	2	no	—
588	C₄×C₂₃	—	2	1	no	—
589	C₄×C₂₃	—	2	4	no	—
590	C₄×C₂₃	—	2	2	no	—
591	C₄×C₂₃	—	2	2	no	—
592	C₄×C₂₃	—	4	2	no	—
593	C₄×C₂₃	—	4	1	no	—
594	C₄×C₂₃	—	4	2	no	—
595	C₄×C₂₃	—	4	1	no	—
596	C₄×C₂₃	—	4	2	no	—
597	C₄×C₂₃	—	4	1	no	—
598	C₄×C₂₃	—	4	1	no	—
599	C₄×C₂₃	#525	1	2	yes	—
600	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
601	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
602	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
603	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
604	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
605	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
606	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
607	#553	—	2	2	no	—
608	#553	—	2	2	no	—
609	#553	—	2	1	no	—
610	#553	—	2	1	no	—
611	#552	—	2	1	no	—
612	#552	—	2	1	no	—
613	#541	C₂²×C₂₃	1	2	yes	—
614	#540	C₂²×C₂₃	1	2	yes	—
615	#537	C₂²×C₂₃	1	1	yes	characteristic
616	#537	C₂²×C₂₃	1	1	yes	characteristic
617	#532	C₂²×C₂₃	1	1	yes	characteristic
618	#529	C₂²×C₂₃	1	2	yes	—
619	#529	C₂²×C₂₃	1	2	yes	—
620	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
621	#520	—	2	2	no	—
622	#520	—	2	1	no	—
623	#520	C₂²×C₂₃	1	2	yes	—
624	#520	C₂²×C₂₃	1	1	yes	characteristic
625	#520	C₂²×C₂₃	1	1	yes	characteristic
626	#520	C₂²×C₂₃	1	1	yes	characteristic
627	#520	C₂²×C₂₃	1	1	yes	characteristic
628	#519	—	2	1	no	—
629	#519	C₂²×C₂₃	1	2	yes	—
630	#519	C₂²×C₂₃	1	1	yes	characteristic
631	C₄×#41	—	2	2	no	—
632	C₄×#41	—	2	1	no	—
633	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
634	C₄×#41	C₂²×C₂₃	1	2	yes	—
635	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
636	C₂×C₄×Q₈	—	2	1	no	—
637	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
638	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
639	#485	C₂²×C₂₃	1	2	yes	—
640	#485	C₂²×C₂₃	1	2	yes	—
641	#484	C₂²×C₂₃	1	2	yes	—
642	#483	C₂²×C₂₃	1	2	yes	—
643	#482	C₂²×C₂₃	1	2	yes	—
644	#482	C₂²×C₂₃	1	2	yes	—
645	#481	C₂²×C₂₃	1	2	yes	—
646	#480	C₂²×C₂₃	1	2	yes	—
647	#479	C₂²×C₂₃	1	2	yes	—
648	#479	C₂²×C₂₃	1	2	yes	—
649	#479	C₂²×C₂₃	1	2	yes	—
650	#479	C₂²×C₂₃	1	2	yes	—
651	#479	C₂²×C₂₃	1	2	yes	—
652	#479	C₂²×C₂₃	1	2	yes	—
653	#478	C₂²×C₂₃	1	2	yes	—
654	#478	C₂²×C₂₃	1	2	yes	—
655	#464	C₂²×C₂₃	1	2	yes	—
656	#464	C₂²×C₂₃	1	1	yes	characteristic
657	#464	C₂²×C₂₃	1	2	yes	—
658	#464	C₂²×C₂₃	1	1	yes	characteristic
659	#463	C₂²×C₂₃	1	1	yes	characteristic
660	#463	C₂²×C₂₃	1	1	yes	characteristic
661	#462	C₂²×C₂₃	1	2	yes	—
662	#462	C₂²×C₂₃	1	1	yes	characteristic
663	#461	C₂²×C₂₃	1	1	yes	characteristic
664	#460	C₂²×C₂₃	1	2	yes	—
665	#460	C₂²×C₂₃	1	1	yes	characteristic
666	#459	C₂²×C₂₃	1	1	yes	characteristic
667	#452	C₂²×C₂₃	1	2	yes	—
668	#452	C₂²×C₂₃	1	2	yes	—
669	#451	C₂²×C₂₃	1	2	yes	—
670	#451	C₂²×C₂₃	1	2	yes	—
671	#449	C₂²×C₂₃	1	2	yes	—
672	#449	C₂²×C₂₃	1	2	yes	—
673	#448	C₂²×C₂₃	1	2	yes	—
674	#448	C₂²×C₂₃	1	2	yes	—
675	#442	C₂²×C₂₃	1	2	yes	—
676	#441	C₂²×C₂₃	1	2	yes	—
677	#441	C₂²×C₂₃	1	2	yes	—
678	#441	C₂²×C₂₃	1	2	yes	—
679	#440	C₂²×C₂₃	1	2	yes	—
680	#440	C₂²×C₂₃	1	2	yes	—
681	#440	C₂²×C₂₃	1	2	yes	—
682	#440	C₂²×C₂₃	1	2	yes	—
683	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
684	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
685	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
687	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
690	C₄×D₈	C₂²×C₂₃	1	2	yes	—
691	#433	C₂²×C₂₃	1	2	yes	—
692	#433	C₂²×C₂₃	1	2	yes	—
693	#432	C₂²×C₂₃	1	2	yes	—
694	#431	C₂²×C₂₃	1	2	yes	—
695	#428	C₂²×C₂₃	1	1	yes	characteristic
696	#428	C₂²×C₂₃	1	1	yes	characteristic
697	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
698	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
699	#423	C₂²×C₂₃	1	1	yes	characteristic
700	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
701	#417	C₂²×C₂₃	1	1	yes	characteristic
702	#417	C₂²×C₂₃	1	1	yes	characteristic
703	#417	C₂²×C₂₃	1	1	yes	characteristic
704	#417	C₂²×C₂₃	1	1	yes	characteristic
705	#416	C₂²×C₂₃	1	1	yes	characteristic
706	#416	C₂²×C₂₃	1	1	yes	characteristic
707	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
708	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
709	#408	C₂²×C₂₃	1	1	yes	characteristic
710	#408	C₂²×C₂₃	1	1	yes	characteristic
711	#405	C₂²×C₂₃	1	1	yes	characteristic
712	#405	C₂²×C₂₃	1	1	yes	characteristic
713	C₂×C₂₃	—	2	2	no	—
714	C₂×C₂₃	—	4	2	no	—
715	C₂×C₂₃	—	4	2	no	—
716	C₂×C₂₃	—	8	1	no	—
717	C₂×C₂₃	—	8	1	no	—
718	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
719	C₂×C₂₃	#3584	1	1	yes	characteristic
720	C₂×C₂₃	#3586	1	1	yes	characteristic
721	2₋¹⁺⁴	—	2	4	no	—
722	2₋¹⁺⁴	—	2	4	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	2	no	—
725	C₂×#41	C₂³×C₂₃	1	2	yes	—
726	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
727	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
728	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
729	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
730	C₂²×Q₈	—	2	1	no	—
731	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
732	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
733	#137	—	2	4	no	—
734	#137	—	2	4	no	—
735	#135	—	2	4	no	—
736	#135	—	2	4	no	—
737	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
740	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
747	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
748	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
750	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
754	#127	C₂³×C₂₃	1	1	yes	characteristic
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	—	2	1	no	—
763	#125	C₂³×C₂₃	1	2	yes	—
764	#125	C₂³×C₂₃	1	2	yes	—
765	#124	C₂³×C₂₃	1	1	yes	characteristic
766	#124	C₂³×C₂₃	1	1	yes	characteristic
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	C₂³×C₂₃	1	2	yes	—
784	#121	C₂³×C₂₃	1	2	yes	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	2	no	—
790	C₄×Q₈	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
795	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
797	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
799	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
800	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
801	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
802	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
804	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	D₄×C₂₃	1	2	yes	—
821	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
822	C₄×D₄	D₄×C₂₃	1	2	yes	—
823	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₂₃	1	2	yes	—
826	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₂₃	1	2	yes	—
828	C₄×D₄	C₂³×C₂₃	1	2	yes	—
829	#117	—	2	1	no	—
830	#117	—	2	2	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	2	no	—
840	#117	C₂³×C₂₃	1	1	yes	characteristic
841	#117	C₂³×C₂₃	1	2	yes	—
842	#117	C₂³×C₂₃	1	1	yes	characteristic
843	#117	C₂³×C₂₃	1	2	yes	—
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
854	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
856	C₂×C₄²	—	2	1	no	—
857	C₂×C₄²	—	2	2	no	—
858	C₂×C₄²	—	2	2	no	—
859	C₂×C₄²	—	2	1	no	—
860	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
861	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
862	#107	C₂³×C₂₃	1	2	yes	—
863	#107	C₂³×C₂₃	1	2	yes	—
864	#107	C₂³×C₂₃	1	2	yes	—
865	#107	C₂³×C₂₃	1	2	yes	—
866	#106	C₂³×C₂₃	1	2	yes	—
867	#106	C₂³×C₂₃	1	2	yes	—
868	#106	C₂³×C₂₃	1	2	yes	—
869	#106	C₂³×C₂₃	1	2	yes	—
870	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
875	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
876	#103	C₂³×C₂₃	1	2	yes	—
877	#103	C₂³×C₂₃	1	2	yes	—
878	#103	C₂³×C₂₃	1	2	yes	—
879	#103	C₂³×C₂₃	1	2	yes	—
880	#103	C₂³×C₂₃	1	1	yes	characteristic
881	#103	C₂³×C₂₃	1	1	yes	characteristic
882	#103	C₂³×C₂₃	1	1	yes	characteristic
883	#103	C₂³×C₂₃	1	1	yes	characteristic
884	#103	C₂³×C₂₃	1	2	yes	—
885	#103	C₂³×C₂₃	1	2	yes	—
886	#103	C₂³×C₂₃	1	2	yes	—
887	#103	C₂³×C₂₃	1	2	yes	—
888	#102	C₂³×C₂₃	1	1	yes	characteristic
889	#102	C₂³×C₂₃	1	1	yes	characteristic
890	#102	C₂³×C₂₃	1	1	yes	characteristic
891	#102	C₂³×C₂₃	1	1	yes	characteristic
892	#102	C₂³×C₂₃	1	2	yes	—
893	#102	C₂³×C₂₃	1	2	yes	—
894	#102	C₂³×C₂₃	1	2	yes	—
895	#102	C₂³×C₂₃	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
899	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
900	#97	C₂³×C₂₃	1	2	yes	—
901	#97	C₂³×C₂₃	1	2	yes	—
902	C₄×C₈	C₂³×C₂₃	1	2	yes	—
903	C₄×C₈	C₂³×C₂₃	1	2	yes	—
904	C₂₃	#60598	1	1	yes	characteristic, direct product factor, Sylow
905	#41	—	2	16	no	—
906	#41	—	2	8	no	—
907	#41	—	2	4	no	—
908	#41	—	2	4	no	—
909	#41	—	2	2	no	—
910	#41	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	2	2	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	#41×C₂₃	1	4	yes	—
917	C₂×Q₈	—	2	8	no	—
918	C₂×Q₈	—	2	4	no	—
919	C₂×Q₈	—	2	4	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
924	C₂×Q₈	#41×C₂₃	1	4	yes	—
925	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
927	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
938	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
939	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
940	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
959	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
960	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
963	Q₁₆	—	2	2	no	—
964	Q₁₆	—	2	2	no	—
965	Q₁₆	—	2	4	no	—
966	Q₁₆	—	2	4	no	—
967	SD₁₆	—	2	2	no	—
968	SD₁₆	—	2	2	no	—
969	SD₁₆	—	2	4	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	2	2	no	—
973	D₈	—	2	2	no	—
974	D₈	—	2	2	no	—
975	M₁₆	—	2	2	no	—
976	M₁₆	—	2	2	no	—
977	C₂×C₈	—	2	2	no	—
978	C₂×C₈	—	2	2	no	—
979	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
982	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
983	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1010	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1011	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	2	no	—
1044	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1045	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1046	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1047	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1048	C₄²	C₂⁴×C₂₃	1	2	yes	—
1049	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1050	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1055	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1056	Q₈	—	2	8	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	4	no	—
1061	Q₈	—	2	1	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	C₂×#41×C₂₃	1	2	yes	—
1066	Q₈	C₂×#41×C₂₃	1	4	yes	—
1067	D₄	—	2	8	no	—
1068	D₄	—	2	4	no	—
1069	D₄	—	2	4	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	C₂×#41×C₂₃	1	2	yes	—
1083	C₂×C₄	—	2	8	no	—
1084	C₂×C₄	—	2	8	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	4	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	4	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	1	no	—
1112	C₂×C₄	—	8	1	no	—
1113	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1121	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1122	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1123	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	2	no	—
1129	C₈	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	C₂₃×#525	1	2	yes	—
1145	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1146	C₄	—	2	4	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	C₂₃×#525	1	2	yes	—
1163	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1164	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1165	C₂	—	2	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	1	no	—
1170	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
1171	C₂	C₂₃×#3584	1	1	yes	characteristic
1172	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3512	C₂	semidirect
2. C₄×C₂₃×2₋¹⁺⁴	C₂	semidirect
3. C₂₃×#3127	C₂	semidirect
4. C₂₃×#3126	C₂	semidirect
5. C₂₃×#3120	C₂	semidirect
6. C₂₃×#3119	C₂	semidirect
7. C₂₃×#3117	C₂	semidirect
8. C₂₃×#3111	C₂	semidirect
9. C₂₃×#3108	C₂	semidirect
10. C₂₃×#3102	C₂	semidirect
11. C₂₃×#3099	C₂	semidirect
12. C₂₃×#3098	C₂	semidirect
13. C₂₃×#3080	C₂	semidirect
14. C₂×C₂₃×#479	C₂	semidirect
15. C₂₃×#3037	C₂	semidirect
16. C₂₃×#3035	C₂	semidirect
17. C₂₃×#3013	C₂	semidirect
18. C₂₃×#3013	C₂	semidirect
19. C₂₃×#2952	C₂	semidirect
20. C₂₃×#2951	C₂	semidirect
21. C₂₃×#2947	C₂	semidirect
22. C₂₃×#2947	C₂	semidirect
23. C₂₃×#2925	C₂	semidirect
464. #60598	C₂₃	direct (N × H)
544. #3512	C₂×C₂₃	semidirect
545. C₄×2₋¹⁺⁴	C₂×C₂₃	semidirect
546. #3127	C₂×C₂₃	semidirect
547. #3126	C₂×C₂₃	semidirect
548. #3120	C₂×C₂₃	semidirect
549. #3119	C₂×C₂₃	semidirect
550. #3117	C₂×C₂₃	semidirect
551. #3111	C₂×C₂₃	semidirect
552. #3108	C₂×C₂₃	semidirect
553. #3102	C₂×C₂₃	semidirect
554. #3099	C₂×C₂₃	semidirect
555. #3098	C₂×C₂₃	semidirect
556. #3080	C₂×C₂₃	semidirect
557. C₂×#479	C₂×C₂₃	semidirect
558. #3037	C₂×C₂₃	semidirect
559. #3035	C₂×C₂₃	semidirect
560. #3013	C₂×C₂₃	semidirect
561. #3013	C₂×C₂₃	semidirect
562. #2952	C₂×C₂₃	semidirect
563. #2951	C₂×C₂₃	semidirect
564. #2947	C₂×C₂₃	semidirect
565. #2947	C₂×C₂₃	semidirect
566. #2925	C₂×C₂₃	semidirect
904. C₂₃	#60598	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×#3512	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂₃×#3127	2
C₂₃×#3126	2
C₂₃×#3120	2
C₂₃×#3119	2
C₂₃×#3117	2
C₂₃×#3111	2
C₂₃×#3108	2
C₂₃×#3102	2
C₂₃×#3099	2
C₂₃×#3098	2
C₂₃×#3080	2
C₂×C₂₃×#479	2
C₂₃×#3037	2
C₂₃×#3035	2
C₂₃×#3013	2
C₂₃×#2952	2
C₂₃×#2951	2
C₂₃×#2947	2
C₂₃×#2925	2
#60598	23

Subgroups — C23×#60598 #19208224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60598 #19208224