Subgroups — C₂₃×#61448 #19209074

Order 5888.

1904 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3350	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3307	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3172	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3101	C₂	1	2	yes	maximal, complemented
21	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
23	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
26	C₂₃×#559	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#556	C₂²	1	1	yes	characteristic
29	C₂₃×#556	C₂²	1	2	yes	complemented
30	C₂₃×#554	C₂²	1	1	yes	characteristic
31	C₂₃×#554	C₂²	1	1	yes	characteristic
32	C₂₃×#553	—	2	1	no	—
33	C₂₃×#553	C₂²	1	2	yes	—
34	C₂₃×#552	—	2	1	no	—
35	C₂₃×#552	—	2	2	no	—
36	C₂₃×#551	—	2	2	no	—
37	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#548	—	2	1	no	—
39	C₂₃×#547	C₂²	1	1	yes	characteristic
40	C₂₃×#547	C₂²	1	2	yes	complemented
41	C₂₃×#546	—	2	1	no	—
42	C₂₃×#546	C₂²	1	2	yes	—
43	D₄²×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#533	C₂²	1	2	yes	complemented
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#529	—	2	1	no	—
48	C₂₃×#529	—	2	1	no	—
49	C₂₃×#529	—	2	2	no	—
50	C₂₃×#529	C₂²	1	2	yes	—
51	C₂₃×#525	—	2	2	no	—
52	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
53	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
55	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
57	C₂×C₄×D₄×C₂₃	—	2	1	no	—
58	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
59	C₂₃×#501	C₂²	1	2	yes	complemented
60	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#497	C₂²	1	2	yes	complemented
62	C₂₃×#492	C₂²	1	1	yes	characteristic
63	C₂₃×#491	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	1	yes	characteristic
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#485	C₂²	1	2	yes	complemented
69	C₂₃×#483	C₂²	1	2	yes	complemented
70	C₂₃×#483	C₂²	1	2	yes	complemented
71	C₂₃×#482	C₂²	1	2	yes	—
72	C₂₃×#482	C₂²	1	2	yes	complemented
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#476	C₂²	1	2	yes	—
77	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#476	C₂²	1	2	yes	complemented
79	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#474	C₂²	1	1	yes	characteristic
81	C₂₃×#470	C₂²	1	2	yes	complemented
82	C₂₃×#470	C₂²	1	2	yes	complemented
83	C₂₃×#468	C₂²	1	2	yes	—
84	C₂₃×#468	C₂²	1	2	yes	—
85	C₂₃×#465	C₂²	1	2	yes	complemented
86	C₂₃×#465	C₂²	1	2	yes	complemented
87	C₂₃×#464	C₂²	1	2	yes	complemented
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#461	C₂²	1	2	yes	—
91	C₂₃×#461	C₂²	1	1	yes	characteristic
92	C₂₃×#461	C₂²	1	2	yes	complemented
93	C₂₃×#460	C₂²	1	1	yes	characteristic
94	C₂₃×#459	C₂²	1	1	yes	characteristic
95	C₂₃×#452	C₂²	1	2	yes	—
96	C₂₃×#452	C₂²	1	2	yes	complemented
97	C₂₃×#450	C₂²	1	2	yes	—
98	C₂₃×#450	C₂²	1	2	yes	—
99	C₂₃×#449	C₂²	1	2	yes	—
100	C₂₃×#449	C₂²	1	2	yes	complemented
101	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#442	C₂²	1	2	yes	—
104	C₂₃×#442	C₂²	1	2	yes	complemented
105	C₂₃×#440	C₂²	1	2	yes	—
106	C₂₃×#440	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic
122	C₂₃×#436	C₂²	1	1	yes	characteristic
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₂₃×#431	C₂²	1	2	yes	complemented
126	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#428	C₂²	1	2	yes	complemented
128	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#418	C₂²	1	2	yes	—
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂₃×#416	C₂²	1	1	yes	characteristic
132	C₂₃×#416	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₂₃	—	2	1	no	—
141	C₂²×D₄×C₂₃	—	2	1	no	—
142	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₂₃	—	2	2	no	—
144	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
145	C₂₃×#135	—	2	4	no	—
146	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×D₈×C₂₃	C₂³	1	2	yes	—
155	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×#127	C₂³	1	1	yes	characteristic
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#125	—	2	1	no	—
172	C₂₃×#125	—	2	2	no	—
173	C₂₃×#125	—	2	1	no	—
174	C₂₃×#125	—	2	1	no	—
175	C₂₃×#125	—	2	2	no	—
176	C₂₃×#125	C₂³	1	2	yes	—
177	C₂₃×#124	—	2	1	no	—
178	C₂₃×#124	—	2	1	no	—
179	C₂₃×#124	—	2	2	no	—
180	C₂₃×#124	—	2	1	no	—
181	C₂₃×#124	C₂³	1	2	yes	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×#123	—	2	2	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	1	no	—
190	C₂₃×C₂²⋊Q₈	—	2	1	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	1	no	—
193	C₂₃×C₂²⋊Q₈	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×#121	—	2	1	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	—	2	1	no	—
205	C₂₃×#121	—	2	2	no	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#121	C₂³	1	2	yes	—
208	C₂₃×#120	—	2	2	no	—
209	C₂₃×#120	—	2	2	no	—
210	C₄×Q₈×C₂₃	—	2	1	no	—
211	C₄×Q₈×C₂₃	—	2	1	no	—
212	C₄×Q₈×C₂₃	—	2	2	no	—
213	C₄×Q₈×C₂₃	—	2	1	no	—
214	C₄×Q₈×C₂₃	—	2	2	no	—
215	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
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×Q₈×C₂₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	1	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	1	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	1	no	—
231	C₄×D₄×C₂₃	—	2	1	no	—
232	C₄×D₄×C₂₃	—	2	2	no	—
233	C₄×D₄×C₂₃	—	2	2	no	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	—	2	2	no	—
236	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
237	C₄×D₄×C₂₃	D₄	1	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	2	yes	—
246	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂³	1	2	yes	—
248	C₂₃×#117	—	2	2	no	—
249	C₂₃×#117	—	2	1	no	—
250	C₂₃×#117	—	2	1	no	—
251	C₂₃×#117	—	2	1	no	—
252	C₂₃×#117	—	2	2	no	—
253	C₂₃×#117	—	2	2	no	—
254	C₂₃×#117	D₄	1	2	yes	—
255	C₂₃×#117	D₄	1	1	yes	characteristic
256	C₂₃×#117	C₂³	1	1	yes	characteristic
257	C₂₃×#117	C₂³	1	2	yes	—
258	C₂₃×#117	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
261	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄²×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂×C₄²×C₂₃	—	2	2	no	—
268	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	1	yes	characteristic
271	C₂₃×#107	C₂³	1	1	yes	characteristic
272	C₂₃×#107	C₂³	1	2	yes	—
273	C₂₃×#107	C₂³	1	2	yes	—
274	C₂₃×#106	C₂³	1	1	yes	characteristic
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	2	yes	—
277	C₂₃×#106	C₂³	1	2	yes	—
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	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×#102	C₂³	1	1	yes	characteristic
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	C₂⁴×C₂₃	—	2	2	no	—
315	#41×C₂₃	—	2	2	no	—
316	#41×C₂₃	—	2	2	no	—
317	#41×C₂₃	—	2	4	no	—
318	#41×C₂₃	—	4	2	no	—
319	#41×C₂₃	—	4	1	no	—
320	#41×C₂₃	—	4	1	no	—
321	#41×C₂₃	—	4	2	no	—
322	#41×C₂₃	—	8	2	no	—
323	C₂×Q₈×C₂₃	—	2	2	no	—
324	C₂×Q₈×C₂₃	—	2	1	no	—
325	C₂×Q₈×C₂₃	—	2	1	no	—
326	C₂×Q₈×C₂₃	—	4	4	no	—
327	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₂₃	—	2	4	no	—
332	C₂×D₄×C₂₃	—	2	1	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	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	1	no	—
339	C₂×D₄×C₂₃	—	2	1	no	—
340	C₂×D₄×C₂₃	—	4	2	no	—
341	C₂×D₄×C₂₃	—	4	4	no	—
342	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₂₃	—	2	2	no	—
348	C₂²×C₄×C₂₃	—	2	1	no	—
349	C₂²×C₄×C₂₃	—	2	1	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	1	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	—	2	1	no	—
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	1	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	2	2	no	—
358	C₂²×C₄×C₂₃	—	2	2	no	—
359	C₂²×C₄×C₂₃	—	8	4	no	—
360	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
366	Q₁₆×C₂₃	—	2	2	no	—
367	Q₁₆×C₂₃	—	4	2	no	—
368	SD₁₆×C₂₃	—	2	2	no	—
369	SD₁₆×C₂₃	—	2	2	no	—
370	SD₁₆×C₂₃	—	2	4	no	—
371	SD₁₆×C₂₃	—	2	4	no	—
372	SD₁₆×C₂₃	—	4	2	no	—
373	SD₁₆×C₂₃	—	4	2	no	—
374	D₈×C₂₃	—	2	4	no	—
375	D₈×C₂₃	#41	1	4	yes	complemented
376	M₁₆×C₂₃	—	2	4	no	—
377	M₁₆×C₂₃	—	4	2	no	—
378	C₂×C₈×C₂₃	—	2	2	no	—
379	C₂×C₈×C₂₃	—	4	1	no	—
380	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
385	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	2	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	1	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	1	no	—
406	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	1	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
438	C₄²×C₂₃	—	2	1	no	—
439	C₄²×C₂₃	—	2	1	no	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	—	2	1	no	—
445	C₄²×C₂₃	—	2	1	no	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₂₃	C₂×D₄	1	2	yes	—
449	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₂₃	C₂×D₄	1	2	yes	—
451	C₄²×C₂₃	C₂⁴	1	2	yes	—
452	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
454	#61448	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₂₃	—	2	1	no	—
456	C₂³×C₂₃	—	2	1	no	—
457	C₂³×C₂₃	—	2	2	no	—
458	C₂³×C₂₃	—	4	4	no	—
459	C₂³×C₂₃	—	4	4	no	—
460	C₂³×C₂₃	—	8	2	no	—
461	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
462	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₂₃	—	2	2	no	—
464	Q₈×C₂₃	—	2	2	no	—
465	Q₈×C₂₃	—	2	1	no	—
466	Q₈×C₂₃	—	2	1	no	—
467	Q₈×C₂₃	—	2	1	no	—
468	Q₈×C₂₃	—	2	2	no	—
469	Q₈×C₂₃	—	2	1	no	—
470	Q₈×C₂₃	—	4	4	no	—
471	Q₈×C₂₃	—	4	2	no	—
472	Q₈×C₂₃	—	8	1	no	—
473	D₄×C₂₃	—	2	2	no	—
474	D₄×C₂₃	—	2	2	no	—
475	D₄×C₂₃	—	2	1	no	—
476	D₄×C₂₃	—	2	1	no	—
477	D₄×C₂₃	—	2	2	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	4	no	—
480	D₄×C₂₃	—	4	2	no	—
481	D₄×C₂₃	—	4	2	no	—
482	D₄×C₂₃	—	4	4	no	—
483	D₄×C₂₃	—	4	4	no	—
484	D₄×C₂₃	—	4	2	no	—
485	D₄×C₂₃	—	8	1	no	—
486	D₄×C₂₃	—	8	2	no	—
487	D₄×C₂₃	C₂×#41	1	2	yes	—
488	D₄×C₂₃	C₂×#41	1	2	yes	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	4	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	2	1	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	2	no	—
496	C₂×C₄×C₂₃	—	2	1	no	—
497	C₂×C₄×C₂₃	—	2	1	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	1	no	—
501	C₂×C₄×C₂₃	—	2	1	no	—
502	C₂×C₄×C₂₃	—	2	2	no	—
503	C₂×C₄×C₂₃	—	2	1	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	4	2	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	4	2	no	—
508	C₂×C₄×C₂₃	—	4	4	no	—
509	C₂×C₄×C₂₃	—	4	4	no	—
510	C₂×C₄×C₂₃	—	4	2	no	—
511	C₂×C₄×C₂₃	—	4	2	no	—
512	C₂×C₄×C₂₃	—	4	2	no	—
513	C₂×C₄×C₂₃	—	4	2	no	—
514	C₂×C₄×C₂₃	—	4	4	no	—
515	C₂×C₄×C₂₃	—	8	2	no	—
516	C₂×C₄×C₂₃	—	8	2	no	—
517	C₂×C₄×C₂₃	—	8	2	no	—
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
527	C₈×C₂₃	—	2	1	no	—
528	C₈×C₂₃	—	2	2	no	—
529	C₈×C₂₃	—	2	1	no	—
530	C₈×C₂₃	—	2	1	no	—
531	C₈×C₂₃	—	2	2	no	—
532	C₈×C₂₃	C₂×#41	1	2	yes	—
533	#3482	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3481	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3400	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3384	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3372	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3356	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3350	C₂×C₂₃	1	2	yes	complemented
541	#3331	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3311	C₂×C₂₃	1	2	yes	complemented
544	#3307	C₂×C₂₃	1	2	yes	complemented
545	#3272	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#3267	C₂×C₂₃	1	2	yes	complemented
547	#3172	C₂×C₂₃	1	2	yes	complemented
548	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3107	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#3102	C₂×C₂₃	1	2	yes	complemented
552	#3101	C₂×C₂₃	1	2	yes	complemented
553	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
554	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
555	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
556	C₂²×C₂₃	—	2	1	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	2	no	—
559	C₂²×C₂₃	—	2	2	no	—
560	C₂²×C₂₃	—	2	1	no	—
561	C₂²×C₂₃	—	2	2	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	1	no	—
564	C₂²×C₂₃	—	4	1	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	1	no	—
568	C₂²×C₂₃	—	4	2	no	—
569	C₂²×C₂₃	—	4	2	no	—
570	C₂²×C₂₃	—	4	2	no	—
571	C₂²×C₂₃	—	8	8	no	—
572	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₂₃	—	2	1	no	—
574	C₄×C₂₃	—	2	2	no	—
575	C₄×C₂₃	—	2	1	no	—
576	C₄×C₂₃	—	2	2	no	—
577	C₄×C₂₃	—	2	2	no	—
578	C₄×C₂₃	—	2	1	no	—
579	C₄×C₂₃	—	4	1	no	—
580	C₄×C₂₃	—	4	2	no	—
581	C₄×C₂₃	—	4	1	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	2	no	—
584	C₄×C₂₃	—	4	1	no	—
585	C₄×C₂₃	—	4	1	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	—	4	2	no	—
588	C₄×C₂₃	#575	1	2	yes	—
589	C₄×C₂₃	#577	1	2	yes	—
590	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
591	C₄×C₂₃	#585	1	1	yes	characteristic
592	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
593	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
594	#559	C₂²×C₂₃	1	1	yes	characteristic
595	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
596	#556	C₂²×C₂₃	1	1	yes	characteristic
597	#556	C₂²×C₂₃	1	2	yes	complemented
598	#554	C₂²×C₂₃	1	1	yes	characteristic
599	#554	C₂²×C₂₃	1	1	yes	characteristic
600	#553	—	2	1	no	—
601	#553	C₂²×C₂₃	1	2	yes	—
602	#552	—	2	1	no	—
603	#552	—	2	2	no	—
604	#551	—	2	2	no	—
605	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
606	#548	—	2	1	no	—
607	#547	C₂²×C₂₃	1	1	yes	characteristic
608	#547	C₂²×C₂₃	1	2	yes	complemented
609	#546	—	2	1	no	—
610	#546	C₂²×C₂₃	1	2	yes	—
611	D₄²	C₂²×C₂₃	1	1	yes	characteristic
612	#533	C₂²×C₂₃	1	2	yes	complemented
613	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
614	#532	C₂²×C₂₃	1	1	yes	characteristic
615	#529	—	2	1	no	—
616	#529	—	2	1	no	—
617	#529	—	2	2	no	—
618	#529	C₂²×C₂₃	1	2	yes	—
619	#525	—	2	2	no	—
620	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
621	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
622	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
623	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	C₂×C₄×Q₈	—	2	1	no	—
625	C₂×C₄×D₄	—	2	1	no	—
626	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
627	#501	C₂²×C₂₃	1	2	yes	complemented
628	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#497	C₂²×C₂₃	1	2	yes	complemented
630	#492	C₂²×C₂₃	1	1	yes	characteristic
631	#491	C₂²×C₂₃	1	2	yes	complemented
632	#489	C₂²×C₂₃	1	2	yes	complemented
633	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
634	#486	C₂²×C₂₃	1	1	yes	characteristic
635	#485	C₂²×C₂₃	1	2	yes	complemented
636	#485	C₂²×C₂₃	1	2	yes	complemented
637	#483	C₂²×C₂₃	1	2	yes	complemented
638	#483	C₂²×C₂₃	1	2	yes	complemented
639	#482	C₂²×C₂₃	1	2	yes	—
640	#482	C₂²×C₂₃	1	2	yes	complemented
641	#479	C₂²×C₂₃	1	2	yes	complemented
642	#478	C₂²×C₂₃	1	2	yes	complemented
643	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#476	C₂²×C₂₃	1	2	yes	—
645	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#476	C₂²×C₂₃	1	2	yes	complemented
647	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#474	C₂²×C₂₃	1	1	yes	characteristic
649	#470	C₂²×C₂₃	1	2	yes	complemented
650	#470	C₂²×C₂₃	1	2	yes	complemented
651	#468	C₂²×C₂₃	1	2	yes	—
652	#468	C₂²×C₂₃	1	2	yes	—
653	#465	C₂²×C₂₃	1	2	yes	complemented
654	#465	C₂²×C₂₃	1	2	yes	complemented
655	#464	C₂²×C₂₃	1	2	yes	complemented
656	#463	C₂²×C₂₃	1	2	yes	complemented
657	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#461	C₂²×C₂₃	1	2	yes	—
659	#461	C₂²×C₂₃	1	1	yes	characteristic
660	#461	C₂²×C₂₃	1	2	yes	complemented
661	#460	C₂²×C₂₃	1	1	yes	characteristic
662	#459	C₂²×C₂₃	1	1	yes	characteristic
663	#452	C₂²×C₂₃	1	2	yes	—
664	#452	C₂²×C₂₃	1	2	yes	complemented
665	#450	C₂²×C₂₃	1	2	yes	—
666	#450	C₂²×C₂₃	1	2	yes	—
667	#449	C₂²×C₂₃	1	2	yes	—
668	#449	C₂²×C₂₃	1	2	yes	complemented
669	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#442	C₂²×C₂₃	1	2	yes	—
672	#442	C₂²×C₂₃	1	2	yes	complemented
673	#440	C₂²×C₂₃	1	2	yes	—
674	#440	C₂²×C₂₃	1	2	yes	complemented
675	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
677	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
686	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
687	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
688	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
689	#436	C₂²×C₂₃	1	1	yes	characteristic
690	#436	C₂²×C₂₃	1	1	yes	characteristic
691	#435	C₂²×C₂₃	1	2	yes	complemented
692	#435	C₂²×C₂₃	1	2	yes	complemented
693	#431	C₂²×C₂₃	1	2	yes	complemented
694	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#428	C₂²×C₂₃	1	2	yes	complemented
696	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	#418	C₂²×C₂₃	1	2	yes	—
698	#417	C₂²×C₂₃	1	2	yes	complemented
699	#416	C₂²×C₂₃	1	1	yes	characteristic
700	#416	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
702	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	C₂×C₂₃	—	4	1	no	—
704	C₂×C₂₃	—	4	2	no	—
705	C₂×C₂₃	—	4	2	no	—
706	C₂×C₂₃	—	4	2	no	—
707	C₂×C₂₃	—	8	2	no	—
708	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
709	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
710	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
711	C₂×#41	—	2	1	no	—
712	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
713	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
714	C₂×#41	C₂³×C₂₃	1	2	yes	—
715	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
716	C₂²×Q₈	—	2	1	no	—
717	C₂²×D₄	—	2	1	no	—
718	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
719	C₂³×C₄	—	2	2	no	—
720	AGL(1,ℤ/8)	—	2	8	no	—
721	#135	—	2	4	no	—
722	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
723	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
730	C₂×D₈	C₂³×C₂₃	1	2	yes	—
731	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
733	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
734	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
741	#127	C₂³×C₂₃	1	1	yes	characteristic
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	—	2	1	no	—
751	#125	—	2	2	no	—
752	#125	C₂³×C₂₃	1	2	yes	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	1	no	—
757	#124	C₂³×C₂₃	1	2	yes	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
775	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
776	#121	—	2	2	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	—	2	1	no	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	C₂³×C₂₃	1	2	yes	—
783	#121	C₂³×C₂₃	1	2	yes	—
784	#120	—	2	2	no	—
785	#120	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	2	no	—
791	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
795	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
798	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	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	D₄×C₂₃	1	1	yes	characteristic
813	C₄×D₄	D₄×C₂₃	1	2	yes	—
814	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₂₃	1	2	yes	—
816	C₄×D₄	C₂³×C₂₃	1	2	yes	—
817	C₄×D₄	C₂³×C₂₃	1	2	yes	—
818	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₂₃	1	2	yes	—
822	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₂₃	1	2	yes	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	D₄×C₂₃	1	2	yes	—
831	#117	D₄×C₂₃	1	1	yes	characteristic
832	#117	C₂³×C₂₃	1	1	yes	characteristic
833	#117	C₂³×C₂₃	1	2	yes	—
834	#117	C₂³×C₂₃	1	1	yes	characteristic
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	—	2	2	no	—
844	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
845	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
846	#107	C₂³×C₂₃	1	1	yes	characteristic
847	#107	C₂³×C₂₃	1	1	yes	characteristic
848	#107	C₂³×C₂₃	1	2	yes	—
849	#107	C₂³×C₂₃	1	2	yes	—
850	#106	C₂³×C₂₃	1	1	yes	characteristic
851	#106	C₂³×C₂₃	1	1	yes	characteristic
852	#106	C₂³×C₂₃	1	2	yes	—
853	#106	C₂³×C₂₃	1	2	yes	—
854	#106	C₂³×C₂₃	1	2	yes	—
855	#106	C₂³×C₂₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
858	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
860	#103	C₂³×C₂₃	1	1	yes	characteristic
861	#103	C₂³×C₂₃	1	1	yes	characteristic
862	#103	C₂³×C₂₃	1	1	yes	characteristic
863	#103	C₂³×C₂₃	1	1	yes	characteristic
864	#103	C₂³×C₂₃	1	2	yes	—
865	#103	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	2	yes	—
867	#103	C₂³×C₂₃	1	2	yes	—
868	#103	C₂³×C₂₃	1	2	yes	—
869	#103	C₂³×C₂₃	1	2	yes	—
870	#102	C₂³×C₂₃	1	1	yes	characteristic
871	#102	C₂³×C₂₃	1	1	yes	characteristic
872	#102	C₂³×C₂₃	1	1	yes	characteristic
873	#102	C₂³×C₂₃	1	1	yes	characteristic
874	#102	C₂³×C₂₃	1	2	yes	—
875	#102	C₂³×C₂₃	1	2	yes	—
876	#102	C₂³×C₂₃	1	2	yes	—
877	#102	C₂³×C₂₃	1	2	yes	—
878	#102	C₂³×C₂₃	1	2	yes	—
879	#102	C₂³×C₂₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
883	#97	C₂³×C₂₃	1	2	yes	—
884	#97	C₂³×C₂₃	1	2	yes	—
885	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
889	C₄×C₈	C₂³×C₂₃	1	2	yes	—
890	C₂₃	#61448	1	1	yes	characteristic, direct product factor, Sylow
891	C₂⁴	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	4	no	—
895	#41	—	4	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	1	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	4	4	no	—
904	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
907	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
908	C₂×D₄	—	2	4	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	4	no	—
919	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
920	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
921	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
922	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	8	4	no	—
937	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
938	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
943	Q₁₆	—	2	2	no	—
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	2	no	—
951	D₈	—	2	4	no	—
952	D₈	#41×C₂₃	1	4	yes	complemented
953	M₁₆	—	2	4	no	—
954	M₁₆	—	4	2	no	—
955	C₂×C₈	—	2	2	no	—
956	C₂×C₈	—	4	1	no	—
957	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
961	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
962	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1025	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1026	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1027	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1028	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₂₃	1	2	yes	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	4	4	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1038	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	4	4	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	8	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	C₂×#41×C₂₃	1	2	yes	—
1064	D₄	C₂×#41×C₂₃	1	2	yes	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	4	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1102	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	2	no	—
1108	C₈	C₂×#41×C₂₃	1	2	yes	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	8	8	no	—
1125	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	C₂₃×#575	1	2	yes	—
1142	C₄	C₂₃×#577	1	2	yes	—
1143	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1144	C₄	C₂₃×#585	1	1	yes	characteristic
1145	C₂	—	4	2	no	—
1146	C₂	—	4	1	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	2	no	—
1150	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1151	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1152	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3482	C₂	semidirect
2. C₂₃×#3481	C₂	semidirect
3. C₂₃×#3400	C₂	semidirect
4. C₂₃×#3384	C₂	semidirect
5. C₂₃×#3373	C₂	semidirect
6. C₂₃×#3372	C₂	semidirect
7. C₂₃×#3356	C₂	semidirect
8. C₂₃×#3350	C₂	semidirect
9. C₂₃×#3331	C₂	semidirect
10. C₂₃×#3324	C₂	semidirect
11. C₂₃×#3311	C₂	semidirect
12. C₂₃×#3307	C₂	semidirect
13. C₂₃×#3272	C₂	semidirect
14. C₂₃×#3267	C₂	semidirect
15. C₂₃×#3172	C₂	semidirect
16. C₂₃×#3167	C₂	semidirect
17. C₂₃×#3107	C₂	semidirect
18. C₂₃×#3106	C₂	semidirect
19. C₂₃×#3102	C₂	semidirect
20. C₂₃×#3101	C₂	semidirect
21. C₂₃×#2965	C₂	semidirect
22. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₄×C₂₃×#135	C₂	semidirect
27. C₂₃×#557	C₂²	semidirect
29. C₂₃×#556	C₂²	semidirect
37. D₄×Q₈×C₂₃	C₂²	semidirect
40. C₂₃×#547	C₂²	semidirect
44. C₂₃×#533	C₂²	semidirect
45. C₂₃×#533	C₂²	semidirect
54. C₄×#41×C₂₃	C₂²	semidirect
55. C₄×#41×C₂₃	C₂²	semidirect
59. C₂₃×#501	C₂²	semidirect
60. C₂₃×#498	C₂²	semidirect
61. C₂₃×#497	C₂²	semidirect
63. C₂₃×#491	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
69. C₂₃×#483	C₂²	semidirect
70. C₂₃×#483	C₂²	semidirect
72. C₂₃×#482	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#476	C₂²	semidirect
79. C₂₃×#475	C₂²	semidirect
81. C₂₃×#470	C₂²	semidirect
82. C₂₃×#470	C₂²	semidirect
85. C₂₃×#465	C₂²	semidirect
86. C₂₃×#465	C₂²	semidirect
87. C₂₃×#464	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
89. C₂₃×#462	C₂²	semidirect
92. C₂₃×#461	C₂²	semidirect
96. C₂₃×#452	C₂²	semidirect
100. C₂₃×#449	C₂²	semidirect
101. C₂₃×#446	C₂²	semidirect
102. C₂₃×#446	C₂²	semidirect
104. C₂₃×#442	C₂²	semidirect
106. C₂₃×#440	C₂²	semidirect
107. C₄×Q₁₆×C₂₃	C₂²	semidirect
108. C₄×Q₁₆×C₂₃	C₂²	semidirect
109. C₄×Q₁₆×C₂₃	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
117. C₄×SD₁₆×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₂₃×#431	C₂²	semidirect
126. C₂₃×#431	C₂²	semidirect
127. C₂₃×#428	C₂²	semidirect
128. C₂₃×#427	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
375. D₈×C₂₃	#41	semidirect
454. #61448	C₂₃	direct (N × H)
533. #3482	C₂×C₂₃	semidirect
534. #3481	C₂×C₂₃	semidirect
535. #3400	C₂×C₂₃	semidirect
536. #3384	C₂×C₂₃	semidirect
537. #3373	C₂×C₂₃	semidirect
538. #3372	C₂×C₂₃	semidirect
539. #3356	C₂×C₂₃	semidirect
540. #3350	C₂×C₂₃	semidirect
541. #3331	C₂×C₂₃	semidirect
542. #3324	C₂×C₂₃	semidirect
543. #3311	C₂×C₂₃	semidirect
544. #3307	C₂×C₂₃	semidirect
545. #3272	C₂×C₂₃	semidirect
546. #3267	C₂×C₂₃	semidirect
547. #3172	C₂×C₂₃	semidirect
548. #3167	C₂×C₂₃	semidirect
549. #3107	C₂×C₂₃	semidirect
550. #3106	C₂×C₂₃	semidirect
551. #3102	C₂×C₂₃	semidirect
552. #3101	C₂×C₂₃	semidirect
553. #2965	C₂×C₂₃	semidirect
554. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
555. C₄×#135	C₂×C₂₃	semidirect
595. #557	C₂²×C₂₃	semidirect
597. #556	C₂²×C₂₃	semidirect
605. D₄×Q₈	C₂²×C₂₃	semidirect
608. #547	C₂²×C₂₃	semidirect
612. #533	C₂²×C₂₃	semidirect
613. #533	C₂²×C₂₃	semidirect
622. C₄×#41	C₂²×C₂₃	semidirect
623. C₄×#41	C₂²×C₂₃	semidirect
627. #501	C₂²×C₂₃	semidirect
628. #498	C₂²×C₂₃	semidirect
629. #497	C₂²×C₂₃	semidirect
631. #491	C₂²×C₂₃	semidirect
632. #489	C₂²×C₂₃	semidirect
633. #487	C₂²×C₂₃	semidirect
635. #485	C₂²×C₂₃	semidirect
636. #485	C₂²×C₂₃	semidirect
637. #483	C₂²×C₂₃	semidirect
638. #483	C₂²×C₂₃	semidirect
640. #482	C₂²×C₂₃	semidirect
641. #479	C₂²×C₂₃	semidirect
642. #478	C₂²×C₂₃	semidirect
643. #477	C₂²×C₂₃	semidirect
645. #476	C₂²×C₂₃	semidirect
646. #476	C₂²×C₂₃	semidirect
647. #475	C₂²×C₂₃	semidirect
649. #470	C₂²×C₂₃	semidirect
650. #470	C₂²×C₂₃	semidirect
653. #465	C₂²×C₂₃	semidirect
654. #465	C₂²×C₂₃	semidirect
655. #464	C₂²×C₂₃	semidirect
656. #463	C₂²×C₂₃	semidirect
657. #462	C₂²×C₂₃	semidirect
660. #461	C₂²×C₂₃	semidirect
664. #452	C₂²×C₂₃	semidirect
668. #449	C₂²×C₂₃	semidirect
669. #446	C₂²×C₂₃	semidirect
670. #446	C₂²×C₂₃	semidirect
672. #442	C₂²×C₂₃	semidirect
674. #440	C₂²×C₂₃	semidirect
675. C₄×Q₁₆	C₂²×C₂₃	semidirect
676. C₄×Q₁₆	C₂²×C₂₃	semidirect
677. C₄×Q₁₆	C₂²×C₂₃	semidirect
681. C₄×SD₁₆	C₂²×C₂₃	semidirect
682. C₄×SD₁₆	C₂²×C₂₃	semidirect
683. C₄×SD₁₆	C₂²×C₂₃	semidirect
684. C₄×SD₁₆	C₂²×C₂₃	semidirect
685. C₄×SD₁₆	C₂²×C₂₃	semidirect
688. C₄×D₈	C₂²×C₂₃	semidirect
691. #435	C₂²×C₂₃	semidirect
692. #435	C₂²×C₂₃	semidirect
693. #431	C₂²×C₂₃	semidirect
694. #431	C₂²×C₂₃	semidirect
695. #428	C₂²×C₂₃	semidirect
696. #427	C₂²×C₂₃	semidirect
698. #417	C₂²×C₂₃	semidirect
700. #416	C₂²×C₂₃	semidirect
701. C₄×M₁₆	C₂²×C₂₃	semidirect
702. C₂×C₄×C₈	C₂²×C₂₃	semidirect
890. C₂₃	#61448	direct (N × H)
952. D₈	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3482	2
C₂₃×#3481	2
C₂₃×#3400	2
C₂₃×#3384	2
C₂₃×#3373	2
C₂₃×#3372	2
C₂₃×#3356	2
C₂₃×#3350	2
C₂₃×#3331	2
C₂₃×#3324	2
C₂₃×#3311	2
C₂₃×#3307	2
C₂₃×#3272	2
C₂₃×#3267	2
C₂₃×#3172	2
C₂₃×#3167	2
C₂₃×#3107	2
C₂₃×#3106	2
C₂₃×#3102	2
C₂₃×#3101	2
C₂₃×#2965	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₄×C₂₃×#135	2
#61448	23

Subgroups — C23×#61448 #19209074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61448 #19209074