Subgroups — C₂₃×#61323 #19208949

Order 5888.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3376	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3367	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3364	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3140	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3078	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3040	C₂	1	2	yes	maximal
14	C₂₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×#137	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
18	C₂×C₂₃×#137	C₂²	1	2	yes	—
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#557	C₂²	1	2	yes	complemented
23	C₂₃×#556	—	2	1	no	—
24	C₂₃×#556	—	2	2	no	—
25	C₂₃×#556	—	2	1	no	—
26	C₂₃×#556	C₂²	1	2	yes	—
27	C₂₃×#556	C₂²	1	2	yes	—
28	C₂₃×#556	C₂²	1	4	yes	—
29	C₂₃×#554	—	2	1	no	—
30	C₂₃×#554	—	2	2	no	—
31	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#554	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₂₃	—	2	1	no	—
34	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#533	—	2	1	no	—
36	C₂₃×#533	—	2	2	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#533	C₂²	1	2	yes	—
39	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#126	—	2	2	no	—
41	C₂×C₂₃×#124	C₂²	1	2	yes	—
42	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
43	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
44	C₄×#41×C₂₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
46	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#117	—	2	1	no	—
50	C₂₃×#491	C₂²	1	4	yes	complemented
51	C₂₃×#489	C₂²	1	4	yes	—
52	C₂₃×#489	C₂²	1	4	yes	—
53	C₂₃×#488	C₂²	1	4	yes	—
54	C₂₃×#488	C₂²	1	4	yes	—
55	C₂₃×#487	C₂²	1	2	yes	complemented
56	C₂₃×#487	C₂²	1	2	yes	complemented
57	C₂₃×#479	C₂²	1	4	yes	complemented
58	C₂₃×#479	C₂²	1	4	yes	complemented
59	C₂₃×#478	C₂²	1	4	yes	—
60	C₂₃×#477	C₂²	1	4	yes	complemented
61	C₂₃×#476	C₂²	1	2	yes	—
62	C₂₃×#475	C₂²	1	4	yes	complemented
63	C₂₃×#474	C₂²	1	2	yes	—
64	C₂₃×#464	C₂²	1	4	yes	—
65	C₂₃×#464	C₂²	1	4	yes	—
66	C₂₃×#463	C₂²	1	4	yes	—
67	C₂₃×#463	C₂²	1	4	yes	—
68	C₂₃×#462	C₂²	1	2	yes	complemented
69	C₂₃×#462	C₂²	1	2	yes	complemented
70	C₂₃×#461	C₂²	1	2	yes	complemented
71	C₂₃×#461	C₂²	1	2	yes	complemented
72	C₂₃×#446	C₂²	1	2	yes	complemented
73	C₂₃×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
75	C₂₃×#442	C₂²	1	2	yes	—
76	C₂₃×#441	C₂²	1	4	yes	complemented
77	C₂₃×#440	C₂²	1	2	yes	—
78	C₂₃×#440	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
82	C₄×D₈×C₂₃	C₂²	1	2	yes	—
83	C₂₃×#428	C₂²	1	1	yes	characteristic
84	C₂₃×#428	C₂²	1	2	yes	—
85	C₂₃×#423	C₂²	1	1	yes	characteristic
86	C₂₃×#423	C₂²	1	2	yes	—
87	C₂₃×#419	C₂²	1	2	yes	—
88	C₂₃×#419	C₂²	1	2	yes	—
89	C₂₃×#419	C₂²	1	2	yes	—
90	C₂₃×#418	C₂²	1	1	yes	characteristic
91	C₂₃×#418	C₂²	1	2	yes	—
92	C₂₃×#417	C₂²	1	1	yes	characteristic
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	—	2	1	no	—
97	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₂₃	—	2	1	no	—
101	C₂₃×#137	—	2	8	no	—
102	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
103	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×D₈×C₂₃	C₂³	1	2	yes	—
107	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	—	2	2	no	—
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	—	2	2	no	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	—	2	1	no	—
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₂₃×#126	—	2	4	no	—
123	C₂₃×#126	—	2	4	no	—
124	C₂₃×#126	—	2	4	no	—
125	C₂₃×#126	—	2	4	no	—
126	C₂₃×#125	—	2	2	no	—
127	C₂₃×#125	—	2	2	no	—
128	C₂₃×#125	—	2	2	no	—
129	C₂₃×#125	C₂³	1	2	yes	—
130	C₂₃×#125	C₂³	1	2	yes	—
131	C₂₃×#125	C₂³	1	2	yes	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	—	2	2	no	—
134	C₂₃×#124	C₂³	1	4	yes	—
135	C₂₃×#124	C₂³	1	4	yes	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	2	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	4	no	—
141	C₂₃×C₂²⋊Q₈	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	—	2	2	no	—
143	C₂₃×C₂²⋊Q₈	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	—	2	1	no	—
145	C₂₃×C₂²⋊Q₈	—	2	1	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	2	no	—
154	C₄×Q₈×C₂₃	—	2	2	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
160	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₂₃	D₄	1	2	yes	—
162	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
163	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₃	C₂³	1	2	yes	—
182	C₄×D₄×C₂₃	C₂³	1	2	yes	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	4	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	1	no	—
187	C₂₃×#117	—	2	2	no	—
188	C₂₃×#117	C₂³	1	1	yes	characteristic
189	C₂₃×#117	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
195	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₄²×C₂₃	—	2	2	no	—
202	C₂×C₄²×C₂₃	—	2	1	no	—
203	C₂×C₄²×C₂₃	—	2	2	no	—
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
206	C₂₃×#107	C₂³	1	2	yes	—
207	C₂₃×#107	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	2	yes	—
209	C₂₃×#106	C₂³	1	4	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	2	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#103	C₂³	1	4	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#102	C₂³	1	2	yes	—
222	C₂₃×#102	C₂³	1	2	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×#102	C₂³	1	4	yes	—
225	C₂₃×#102	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₂₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₂₃	C₂³	1	2	yes	—
229	C₄×C₈×C₂₃	C₂³	1	4	yes	—
230	C₂⁴×C₂₃	—	2	1	no	—
231	#41×C₂₃	—	2	2	no	—
232	#41×C₂₃	#41	1	4	yes	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	1	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	—	2	1	no	—
238	C₂×Q₈×C₂₃	—	2	4	no	—
239	C₂×Q₈×C₂₃	—	2	4	no	—
240	C₂×Q₈×C₂₃	—	4	2	no	—
241	C₂×Q₈×C₂₃	—	4	4	no	—
242	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₂₃	—	2	1	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	—	2	1	no	—
254	C₂²×C₄×C₂₃	—	2	1	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	1	no	—
262	C₂²×C₄×C₂₃	—	4	4	no	—
263	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₂₃	—	2	8	no	—
269	SD₁₆×C₂₃	—	2	4	no	—
270	SD₁₆×C₂₃	—	2	8	no	—
271	D₈×C₂₃	—	2	4	no	—
272	M₁₆×C₂₃	—	2	2	no	—
273	M₁₆×C₂₃	—	2	4	no	—
274	M₁₆×C₂₃	—	2	2	no	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
277	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	4	no	—
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	4	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	1	no	—
323	C₄²×C₂₃	—	2	4	no	—
324	C₄²×C₂₃	—	2	4	no	—
325	C₄²×C₂₃	—	2	1	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	1	no	—
329	C₄²×C₂₃	—	2	2	no	—
330	C₄²×C₂₃	—	2	1	no	—
331	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₂₃	C₂×D₄	1	2	yes	—
333	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₂₃	C₂×D₄	1	2	yes	—
335	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
337	C₄²×C₂₃	C₂⁴	1	2	yes	—
338	C₄²×C₂₃	C₂⁴	1	2	yes	—
339	#61323	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂³×C₂₃	—	2	1	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	4	2	no	—
344	C₂³×C₂₃	—	4	2	no	—
345	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	1	no	—
349	Q₈×C₂₃	—	2	4	no	—
350	Q₈×C₂₃	—	2	4	no	—
351	Q₈×C₂₃	—	4	2	no	—
352	Q₈×C₂₃	—	4	4	no	—
353	Q₈×C₂₃	—	4	4	no	—
354	Q₈×C₂₃	—	4	2	no	—
355	Q₈×C₂₃	—	8	2	no	—
356	Q₈×C₂₃	—	8	1	no	—
357	Q₈×C₂₃	C₂×#41	1	2	yes	—
358	D₄×C₂₃	—	2	4	no	—
359	D₄×C₂₃	—	2	2	no	—
360	D₄×C₂₃	—	2	1	no	—
361	D₄×C₂₃	—	2	2	no	—
362	D₄×C₂₃	—	4	2	no	—
363	D₄×C₂₃	C₂×#41	1	2	yes	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	4	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	4	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	2	no	—
376	C₂×C₄×C₂₃	—	4	4	no	—
377	C₂×C₄×C₂₃	—	4	4	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	4	no	—
380	C₂×C₄×C₂₃	—	4	4	no	—
381	C₂×C₄×C₂₃	—	4	2	no	—
382	C₂×C₄×C₂₃	—	8	2	no	—
383	C₂×C₄×C₂₃	—	8	1	no	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
394	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
395	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
396	C₈×C₂₃	—	2	2	no	—
397	C₈×C₂₃	—	2	4	no	—
398	C₈×C₂₃	—	2	2	no	—
399	Q₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
400	C₂×#556	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3377	C₂×C₂₃	1	4	yes	complemented
402	#3376	C₂×C₂₃	1	4	yes	complemented
403	#3369	C₂×C₂₃	1	2	yes	complemented
404	#3367	C₂×C₂₃	1	2	yes	complemented
405	#3364	C₂×C₂₃	1	2	yes	complemented
406	#3360	C₂×C₂₃	1	2	yes	complemented
407	#3140	C₂×C₂₃	1	2	yes	complemented
408	#3139	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3078	C₂×C₂₃	1	2	yes	complemented
410	#3077	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3040	C₂×C₂₃	1	2	yes	—
412	#3039	C₂×C₂₃	1	1	yes	characteristic, complemented
413	Q₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
414	C₄×#137	C₂×C₂₃	1	2	yes	complemented
415	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	4	1	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	—	4	2	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	8	4	no	—
425	C₂²×C₂₃	#548	1	2	yes	—
426	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	2	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	2	no	—
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	—	4	1	no	—
437	C₄×C₂₃	—	4	4	no	—
438	C₄×C₂₃	—	4	2	no	—
439	C₄×C₂₃	—	4	2	no	—
440	C₄×C₂₃	—	4	1	no	—
441	C₄×C₂₃	#548	1	2	yes	—
442	C₄×C₂₃	#575	1	2	yes	—
443	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
444	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂×#137	C₂²×C₂₃	1	2	yes	—
446	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
447	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	#557	C₂²×C₂₃	1	2	yes	complemented
450	#556	—	2	1	no	—
451	#556	—	2	2	no	—
452	#556	—	2	1	no	—
453	#556	C₂²×C₂₃	1	2	yes	—
454	#556	C₂²×C₂₃	1	2	yes	—
455	#556	C₂²×C₂₃	1	4	yes	—
456	#554	—	2	1	no	—
457	#554	—	2	2	no	—
458	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#554	C₂²×C₂₃	1	2	yes	complemented
460	D₄×Q₈	—	2	1	no	—
461	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#533	—	2	1	no	—
463	#533	—	2	2	no	—
464	#533	C₂²×C₂₃	1	1	yes	characteristic
465	#533	C₂²×C₂₃	1	2	yes	—
466	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×#126	—	2	2	no	—
468	C₂×#124	C₂²×C₂₃	1	2	yes	—
469	C₂×C₂²⋊Q₈	—	2	1	no	—
470	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
471	C₄×#41	C₂²×C₂₃	1	2	yes	—
472	C₂×C₄×Q₈	—	2	1	no	—
473	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
474	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×#117	—	2	1	no	—
477	#491	C₂²×C₂₃	1	4	yes	complemented
478	#489	C₂²×C₂₃	1	4	yes	—
479	#489	C₂²×C₂₃	1	4	yes	—
480	#488	C₂²×C₂₃	1	4	yes	—
481	#488	C₂²×C₂₃	1	4	yes	—
482	#487	C₂²×C₂₃	1	2	yes	complemented
483	#487	C₂²×C₂₃	1	2	yes	complemented
484	#479	C₂²×C₂₃	1	4	yes	complemented
485	#479	C₂²×C₂₃	1	4	yes	complemented
486	#478	C₂²×C₂₃	1	4	yes	—
487	#477	C₂²×C₂₃	1	4	yes	complemented
488	#476	C₂²×C₂₃	1	2	yes	—
489	#475	C₂²×C₂₃	1	4	yes	complemented
490	#474	C₂²×C₂₃	1	2	yes	—
491	#464	C₂²×C₂₃	1	4	yes	—
492	#464	C₂²×C₂₃	1	4	yes	—
493	#463	C₂²×C₂₃	1	4	yes	—
494	#463	C₂²×C₂₃	1	4	yes	—
495	#462	C₂²×C₂₃	1	2	yes	complemented
496	#462	C₂²×C₂₃	1	2	yes	complemented
497	#461	C₂²×C₂₃	1	2	yes	complemented
498	#461	C₂²×C₂₃	1	2	yes	complemented
499	#446	C₂²×C₂₃	1	2	yes	complemented
500	#446	C₂²×C₂₃	1	4	yes	complemented
501	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
502	#442	C₂²×C₂₃	1	2	yes	—
503	#441	C₂²×C₂₃	1	4	yes	complemented
504	#440	C₂²×C₂₃	1	2	yes	—
505	#440	C₂²×C₂₃	1	4	yes	complemented
506	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
507	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
508	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
509	C₄×D₈	C₂²×C₂₃	1	2	yes	—
510	#428	C₂²×C₂₃	1	2	yes	—
511	#428	C₂²×C₂₃	1	1	yes	characteristic
512	#423	C₂²×C₂₃	1	1	yes	characteristic
513	#423	C₂²×C₂₃	1	2	yes	—
514	#419	C₂²×C₂₃	1	2	yes	—
515	#419	C₂²×C₂₃	1	2	yes	—
516	#419	C₂²×C₂₃	1	2	yes	—
517	#418	C₂²×C₂₃	1	2	yes	—
518	#418	C₂²×C₂₃	1	1	yes	characteristic
519	#417	C₂²×C₂₃	1	1	yes	characteristic
520	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
521	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
522	C₂×C₂₃	—	2	2	no	—
523	C₂×C₂₃	—	4	2	no	—
524	C₂×C₂₃	—	8	2	no	—
525	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
526	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
527	C₂×C₂₃	#3586	1	1	yes	characteristic
528	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
532	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
533	C₂³×C₄	—	2	1	no	—
534	#137	—	2	8	no	—
535	AGL(1,ℤ/8)	—	2	4	no	—
536	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
537	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
539	C₂×D₈	C₂³×C₂₃	1	2	yes	—
540	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
542	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	—	2	2	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
552	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
555	#126	—	2	4	no	—
556	#126	—	2	4	no	—
557	#126	—	2	4	no	—
558	#126	—	2	4	no	—
559	#125	—	2	2	no	—
560	#125	—	2	2	no	—
561	#125	—	2	2	no	—
562	#125	C₂³×C₂₃	1	2	yes	—
563	#125	C₂³×C₂₃	1	2	yes	—
564	#125	C₂³×C₂₃	1	2	yes	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	C₂³×C₂₃	1	4	yes	—
568	#124	C₂³×C₂₃	1	4	yes	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
593	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
594	C₄×Q₈	D₄×C₂₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
596	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
597	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
601	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	C₂³×C₂₃	1	2	yes	—
611	C₄×D₄	C₂³×C₂₃	1	2	yes	—
612	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₂₃	1	2	yes	—
614	C₄×D₄	C₂³×C₂₃	1	2	yes	—
615	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
616	#117	—	2	2	no	—
617	#117	—	2	4	no	—
618	#117	—	2	2	no	—
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	C₂³×C₂₃	1	1	yes	characteristic
622	#117	C₂³×C₂₃	1	2	yes	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₄²	—	2	2	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	2	no	—
637	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
639	#107	C₂³×C₂₃	1	2	yes	—
640	#107	C₂³×C₂₃	1	4	yes	—
641	#106	C₂³×C₂₃	1	2	yes	—
642	#106	C₂³×C₂₃	1	4	yes	—
643	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
644	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
647	#103	C₂³×C₂₃	1	2	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#103	C₂³×C₂₃	1	4	yes	—
650	#103	C₂³×C₂₃	1	4	yes	—
651	#103	C₂³×C₂₃	1	4	yes	—
652	#103	C₂³×C₂₃	1	4	yes	—
653	#103	C₂³×C₂₃	1	4	yes	—
654	#102	C₂³×C₂₃	1	2	yes	—
655	#102	C₂³×C₂₃	1	2	yes	—
656	#102	C₂³×C₂₃	1	2	yes	—
657	#102	C₂³×C₂₃	1	4	yes	—
658	#102	C₂³×C₂₃	1	4	yes	—
659	#97	C₂³×C₂₃	1	2	yes	—
660	#97	C₂³×C₂₃	1	4	yes	—
661	C₄×C₈	C₂³×C₂₃	1	2	yes	—
662	C₄×C₈	C₂³×C₂₃	1	4	yes	—
663	C₂₃	#61323	1	1	yes	characteristic, direct product factor, Sylow
664	C₂⁴	—	2	1	no	—
665	#41	—	2	2	no	—
666	#41	#41×C₂₃	1	4	yes	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
680	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
686	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	4	4	no	—
697	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
702	Q₁₆	—	2	8	no	—
703	SD₁₆	—	2	4	no	—
704	SD₁₆	—	2	8	no	—
705	D₈	—	2	4	no	—
706	M₁₆	—	2	2	no	—
707	M₁₆	—	2	4	no	—
708	M₁₆	—	2	2	no	—
709	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
710	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
711	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	1	no	—
765	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₂₃	1	2	yes	—
767	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₂₃	1	2	yes	—
769	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
770	C₄²	C₂⁴×C₂₃	1	2	yes	—
771	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₂₃	1	2	yes	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	4	no	—
787	Q₈	—	4	2	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	1	no	—
790	Q₈	C₂×#41×C₂₃	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	2	no	—
795	D₄	—	4	2	no	—
796	D₄	C₂×#41×C₂₃	1	2	yes	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	8	2	no	—
816	C₂×C₄	—	8	1	no	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
826	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
827	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
828	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
829	C₈	—	2	2	no	—
830	C₈	—	2	4	no	—
831	C₈	—	2	2	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	4	no	—
841	C₂²	C₂₃×#548	1	2	yes	—
842	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	4	4	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	C₂₃×#548	1	2	yes	—
858	C₄	C₂₃×#575	1	2	yes	—
859	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
860	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
861	C₂	—	2	2	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
865	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
866	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×AGL(1,ℤ/8)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×#41×C₂₃	C₂	semidirect
2. C₂×C₂₃×#556	C₂	semidirect
3. C₂₃×#3377	C₂	semidirect
4. C₂₃×#3376	C₂	semidirect
5. C₂₃×#3369	C₂	semidirect
6. C₂₃×#3367	C₂	semidirect
7. C₂₃×#3364	C₂	semidirect
8. C₂₃×#3360	C₂	semidirect
9. C₂₃×#3140	C₂	semidirect
10. C₂₃×#3139	C₂	semidirect
11. C₂₃×#3078	C₂	semidirect
12. C₂₃×#3077	C₂	semidirect
14. C₂₃×#3039	C₂	semidirect
15. Q₈×M₁₆×C₂₃	C₂	semidirect
16. C₄×C₂₃×#137	C₂	semidirect
20. Q₈²×C₂₃	C₂²	semidirect
21. C₂₃×#557	C₂²	semidirect
22. C₂₃×#557	C₂²	semidirect
31. C₂₃×#554	C₂²	semidirect
32. C₂₃×#554	C₂²	semidirect
34. D₄×Q₈×C₂₃	C₂²	semidirect
50. C₂₃×#491	C₂²	semidirect
55. C₂₃×#487	C₂²	semidirect
56. C₂₃×#487	C₂²	semidirect
57. C₂₃×#479	C₂²	semidirect
58. C₂₃×#479	C₂²	semidirect
60. C₂₃×#477	C₂²	semidirect
62. C₂₃×#475	C₂²	semidirect
68. C₂₃×#462	C₂²	semidirect
69. C₂₃×#462	C₂²	semidirect
70. C₂₃×#461	C₂²	semidirect
71. C₂₃×#461	C₂²	semidirect
72. C₂₃×#446	C₂²	semidirect
73. C₂₃×#446	C₂²	semidirect
74. C₈×Q₈×C₂₃	C₂²	semidirect
76. C₂₃×#441	C₂²	semidirect
78. C₂₃×#440	C₂²	semidirect
79. C₄×Q₁₆×C₂₃	C₂²	semidirect
81. C₄×SD₁₆×C₂₃	C₂²	semidirect
339. #61323	C₂₃	direct (N × H)
399. Q₈×#41	C₂×C₂₃	semidirect
400. C₂×#556	C₂×C₂₃	semidirect
401. #3377	C₂×C₂₃	semidirect
402. #3376	C₂×C₂₃	semidirect
403. #3369	C₂×C₂₃	semidirect
404. #3367	C₂×C₂₃	semidirect
405. #3364	C₂×C₂₃	semidirect
406. #3360	C₂×C₂₃	semidirect
407. #3140	C₂×C₂₃	semidirect
408. #3139	C₂×C₂₃	semidirect
409. #3078	C₂×C₂₃	semidirect
410. #3077	C₂×C₂₃	semidirect
412. #3039	C₂×C₂₃	semidirect
413. Q₈×M₁₆	C₂×C₂₃	semidirect
414. C₄×#137	C₂×C₂₃	semidirect
447. Q₈²	C₂²×C₂₃	semidirect
448. #557	C₂²×C₂₃	semidirect
449. #557	C₂²×C₂₃	semidirect
458. #554	C₂²×C₂₃	semidirect
459. #554	C₂²×C₂₃	semidirect
461. D₄×Q₈	C₂²×C₂₃	semidirect
477. #491	C₂²×C₂₃	semidirect
482. #487	C₂²×C₂₃	semidirect
483. #487	C₂²×C₂₃	semidirect
484. #479	C₂²×C₂₃	semidirect
485. #479	C₂²×C₂₃	semidirect
487. #477	C₂²×C₂₃	semidirect
489. #475	C₂²×C₂₃	semidirect
495. #462	C₂²×C₂₃	semidirect
496. #462	C₂²×C₂₃	semidirect
497. #461	C₂²×C₂₃	semidirect
498. #461	C₂²×C₂₃	semidirect
499. #446	C₂²×C₂₃	semidirect
500. #446	C₂²×C₂₃	semidirect
501. C₈×Q₈	C₂²×C₂₃	semidirect
503. #441	C₂²×C₂₃	semidirect
505. #440	C₂²×C₂₃	semidirect
506. C₄×Q₁₆	C₂²×C₂₃	semidirect
508. C₄×SD₁₆	C₂²×C₂₃	semidirect
663. C₂₃	#61323	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×#41×C₂₃	2
C₂×C₂₃×#556	2
C₂₃×#3377	2
C₂₃×#3376	2
C₂₃×#3369	2
C₂₃×#3367	2
C₂₃×#3364	2
C₂₃×#3360	2
C₂₃×#3140	2
C₂₃×#3139	2
C₂₃×#3078	2
C₂₃×#3077	2
C₂₃×#3040	2
C₂₃×#3039	2
Q₈×M₁₆×C₂₃	2
C₄×C₂₃×#137	2
C₄×C₂₃×AGL(1,ℤ/8)	2
#61323	23

Subgroups — C23×#61323 #19208949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61323 #19208949