Subgroups — C₂₃×#60933 #19208559

Order 5888.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1188 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	C₂₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3260	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3259	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3258	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3257	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3256	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3251	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3250	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3247	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
30	C₂₃×#553	—	2	2	no	—
31	C₂₃×#553	—	2	2	no	—
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	—	2	1	no	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	—	2	1	no	—
36	C₂₃×#544	C₂²	1	1	yes	characteristic
37	C₂₃×#542	—	2	1	no	—
38	C₂₃×#542	C₂²	1	2	yes	—
39	C₂₃×#541	C₂²	1	2	yes	complemented
40	C₂₃×#540	—	2	1	no	—
41	C₂₃×#540	C₂²	1	2	yes	—
42	C₂₃×#540	C₂²	1	2	yes	complemented
43	C₂₃×#538	—	2	2	no	—
44	C₂₃×#537	C₂²	1	1	yes	characteristic
45	C₂₃×#537	C₂²	1	1	yes	characteristic
46	C₂₃×#537	C₂²	1	1	yes	characteristic
47	C₂₃×#535	C₂²	1	1	yes	characteristic
48	C₂₃×#535	C₂²	1	1	yes	characteristic
49	C₂₃×#532	—	2	1	no	—
50	C₂₃×#532	C₂²	1	1	yes	characteristic
51	C₂₃×#532	C₂²	1	2	yes	—
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#529	C₂²	1	2	yes	—
54	C₂₃×#529	C₂²	1	2	yes	complemented
55	C₂₃×#529	C₂²	1	2	yes	complemented
56	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
57	C₂₃×#525	—	2	2	no	—
58	C₂₃×#520	C₂²	1	1	yes	characteristic
59	C₂₃×#520	C₂²	1	1	yes	characteristic
60	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
61	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₂₃×#479	C₂²	1	2	yes	complemented
64	C₂₃×#479	C₂²	1	2	yes	complemented
65	C₂₃×#479	C₂²	1	2	yes	complemented
66	C₂₃×#479	C₂²	1	2	yes	complemented
67	C₂₃×#478	C₂²	1	2	yes	—
68	C₂₃×#478	C₂²	1	2	yes	—
69	C₂₃×#478	C₂²	1	2	yes	—
70	C₂₃×#478	C₂²	1	2	yes	—
71	C₂₃×#478	C₂²	1	2	yes	complemented
72	C₂₃×#478	C₂²	1	2	yes	complemented
73	C₂₃×#478	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#477	C₂²	1	2	yes	complemented
76	C₂₃×#476	C₂²	1	2	yes	complemented
77	C₂₃×#475	C₂²	1	2	yes	complemented
78	C₂₃×#474	C₂²	1	2	yes	complemented
79	C₂₃×#470	C₂²	1	2	yes	complemented
80	C₂₃×#469	C₂²	1	2	yes	—
81	C₂₃×#469	C₂²	1	2	yes	—
82	C₂₃×#469	C₂²	1	2	yes	complemented
83	C₂₃×#468	C₂²	1	2	yes	—
84	C₂₃×#468	C₂²	1	2	yes	—
85	C₂₃×#468	C₂²	1	2	yes	complemented
86	C₂₃×#468	C₂²	1	2	yes	complemented
87	C₂₃×#467	C₂²	1	2	yes	complemented
88	C₂₃×#466	C₂²	1	2	yes	—
89	C₂₃×#466	C₂²	1	2	yes	—
90	C₂₃×#466	C₂²	1	2	yes	complemented
91	C₂₃×#465	C₂²	1	2	yes	—
92	C₂₃×#465	C₂²	1	2	yes	—
93	C₂₃×#465	C₂²	1	2	yes	complemented
94	C₂₃×#465	C₂²	1	2	yes	complemented
95	C₂₃×#464	C₂²	1	2	yes	—
96	C₂₃×#464	C₂²	1	2	yes	—
97	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
98	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#463	C₂²	1	2	yes	—
100	C₂₃×#463	C₂²	1	2	yes	—
101	C₂₃×#463	C₂²	1	2	yes	—
102	C₂₃×#463	C₂²	1	2	yes	—
103	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#463	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#461	C₂²	1	2	yes	—
107	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#460	C₂²	1	2	yes	—
109	C₂₃×#460	C₂²	1	2	yes	—
110	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#459	C₂²	1	2	yes	—
112	C₂₃×#459	C₂²	1	2	yes	—
113	C₂₃×#459	C₂²	1	2	yes	—
114	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#428	C₂²	1	1	yes	characteristic
116	C₂₃×#428	C₂²	1	1	yes	characteristic
117	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
118	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
119	C₂₃×#424	C₂²	1	1	yes	characteristic
120	C₂₃×#424	C₂²	1	1	yes	characteristic
121	C₂₃×#424	C₂²	1	2	yes	complemented
122	C₂₃×#424	C₂²	1	2	yes	complemented
123	C₂₃×#423	C₂²	1	1	yes	characteristic
124	C₂₃×#423	C₂²	1	2	yes	complemented
125	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
127	C₂₃×#417	C₂²	1	1	yes	characteristic
128	C₂₃×#417	C₂²	1	1	yes	characteristic
129	C₂₃×#417	C₂²	1	1	yes	characteristic
130	C₂₃×#417	C₂²	1	1	yes	characteristic
131	C₂₃×#416	C₂²	1	1	yes	characteristic
132	C₂₃×#416	C₂²	1	1	yes	characteristic
133	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
134	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	—	2	1	no	—
142	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
143	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
144	C₂₃×#135	—	4	2	no	—
145	C₂₃×#135	—	4	2	no	—
146	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₂₃	C₂³	1	2	yes	—
157	C₂×D₈×C₂₃	C₂³	1	2	yes	—
158	C₂₃×#131	—	4	2	no	—
159	C₂₃×#131	—	4	2	no	—
160	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
168	C₂₃×C₄⋊Q₈	—	2	1	no	—
169	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×#127	—	2	1	no	—
172	C₂₃×#127	C₂³	1	1	yes	characteristic
173	C₂₃×#127	C₂³	1	2	yes	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	2	no	—
178	C₂₃×#126	—	2	2	no	—
179	C₂₃×#126	—	2	2	no	—
180	C₂₃×#125	—	2	2	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	—	2	1	no	—
183	C₂₃×#125	—	2	1	no	—
184	C₂₃×#125	—	2	1	no	—
185	C₂₃×#125	C₂³	1	2	yes	—
186	C₂₃×#125	C₂³	1	2	yes	—
187	C₂₃×#125	C₂³	1	2	yes	—
188	C₂₃×#124	—	2	1	no	—
189	C₂₃×#124	—	2	2	no	—
190	C₂₃×#124	—	2	2	no	—
191	C₂₃×#124	C₂³	1	1	yes	characteristic
192	C₂₃×#124	C₂³	1	1	yes	characteristic
193	C₂₃×#124	C₂³	1	2	yes	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	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×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₃×#121	—	2	1	no	—
211	C₂₃×#121	—	2	1	no	—
212	C₂₃×#121	—	2	2	no	—
213	C₂₃×#121	—	2	2	no	—
214	C₂₃×#121	—	2	2	no	—
215	C₂₃×#121	—	2	1	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	1	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#121	C₂³	1	2	yes	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
233	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	1	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	D₄	1	2	yes	—
251	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
252	C₄×D₄×C₂₃	D₄	1	2	yes	—
253	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	2	yes	—
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	1	2	yes	—
259	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	2	no	—
263	C₂₃×#117	—	2	2	no	—
264	C₂₃×#117	—	2	1	no	—
265	C₂₃×#117	—	2	2	no	—
266	C₂₃×#117	C₂³	1	1	yes	characteristic
267	C₂₃×#117	C₂³	1	1	yes	characteristic
268	C₂₃×#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
277	C₂×C₄²×C₂₃	—	2	1	no	—
278	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₂₃	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×#107	C₂³	1	2	yes	—
284	C₂₃×#106	C₂³	1	2	yes	—
285	C₂₃×#106	C₂³	1	2	yes	—
286	C₂₃×#106	C₂³	1	2	yes	—
287	C₂₃×#106	C₂³	1	2	yes	—
288	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
293	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
294	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
295	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
296	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
297	C₂₃×C₄⋊C₈	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	1	yes	characteristic
301	C₂₃×#103	C₂³	1	1	yes	characteristic
302	C₂₃×#103	C₂³	1	2	yes	—
303	C₂₃×#103	C₂³	1	2	yes	—
304	C₂₃×#103	C₂³	1	2	yes	—
305	C₂₃×#103	C₂³	1	2	yes	—
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×#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	1	yes	characteristic
314	C₂₃×#102	C₂³	1	2	yes	—
315	C₂₃×#102	C₂³	1	2	yes	—
316	C₂₃×#102	C₂³	1	2	yes	—
317	C₂₃×#102	C₂³	1	2	yes	—
318	C₂⁴×C₂₃	—	2	1	no	—
319	#41×C₂₃	—	2	2	no	—
320	#41×C₂₃	—	2	2	no	—
321	#41×C₂₃	—	2	2	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	—	8	4	no	—
328	C₂×Q₈×C₂₃	—	2	2	no	—
329	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	1	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	2	no	—
339	C₂×D₄×C₂₃	—	2	2	no	—
340	C₂×D₄×C₂₃	—	2	2	no	—
341	C₂×D₄×C₂₃	—	2	1	no	—
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	2	no	—
346	C₂×D₄×C₂₃	—	2	2	no	—
347	C₂×D₄×C₂₃	—	2	2	no	—
348	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	1	no	—
356	C₂²×C₄×C₂₃	—	2	1	no	—
357	C₂²×C₄×C₂₃	—	2	1	no	—
358	C₂²×C₄×C₂₃	—	2	1	no	—
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	2	no	—
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	2	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	—	2	2	no	—
366	C₂²×C₄×C₂₃	—	8	2	no	—
367	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	Q₁₆×C₂₃	—	4	1	no	—
374	Q₁₆×C₂₃	—	4	1	no	—
375	SD₁₆×C₂₃	—	4	1	no	—
376	SD₁₆×C₂₃	—	4	1	no	—
377	SD₁₆×C₂₃	—	4	1	no	—
378	SD₁₆×C₂₃	—	4	1	no	—
379	SD₁₆×C₂₃	—	4	2	no	—
380	SD₁₆×C₂₃	—	4	2	no	—
381	D₈×C₂₃	—	4	1	no	—
382	D₈×C₂₃	—	4	1	no	—
383	D₈×C₂₃	—	4	2	no	—
384	D₈×C₂₃	—	4	2	no	—
385	M₁₆×C₂₃	—	2	2	no	—
386	M₁₆×C₂₃	—	2	2	no	—
387	M₁₆×C₂₃	—	4	2	no	—
388	M₁₆×C₂₃	—	4	2	no	—
389	C₂×C₈×C₂₃	—	2	2	no	—
390	C₂×C₈×C₂₃	—	2	2	no	—
391	C₂×C₈×C₂₃	—	4	2	no	—
392	C₂×C₈×C₂₃	—	4	2	no	—
393	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
398	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	1	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	—	2	1	no	—
408	C₄⋊C₄×C₂₃	—	2	1	no	—
409	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	1	no	—
417	C₄⋊C₄×C₂₃	—	2	1	no	—
418	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₂₃	—	2	1	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
442	C₂²⋊C₄×C₂₃	—	2	2	no	—
443	C₂²⋊C₄×C₂₃	—	2	1	no	—
444	C₂²⋊C₄×C₂₃	—	2	1	no	—
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	—	2	2	no	—
447	C₂²⋊C₄×C₂₃	—	2	2	no	—
448	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
451	C₄²×C₂₃	—	2	1	no	—
452	C₄²×C₂₃	—	2	1	no	—
453	C₄²×C₂₃	—	2	1	no	—
454	C₄²×C₂₃	—	2	2	no	—
455	C₄²×C₂₃	—	2	2	no	—
456	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
461	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
462	C₄²×C₂₃	C₂⁴	1	2	yes	—
463	#60933	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂³×C₂₃	—	2	1	no	—
465	C₂³×C₂₃	—	2	1	no	—
466	C₂³×C₂₃	—	2	2	no	—
467	C₂³×C₂₃	—	2	1	no	—
468	C₂³×C₂₃	—	4	2	no	—
469	C₂³×C₂₃	—	8	1	no	—
470	C₂³×C₂₃	—	8	1	no	—
471	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
472	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
473	Q₈×C₂₃	—	2	2	no	—
474	Q₈×C₂₃	—	2	1	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	—	2	1	no	—
480	Q₈×C₂₃	—	8	2	no	—
481	D₄×C₂₃	—	2	4	no	—
482	D₄×C₂₃	—	2	2	no	—
483	D₄×C₂₃	—	2	1	no	—
484	D₄×C₂₃	—	2	1	no	—
485	D₄×C₂₃	—	2	2	no	—
486	D₄×C₂₃	—	2	1	no	—
487	D₄×C₂₃	—	2	2	no	—
488	D₄×C₂₃	—	2	1	no	—
489	D₄×C₂₃	—	2	1	no	—
490	D₄×C₂₃	—	2	1	no	—
491	D₄×C₂₃	—	4	2	no	—
492	D₄×C₂₃	—	4	2	no	—
493	D₄×C₂₃	—	4	2	no	—
494	D₄×C₂₃	—	4	2	no	—
495	D₄×C₂₃	—	8	1	no	—
496	D₄×C₂₃	—	8	2	no	—
497	D₄×C₂₃	—	8	1	no	—
498	D₄×C₂₃	—	8	2	no	—
499	D₄×C₂₃	—	8	2	no	—
500	D₄×C₂₃	—	8	2	no	—
501	D₄×C₂₃	—	8	2	no	—
502	D₄×C₂₃	—	8	2	no	—
503	D₄×C₂₃	—	8	2	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	2	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	1	no	—
510	C₂×C₄×C₂₃	—	2	1	no	—
511	C₂×C₄×C₂₃	—	2	2	no	—
512	C₂×C₄×C₂₃	—	2	2	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	4	1	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	4	no	—
519	C₂×C₄×C₂₃	—	4	2	no	—
520	C₂×C₄×C₂₃	—	4	2	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	2	no	—
523	C₂×C₄×C₂₃	—	8	2	no	—
524	C₂×C₄×C₂₃	—	8	1	no	—
525	C₂×C₄×C₂₃	—	8	2	no	—
526	C₂×C₄×C₂₃	—	8	2	no	—
527	C₂×C₄×C₂₃	—	8	1	no	—
528	C₂×C₄×C₂₃	—	8	1	no	—
529	C₂×C₄×C₂₃	—	8	1	no	—
530	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
539	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
540	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
541	C₈×C₂₃	—	2	1	no	—
542	C₈×C₂₃	—	2	1	no	—
543	C₈×C₂₃	—	2	1	no	—
544	C₈×C₂₃	—	2	1	no	—
545	C₈×C₂₃	—	2	2	no	—
546	C₈×C₂₃	—	2	2	no	—
547	#3512	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3460	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3260	C₂×C₂₃	1	2	yes	complemented
550	#3259	C₂×C₂₃	1	2	yes	complemented
551	#3258	C₂×C₂₃	1	2	yes	complemented
552	#3257	C₂×C₂₃	1	2	yes	complemented
553	#3256	C₂×C₂₃	1	2	yes	complemented
554	#3251	C₂×C₂₃	1	2	yes	complemented
555	#3250	C₂×C₂₃	1	2	yes	complemented
556	#3247	C₂×C₂₃	1	2	yes	complemented
557	#3084	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#3083	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3080	C₂×C₂₃	1	1	yes	characteristic, complemented
560	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
561	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
563	#3061	C₂×C₂₃	1	1	yes	characteristic, complemented
564	#3060	C₂×C₂₃	1	1	yes	characteristic, complemented
565	#3045	C₂×C₂₃	1	1	yes	characteristic, complemented
566	#3045	C₂×C₂₃	1	1	yes	characteristic, complemented
567	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
568	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
569	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
570	C₂²×C₂₃	—	2	1	no	—
571	C₂²×C₂₃	—	2	1	no	—
572	C₂²×C₂₃	—	2	2	no	—
573	C₂²×C₂₃	—	2	2	no	—
574	C₂²×C₂₃	—	2	2	no	—
575	C₂²×C₂₃	—	4	1	no	—
576	C₂²×C₂₃	—	4	1	no	—
577	C₂²×C₂₃	—	4	1	no	—
578	C₂²×C₂₃	—	4	2	no	—
579	C₂²×C₂₃	—	4	2	no	—
580	C₂²×C₂₃	—	4	1	no	—
581	C₂²×C₂₃	—	4	1	no	—
582	C₂²×C₂₃	—	4	1	no	—
583	C₂²×C₂₃	—	4	1	no	—
584	C₂²×C₂₃	—	4	1	no	—
585	C₂²×C₂₃	—	4	1	no	—
586	C₂²×C₂₃	—	4	2	no	—
587	C₂²×C₂₃	—	8	4	no	—
588	C₂²×C₂₃	#537	1	2	yes	—
589	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
590	C₄×C₂₃	—	2	1	no	—
591	C₄×C₂₃	—	2	1	no	—
592	C₄×C₂₃	—	2	2	no	—
593	C₄×C₂₃	—	2	1	no	—
594	C₄×C₂₃	—	2	1	no	—
595	C₄×C₂₃	—	2	2	no	—
596	C₄×C₂₃	—	2	2	no	—
597	C₄×C₂₃	—	4	2	no	—
598	C₄×C₂₃	—	4	1	no	—
599	C₄×C₂₃	—	4	2	no	—
600	C₄×C₂₃	—	4	1	no	—
601	C₄×C₂₃	—	4	2	no	—
602	C₄×C₂₃	—	4	1	no	—
603	C₄×C₂₃	—	4	1	no	—
604	C₄×C₂₃	—	4	1	no	—
605	C₄×C₂₃	#537	1	2	yes	—
606	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
608	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
609	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
610	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
611	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
612	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
613	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
614	#553	—	2	2	no	—
615	#553	—	2	2	no	—
616	#553	—	2	1	no	—
617	#553	—	2	1	no	—
618	#552	—	2	1	no	—
619	#552	—	2	1	no	—
620	#544	C₂²×C₂₃	1	1	yes	characteristic
621	#542	—	2	1	no	—
622	#542	C₂²×C₂₃	1	2	yes	—
623	#541	C₂²×C₂₃	1	2	yes	complemented
624	#540	—	2	1	no	—
625	#540	C₂²×C₂₃	1	2	yes	—
626	#540	C₂²×C₂₃	1	2	yes	complemented
627	#538	—	2	2	no	—
628	#537	C₂²×C₂₃	1	1	yes	characteristic
629	#537	C₂²×C₂₃	1	1	yes	characteristic
630	#537	C₂²×C₂₃	1	1	yes	characteristic
631	#535	C₂²×C₂₃	1	1	yes	characteristic
632	#535	C₂²×C₂₃	1	1	yes	characteristic
633	#532	—	2	1	no	—
634	#532	C₂²×C₂₃	1	1	yes	characteristic
635	#532	C₂²×C₂₃	1	2	yes	—
636	#529	—	2	1	no	—
637	#529	C₂²×C₂₃	1	2	yes	—
638	#529	C₂²×C₂₃	1	2	yes	complemented
639	#529	C₂²×C₂₃	1	2	yes	complemented
640	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
641	#525	—	2	2	no	—
642	#520	C₂²×C₂₃	1	1	yes	characteristic
643	#520	C₂²×C₂₃	1	1	yes	characteristic
644	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
645	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
646	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
647	#479	C₂²×C₂₃	1	2	yes	complemented
648	#479	C₂²×C₂₃	1	2	yes	complemented
649	#479	C₂²×C₂₃	1	2	yes	complemented
650	#479	C₂²×C₂₃	1	2	yes	complemented
651	#478	C₂²×C₂₃	1	2	yes	—
652	#478	C₂²×C₂₃	1	2	yes	—
653	#478	C₂²×C₂₃	1	2	yes	—
654	#478	C₂²×C₂₃	1	2	yes	—
655	#478	C₂²×C₂₃	1	2	yes	complemented
656	#478	C₂²×C₂₃	1	2	yes	complemented
657	#478	C₂²×C₂₃	1	2	yes	complemented
658	#478	C₂²×C₂₃	1	2	yes	complemented
659	#477	C₂²×C₂₃	1	2	yes	complemented
660	#476	C₂²×C₂₃	1	2	yes	complemented
661	#475	C₂²×C₂₃	1	2	yes	complemented
662	#474	C₂²×C₂₃	1	2	yes	complemented
663	#470	C₂²×C₂₃	1	2	yes	complemented
664	#469	C₂²×C₂₃	1	2	yes	—
665	#469	C₂²×C₂₃	1	2	yes	—
666	#469	C₂²×C₂₃	1	2	yes	complemented
667	#468	C₂²×C₂₃	1	2	yes	—
668	#468	C₂²×C₂₃	1	2	yes	—
669	#468	C₂²×C₂₃	1	2	yes	complemented
670	#468	C₂²×C₂₃	1	2	yes	complemented
671	#467	C₂²×C₂₃	1	2	yes	complemented
672	#466	C₂²×C₂₃	1	2	yes	—
673	#466	C₂²×C₂₃	1	2	yes	—
674	#466	C₂²×C₂₃	1	2	yes	complemented
675	#465	C₂²×C₂₃	1	2	yes	—
676	#465	C₂²×C₂₃	1	2	yes	—
677	#465	C₂²×C₂₃	1	2	yes	complemented
678	#465	C₂²×C₂₃	1	2	yes	complemented
679	#464	C₂²×C₂₃	1	2	yes	—
680	#464	C₂²×C₂₃	1	2	yes	—
681	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#463	C₂²×C₂₃	1	2	yes	—
684	#463	C₂²×C₂₃	1	2	yes	—
685	#463	C₂²×C₂₃	1	2	yes	—
686	#463	C₂²×C₂₃	1	2	yes	—
687	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	#463	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#461	C₂²×C₂₃	1	2	yes	—
691	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#460	C₂²×C₂₃	1	2	yes	—
693	#460	C₂²×C₂₃	1	2	yes	—
694	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#459	C₂²×C₂₃	1	2	yes	—
696	#459	C₂²×C₂₃	1	2	yes	—
697	#459	C₂²×C₂₃	1	2	yes	—
698	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	#428	C₂²×C₂₃	1	1	yes	characteristic
700	#428	C₂²×C₂₃	1	1	yes	characteristic
701	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
702	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
703	#424	C₂²×C₂₃	1	1	yes	characteristic
704	#424	C₂²×C₂₃	1	1	yes	characteristic
705	#424	C₂²×C₂₃	1	2	yes	complemented
706	#424	C₂²×C₂₃	1	2	yes	complemented
707	#423	C₂²×C₂₃	1	1	yes	characteristic
708	#423	C₂²×C₂₃	1	2	yes	complemented
709	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
710	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
711	#417	C₂²×C₂₃	1	1	yes	characteristic
712	#417	C₂²×C₂₃	1	1	yes	characteristic
713	#417	C₂²×C₂₃	1	1	yes	characteristic
714	#417	C₂²×C₂₃	1	1	yes	characteristic
715	#416	C₂²×C₂₃	1	1	yes	characteristic
716	#416	C₂²×C₂₃	1	1	yes	characteristic
717	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
718	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
719	C₂×C₂₃	—	2	2	no	—
720	C₂×C₂₃	—	4	2	no	—
721	C₂×C₂₃	—	8	1	no	—
722	C₂×C₂₃	—	8	1	no	—
723	C₂×C₂₃	—	8	1	no	—
724	C₂×C₂₃	—	8	2	no	—
725	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
726	C₂×C₂₃	#3584	1	1	yes	characteristic
727	C₂×C₂₃	#3585	1	1	yes	characteristic
728	C₂×#41	—	2	2	no	—
729	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
731	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
732	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
733	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
734	C₂³×C₄	—	2	1	no	—
735	AGL(1,ℤ/8)	—	4	2	no	—
736	AGL(1,ℤ/8)	—	4	2	no	—
737	#135	—	4	2	no	—
738	#135	—	4	2	no	—
739	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
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×D₈	C₂³×C₂₃	1	2	yes	—
750	C₂×D₈	C₂³×C₂₃	1	2	yes	—
751	#131	—	4	2	no	—
752	#131	—	4	2	no	—
753	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
754	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
756	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
757	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
758	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
759	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
760	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
761	C₄⋊Q₈	—	2	1	no	—
762	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
764	#127	—	2	1	no	—
765	#127	C₂³×C₂₃	1	2	yes	—
766	#127	C₂³×C₂₃	1	1	yes	characteristic
767	#126	—	2	2	no	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#125	—	2	1	no	—
774	#125	—	2	2	no	—
775	#125	—	2	2	no	—
776	#125	—	2	1	no	—
777	#125	—	2	1	no	—
778	#125	C₂³×C₂₃	1	2	yes	—
779	#125	C₂³×C₂₃	1	2	yes	—
780	#125	C₂³×C₂₃	1	2	yes	—
781	#124	—	2	1	no	—
782	#124	—	2	2	no	—
783	#124	—	2	2	no	—
784	#124	C₂³×C₂₃	1	2	yes	—
785	#124	C₂³×C₂₃	1	1	yes	characteristic
786	#124	C₂³×C₂₃	1	1	yes	characteristic
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	C₂³×C₂₃	1	2	yes	—
819	#121	C₂³×C₂₃	1	2	yes	—
820	#121	C₂³×C₂₃	1	2	yes	—
821	#121	C₂³×C₂₃	1	2	yes	—
822	#121	C₂³×C₂₃	1	2	yes	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
826	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
830	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	D₄×C₂₃	1	2	yes	—
844	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
845	C₄×D₄	D₄×C₂₃	1	2	yes	—
846	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₂₃	1	2	yes	—
848	C₄×D₄	C₂³×C₂₃	1	2	yes	—
849	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₂₃	1	2	yes	—
852	C₄×D₄	C₂³×C₂₃	1	2	yes	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	2	no	—
857	#117	—	2	2	no	—
858	#117	—	2	2	no	—
859	#117	C₂³×C₂₃	1	1	yes	characteristic
860	#117	C₂³×C₂₃	1	1	yes	characteristic
861	#117	C₂³×C₂₃	1	2	yes	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
869	C₂×C₂²⋊C₄	—	2	1	no	—
870	C₂×C₄²	—	2	1	no	—
871	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
872	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
873	#107	C₂³×C₂₃	1	2	yes	—
874	#107	C₂³×C₂₃	1	2	yes	—
875	#107	C₂³×C₂₃	1	2	yes	—
876	#107	C₂³×C₂₃	1	2	yes	—
877	#106	C₂³×C₂₃	1	2	yes	—
878	#106	C₂³×C₂₃	1	2	yes	—
879	#106	C₂³×C₂₃	1	2	yes	—
880	#106	C₂³×C₂₃	1	2	yes	—
881	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
886	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
888	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
889	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
890	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
891	#103	C₂³×C₂₃	1	1	yes	characteristic
892	#103	C₂³×C₂₃	1	1	yes	characteristic
893	#103	C₂³×C₂₃	1	1	yes	characteristic
894	#103	C₂³×C₂₃	1	1	yes	characteristic
895	#103	C₂³×C₂₃	1	2	yes	—
896	#103	C₂³×C₂₃	1	2	yes	—
897	#103	C₂³×C₂₃	1	2	yes	—
898	#103	C₂³×C₂₃	1	2	yes	—
899	#102	C₂³×C₂₃	1	2	yes	—
900	#102	C₂³×C₂₃	1	2	yes	—
901	#102	C₂³×C₂₃	1	2	yes	—
902	#102	C₂³×C₂₃	1	2	yes	—
903	#102	C₂³×C₂₃	1	1	yes	characteristic
904	#102	C₂³×C₂₃	1	1	yes	characteristic
905	#102	C₂³×C₂₃	1	1	yes	characteristic
906	#102	C₂³×C₂₃	1	1	yes	characteristic
907	#102	C₂³×C₂₃	1	2	yes	—
908	#102	C₂³×C₂₃	1	2	yes	—
909	#102	C₂³×C₂₃	1	2	yes	—
910	#102	C₂³×C₂₃	1	2	yes	—
911	C₂₃	#60933	1	1	yes	characteristic, direct product factor, Sylow
912	C₂⁴	—	2	1	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	8	4	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
947	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	8	2	no	—
961	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
962	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	Q₁₆	—	4	1	no	—
968	Q₁₆	—	4	1	no	—
969	SD₁₆	—	4	1	no	—
970	SD₁₆	—	4	1	no	—
971	SD₁₆	—	4	1	no	—
972	SD₁₆	—	4	1	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	D₈	—	4	1	no	—
976	D₈	—	4	1	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	2	2	no	—
980	M₁₆	—	2	2	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	2	2	no	—
985	C₂×C₈	—	4	2	no	—
986	C₂×C₈	—	4	2	no	—
987	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
992	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	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	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1051	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1052	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1054	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₂₃	1	2	yes	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	4	2	no	—
1062	C₂³	—	8	1	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1065	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	8	2	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	1	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	8	1	no	—
1122	C₂×C₄	—	8	1	no	—
1123	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1131	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1132	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1133	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	2	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	8	4	no	—
1158	C₂²	C₂₃×#537	1	2	yes	—
1159	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	2	no	—
1175	C₄	C₂₃×#537	1	2	yes	—
1176	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1178	C₂	—	2	2	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	1	no	—
1184	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
1185	C₂	C₂₃×#3584	1	1	yes	characteristic
1186	C₂	C₂₃×#3585	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. C₂₃×#3460	C₂	semidirect
3. C₂₃×#3260	C₂	semidirect
4. C₂₃×#3259	C₂	semidirect
5. C₂₃×#3258	C₂	semidirect
6. C₂₃×#3257	C₂	semidirect
7. C₂₃×#3256	C₂	semidirect
8. C₂₃×#3251	C₂	semidirect
9. C₂₃×#3250	C₂	semidirect
10. C₂₃×#3247	C₂	semidirect
11. C₂₃×#3084	C₂	semidirect
12. C₂₃×#3083	C₂	semidirect
13. C₂₃×#3080	C₂	semidirect
14. C₂×C₂₃×#478	C₂	semidirect
15. C₂₃×#3062	C₂	semidirect
16. C₂₃×#3062	C₂	semidirect
17. C₂₃×#3061	C₂	semidirect
18. C₂₃×#3060	C₂	semidirect
19. C₂₃×#3045	C₂	semidirect
20. C₂₃×#3045	C₂	semidirect
21. C₂₃×#3036	C₂	semidirect
22. C₂₃×#3035	C₂	semidirect
23. C₂₃×#2906	C₂	semidirect
39. C₂₃×#541	C₂²	semidirect
42. C₂₃×#540	C₂²	semidirect
54. C₂₃×#529	C₂²	semidirect
55. C₂₃×#529	C₂²	semidirect
63. C₂₃×#479	C₂²	semidirect
64. C₂₃×#479	C₂²	semidirect
65. C₂₃×#479	C₂²	semidirect
66. C₂₃×#479	C₂²	semidirect
71. C₂₃×#478	C₂²	semidirect
72. C₂₃×#478	C₂²	semidirect
73. C₂₃×#478	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#476	C₂²	semidirect
77. C₂₃×#475	C₂²	semidirect
78. C₂₃×#474	C₂²	semidirect
79. C₂₃×#470	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
85. C₂₃×#468	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#467	C₂²	semidirect
90. C₂₃×#466	C₂²	semidirect
93. C₂₃×#465	C₂²	semidirect
94. C₂₃×#465	C₂²	semidirect
97. C₂₃×#464	C₂²	semidirect
98. C₂₃×#464	C₂²	semidirect
103. C₂₃×#463	C₂²	semidirect
104. C₂₃×#463	C₂²	semidirect
105. C₂₃×#462	C₂²	semidirect
107. C₂₃×#461	C₂²	semidirect
110. C₂₃×#460	C₂²	semidirect
114. C₂₃×#459	C₂²	semidirect
121. C₂₃×#424	C₂²	semidirect
122. C₂₃×#424	C₂²	semidirect
124. C₂₃×#423	C₂²	semidirect
126. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
463. #60933	C₂₃	direct (N × H)
547. #3512	C₂×C₂₃	semidirect
548. #3460	C₂×C₂₃	semidirect
549. #3260	C₂×C₂₃	semidirect
550. #3259	C₂×C₂₃	semidirect
551. #3258	C₂×C₂₃	semidirect
552. #3257	C₂×C₂₃	semidirect
553. #3256	C₂×C₂₃	semidirect
554. #3251	C₂×C₂₃	semidirect
555. #3250	C₂×C₂₃	semidirect
556. #3247	C₂×C₂₃	semidirect
557. #3084	C₂×C₂₃	semidirect
558. #3083	C₂×C₂₃	semidirect
559. #3080	C₂×C₂₃	semidirect
560. C₂×#478	C₂×C₂₃	semidirect
561. #3062	C₂×C₂₃	semidirect
562. #3062	C₂×C₂₃	semidirect
563. #3061	C₂×C₂₃	semidirect
564. #3060	C₂×C₂₃	semidirect
565. #3045	C₂×C₂₃	semidirect
566. #3045	C₂×C₂₃	semidirect
567. #3036	C₂×C₂₃	semidirect
568. #3035	C₂×C₂₃	semidirect
569. #2906	C₂×C₂₃	semidirect
623. #541	C₂²×C₂₃	semidirect
626. #540	C₂²×C₂₃	semidirect
638. #529	C₂²×C₂₃	semidirect
639. #529	C₂²×C₂₃	semidirect
647. #479	C₂²×C₂₃	semidirect
648. #479	C₂²×C₂₃	semidirect
649. #479	C₂²×C₂₃	semidirect
650. #479	C₂²×C₂₃	semidirect
655. #478	C₂²×C₂₃	semidirect
656. #478	C₂²×C₂₃	semidirect
657. #478	C₂²×C₂₃	semidirect
658. #478	C₂²×C₂₃	semidirect
659. #477	C₂²×C₂₃	semidirect
660. #476	C₂²×C₂₃	semidirect
661. #475	C₂²×C₂₃	semidirect
662. #474	C₂²×C₂₃	semidirect
663. #470	C₂²×C₂₃	semidirect
666. #469	C₂²×C₂₃	semidirect
669. #468	C₂²×C₂₃	semidirect
670. #468	C₂²×C₂₃	semidirect
671. #467	C₂²×C₂₃	semidirect
674. #466	C₂²×C₂₃	semidirect
677. #465	C₂²×C₂₃	semidirect
678. #465	C₂²×C₂₃	semidirect
681. #464	C₂²×C₂₃	semidirect
682. #464	C₂²×C₂₃	semidirect
687. #463	C₂²×C₂₃	semidirect
688. #463	C₂²×C₂₃	semidirect
689. #462	C₂²×C₂₃	semidirect
691. #461	C₂²×C₂₃	semidirect
694. #460	C₂²×C₂₃	semidirect
698. #459	C₂²×C₂₃	semidirect
705. #424	C₂²×C₂₃	semidirect
706. #424	C₂²×C₂₃	semidirect
708. #423	C₂²×C₂₃	semidirect
710. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
911. C₂₃	#60933	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
C₂₃×#3460	2
C₂₃×#3260	2
C₂₃×#3259	2
C₂₃×#3258	2
C₂₃×#3257	2
C₂₃×#3256	2
C₂₃×#3251	2
C₂₃×#3250	2
C₂₃×#3247	2
C₂₃×#3084	2
C₂₃×#3083	2
C₂₃×#3080	2
C₂×C₂₃×#478	2
C₂₃×#3062	2
C₂₃×#3061	2
C₂₃×#3060	2
C₂₃×#3045	2
C₂₃×#3036	2
C₂₃×#3035	2
C₂₃×#2906	2
#60933	23

Subgroups — C23×#60933 #19208559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60933 #19208559