Subgroups — C₂×C₂₃×#3345 #19208863

Order 5888.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3345	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	—	2	1	no	—
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#553	—	2	4	no	—
22	C₂₃×#553	C₂²	1	8	yes	complemented
23	C₂₃×#547	—	2	4	no	—
24	C₂₃×#547	C₂²	1	8	yes	complemented
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#126	—	2	1	no	—
27	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#123	—	2	1	no	—
29	C₂×C₂₃×#123	—	2	1	no	—
30	C₂×C₂₃×#123	—	2	1	no	—
31	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂×C₂₃×#121	—	2	1	no	—
33	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	—	2	1	no	—
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#501	C₂²	1	8	yes	complemented
46	C₂₃×#482	C₂²	1	8	yes	complemented
47	C₂₃×#481	C₂²	1	8	yes	complemented
48	C₂₃×#481	C₂²	1	8	yes	complemented
49	C₂₃×#480	C₂²	1	8	yes	complemented
50	C₂₃×#478	C₂²	1	8	yes	complemented
51	C₂₃×#476	C₂²	1	8	yes	complemented
52	C₂₃×#469	C₂²	1	8	yes	complemented
53	C₂₃×#466	C₂²	1	8	yes	complemented
54	C₂₃×#442	C₂²	1	8	yes	complemented
55	C₂₃×#435	C₂²	1	8	yes	complemented
56	C₂₃×#428	C₂²	1	8	yes	complemented
57	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#106	C₂²	1	8	yes	complemented
67	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	2	8	no	—
78	C₂×#41×C₂₃	—	4	8	no	—
79	C₂²×Q₈×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	—	2	1	no	—
84	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	—	2	1	no	—
89	C₂³×C₄×C₂₃	—	2	1	no	—
90	C₂³×C₄×C₂₃	—	2	1	no	—
91	C₂³×C₄×C₂₃	—	2	1	no	—
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×D₈×C₂₃	—	2	4	no	—
95	C₂×D₈×C₂₃	C₂³	1	4	yes	—
96	C₂×M₁₆×C₂₃	—	2	4	no	—
97	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂²×C₈×C₂₃	—	2	4	no	—
99	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂₃×C₄⋊Q₈	—	2	2	no	—
105	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₂₃×#126	—	2	8	no	—
107	C₂₃×#125	—	2	2	no	—
108	C₂₃×#125	C₂³	1	4	yes	—
109	C₂₃×#123	—	2	8	no	—
110	C₂₃×#123	—	2	8	no	—
111	C₂₃×#123	—	2	8	no	—
112	C₂₃×C₂²⋊Q₈	—	2	8	no	—
113	C₂₃×#121	—	2	8	no	—
114	C₂₃×#121	—	2	2	no	—
115	C₂₃×#121	—	2	2	no	—
116	C₂₃×#121	—	2	2	no	—
117	C₂₃×#121	—	2	2	no	—
118	C₂₃×#121	C₂³	1	4	yes	—
119	C₂₃×#121	C₂³	1	4	yes	—
120	C₂₃×#121	C₂³	1	4	yes	—
121	C₂₃×#121	C₂³	1	4	yes	—
122	C₄×D₄×C₂₃	—	2	8	no	—
123	C₄×D₄×C₂₃	—	2	2	no	—
124	C₄×D₄×C₂₃	—	2	2	no	—
125	C₄×D₄×C₂₃	D₄	1	4	yes	—
126	C₄×D₄×C₂₃	C₂³	1	4	yes	—
127	C₄×D₄×C₂₃	C₂³	1	4	yes	—
128	C₄×D₄×C₂₃	C₂³	1	4	yes	—
129	C₂₃×#117	—	2	2	no	—
130	C₂₃×#117	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
132	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
133	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
134	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
140	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
159	C₂×C₄²×C₂₃	—	2	1	no	—
160	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
161	C₂₃×#107	C₂³	1	4	yes	—
162	C₂₃×#107	C₂³	1	4	yes	—
163	C₂₃×#107	C₂³	1	4	yes	—
164	C₂₃×#106	C₂³	1	4	yes	—
165	C₂₃×#106	C₂³	1	4	yes	—
166	C₂₃×#106	C₂³	1	4	yes	—
167	C₂₃×#106	C₂³	1	4	yes	—
168	C₂₃×#106	C₂³	1	4	yes	—
169	C₂₃×#106	C₂³	1	4	yes	—
170	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₂₃×#102	C₂³	1	4	yes	—
172	C₂₃×#102	C₂³	1	4	yes	—
173	C₂₃×#102	C₂³	1	4	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×#102	C₂³	1	4	yes	—
176	C₂₃×#102	C₂³	1	4	yes	—
177	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₂₃×#97	C₂³	1	4	yes	—
180	C₂⁴×C₂₃	—	2	1	no	—
181	C₂⁴×C₂₃	—	2	1	no	—
182	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
183	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
184	#41×C₂₃	—	4	32	no	—
185	C₂×Q₈×C₂₃	—	2	4	no	—
186	C₂×Q₈×C₂₃	—	4	4	no	—
187	C₂×D₄×C₂₃	—	2	4	no	—
188	C₂×D₄×C₂₃	—	2	4	no	—
189	C₂×D₄×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	4	no	—
191	C₂×D₄×C₂₃	—	2	4	no	—
192	C₂×D₄×C₂₃	—	2	1	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂×D₄×C₂₃	—	2	2	no	—
196	C₂×D₄×C₂₃	—	2	2	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	4	4	no	—
199	C₂×D₄×C₂₃	—	4	4	no	—
200	C₂×D₄×C₂₃	—	4	4	no	—
201	C₂×D₄×C₂₃	—	8	2	no	—
202	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
203	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
204	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	2	no	—
207	C₂²×C₄×C₂₃	—	2	2	no	—
208	C₂²×C₄×C₂₃	—	2	2	no	—
209	C₂²×C₄×C₂₃	—	2	4	no	—
210	C₂²×C₄×C₂₃	—	2	4	no	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	1	no	—
213	C₂²×C₄×C₂₃	—	2	1	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	2	4	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	—	2	4	no	—
220	C₂²×C₄×C₂₃	—	4	4	no	—
221	C₂²×C₄×C₂₃	—	4	4	no	—
222	C₂²×C₄×C₂₃	—	4	4	no	—
223	C₂²×C₄×C₂₃	—	8	2	no	—
224	C₂²×C₄×C₂₃	—	8	2	no	—
225	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
234	D₈×C₂₃	—	2	8	no	—
235	M₁₆×C₂₃	—	2	8	no	—
236	C₂×C₈×C₂₃	—	2	2	no	—
237	C₂×C₈×C₂₃	—	2	2	no	—
238	C₂×C₈×C₂₃	—	2	2	no	—
239	C₂×C₈×C₂₃	—	2	8	no	—
240	C₂×C₈×C₂₃	#41	1	4	yes	complemented
241	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	1	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	—	2	1	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	4	no	—
256	C₄⋊C₄×C₂₃	—	2	1	no	—
257	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
272	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
273	C₄²×C₂₃	—	2	4	no	—
274	C₄²×C₂₃	C₂×D₄	1	2	yes	—
275	C₄²×C₂₃	C₂⁴	1	2	yes	—
276	C₂×#3345	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	2	2	no	—
284	C₂³×C₂₃	—	4	2	no	—
285	C₂³×C₂₃	—	4	2	no	—
286	C₂³×C₂₃	—	4	2	no	—
287	C₂³×C₂₃	—	4	2	no	—
288	C₂³×C₂₃	—	4	2	no	—
289	C₂³×C₂₃	—	4	2	no	—
290	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
291	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
292	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
293	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
294	Q₈×C₂₃	—	4	8	no	—
295	D₄×C₂₃	—	2	8	no	—
296	D₄×C₂₃	—	2	2	no	—
297	D₄×C₂₃	—	2	2	no	—
298	D₄×C₂₃	—	2	2	no	—
299	D₄×C₂₃	—	2	2	no	—
300	D₄×C₂₃	—	4	8	no	—
301	D₄×C₂₃	—	4	8	no	—
302	D₄×C₂₃	—	4	8	no	—
303	D₄×C₂₃	—	4	2	no	—
304	D₄×C₂₃	—	4	2	no	—
305	D₄×C₂₃	—	8	4	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	4	no	—
311	C₂×C₄×C₂₃	—	2	4	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	4	8	no	—
323	C₂×C₄×C₂₃	—	4	8	no	—
324	C₂×C₄×C₂₃	—	4	2	no	—
325	C₂×C₄×C₂₃	—	4	2	no	—
326	C₂×C₄×C₂₃	—	4	2	no	—
327	C₂×C₄×C₂₃	—	4	8	no	—
328	C₂×C₄×C₂₃	—	4	2	no	—
329	C₂×C₄×C₂₃	—	4	2	no	—
330	C₂×C₄×C₂₃	—	4	2	no	—
331	C₂×C₄×C₂₃	—	8	4	no	—
332	C₂×C₄×C₂₃	—	8	4	no	—
333	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
339	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
340	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
341	C₈×C₂₃	—	2	2	no	—
342	C₈×C₂₃	—	2	2	no	—
343	C₈×C₂₃	—	2	2	no	—
344	C₈×C₂₃	C₂×#41	1	4	yes	complemented
345	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#3345	C₂×C₂₃	1	16	yes	direct product factor
348	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
355	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
357	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
358	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
360	C₂²×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
361	C₂²×C₂₃	—	2	8	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	4	4	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	4	2	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	8	4	no	—
375	C₂²×C₂₃	—	8	4	no	—
376	C₂²×C₂₃	#547	1	2	yes	—
377	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
378	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
379	C₂²×C₂₃	#577	1	2	yes	—
380	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₂₃	—	2	2	no	—
382	C₄×C₂₃	—	2	2	no	—
383	C₄×C₂₃	—	2	2	no	—
384	C₄×C₂₃	—	2	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	2	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	#547	1	2	yes	—
392	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
393	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
394	C₂²×#41	—	2	1	no	—
395	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
397	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
398	#553	—	2	4	no	—
399	#553	C₂²×C₂₃	1	8	yes	complemented
400	#547	—	2	4	no	—
401	#547	C₂²×C₂₃	1	8	yes	complemented
402	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#126	—	2	1	no	—
404	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#123	—	2	1	no	—
406	C₂×#123	—	2	1	no	—
407	C₂×#123	—	2	1	no	—
408	C₂×C₂²⋊Q₈	—	2	1	no	—
409	C₂×#121	—	2	1	no	—
410	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×C₄×D₄	—	2	1	no	—
415	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
421	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
422	#501	C₂²×C₂₃	1	8	yes	complemented
423	#482	C₂²×C₂₃	1	8	yes	complemented
424	#481	C₂²×C₂₃	1	8	yes	complemented
425	#481	C₂²×C₂₃	1	8	yes	complemented
426	#480	C₂²×C₂₃	1	8	yes	complemented
427	#478	C₂²×C₂₃	1	8	yes	complemented
428	#476	C₂²×C₂₃	1	8	yes	complemented
429	#469	C₂²×C₂₃	1	8	yes	complemented
430	#466	C₂²×C₂₃	1	8	yes	complemented
431	#442	C₂²×C₂₃	1	8	yes	complemented
432	#435	C₂²×C₂₃	1	8	yes	complemented
433	#428	C₂²×C₂₃	1	8	yes	complemented
434	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#106	C₂²×C₂₃	1	8	yes	complemented
444	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×C₂₃	—	2	4	no	—
455	C₂×C₂₃	—	4	2	no	—
456	C₂×C₂₃	—	8	2	no	—
457	C₂×C₂₃	—	8	2	no	—
458	C₂×C₂₃	#3345	1	4	yes	direct product factor
459	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
460	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
462	C₂×#41	—	2	8	no	—
463	C₂×#41	—	4	8	no	—
464	C₂²×Q₈	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	—	2	1	no	—
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×D₈	—	2	4	no	—
480	C₂×D₈	C₂³×C₂₃	1	4	yes	—
481	C₂×M₁₆	—	2	4	no	—
482	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
483	C₂²×C₈	—	2	4	no	—
484	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
485	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
486	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
491	#126	—	2	8	no	—
492	#125	—	2	2	no	—
493	#125	C₂³×C₂₃	1	4	yes	—
494	#123	—	2	8	no	—
495	#123	—	2	8	no	—
496	#123	—	2	8	no	—
497	C₂²⋊Q₈	—	2	8	no	—
498	#121	—	2	8	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	C₂³×C₂₃	1	4	yes	—
504	#121	C₂³×C₂₃	1	4	yes	—
505	#121	C₂³×C₂₃	1	4	yes	—
506	#121	C₂³×C₂₃	1	4	yes	—
507	C₄×D₄	—	2	8	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	D₄×C₂₃	1	4	yes	—
511	C₄×D₄	C₂³×C₂₃	1	4	yes	—
512	C₄×D₄	C₂³×C₂₃	1	4	yes	—
513	C₄×D₄	C₂³×C₂₃	1	4	yes	—
514	#117	—	2	2	no	—
515	#117	C₂³×C₂₃	1	4	yes	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	—	2	1	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
546	#107	C₂³×C₂₃	1	4	yes	—
547	#107	C₂³×C₂₃	1	4	yes	—
548	#107	C₂³×C₂₃	1	4	yes	—
549	#106	C₂³×C₂₃	1	4	yes	—
550	#106	C₂³×C₂₃	1	4	yes	—
551	#106	C₂³×C₂₃	1	4	yes	—
552	#106	C₂³×C₂₃	1	4	yes	—
553	#106	C₂³×C₂₃	1	4	yes	—
554	#106	C₂³×C₂₃	1	4	yes	—
555	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
556	#102	C₂³×C₂₃	1	4	yes	—
557	#102	C₂³×C₂₃	1	4	yes	—
558	#102	C₂³×C₂₃	1	4	yes	—
559	#102	C₂³×C₂₃	1	4	yes	—
560	#102	C₂³×C₂₃	1	4	yes	—
561	#102	C₂³×C₂₃	1	4	yes	—
562	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
563	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
564	#97	C₂³×C₂₃	1	4	yes	—
565	C₂₃	C₂×#3345	1	1	yes	characteristic, direct product factor, Sylow
566	C₂⁴	—	2	1	no	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
569	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
570	#41	—	4	32	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	4	4	no	—
585	C₂×D₄	—	4	4	no	—
586	C₂×D₄	—	4	4	no	—
587	C₂×D₄	—	8	2	no	—
588	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
589	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
590	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	8	2	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
616	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
620	D₈	—	2	8	no	—
621	M₁₆	—	2	8	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	8	no	—
626	C₂×C₈	#41×C₂₃	1	4	yes	complemented
627	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
628	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
629	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
630	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
644	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
647	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
649	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
658	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₂₃	1	2	yes	—
661	C₄²	C₂⁴×C₂₃	1	2	yes	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
676	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
677	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
678	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
679	Q₈	—	4	8	no	—
680	D₄	—	2	8	no	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	8	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	8	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
721	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
722	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
723	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
724	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
725	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₈	C₂×#41×C₂₃	1	4	yes	complemented
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	8	4	no	—
744	C₂²	—	8	4	no	—
745	C₂²	C₂₃×#547	1	2	yes	—
746	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
747	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
748	C₂²	C₂₃×#577	1	2	yes	—
749	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	C₂₃×#547	1	2	yes	—
761	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
762	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
763	C₂	—	2	4	no	—
764	C₂	—	4	2	no	—
765	C₂	—	8	2	no	—
766	C₂	—	8	2	no	—
767	C₂	C₂₃×#3345	1	4	yes	direct product factor
768	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
769	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
770	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#553	C₂	semidirect
2. C₂×C₂₃×#547	C₂	semidirect
3. C₂₃×#3345	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#481	C₂	semidirect
6. C₂×C₂₃×#481	C₂	semidirect
7. C₂×C₂₃×#482	C₂	semidirect
8. C₂×C₂₃×#480	C₂	semidirect
9. C₂×C₂₃×#478	C₂	semidirect
10. C₂×C₂₃×#476	C₂	semidirect
11. C₂×C₂₃×#469	C₂	semidirect
12. C₂×C₂₃×#466	C₂	semidirect
13. C₂×C₂₃×#442	C₂	semidirect
14. C₂×C₂₃×#435	C₂	semidirect
15. C₂×C₂₃×#428	C₂	semidirect
16. C₂²×C₂₃×#106	C₂	semidirect
22. C₂₃×#553	C₂²	semidirect
24. C₂₃×#547	C₂²	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#482	C₂²	semidirect
47. C₂₃×#481	C₂²	semidirect
48. C₂₃×#481	C₂²	semidirect
49. C₂₃×#480	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#476	C₂²	semidirect
52. C₂₃×#469	C₂²	semidirect
53. C₂₃×#466	C₂²	semidirect
54. C₂₃×#442	C₂²	semidirect
55. C₂₃×#435	C₂²	semidirect
56. C₂₃×#428	C₂²	semidirect
66. C₂×C₂₃×#106	C₂²	semidirect
240. C₂×C₈×C₂₃	#41	semidirect
276. C₂×#3345	C₂₃	direct (N × H)
344. C₈×C₂₃	C₂×#41	semidirect
345. C₂×#553	C₂×C₂₃	semidirect
346. C₂×#547	C₂×C₂₃	semidirect
347. #3345	C₂×C₂₃	direct (N × H)
348. C₂×#501	C₂×C₂₃	semidirect
349. C₂×#481	C₂×C₂₃	semidirect
350. C₂×#481	C₂×C₂₃	semidirect
351. C₂×#482	C₂×C₂₃	semidirect
352. C₂×#480	C₂×C₂₃	semidirect
353. C₂×#478	C₂×C₂₃	semidirect
354. C₂×#476	C₂×C₂₃	semidirect
355. C₂×#469	C₂×C₂₃	semidirect
356. C₂×#466	C₂×C₂₃	semidirect
357. C₂×#442	C₂×C₂₃	semidirect
358. C₂×#435	C₂×C₂₃	semidirect
359. C₂×#428	C₂×C₂₃	semidirect
360. C₂²×#106	C₂×C₂₃	semidirect
399. #553	C₂²×C₂₃	semidirect
401. #547	C₂²×C₂₃	semidirect
422. #501	C₂²×C₂₃	semidirect
423. #482	C₂²×C₂₃	semidirect
424. #481	C₂²×C₂₃	semidirect
425. #481	C₂²×C₂₃	semidirect
426. #480	C₂²×C₂₃	semidirect
427. #478	C₂²×C₂₃	semidirect
428. #476	C₂²×C₂₃	semidirect
429. #469	C₂²×C₂₃	semidirect
430. #466	C₂²×C₂₃	semidirect
431. #442	C₂²×C₂₃	semidirect
432. #435	C₂²×C₂₃	semidirect
433. #428	C₂²×C₂₃	semidirect
443. C₂×#106	C₂²×C₂₃	semidirect
458. C₂×C₂₃	#3345	direct (N × H)
565. C₂₃	C₂×#3345	direct (N × H)
626. C₂×C₈	#41×C₂₃	semidirect
729. C₈	C₂×#41×C₂₃	semidirect
767. C₂	C₂₃×#3345	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#553	2
C₂×C₂₃×#547	2
C₂₃×#3345	2
C₂×C₂₃×#501	2
C₂×C₂₃×#481	2
C₂×C₂₃×#482	2
C₂×C₂₃×#480	2
C₂×C₂₃×#478	2
C₂×C₂₃×#476	2
C₂×C₂₃×#469	2
C₂×C₂₃×#466	2
C₂×C₂₃×#442	2
C₂×C₂₃×#435	2
C₂×C₂₃×#428	2
C₂²×C₂₃×#106	2
C₂×#3345	23

Subgroups — C2×C23×#3345 #19208863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3345 #19208863