Subgroups — C₂₃×#61318 #19208944

Order 5888.

1880 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3370	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3366	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3361	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3142	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3080	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3036	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#559	C₂²	1	2	yes	complemented
22	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#556	C₂²	1	2	yes	complemented
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#554	—	2	1	no	—
27	C₂₃×#554	—	2	2	no	—
28	C₂₃×#554	C₂²	1	2	yes	—
29	C₂₃×#554	C₂²	1	2	yes	—
30	C₂₃×#554	C₂²	1	4	yes	—
31	C₂₃×#553	—	2	1	no	—
32	C₂₃×#553	—	2	2	no	—
33	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#548	—	2	1	no	—
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂₃×#532	C₂²	1	2	yes	—
37	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂₃×#529	—	2	2	no	—
39	C₂₃×#529	—	2	1	no	—
40	C₂×C₂₃×#125	C₂²	1	2	yes	—
41	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
43	C₄×#41×C₂₃	—	2	1	no	—
44	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
45	C₄×#41×C₂₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
50	C₂₃×#491	C₂²	1	4	yes	complemented
51	C₂₃×#490	C₂²	1	4	yes	complemented
52	C₂₃×#489	C₂²	1	4	yes	complemented
53	C₂₃×#488	C₂²	1	4	yes	complemented
54	C₂₃×#488	C₂²	1	4	yes	complemented
55	C₂₃×#487	C₂²	1	2	yes	complemented
56	C₂₃×#486	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	complemented
60	C₂₃×#478	C₂²	1	4	yes	complemented
61	C₂₃×#477	C₂²	1	2	yes	complemented
62	C₂₃×#476	C₂²	1	2	yes	complemented
63	C₂₃×#475	C₂²	1	2	yes	complemented
64	C₂₃×#474	C₂²	1	2	yes	complemented
65	C₂₃×#463	C₂²	1	4	yes	—
66	C₂₃×#463	C₂²	1	4	yes	—
67	C₂₃×#463	C₂²	1	4	yes	—
68	C₂₃×#461	C₂²	1	2	yes	—
69	C₂₃×#461	C₂²	1	4	yes	—
70	C₂₃×#459	C₂²	1	2	yes	—
71	C₂₃×#459	C₂²	1	4	yes	—
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	4	yes	—
76	C₂₃×#442	C₂²	1	2	yes	—
77	C₂₃×#440	C₂²	1	4	yes	—
78	C₂₃×#440	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
81	C₄×D₈×C₂₃	C₂²	1	2	yes	—
82	C₄×D₈×C₂₃	C₂²	1	4	yes	—
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	1	yes	characteristic
85	C₂₃×#423	C₂²	1	1	yes	characteristic
86	C₂₃×#423	C₂²	1	2	yes	—
87	C₂₃×#418	C₂²	1	1	yes	characteristic
88	C₂₃×#417	C₂²	1	2	yes	—
89	C₂₃×#417	C₂²	1	1	yes	characteristic
90	C₂₃×#417	C₂²	1	2	yes	—
91	C₂₃×#417	C₂²	1	2	yes	—
92	C₂₃×#417	C₂²	1	2	yes	—
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	—	2	1	no	—
99	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
100	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	—	2	1	no	—
102	C₂³×C₄×C₂₃	—	2	2	no	—
103	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
104	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×D₈×C₂₃	C₂³	1	2	yes	—
108	C₂×D₈×C₂₃	C₂³	1	4	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
111	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	—	2	1	no	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#127	C₂³	1	2	yes	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#125	—	2	1	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	—	2	2	no	—
126	C₂₃×#125	—	2	2	no	—
127	C₂₃×#125	C₂³	1	4	yes	—
128	C₂₃×#125	C₂³	1	4	yes	—
129	C₂₃×#124	—	2	1	no	—
130	C₂₃×#124	—	2	2	no	—
131	C₂₃×#124	C₂³	1	2	yes	—
132	C₂₃×#124	C₂³	1	2	yes	—
133	C₂₃×#124	C₂³	1	2	yes	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×#123	—	2	2	no	—
136	C₂₃×#123	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	—	2	4	no	—
145	C₂₃×C₂²⋊Q₈	—	2	4	no	—
146	C₂₃×#121	—	2	1	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	1	no	—
149	C₂₃×#121	—	2	2	no	—
150	C₂₃×#121	—	2	1	no	—
151	C₂₃×#121	—	2	2	no	—
152	C₄×Q₈×C₂₃	—	2	1	no	—
153	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
154	C₄×Q₈×C₂₃	D₄	1	2	yes	—
155	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
156	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	2	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	4	yes	—
181	C₄×D₄×C₂₃	C₂³	1	4	yes	—
182	C₄×D₄×C₂₃	C₂³	1	2	yes	—
183	C₄×D₄×C₂₃	C₂³	1	2	yes	—
184	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂₃×#117	—	2	1	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	2	no	—
188	C₂₃×#117	—	2	1	no	—
189	C₂₃×#117	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
195	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
196	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
198	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
202	C₂×C₄²×C₂₃	—	2	2	no	—
203	C₂×C₄²×C₂₃	—	2	1	no	—
204	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
206	C₂₃×#107	C₂³	1	4	yes	—
207	C₂₃×#107	C₂³	1	2	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×#106	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	2	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×#102	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	—
225	C₂₃×#102	C₂³	1	2	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	4	no	—
232	#41×C₂₃	—	2	2	no	—
233	#41×C₂₃	—	2	4	no	—
234	#41×C₂₃	—	2	2	no	—
235	#41×C₂₃	—	4	4	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	4	2	no	—
239	C₂×Q₈×C₂₃	—	8	2	no	—
240	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
243	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	1	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	#41	1	4	yes	complemented
254	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
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	1	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	1	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	4	no	—
268	C₂²×C₄×C₂₃	—	2	4	no	—
269	C₂²×C₄×C₂₃	—	4	4	no	—
270	C₂²×C₄×C₂₃	—	8	4	no	—
271	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
276	SD₁₆×C₂₃	—	2	8	no	—
277	SD₁₆×C₂₃	—	2	4	no	—
278	D₈×C₂₃	—	2	4	no	—
279	D₈×C₂₃	—	2	8	no	—
280	M₁₆×C₂₃	—	2	2	no	—
281	M₁₆×C₂₃	—	2	4	no	—
282	M₁₆×C₂₃	—	2	2	no	—
283	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
285	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	2	4	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	4	no	—
291	C₄⋊C₄×C₂₃	—	2	4	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	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	1	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	4	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	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	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	—	2	1	no	—
325	C₂²⋊C₄×C₂₃	—	2	2	no	—
326	C₂²⋊C₄×C₂₃	—	2	2	no	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	1	no	—
329	C₄²×C₂₃	—	2	1	no	—
330	C₄²×C₂₃	—	2	2	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	—	2	1	no	—
333	C₄²×C₂₃	C₂×D₄	1	2	yes	—
334	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₂₃	C₂×D₄	1	2	yes	—
336	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₂₃	C₂⁴	1	2	yes	—
338	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₂₃	C₂⁴	1	2	yes	—
340	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
341	#61318	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂³×C₂₃	—	2	4	no	—
343	C₂³×C₂₃	—	2	2	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	2	1	no	—
346	C₂³×C₂₃	—	4	2	no	—
347	C₂³×C₂₃	—	4	2	no	—
348	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	2	2	no	—
351	Q₈×C₂₃	—	2	2	no	—
352	Q₈×C₂₃	—	2	1	no	—
353	Q₈×C₂₃	—	2	2	no	—
354	Q₈×C₂₃	—	2	1	no	—
355	Q₈×C₂₃	—	4	2	no	—
356	Q₈×C₂₃	—	8	2	no	—
357	Q₈×C₂₃	—	8	2	no	—
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	—	2	2	no	—
363	D₄×C₂₃	—	2	1	no	—
364	D₄×C₂₃	—	4	4	no	—
365	D₄×C₂₃	—	4	2	no	—
366	D₄×C₂₃	—	4	4	no	—
367	D₄×C₂₃	—	4	2	no	—
368	D₄×C₂₃	—	8	2	no	—
369	D₄×C₂₃	—	8	1	no	—
370	D₄×C₂₃	C₂×#41	1	4	yes	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	4	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	1	no	—
381	C₂×C₄×C₂₃	—	4	4	no	—
382	C₂×C₄×C₂₃	—	4	4	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	4	4	no	—
385	C₂×C₄×C₂₃	—	4	4	no	—
386	C₂×C₄×C₂₃	—	4	2	no	—
387	C₂×C₄×C₂₃	—	4	4	no	—
388	C₂×C₄×C₂₃	—	4	2	no	—
389	C₂×C₄×C₂₃	—	8	2	no	—
390	C₂×C₄×C₂₃	—	8	1	no	—
391	C₂×C₄×C₂₃	—	8	4	no	—
392	C₂×C₄×C₂₃	—	8	4	no	—
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
403	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
404	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
405	C₈×C₂₃	—	2	4	no	—
406	C₈×C₂₃	—	2	2	no	—
407	C₈×C₂₃	—	2	2	no	—
408	#3480	C₂×C₂₃	1	1	yes	characteristic, complemented
409	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#3376	C₂×C₂₃	1	4	yes	complemented
411	#3372	C₂×C₂₃	1	2	yes	complemented
412	#3370	C₂×C₂₃	1	4	yes	complemented
413	#3366	C₂×C₂₃	1	2	yes	complemented
414	#3361	C₂×C₂₃	1	2	yes	complemented
415	#3360	C₂×C₂₃	1	2	yes	complemented
416	#3142	C₂×C₂₃	1	2	yes	complemented
417	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#3080	C₂×C₂₃	1	2	yes	complemented
419	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#3036	C₂×C₂₃	1	2	yes	complemented
422	Q₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
424	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
425	C₂²×C₂₃	—	2	1	no	—
426	C₂²×C₂₃	—	2	1	no	—
427	C₂²×C₂₃	—	2	4	no	—
428	C₂²×C₂₃	—	4	8	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	1	no	—
435	C₂²×C₂₃	—	4	2	no	—
436	C₂²×C₂₃	—	4	1	no	—
437	C₂²×C₂₃	#548	1	2	yes	—
438	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₂₃	—	2	2	no	—
440	C₄×C₂₃	—	2	2	no	—
441	C₄×C₂₃	—	2	1	no	—
442	C₄×C₂₃	—	2	1	no	—
443	C₄×C₂₃	—	2	1	no	—
444	C₄×C₂₃	—	2	2	no	—
445	C₄×C₂₃	—	2	2	no	—
446	C₄×C₂₃	—	4	4	no	—
447	C₄×C₂₃	—	4	1	no	—
448	C₄×C₂₃	—	4	1	no	—
449	C₄×C₂₃	—	4	2	no	—
450	C₄×C₂₃	—	4	1	no	—
451	C₄×C₂₃	—	4	2	no	—
452	C₄×C₂₃	#548	1	2	yes	—
453	C₄×C₂₃	#575	1	2	yes	—
454	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
455	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
458	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#559	C₂²×C₂₃	1	2	yes	complemented
460	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	#556	C₂²×C₂₃	1	2	yes	complemented
463	#554	—	2	1	no	—
464	#554	—	2	1	no	—
465	#554	—	2	2	no	—
466	#554	C₂²×C₂₃	1	2	yes	—
467	#554	C₂²×C₂₃	1	2	yes	—
468	#554	C₂²×C₂₃	1	4	yes	—
469	#553	—	2	1	no	—
470	#553	—	2	2	no	—
471	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	#548	—	2	1	no	—
473	#532	C₂²×C₂₃	1	1	yes	characteristic
474	#532	C₂²×C₂₃	1	2	yes	—
475	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
476	#529	—	2	2	no	—
477	#529	—	2	1	no	—
478	C₂×#125	C₂²×C₂₃	1	2	yes	—
479	C₂×C₂²⋊Q₈	—	2	1	no	—
480	C₂×C₂²⋊Q₈	—	2	2	no	—
481	C₄×#41	—	2	1	no	—
482	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
483	C₄×#41	C₂²×C₂₃	1	2	yes	—
484	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
487	C₂²×C₄⋊C₄	—	2	1	no	—
488	#491	C₂²×C₂₃	1	4	yes	complemented
489	#490	C₂²×C₂₃	1	4	yes	complemented
490	#489	C₂²×C₂₃	1	4	yes	complemented
491	#488	C₂²×C₂₃	1	4	yes	complemented
492	#488	C₂²×C₂₃	1	4	yes	complemented
493	#487	C₂²×C₂₃	1	2	yes	complemented
494	#486	C₂²×C₂₃	1	2	yes	complemented
495	#479	C₂²×C₂₃	1	4	yes	complemented
496	#479	C₂²×C₂₃	1	4	yes	complemented
497	#478	C₂²×C₂₃	1	4	yes	complemented
498	#478	C₂²×C₂₃	1	4	yes	complemented
499	#477	C₂²×C₂₃	1	2	yes	complemented
500	#476	C₂²×C₂₃	1	2	yes	complemented
501	#475	C₂²×C₂₃	1	2	yes	complemented
502	#474	C₂²×C₂₃	1	2	yes	complemented
503	#463	C₂²×C₂₃	1	4	yes	—
504	#463	C₂²×C₂₃	1	4	yes	—
505	#463	C₂²×C₂₃	1	4	yes	—
506	#461	C₂²×C₂₃	1	2	yes	—
507	#461	C₂²×C₂₃	1	4	yes	—
508	#459	C₂²×C₂₃	1	2	yes	—
509	#459	C₂²×C₂₃	1	4	yes	—
510	#446	C₂²×C₂₃	1	2	yes	complemented
511	#446	C₂²×C₂₃	1	4	yes	complemented
512	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
513	#442	C₂²×C₂₃	1	4	yes	—
514	#442	C₂²×C₂₃	1	2	yes	—
515	#440	C₂²×C₂₃	1	4	yes	—
516	#440	C₂²×C₂₃	1	2	yes	—
517	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
518	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
519	C₄×D₈	C₂²×C₂₃	1	2	yes	—
520	C₄×D₈	C₂²×C₂₃	1	4	yes	—
521	#428	C₂²×C₂₃	1	2	yes	—
522	#428	C₂²×C₂₃	1	1	yes	characteristic
523	#423	C₂²×C₂₃	1	1	yes	characteristic
524	#423	C₂²×C₂₃	1	2	yes	—
525	#418	C₂²×C₂₃	1	1	yes	characteristic
526	#417	C₂²×C₂₃	1	2	yes	—
527	#417	C₂²×C₂₃	1	2	yes	—
528	#417	C₂²×C₂₃	1	2	yes	—
529	#417	C₂²×C₂₃	1	2	yes	—
530	#417	C₂²×C₂₃	1	1	yes	characteristic
531	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
532	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
533	C₂×C₂₃	—	2	2	no	—
534	C₂×C₂₃	—	4	4	no	—
535	C₂×C₂₃	—	8	2	no	—
536	C₂×C₂₃	—	8	1	no	—
537	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
538	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
539	C₂×C₂₃	#3585	1	1	yes	characteristic
540	C₂×#41	—	2	1	no	—
541	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×#41	C₂³×C₂₃	1	2	yes	—
543	C₂²×Q₈	—	2	1	no	—
544	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
546	C₂³×C₄	—	2	1	no	—
547	C₂³×C₄	—	2	2	no	—
548	AGL(1,ℤ/8)	—	2	4	no	—
549	AGL(1,ℤ/8)	—	2	8	no	—
550	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
551	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
552	C₂×D₈	C₂³×C₂₃	1	2	yes	—
553	C₂×D₈	C₂³×C₂₃	1	4	yes	—
554	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
555	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
556	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
563	#127	C₂³×C₂₃	1	1	yes	characteristic
564	#127	C₂³×C₂₃	1	2	yes	—
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#126	—	2	2	no	—
568	#125	—	2	1	no	—
569	#125	—	2	2	no	—
570	#125	—	2	2	no	—
571	#125	—	2	2	no	—
572	#125	C₂³×C₂₃	1	4	yes	—
573	#125	C₂³×C₂₃	1	4	yes	—
574	#124	—	2	1	no	—
575	#124	—	2	2	no	—
576	#124	C₂³×C₂₃	1	2	yes	—
577	#124	C₂³×C₂₃	1	2	yes	—
578	#124	C₂³×C₂₃	1	2	yes	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	—	2	1	no	—
596	#121	—	2	2	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
599	C₄×Q₈	D₄×C₂₃	1	2	yes	—
600	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
602	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	C₂³×C₂₃	1	2	yes	—
623	C₄×D₄	C₂³×C₂₃	1	4	yes	—
624	C₄×D₄	C₂³×C₂₃	1	4	yes	—
625	C₄×D₄	C₂³×C₂₃	1	2	yes	—
626	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₂₃	1	2	yes	—
628	C₄×D₄	C₂³×C₂₃	1	2	yes	—
629	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
630	#117	—	2	1	no	—
631	#117	—	2	2	no	—
632	#117	—	2	2	no	—
633	#117	—	2	1	no	—
634	#117	C₂³×C₂₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	—	2	2	no	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	4	no	—
641	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	2	no	—
647	C₂×C₄²	—	2	2	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
651	#107	C₂³×C₂₃	1	4	yes	—
652	#107	C₂³×C₂₃	1	2	yes	—
653	#106	C₂³×C₂₃	1	4	yes	—
654	#106	C₂³×C₂₃	1	2	yes	—
655	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
656	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
657	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
658	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
659	#103	C₂³×C₂₃	1	4	yes	—
660	#103	C₂³×C₂₃	1	2	yes	—
661	#103	C₂³×C₂₃	1	4	yes	—
662	#103	C₂³×C₂₃	1	4	yes	—
663	#103	C₂³×C₂₃	1	4	yes	—
664	#102	C₂³×C₂₃	1	4	yes	—
665	#102	C₂³×C₂₃	1	2	yes	—
666	#102	C₂³×C₂₃	1	4	yes	—
667	#102	C₂³×C₂₃	1	4	yes	—
668	#102	C₂³×C₂₃	1	4	yes	—
669	#102	C₂³×C₂₃	1	2	yes	—
670	#102	C₂³×C₂₃	1	2	yes	—
671	#97	C₂³×C₂₃	1	2	yes	—
672	#97	C₂³×C₂₃	1	4	yes	—
673	C₄×C₈	C₂³×C₂₃	1	2	yes	—
674	C₄×C₈	C₂³×C₂₃	1	4	yes	—
675	C₂₃	#61318	1	1	yes	characteristic, direct product factor, Sylow
676	C₂⁴	—	2	1	no	—
677	#41	—	2	2	no	—
678	#41	—	2	4	no	—
679	#41	—	2	2	no	—
680	#41	—	2	4	no	—
681	#41	—	4	4	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	8	2	no	—
686	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
687	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
688	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
689	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
690	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	#41×C₂₃	1	4	yes	complemented
700	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
701	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
702	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	4	4	no	—
716	C₂²×C₄	—	8	4	no	—
717	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
722	SD₁₆	—	2	8	no	—
723	SD₁₆	—	2	4	no	—
724	D₈	—	2	4	no	—
725	D₈	—	2	8	no	—
726	M₁₆	—	2	2	no	—
727	M₁₆	—	2	4	no	—
728	M₁₆	—	2	2	no	—
729	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
731	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
751	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
752	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
753	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
754	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
757	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	1	no	—
779	C₄²	C₂×D₄×C₂₃	1	2	yes	—
780	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₂₃	1	2	yes	—
782	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₂₃	1	2	yes	—
784	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
786	C₄²	C₂⁴×C₂₃	1	2	yes	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	4	2	no	—
792	C₂³	—	4	2	no	—
793	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
794	Q₈	—	2	2	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	1	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	Q₈	—	8	2	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	1	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	1	no	—
815	D₄	C₂×#41×C₂₃	1	4	yes	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
841	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
845	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
847	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
848	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
849	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	8	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	1	no	—
865	C₂²	C₂₃×#548	1	2	yes	—
866	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
867	C₄	—	2	1	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	4	no	—
879	C₄	—	4	1	no	—
880	C₄	C₂₃×#548	1	2	yes	—
881	C₄	C₂₃×#575	1	2	yes	—
882	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
883	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
884	C₂	—	2	2	no	—
885	C₂	—	4	4	no	—
886	C₂	—	8	2	no	—
887	C₂	—	8	1	no	—
888	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
889	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
890	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 ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3480	C₂	semidirect
2. C₂×C₂₃×#554	C₂	semidirect
3. C₂₃×#3376	C₂	semidirect
4. C₂₃×#3372	C₂	semidirect
5. C₂₃×#3370	C₂	semidirect
6. C₂₃×#3366	C₂	semidirect
7. C₂₃×#3361	C₂	semidirect
8. C₂₃×#3360	C₂	semidirect
9. C₂₃×#3142	C₂	semidirect
10. C₂₃×#3141	C₂	semidirect
11. C₂₃×#3080	C₂	semidirect
12. C₂₃×#3079	C₂	semidirect
13. C₂₃×#3036	C₂	semidirect
14. C₂₃×#3036	C₂	semidirect
15. Q₈×M₁₆×C₂₃	C₂	semidirect
16. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
17. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
20. C₂₃×#559	C₂²	semidirect
21. C₂₃×#559	C₂²	semidirect
22. C₂₃×#557	C₂²	semidirect
23. C₂₃×#556	C₂²	semidirect
24. C₂₃×#556	C₂²	semidirect
33. C₂₃×#550	C₂²	semidirect
50. C₂₃×#491	C₂²	semidirect
51. C₂₃×#490	C₂²	semidirect
52. C₂₃×#489	C₂²	semidirect
53. C₂₃×#488	C₂²	semidirect
54. C₂₃×#488	C₂²	semidirect
55. C₂₃×#487	C₂²	semidirect
56. C₂₃×#486	C₂²	semidirect
57. C₂₃×#479	C₂²	semidirect
58. C₂₃×#479	C₂²	semidirect
59. C₂₃×#478	C₂²	semidirect
60. C₂₃×#478	C₂²	semidirect
61. C₂₃×#477	C₂²	semidirect
62. C₂₃×#476	C₂²	semidirect
63. C₂₃×#475	C₂²	semidirect
64. C₂₃×#474	C₂²	semidirect
72. C₂₃×#446	C₂²	semidirect
73. C₂₃×#446	C₂²	semidirect
74. C₈×Q₈×C₂₃	C₂²	semidirect
253. C₂×D₄×C₂₃	#41	semidirect
341. #61318	C₂₃	direct (N × H)
408. #3480	C₂×C₂₃	semidirect
409. C₂×#554	C₂×C₂₃	semidirect
410. #3376	C₂×C₂₃	semidirect
411. #3372	C₂×C₂₃	semidirect
412. #3370	C₂×C₂₃	semidirect
413. #3366	C₂×C₂₃	semidirect
414. #3361	C₂×C₂₃	semidirect
415. #3360	C₂×C₂₃	semidirect
416. #3142	C₂×C₂₃	semidirect
417. #3141	C₂×C₂₃	semidirect
418. #3080	C₂×C₂₃	semidirect
419. #3079	C₂×C₂₃	semidirect
420. #3036	C₂×C₂₃	semidirect
421. #3036	C₂×C₂₃	semidirect
422. Q₈×M₁₆	C₂×C₂₃	semidirect
423. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
424. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
458. #559	C₂²×C₂₃	semidirect
459. #559	C₂²×C₂₃	semidirect
460. #557	C₂²×C₂₃	semidirect
461. #556	C₂²×C₂₃	semidirect
462. #556	C₂²×C₂₃	semidirect
471. #550	C₂²×C₂₃	semidirect
488. #491	C₂²×C₂₃	semidirect
489. #490	C₂²×C₂₃	semidirect
490. #489	C₂²×C₂₃	semidirect
491. #488	C₂²×C₂₃	semidirect
492. #488	C₂²×C₂₃	semidirect
493. #487	C₂²×C₂₃	semidirect
494. #486	C₂²×C₂₃	semidirect
495. #479	C₂²×C₂₃	semidirect
496. #479	C₂²×C₂₃	semidirect
497. #478	C₂²×C₂₃	semidirect
498. #478	C₂²×C₂₃	semidirect
499. #477	C₂²×C₂₃	semidirect
500. #476	C₂²×C₂₃	semidirect
501. #475	C₂²×C₂₃	semidirect
502. #474	C₂²×C₂₃	semidirect
510. #446	C₂²×C₂₃	semidirect
511. #446	C₂²×C₂₃	semidirect
512. C₈×Q₈	C₂²×C₂₃	semidirect
675. C₂₃	#61318	direct (N × H)
699. C₂×D₄	#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×#3480	2
C₂×C₂₃×#554	2
C₂₃×#3376	2
C₂₃×#3372	2
C₂₃×#3370	2
C₂₃×#3366	2
C₂₃×#3361	2
C₂₃×#3360	2
C₂₃×#3142	2
C₂₃×#3141	2
C₂₃×#3080	2
C₂₃×#3079	2
C₂₃×#3036	2
Q₈×M₁₆×C₂₃	2
C₄×C₂₃×AGL(1,ℤ/8)	2
#61318	23

Subgroups — C23×#61318 #19208944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61318 #19208944