Subgroups — C₂×C₂₃×#3318 #19208754

Order 5888.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 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×D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3318	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#447	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×#418	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₂₃	—	2	1	no	—
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#553	—	2	4	no	—
26	C₂₃×#553	C₂²	1	8	yes	complemented
27	D₄²×C₂₃	—	2	4	no	—
28	D₄²×C₂₃	C₂²	1	8	yes	complemented
29	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#126	—	2	1	no	—
31	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×#123	—	2	1	no	—
33	C₂×C₂₃×#121	—	2	1	no	—
34	C₂×C₂₃×#121	—	2	1	no	—
35	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₃×#120	—	2	1	no	—
40	C₂×C₂₃×#120	—	2	1	no	—
41	C₂×C₄×D₄×C₂₃	—	2	1	no	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#490	C₂²	1	8	yes	complemented
48	C₂₃×#482	C₂²	1	8	yes	complemented
49	C₂₃×#481	C₂²	1	8	yes	complemented
50	C₂₃×#478	C₂²	1	8	yes	complemented
51	C₂₃×#469	C₂²	1	8	yes	complemented
52	C₂₃×#466	C₂²	1	8	yes	complemented
53	C₂₃×#459	C₂²	1	8	yes	complemented
54	C₂₃×#447	C₂²	1	8	yes	complemented
55	C₂₃×#447	C₂²	1	8	yes	complemented
56	C₂₃×#442	C₂²	1	8	yes	complemented
57	C₂₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#418	C₂²	1	8	yes	complemented
63	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#102	C₂²	1	8	yes	complemented
67	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₂₃	—	2	1	no	—
78	C₂⁵×C₂₃	—	2	1	no	—
79	C₂²×D₄×C₂₃	—	2	4	no	—
80	C₂²×D₄×C₂₃	—	2	4	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	—	2	1	no	—
85	C₂²×D₄×C₂₃	—	2	8	no	—
86	C₂²×D₄×C₂₃	—	2	1	no	—
87	C₂²×D₄×C₂₃	—	2	1	no	—
88	C₂²×D₄×C₂₃	—	2	1	no	—
89	C₂²×D₄×C₂₃	—	2	2	no	—
90	C₂²×D₄×C₂₃	—	2	2	no	—
91	C₂²×D₄×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	—	4	2	no	—
93	C₂²×D₄×C₂₃	—	4	2	no	—
94	C₂²×D₄×C₂₃	—	4	8	no	—
95	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
96	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₂₃	—	2	1	no	—
103	C₂³×C₄×C₂₃	—	2	1	no	—
104	C₂³×C₄×C₂₃	—	2	1	no	—
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×D₈×C₂₃	—	2	4	no	—
108	C₂×D₈×C₂₃	—	4	2	no	—
109	C₂×D₈×C₂₃	—	4	2	no	—
110	C₂×D₈×C₂₃	C₂³	1	4	yes	—
111	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
112	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
113	C₂×M₁₆×C₂₃	—	4	2	no	—
114	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
115	C₂²×C₈×C₂₃	—	4	2	no	—
116	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₃	C₂³	1	4	yes	complemented
121	C₂₃×#127	—	2	2	no	—
122	C₂₃×#127	C₂³	1	4	yes	—
123	C₂₃×#126	—	2	8	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	C₂³	1	4	yes	complemented
126	C₂₃×#123	—	2	8	no	—
127	C₂₃×#121	—	2	8	no	—
128	C₂₃×#121	—	2	2	no	—
129	C₂₃×#121	—	2	2	no	—
130	C₂₃×#121	—	2	2	no	—
131	C₂₃×#121	—	2	2	no	—
132	C₂₃×#121	—	2	8	no	—
133	C₂₃×#121	C₂³	1	4	yes	—
134	C₂₃×#121	C₂³	1	4	yes	—
135	C₂₃×#121	C₂³	1	4	yes	complemented
136	C₂₃×#121	C₂³	1	4	yes	complemented
137	C₂₃×#120	—	2	8	no	—
138	C₂₃×#120	—	2	8	no	—
139	C₄×D₄×C₂₃	—	2	8	no	—
140	C₄×D₄×C₂₃	—	2	2	no	—
141	C₄×D₄×C₂₃	—	2	2	no	—
142	C₄×D₄×C₂₃	D₄	1	4	yes	—
143	C₄×D₄×C₂₃	C₂³	1	4	yes	—
144	C₄×D₄×C₂₃	C₂³	1	4	yes	—
145	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
146	C₂₃×#117	—	2	2	no	—
147	C₂₃×#117	C₂³	1	4	yes	complemented
148	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
152	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
158	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
167	C₂×C₄²×C₂₃	—	2	1	no	—
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#107	C₂³	1	4	yes	complemented
170	C₂₃×#106	C₂³	1	4	yes	complemented
171	C₂₃×#106	C₂³	1	4	yes	complemented
172	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
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	complemented
177	C₂₃×#102	C₂³	1	4	yes	complemented
178	C₂₃×#102	C₂³	1	4	yes	complemented
179	C₂₃×#102	C₂³	1	4	yes	complemented
180	C₂₃×#102	C₂³	1	4	yes	complemented
181	C₂₃×#102	C₂³	1	4	yes	complemented
182	C₂₃×#102	C₂³	1	4	yes	complemented
183	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
184	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
185	C₂₃×#97	C₂³	1	4	yes	complemented
186	C₂⁴×C₂₃	—	2	1	no	—
187	C₂⁴×C₂₃	—	2	1	no	—
188	C₂⁴×C₂₃	—	2	1	no	—
189	C₂⁴×C₂₃	—	2	1	no	—
190	C₂⁴×C₂₃	—	2	4	no	—
191	C₂⁴×C₂₃	—	2	4	no	—
192	C₂⁴×C₂₃	—	4	4	no	—
193	C₂⁴×C₂₃	—	4	4	no	—
194	C₂⁴×C₂₃	—	4	4	no	—
195	C₂⁴×C₂₃	—	4	4	no	—
196	C₂⁴×C₂₃	—	8	2	no	—
197	C₂⁴×C₂₃	—	8	2	no	—
198	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄×C₂₃	—	2	4	no	—
201	C₂×D₄×C₂₃	—	2	8	no	—
202	C₂×D₄×C₂₃	—	2	8	no	—
203	C₂×D₄×C₂₃	—	2	4	no	—
204	C₂×D₄×C₂₃	—	2	4	no	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	2	1	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	1	no	—
212	C₂×D₄×C₂₃	—	2	1	no	—
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	2	4	no	—
215	C₂×D₄×C₂₃	—	2	2	no	—
216	C₂×D₄×C₂₃	—	2	2	no	—
217	C₂×D₄×C₂₃	—	2	2	no	—
218	C₂×D₄×C₂₃	—	2	2	no	—
219	C₂×D₄×C₂₃	—	2	2	no	—
220	C₂×D₄×C₂₃	—	2	2	no	—
221	C₂×D₄×C₂₃	—	2	2	no	—
222	C₂×D₄×C₂₃	—	4	4	no	—
223	C₂×D₄×C₂₃	—	4	4	no	—
224	C₂×D₄×C₂₃	—	4	8	no	—
225	C₂×D₄×C₂₃	—	4	8	no	—
226	C₂×D₄×C₂₃	—	4	4	no	—
227	C₂×D₄×C₂₃	—	4	4	no	—
228	C₂×D₄×C₂₃	—	4	4	no	—
229	C₂×D₄×C₂₃	—	4	32	no	—
230	C₂×D₄×C₂₃	—	4	4	no	—
231	C₂×D₄×C₂₃	—	4	4	no	—
232	C₂×D₄×C₂₃	—	4	4	no	—
233	C₂×D₄×C₂₃	—	8	2	no	—
234	C₂×D₄×C₂₃	—	8	2	no	—
235	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₂₃	#41	1	4	yes	—
237	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₂₃	—	2	2	no	—
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	1	no	—
246	C₂²×C₄×C₂₃	—	2	1	no	—
247	C₂²×C₄×C₂₃	—	2	1	no	—
248	C₂²×C₄×C₂₃	—	2	1	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	—	2	4	no	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	4	4	no	—
253	C₂²×C₄×C₂₃	—	8	2	no	—
254	C₂²×C₄×C₂₃	—	8	2	no	—
255	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	D₈×C₂₃	—	2	8	no	—
265	D₈×C₂₃	—	4	4	no	—
266	D₈×C₂₃	—	4	4	no	—
267	M₁₆×C₂₃	—	4	4	no	—
268	C₂×C₈×C₂₃	—	2	2	no	—
269	C₂×C₈×C₂₃	—	2	2	no	—
270	C₂×C₈×C₂₃	—	2	2	no	—
271	C₂×C₈×C₂₃	—	2	2	no	—
272	C₂×C₈×C₂₃	—	4	4	no	—
273	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	4	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
285	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²⋊C₄×C₂₃	—	2	4	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	—	2	4	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	no	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
298	C₄²×C₂₃	—	2	4	no	—
299	C₄²×C₂₃	C₂×D₄	1	2	yes	—
300	C₄²×C₂₃	C₂⁴	1	2	yes	—
301	C₂×#3318	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂³×C₂₃	—	2	2	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	—	2	4	no	—
306	C₂³×C₂₃	—	2	2	no	—
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	—	2	2	no	—
310	C₂³×C₂₃	—	2	2	no	—
311	C₂³×C₂₃	—	2	2	no	—
312	C₂³×C₂₃	—	4	8	no	—
313	C₂³×C₂₃	—	4	8	no	—
314	C₂³×C₂₃	—	4	8	no	—
315	C₂³×C₂₃	—	4	2	no	—
316	C₂³×C₂₃	—	4	2	no	—
317	C₂³×C₂₃	—	4	2	no	—
318	C₂³×C₂₃	—	4	2	no	—
319	C₂³×C₂₃	—	4	2	no	—
320	C₂³×C₂₃	—	4	8	no	—
321	C₂³×C₂₃	—	4	2	no	—
322	C₂³×C₂₃	—	4	2	no	—
323	C₂³×C₂₃	—	4	2	no	—
324	C₂³×C₂₃	—	4	2	no	—
325	C₂³×C₂₃	—	4	2	no	—
326	C₂³×C₂₃	—	4	2	no	—
327	C₂³×C₂₃	—	8	4	no	—
328	C₂³×C₂₃	—	8	4	no	—
329	C₂³×C₂₃	—	8	16	no	—
330	C₂³×C₂₃	—	8	16	no	—
331	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
332	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
334	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
335	D₄×C₂₃	—	2	8	no	—
336	D₄×C₂₃	—	2	4	no	—
337	D₄×C₂₃	—	2	2	no	—
338	D₄×C₂₃	—	2	2	no	—
339	D₄×C₂₃	—	2	2	no	—
340	D₄×C₂₃	—	2	2	no	—
341	D₄×C₂₃	—	2	2	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	2	2	no	—
344	D₄×C₂₃	—	4	8	no	—
345	D₄×C₂₃	—	4	8	no	—
346	D₄×C₂₃	—	4	8	no	—
347	D₄×C₂₃	—	4	8	no	—
348	D₄×C₂₃	—	4	8	no	—
349	D₄×C₂₃	—	4	8	no	—
350	D₄×C₂₃	—	4	2	no	—
351	D₄×C₂₃	—	4	2	no	—
352	D₄×C₂₃	—	4	2	no	—
353	D₄×C₂₃	—	8	4	no	—
354	D₄×C₂₃	—	8	4	no	—
355	D₄×C₂₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	4	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	4	8	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	2	no	—
375	C₂×C₄×C₂₃	—	8	4	no	—
376	C₂×C₄×C₂₃	—	8	4	no	—
377	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
383	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
385	C₈×C₂₃	—	2	2	no	—
386	C₈×C₂₃	—	2	2	no	—
387	C₈×C₂₃	—	2	2	no	—
388	C₈×C₂₃	—	2	2	no	—
389	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
390	C₂×D₄²	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3318	C₂×C₂₃	1	16	yes	direct product factor
392	C₂×#490	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
394	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
395	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
396	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
397	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
398	C₂×#459	C₂×C₂₃	1	1	yes	characteristic, complemented
399	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
400	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
401	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
402	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
404	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic, complemented
405	C₂²×C₂₃	—	2	2	no	—
406	C₂²×C₂₃	—	2	8	no	—
407	C₂²×C₂₃	—	2	2	no	—
408	C₂²×C₂₃	—	2	2	no	—
409	C₂²×C₂₃	—	2	4	no	—
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	4	4	no	—
413	C₂²×C₂₃	—	4	8	no	—
414	C₂²×C₂₃	—	4	2	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	2	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	2	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	4	2	no	—
421	C₂²×C₂₃	—	4	2	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	4	2	no	—
425	C₂²×C₂₃	—	8	16	no	—
426	C₂²×C₂₃	—	8	16	no	—
427	C₂²×C₂₃	—	8	4	no	—
428	C₂²×C₂₃	—	8	4	no	—
429	C₂²×C₂₃	—	8	4	no	—
430	C₂²×C₂₃	#546	1	2	yes	—
431	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
432	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
433	C₂²×C₂₃	#576	1	2	yes	—
434	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₂₃	—	2	2	no	—
436	C₄×C₂₃	—	2	2	no	—
437	C₄×C₂₃	—	2	2	no	—
438	C₄×C₂₃	—	2	2	no	—
439	C₄×C₂₃	—	4	2	no	—
440	C₄×C₂₃	—	4	2	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	#546	1	2	yes	—
444	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
445	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂³×D₄	—	2	1	no	—
447	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
448	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
449	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
450	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#553	—	2	4	no	—
455	#553	C₂²×C₂₃	1	8	yes	complemented
456	D₄²	—	2	4	no	—
457	D₄²	C₂²×C₂₃	1	8	yes	complemented
458	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×#126	—	2	1	no	—
460	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂×#123	—	2	1	no	—
462	C₂×#121	—	2	1	no	—
463	C₂×#121	—	2	1	no	—
464	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	C₂×#120	—	2	1	no	—
469	C₂×#120	—	2	1	no	—
470	C₂×C₄×D₄	—	2	1	no	—
471	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	#490	C₂²×C₂₃	1	8	yes	complemented
477	#482	C₂²×C₂₃	1	8	yes	complemented
478	#481	C₂²×C₂₃	1	8	yes	complemented
479	#478	C₂²×C₂₃	1	8	yes	complemented
480	#469	C₂²×C₂₃	1	8	yes	complemented
481	#466	C₂²×C₂₃	1	8	yes	complemented
482	#459	C₂²×C₂₃	1	8	yes	complemented
483	#447	C₂²×C₂₃	1	8	yes	complemented
484	#447	C₂²×C₂₃	1	8	yes	complemented
485	#442	C₂²×C₂₃	1	8	yes	complemented
486	#435	C₂²×C₂₃	1	8	yes	complemented
487	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
490	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#418	C₂²×C₂₃	1	8	yes	complemented
492	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×#102	C₂²×C₂₃	1	8	yes	complemented
496	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
497	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
498	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
502	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
503	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
505	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
506	C₂×C₂₃	—	2	4	no	—
507	C₂×C₂₃	—	4	2	no	—
508	C₂×C₂₃	—	4	4	no	—
509	C₂×C₂₃	—	8	2	no	—
510	C₂×C₂₃	—	8	2	no	—
511	C₂×C₂₃	—	8	2	no	—
512	C₂×C₂₃	#3318	1	4	yes	direct product factor
513	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
514	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
516	C₂⁵	—	2	1	no	—
517	C₂⁵	—	2	1	no	—
518	C₂²×D₄	—	2	4	no	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	8	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	—	2	2	no	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	4	2	no	—
532	C₂²×D₄	—	4	2	no	—
533	C₂²×D₄	—	4	8	no	—
534	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
539	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
540	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
546	C₂×D₈	—	2	4	no	—
547	C₂×D₈	—	4	2	no	—
548	C₂×D₈	—	4	2	no	—
549	C₂×D₈	C₂³×C₂₃	1	4	yes	—
550	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
551	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
552	C₂×M₁₆	—	4	2	no	—
553	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
554	C₂²×C₈	—	4	2	no	—
555	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
556	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
557	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
559	C₂²×C₈	C₂³×C₂₃	1	4	yes	complemented
560	#127	—	2	2	no	—
561	#127	C₂³×C₂₃	1	4	yes	—
562	#126	—	2	8	no	—
563	#125	—	2	2	no	—
564	#125	C₂³×C₂₃	1	4	yes	complemented
565	#123	—	2	8	no	—
566	#121	—	2	8	no	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#121	—	2	8	no	—
572	#121	C₂³×C₂₃	1	4	yes	—
573	#121	C₂³×C₂₃	1	4	yes	—
574	#121	C₂³×C₂₃	1	4	yes	complemented
575	#121	C₂³×C₂₃	1	4	yes	complemented
576	#120	—	2	8	no	—
577	#120	—	2	8	no	—
578	C₄×D₄	—	2	8	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	D₄×C₂₃	1	4	yes	—
582	C₄×D₄	C₂³×C₂₃	1	4	yes	—
583	C₄×D₄	C₂³×C₂₃	1	4	yes	—
584	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
585	#117	—	2	2	no	—
586	#117	C₂³×C₂₃	1	4	yes	complemented
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
606	C₂×C₄²	—	2	1	no	—
607	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
608	#107	C₂³×C₂₃	1	4	yes	complemented
609	#106	C₂³×C₂₃	1	4	yes	complemented
610	#106	C₂³×C₂₃	1	4	yes	complemented
611	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
612	#102	C₂³×C₂₃	1	4	yes	—
613	#102	C₂³×C₂₃	1	4	yes	—
614	#102	C₂³×C₂₃	1	4	yes	—
615	#102	C₂³×C₂₃	1	4	yes	complemented
616	#102	C₂³×C₂₃	1	4	yes	complemented
617	#102	C₂³×C₂₃	1	4	yes	complemented
618	#102	C₂³×C₂₃	1	4	yes	complemented
619	#102	C₂³×C₂₃	1	4	yes	complemented
620	#102	C₂³×C₂₃	1	4	yes	complemented
621	#102	C₂³×C₂₃	1	4	yes	complemented
622	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
623	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
624	#97	C₂³×C₂₃	1	4	yes	complemented
625	C₂₃	C₂×#3318	1	1	yes	characteristic, direct product factor, Sylow
626	C₂⁴	—	2	1	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	—	2	1	no	—
629	C₂⁴	—	2	1	no	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	4	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	4	4	no	—
635	C₂⁴	—	4	4	no	—
636	C₂⁴	—	8	2	no	—
637	C₂⁴	—	8	2	no	—
638	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	8	no	—
642	C₂×D₄	—	2	8	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	8	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	32	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	8	2	no	—
674	C₂×D₄	—	8	2	no	—
675	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
676	C₂×D₄	#41×C₂₃	1	4	yes	—
677	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
678	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
679	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
680	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	—	8	2	no	—
695	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
700	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
704	D₈	—	2	8	no	—
705	D₈	—	4	4	no	—
706	D₈	—	4	4	no	—
707	M₁₆	—	4	4	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	2	2	no	—
710	C₂×C₈	—	2	2	no	—
711	C₂×C₈	—	2	2	no	—
712	C₂×C₈	—	4	4	no	—
713	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
714	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
716	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
737	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
738	C₄²	—	2	4	no	—
739	C₄²	C₂×D₄×C₂₃	1	2	yes	—
740	C₄²	C₂⁴×C₂₃	1	2	yes	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	4	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	4	8	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	4	8	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	8	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	2	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	—	8	16	no	—
769	C₂³	—	8	16	no	—
770	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
771	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
772	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
773	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
774	D₄	—	2	8	no	—
775	D₄	—	2	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	4	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	2	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	C₂×#41×C₂₃	1	4	yes	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	8	4	no	—
815	C₂×C₄	—	8	4	no	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
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	2	yes	—
820	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
822	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
823	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
824	C₈	—	2	2	no	—
825	C₈	—	2	2	no	—
826	C₈	—	2	2	no	—
827	C₈	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	8	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	8	16	no	—
849	C₂²	—	8	16	no	—
850	C₂²	—	8	4	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	8	4	no	—
853	C₂²	C₂₃×#546	1	2	yes	—
854	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
855	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
856	C₂²	C₂₃×#576	1	2	yes	—
857	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	C₂₃×#546	1	2	yes	—
867	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
868	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
869	C₂	—	2	4	no	—
870	C₂	—	4	2	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	2	no	—
874	C₂	—	8	2	no	—
875	C₂	C₂₃×#3318	1	4	yes	direct product factor
876	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
877	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
878	C₂	C₂×C₂₃×#576	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×D₄²×C₂₃	C₂	semidirect
3. C₂₃×#3318	C₂	direct (N × H)
4. C₂×C₂₃×#490	C₂	semidirect
5. C₂×C₂₃×#481	C₂	semidirect
6. C₂×C₂₃×#482	C₂	semidirect
7. C₂×C₂₃×#478	C₂	semidirect
8. C₂×C₂₃×#469	C₂	semidirect
9. C₂×C₂₃×#466	C₂	semidirect
10. C₂×C₂₃×#459	C₂	semidirect
11. C₂×C₂₃×#447	C₂	semidirect
12. C₂×C₂₃×#447	C₂	semidirect
13. C₂×C₂₃×#442	C₂	semidirect
14. C₂×C₂₃×#435	C₂	semidirect
15. C₂×C₂₃×#418	C₂	semidirect
16. C₂²×C₂₃×#102	C₂	semidirect
21. C₂²×D₈×C₂₃	C₂²	semidirect
22. C₂²×D₈×C₂₃	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
24. C₂³×C₈×C₂₃	C₂²	semidirect
26. C₂₃×#553	C₂²	semidirect
28. D₄²×C₂₃	C₂²	semidirect
31. C₂×C₂₃×#125	C₂²	semidirect
37. C₂×C₂₃×#121	C₂²	semidirect
38. C₂×C₂₃×#121	C₂²	semidirect
44. C₂×C₄×D₄×C₂₃	C₂²	semidirect
45. C₂×C₂₃×#117	C₂²	semidirect
46. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
47. C₂₃×#490	C₂²	semidirect
48. C₂₃×#482	C₂²	semidirect
49. C₂₃×#481	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#469	C₂²	semidirect
52. C₂₃×#466	C₂²	semidirect
53. C₂₃×#459	C₂²	semidirect
54. C₂₃×#447	C₂²	semidirect
55. C₂₃×#447	C₂²	semidirect
56. C₂₃×#442	C₂²	semidirect
57. C₂₃×#435	C₂²	semidirect
58. C₂×C₂₃×#107	C₂²	semidirect
59. C₂×C₂₃×#106	C₂²	semidirect
60. C₂×C₂₃×#106	C₂²	semidirect
61. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
62. C₂₃×#418	C₂²	semidirect
66. C₂×C₂₃×#102	C₂²	semidirect
67. C₂×C₂₃×#102	C₂²	semidirect
68. C₂×C₂₃×#102	C₂²	semidirect
69. C₂×C₂₃×#102	C₂²	semidirect
70. C₂×C₂₃×#102	C₂²	semidirect
71. C₂×C₂₃×#102	C₂²	semidirect
72. C₂×C₂₃×#102	C₂²	semidirect
73. C₂×C₂₃×#102	C₂²	semidirect
74. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
75. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₂₃×#97	C₂²	semidirect
111. C₂×D₈×C₂₃	C₂³	semidirect
112. C₂×D₈×C₂₃	C₂³	semidirect
114. C₂×M₁₆×C₂₃	C₂³	semidirect
120. C₂²×C₈×C₂₃	C₂³	semidirect
125. C₂₃×#125	C₂³	semidirect
135. C₂₃×#121	C₂³	semidirect
136. C₂₃×#121	C₂³	semidirect
145. C₄×D₄×C₂₃	C₂³	semidirect
147. C₂₃×#117	C₂³	semidirect
157. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
169. C₂₃×#107	C₂³	semidirect
170. C₂₃×#106	C₂³	semidirect
171. C₂₃×#106	C₂³	semidirect
172. C₂₃×C₄⋊C₈	C₂³	semidirect
176. C₂₃×#102	C₂³	semidirect
177. C₂₃×#102	C₂³	semidirect
178. C₂₃×#102	C₂³	semidirect
179. C₂₃×#102	C₂³	semidirect
180. C₂₃×#102	C₂³	semidirect
181. C₂₃×#102	C₂³	semidirect
182. C₂₃×#102	C₂³	semidirect
183. C₂₃×C₂²⋊C₈	C₂³	semidirect
184. C₂₃×C₂²⋊C₈	C₂³	semidirect
185. C₂₃×#97	C₂³	semidirect
301. C₂×#3318	C₂₃	direct (N × H)
389. C₂×#553	C₂×C₂₃	semidirect
390. C₂×D₄²	C₂×C₂₃	semidirect
391. #3318	C₂×C₂₃	direct (N × H)
392. C₂×#490	C₂×C₂₃	semidirect
393. C₂×#481	C₂×C₂₃	semidirect
394. C₂×#482	C₂×C₂₃	semidirect
395. C₂×#478	C₂×C₂₃	semidirect
396. C₂×#469	C₂×C₂₃	semidirect
397. C₂×#466	C₂×C₂₃	semidirect
398. C₂×#459	C₂×C₂₃	semidirect
399. C₂×#447	C₂×C₂₃	semidirect
400. C₂×#447	C₂×C₂₃	semidirect
401. C₂×#442	C₂×C₂₃	semidirect
402. C₂×#435	C₂×C₂₃	semidirect
403. C₂×#418	C₂×C₂₃	semidirect
404. C₂²×#102	C₂×C₂₃	semidirect
450. C₂²×D₈	C₂²×C₂₃	semidirect
451. C₂²×D₈	C₂²×C₂₃	semidirect
452. C₂²×M₁₆	C₂²×C₂₃	semidirect
453. C₂³×C₈	C₂²×C₂₃	semidirect
455. #553	C₂²×C₂₃	semidirect
457. D₄²	C₂²×C₂₃	semidirect
460. C₂×#125	C₂²×C₂₃	semidirect
466. C₂×#121	C₂²×C₂₃	semidirect
467. C₂×#121	C₂²×C₂₃	semidirect
473. C₂×C₄×D₄	C₂²×C₂₃	semidirect
474. C₂×#117	C₂²×C₂₃	semidirect
475. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
476. #490	C₂²×C₂₃	semidirect
477. #482	C₂²×C₂₃	semidirect
478. #481	C₂²×C₂₃	semidirect
479. #478	C₂²×C₂₃	semidirect
480. #469	C₂²×C₂₃	semidirect
481. #466	C₂²×C₂₃	semidirect
482. #459	C₂²×C₂₃	semidirect
483. #447	C₂²×C₂₃	semidirect
484. #447	C₂²×C₂₃	semidirect
485. #442	C₂²×C₂₃	semidirect
486. #435	C₂²×C₂₃	semidirect
487. C₂×#107	C₂²×C₂₃	semidirect
488. C₂×#106	C₂²×C₂₃	semidirect
489. C₂×#106	C₂²×C₂₃	semidirect
490. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
491. #418	C₂²×C₂₃	semidirect
495. C₂×#102	C₂²×C₂₃	semidirect
496. C₂×#102	C₂²×C₂₃	semidirect
497. C₂×#102	C₂²×C₂₃	semidirect
498. C₂×#102	C₂²×C₂₃	semidirect
499. C₂×#102	C₂²×C₂₃	semidirect
500. C₂×#102	C₂²×C₂₃	semidirect
501. C₂×#102	C₂²×C₂₃	semidirect
502. C₂×#102	C₂²×C₂₃	semidirect
503. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
504. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
505. C₂×#97	C₂²×C₂₃	semidirect
512. C₂×C₂₃	#3318	direct (N × H)
550. C₂×D₈	C₂³×C₂₃	semidirect
551. C₂×D₈	C₂³×C₂₃	semidirect
553. C₂×M₁₆	C₂³×C₂₃	semidirect
559. C₂²×C₈	C₂³×C₂₃	semidirect
564. #125	C₂³×C₂₃	semidirect
574. #121	C₂³×C₂₃	semidirect
575. #121	C₂³×C₂₃	semidirect
584. C₄×D₄	C₂³×C₂₃	semidirect
586. #117	C₂³×C₂₃	semidirect
596. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
608. #107	C₂³×C₂₃	semidirect
609. #106	C₂³×C₂₃	semidirect
610. #106	C₂³×C₂₃	semidirect
611. C₄⋊C₈	C₂³×C₂₃	semidirect
615. #102	C₂³×C₂₃	semidirect
616. #102	C₂³×C₂₃	semidirect
617. #102	C₂³×C₂₃	semidirect
618. #102	C₂³×C₂₃	semidirect
619. #102	C₂³×C₂₃	semidirect
620. #102	C₂³×C₂₃	semidirect
621. #102	C₂³×C₂₃	semidirect
622. C₂²⋊C₈	C₂³×C₂₃	semidirect
623. C₂²⋊C₈	C₂³×C₂₃	semidirect
624. #97	C₂³×C₂₃	semidirect
625. C₂₃	C₂×#3318	direct (N × H)
875. C₂	C₂₃×#3318	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×D₄²×C₂₃	2
C₂₃×#3318	2
C₂×C₂₃×#490	2
C₂×C₂₃×#481	2
C₂×C₂₃×#482	2
C₂×C₂₃×#478	2
C₂×C₂₃×#469	2
C₂×C₂₃×#466	2
C₂×C₂₃×#459	2
C₂×C₂₃×#447	2
C₂×C₂₃×#442	2
C₂×C₂₃×#435	2
C₂×C₂₃×#418	2
C₂²×C₂₃×#102	2
C₂×#3318	23

Subgroups — C2×C23×#3318 #19208754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3318 #19208754