Subgroups — C₂×C₂₃×#3306 #19208751

Order 5888.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3306	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#449	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×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	—	2	1	no	—
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#547	—	2	4	no	—
26	C₂₃×#547	C₂²	1	8	yes	complemented
27	C₂₃×#546	—	2	4	no	—
28	C₂₃×#546	C₂²	1	8	yes	complemented
29	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#123	—	2	1	no	—
32	C₂×C₂₃×#123	—	2	1	no	—
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#121	—	2	1	no	—
37	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₂₃×#120	—	2	1	no	—
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
47	C₂₃×#489	C₂²	1	8	yes	complemented
48	C₂₃×#483	C₂²	1	8	yes	complemented
49	C₂₃×#481	C₂²	1	8	yes	complemented
50	C₂₃×#476	C₂²	1	8	yes	complemented
51	C₂₃×#469	C₂²	1	8	yes	complemented
52	C₂₃×#465	C₂²	1	8	yes	complemented
53	C₂₃×#463	C₂²	1	8	yes	complemented
54	C₂₃×#449	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×#106	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×#417	C₂²	1	8	yes	complemented
63	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#102	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	8	yes	complemented
73	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
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	C₂×#41×C₂₃	—	2	8	no	—
79	C₂×#41×C₂₃	—	2	2	no	—
80	C₂×#41×C₂₃	—	2	4	no	—
81	C₂×#41×C₂₃	—	4	2	no	—
82	C₂×#41×C₂₃	—	4	8	no	—
83	C₂×#41×C₂₃	C₂³	1	4	yes	—
84	C₂²×Q₈×C₂₃	—	2	1	no	—
85	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₂₃	—	2	4	no	—
87	C₂²×D₄×C₂₃	—	2	1	no	—
88	C₂²×D₄×C₂₃	—	2	1	no	—
89	C₂²×D₄×C₂₃	—	2	1	no	—
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	—	2	2	no	—
93	C₂²×D₄×C₂₃	—	4	2	no	—
94	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	—	2	1	no	—
100	C₂³×C₄×C₂₃	—	2	1	no	—
101	C₂³×C₄×C₂₃	—	2	1	no	—
102	C₂³×C₄×C₂₃	—	2	1	no	—
103	C₂³×C₄×C₂₃	—	2	1	no	—
104	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×SD₁₆×C₂₃	—	4	2	no	—
107	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
108	C₂×D₈×C₂₃	—	2	4	no	—
109	C₂×D₈×C₂₃	—	4	2	no	—
110	C₂×D₈×C₂₃	C₂³	1	4	yes	—
111	C₂×D₈×C₂₃	C₂³	1	4	yes	—
112	C₂×M₁₆×C₂₃	—	4	2	no	—
113	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
114	C₂²×C₈×C₂₃	—	4	2	no	—
115	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	4	yes	—
120	C₂₃×C₄⋊Q₈	—	2	2	no	—
121	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
122	C₂₃×#124	—	2	2	no	—
123	C₂₃×#124	C₂³	1	4	yes	—
124	C₂₃×#123	—	2	8	no	—
125	C₂₃×#123	—	2	8	no	—
126	C₂₃×#123	—	2	8	no	—
127	C₂₃×C₂²⋊Q₈	—	2	2	no	—
128	C₂₃×C₂²⋊Q₈	—	2	8	no	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₂₃×#121	—	2	2	no	—
131	C₂₃×#121	—	2	2	no	—
132	C₂₃×#121	—	2	2	no	—
133	C₂₃×#121	—	2	8	no	—
134	C₂₃×#121	C₂³	1	4	yes	—
135	C₂₃×#121	C₂³	1	4	yes	—
136	C₂₃×#121	C₂³	1	4	yes	complemented
137	C₂₃×#120	—	2	8	no	—
138	C₄×D₄×C₂₃	—	2	2	no	—
139	C₄×D₄×C₂₃	—	2	2	no	—
140	C₄×D₄×C₂₃	D₄	1	4	yes	—
141	C₄×D₄×C₂₃	C₂³	1	4	yes	—
142	C₄×D₄×C₂₃	C₂³	1	4	yes	—
143	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
144	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	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	4	yes	complemented
157	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	—	2	8	no	—
166	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#106	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×#103	C₂³	1	4	yes	complemented
174	C₂₃×#103	C₂³	1	4	yes	complemented
175	C₂₃×#103	C₂³	1	4	yes	complemented
176	C₂₃×#102	C₂³	1	4	yes	—
177	C₂₃×#102	C₂³	1	4	yes	—
178	C₂₃×#102	C₂³	1	4	yes	—
179	C₂₃×#102	C₂³	1	4	yes	—
180	C₂₃×#102	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	4	yes	—
182	C₂₃×#102	C₂³	1	4	yes	complemented
183	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
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	4	no	—
190	C₂⁴×C₂₃	—	4	4	no	—
191	C₂⁴×C₂₃	—	4	4	no	—
192	C₂⁴×C₂₃	—	8	2	no	—
193	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
195	#41×C₂₃	—	2	8	no	—
196	#41×C₂₃	—	4	4	no	—
197	#41×C₂₃	—	4	8	no	—
198	#41×C₂₃	—	4	32	no	—
199	C₂×Q₈×C₂₃	—	2	1	no	—
200	C₂×Q₈×C₂₃	—	2	4	no	—
201	C₂×Q₈×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	4	4	no	—
204	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	8	no	—
207	C₂×D₄×C₂₃	—	2	4	no	—
208	C₂×D₄×C₂₃	—	2	4	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	1	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	—	4	4	no	—
221	C₂×D₄×C₂₃	—	4	8	no	—
222	C₂×D₄×C₂₃	—	4	4	no	—
223	C₂×D₄×C₂₃	—	4	4	no	—
224	C₂×D₄×C₂₃	—	4	4	no	—
225	C₂×D₄×C₂₃	—	4	4	no	—
226	C₂×D₄×C₂₃	—	8	2	no	—
227	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
228	C₂×D₄×C₂₃	#41	1	4	yes	complemented
229	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	—	2	2	no	—
233	C₂²×C₄×C₂₃	—	2	2	no	—
234	C₂²×C₄×C₂₃	—	2	2	no	—
235	C₂²×C₄×C₂₃	—	2	2	no	—
236	C₂²×C₄×C₂₃	—	2	4	no	—
237	C₂²×C₄×C₂₃	—	2	4	no	—
238	C₂²×C₄×C₂₃	—	2	1	no	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	1	no	—
243	C₂²×C₄×C₂₃	—	2	4	no	—
244	C₂²×C₄×C₂₃	—	2	4	no	—
245	C₂²×C₄×C₂₃	—	2	4	no	—
246	C₂²×C₄×C₂₃	—	4	4	no	—
247	C₂²×C₄×C₂₃	—	4	4	no	—
248	C₂²×C₄×C₂₃	—	4	4	no	—
249	C₂²×C₄×C₂₃	—	4	4	no	—
250	C₂²×C₄×C₂₃	—	8	2	no	—
251	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	SD₁₆×C₂₃	—	4	4	no	—
261	D₈×C₂₃	—	2	8	no	—
262	D₈×C₂₃	—	4	4	no	—
263	M₁₆×C₂₃	—	4	4	no	—
264	C₂×C₈×C₂₃	—	2	2	no	—
265	C₂×C₈×C₂₃	—	2	2	no	—
266	C₂×C₈×C₂₃	—	2	2	no	—
267	C₂×C₈×C₂₃	—	2	2	no	—
268	C₂×C₈×C₂₃	—	4	4	no	—
269	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
272	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²⋊C₄×C₂₃	—	2	4	no	—
287	C₂²⋊C₄×C₂₃	—	2	4	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
296	C₄²×C₂₃	C₂×D₄	1	2	yes	—
297	C₄²×C₂₃	C₂⁴	1	2	yes	—
298	C₂×#3306	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	—	2	4	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	—	2	2	no	—
306	C₂³×C₂₃	—	2	2	no	—
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	4	8	no	—
309	C₂³×C₂₃	—	4	2	no	—
310	C₂³×C₂₃	—	4	2	no	—
311	C₂³×C₂₃	—	4	2	no	—
312	C₂³×C₂₃	—	4	2	no	—
313	C₂³×C₂₃	—	4	2	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	—	8	4	no	—
319	C₂³×C₂₃	—	8	16	no	—
320	C₂³×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
321	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
322	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
323	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₂₃	—	2	2	no	—
325	Q₈×C₂₃	—	2	2	no	—
326	Q₈×C₂₃	—	4	8	no	—
327	Q₈×C₂₃	—	4	2	no	—
328	D₄×C₂₃	—	2	8	no	—
329	D₄×C₂₃	—	2	4	no	—
330	D₄×C₂₃	—	2	2	no	—
331	D₄×C₂₃	—	2	2	no	—
332	D₄×C₂₃	—	2	2	no	—
333	D₄×C₂₃	—	2	2	no	—
334	D₄×C₂₃	—	2	2	no	—
335	D₄×C₂₃	—	4	8	no	—
336	D₄×C₂₃	—	4	8	no	—
337	D₄×C₂₃	—	4	8	no	—
338	D₄×C₂₃	—	4	8	no	—
339	D₄×C₂₃	—	4	2	no	—
340	D₄×C₂₃	—	4	2	no	—
341	D₄×C₂₃	—	8	4	no	—
342	D₄×C₂₃	C₂×#41	1	4	yes	complemented
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	4	no	—
348	C₂×C₄×C₂₃	—	2	4	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	4	8	no	—
359	C₂×C₄×C₂₃	—	4	8	no	—
360	C₂×C₄×C₂₃	—	4	8	no	—
361	C₂×C₄×C₂₃	—	4	2	no	—
362	C₂×C₄×C₂₃	—	4	2	no	—
363	C₂×C₄×C₂₃	—	4	2	no	—
364	C₂×C₄×C₂₃	—	4	2	no	—
365	C₂×C₄×C₂₃	—	4	8	no	—
366	C₂×C₄×C₂₃	—	4	2	no	—
367	C₂×C₄×C₂₃	—	8	4	no	—
368	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
374	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
376	C₈×C₂₃	—	2	2	no	—
377	C₈×C₂₃	—	2	2	no	—
378	C₈×C₂₃	—	2	2	no	—
379	C₈×C₂₃	—	2	2	no	—
380	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
381	C₂×#546	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#3306	C₂×C₂₃	1	16	yes	direct product factor
383	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
384	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
385	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
386	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
388	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
389	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
390	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
391	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
392	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
394	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
395	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic, complemented
396	C₂²×C₂₃	—	2	2	no	—
397	C₂²×C₂₃	—	2	8	no	—
398	C₂²×C₂₃	—	2	2	no	—
399	C₂²×C₂₃	—	2	2	no	—
400	C₂²×C₂₃	—	2	4	no	—
401	C₂²×C₂₃	—	2	2	no	—
402	C₂²×C₂₃	—	2	2	no	—
403	C₂²×C₂₃	—	4	4	no	—
404	C₂²×C₂₃	—	4	8	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	2	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	8	16	no	—
414	C₂²×C₂₃	—	8	4	no	—
415	C₂²×C₂₃	—	8	4	no	—
416	C₂²×C₂₃	#546	1	2	yes	—
417	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
418	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
419	C₂²×C₂₃	#577	1	2	yes	—
420	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₂₃	—	2	2	no	—
422	C₄×C₂₃	—	2	2	no	—
423	C₄×C₂₃	—	2	2	no	—
424	C₄×C₂₃	—	2	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	2	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	#546	1	2	yes	—
431	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
432	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂²×#41	—	2	1	no	—
434	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
435	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
436	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
441	#547	—	2	4	no	—
442	#547	C₂²×C₂₃	1	8	yes	complemented
443	#546	—	2	4	no	—
444	#546	C₂²×C₂₃	1	8	yes	complemented
445	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#123	—	2	1	no	—
448	C₂×#123	—	2	1	no	—
449	C₂×#123	—	2	1	no	—
450	C₂×C₂²⋊Q₈	—	2	1	no	—
451	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#121	—	2	1	no	—
453	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	C₂×#120	—	2	1	no	—
457	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
461	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	C₂²×C₂²⋊C₄	—	2	1	no	—
463	#489	C₂²×C₂₃	1	8	yes	complemented
464	#483	C₂²×C₂₃	1	8	yes	complemented
465	#481	C₂²×C₂₃	1	8	yes	complemented
466	#476	C₂²×C₂₃	1	8	yes	complemented
467	#469	C₂²×C₂₃	1	8	yes	complemented
468	#465	C₂²×C₂₃	1	8	yes	complemented
469	#463	C₂²×C₂₃	1	8	yes	complemented
470	#449	C₂²×C₂₃	1	8	yes	complemented
471	#447	C₂²×C₂₃	1	8	yes	complemented
472	#442	C₂²×C₂₃	1	8	yes	complemented
473	#435	C₂²×C₂₃	1	8	yes	complemented
474	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#417	C₂²×C₂₃	1	8	yes	complemented
479	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
480	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
483	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
486	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×#102	C₂²×C₂₃	1	8	yes	complemented
489	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
490	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
491	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
493	C₂×C₂₃	—	2	4	no	—
494	C₂×C₂₃	—	4	2	no	—
495	C₂×C₂₃	—	4	4	no	—
496	C₂×C₂₃	—	8	2	no	—
497	C₂×C₂₃	—	8	2	no	—
498	C₂×C₂₃	#3306	1	4	yes	direct product factor
499	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
500	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
501	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
502	C₂⁵	—	2	1	no	—
503	C₂×#41	—	2	8	no	—
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	4	no	—
506	C₂×#41	—	4	2	no	—
507	C₂×#41	—	4	8	no	—
508	C₂×#41	C₂³×C₂₃	1	4	yes	—
509	C₂²×Q₈	—	2	1	no	—
510	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
511	C₂²×D₄	—	2	4	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	4	2	no	—
519	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
523	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
524	C₂³×C₄	—	2	1	no	—
525	C₂³×C₄	—	2	1	no	—
526	C₂³×C₄	—	2	1	no	—
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×SD₁₆	—	4	2	no	—
532	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
533	C₂×D₈	—	2	4	no	—
534	C₂×D₈	—	4	2	no	—
535	C₂×D₈	C₂³×C₂₃	1	4	yes	—
536	C₂×D₈	C₂³×C₂₃	1	4	yes	—
537	C₂×M₁₆	—	4	2	no	—
538	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
539	C₂²×C₈	—	4	2	no	—
540	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
547	#124	—	2	2	no	—
548	#124	C₂³×C₂₃	1	4	yes	—
549	#123	—	2	8	no	—
550	#123	—	2	8	no	—
551	#123	—	2	8	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	8	no	—
554	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
555	#121	—	2	2	no	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	8	no	—
559	#121	C₂³×C₂₃	1	4	yes	—
560	#121	C₂³×C₂₃	1	4	yes	—
561	#121	C₂³×C₂₃	1	4	yes	complemented
562	#120	—	2	8	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	D₄×C₂₃	1	4	yes	—
566	C₄×D₄	C₂³×C₂₃	1	4	yes	—
567	C₄×D₄	C₂³×C₂₃	1	4	yes	—
568	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	2	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	2	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
579	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	8	no	—
591	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
594	#106	C₂³×C₂₃	1	4	yes	complemented
595	#106	C₂³×C₂₃	1	4	yes	complemented
596	#106	C₂³×C₂₃	1	4	yes	complemented
597	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
598	#103	C₂³×C₂₃	1	4	yes	complemented
599	#103	C₂³×C₂₃	1	4	yes	complemented
600	#103	C₂³×C₂₃	1	4	yes	complemented
601	#102	C₂³×C₂₃	1	4	yes	—
602	#102	C₂³×C₂₃	1	4	yes	—
603	#102	C₂³×C₂₃	1	4	yes	—
604	#102	C₂³×C₂₃	1	4	yes	—
605	#102	C₂³×C₂₃	1	4	yes	—
606	#102	C₂³×C₂₃	1	4	yes	—
607	#102	C₂³×C₂₃	1	4	yes	complemented
608	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
609	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
610	#97	C₂³×C₂₃	1	4	yes	complemented
611	C₂₃	C₂×#3306	1	1	yes	characteristic, direct product factor, Sylow
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	4	no	—
616	C₂⁴	—	4	4	no	—
617	C₂⁴	—	4	4	no	—
618	C₂⁴	—	8	2	no	—
619	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
620	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
621	#41	—	2	8	no	—
622	#41	—	4	4	no	—
623	#41	—	4	8	no	—
624	#41	—	4	32	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	4	4	no	—
630	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	4	8	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	8	2	no	—
653	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
654	C₂×D₄	#41×C₂₃	1	4	yes	complemented
655	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
656	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
657	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	—	4	4	no	—
674	C₂²×C₄	—	4	4	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	—	8	2	no	—
677	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
686	SD₁₆	—	4	4	no	—
687	D₈	—	2	8	no	—
688	D₈	—	4	4	no	—
689	M₁₆	—	4	4	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	—	2	2	no	—
694	C₂×C₈	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
696	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
697	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
698	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
708	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
721	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
722	C₄²	C₂×D₄×C₂₃	1	2	yes	—
723	C₄²	C₂⁴×C₂₃	1	2	yes	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	8	no	—
738	C₂³	—	4	2	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	8	4	no	—
744	C₂³	—	8	16	no	—
745	C₂³	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
746	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
747	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
748	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
749	Q₈	—	2	2	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	4	8	no	—
752	Q₈	—	4	2	no	—
753	D₄	—	2	8	no	—
754	D₄	—	2	2	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	4	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	—	4	8	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	8	4	no	—
767	D₄	C₂×#41×C₂₃	1	4	yes	complemented
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	8	4	no	—
793	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
799	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
800	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
801	C₈	—	2	2	no	—
802	C₈	—	2	2	no	—
803	C₈	—	2	2	no	—
804	C₈	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	8	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	4	4	no	—
813	C₂²	—	4	8	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	16	no	—
823	C₂²	—	8	4	no	—
824	C₂²	—	8	4	no	—
825	C₂²	C₂₃×#546	1	2	yes	—
826	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
827	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
828	C₂²	C₂₃×#577	1	2	yes	—
829	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	C₂₃×#546	1	2	yes	—
840	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
841	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
842	C₂	—	2	4	no	—
843	C₂	—	4	2	no	—
844	C₂	—	4	4	no	—
845	C₂	—	8	2	no	—
846	C₂	—	8	2	no	—
847	C₂	C₂₃×#3306	1	4	yes	direct product factor
848	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
849	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
850	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×#547	C₂	semidirect
2. C₂×C₂₃×#546	C₂	semidirect
3. C₂₃×#3306	C₂	direct (N × H)
4. C₂×C₂₃×#489	C₂	semidirect
5. C₂×C₂₃×#481	C₂	semidirect
6. C₂×C₂₃×#483	C₂	semidirect
7. C₂×C₂₃×#476	C₂	semidirect
8. C₂×C₂₃×#469	C₂	semidirect
9. C₂×C₂₃×#465	C₂	semidirect
10. C₂×C₂₃×#463	C₂	semidirect
11. C₂×C₂₃×#449	C₂	semidirect
12. C₂×C₂₃×#447	C₂	semidirect
13. C₂×C₂₃×#442	C₂	semidirect
14. C₂×C₂₃×#435	C₂	semidirect
15. C₂×C₂₃×#417	C₂	semidirect
16. C₂²×C₂₃×#102	C₂	semidirect
20. C₂²×SD₁₆×C₂₃	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
26. C₂₃×#547	C₂²	semidirect
28. C₂₃×#546	C₂²	semidirect
29. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₂₃×#121	C₂²	semidirect
43. C₂×C₄×D₄×C₂₃	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
47. C₂₃×#489	C₂²	semidirect
48. C₂₃×#483	C₂²	semidirect
49. C₂₃×#481	C₂²	semidirect
50. C₂₃×#476	C₂²	semidirect
51. C₂₃×#469	C₂²	semidirect
52. C₂₃×#465	C₂²	semidirect
53. C₂₃×#463	C₂²	semidirect
54. C₂₃×#449	C₂²	semidirect
55. C₂₃×#447	C₂²	semidirect
56. C₂₃×#442	C₂²	semidirect
57. C₂₃×#435	C₂²	semidirect
58. C₂×C₂₃×#106	C₂²	semidirect
59. C₂×C₂₃×#106	C₂²	semidirect
60. C₂×C₂₃×#106	C₂²	semidirect
61. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
62. C₂₃×#417	C₂²	semidirect
63. C₂×C₂₃×#103	C₂²	semidirect
64. C₂×C₂₃×#103	C₂²	semidirect
65. C₂×C₂₃×#103	C₂²	semidirect
72. C₂×C₂₃×#102	C₂²	semidirect
73. C₂×C₂₃×#102	C₂²	semidirect
75. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₂₃×#97	C₂²	semidirect
107. C₂×SD₁₆×C₂₃	C₂³	semidirect
113. C₂×M₁₆×C₂₃	C₂³	semidirect
121. C₂₃×C₄⋊Q₈	C₂³	semidirect
136. C₂₃×#121	C₂³	semidirect
143. C₄×D₄×C₂₃	C₂³	semidirect
156. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
169. C₂₃×#106	C₂³	semidirect
170. C₂₃×#106	C₂³	semidirect
171. C₂₃×#106	C₂³	semidirect
172. C₂₃×C₄⋊C₈	C₂³	semidirect
173. C₂₃×#103	C₂³	semidirect
174. C₂₃×#103	C₂³	semidirect
175. C₂₃×#103	C₂³	semidirect
182. C₂₃×#102	C₂³	semidirect
184. C₂₃×C₂²⋊C₈	C₂³	semidirect
185. C₂₃×#97	C₂³	semidirect
228. C₂×D₄×C₂₃	#41	semidirect
298. C₂×#3306	C₂₃	direct (N × H)
342. D₄×C₂₃	C₂×#41	semidirect
380. C₂×#547	C₂×C₂₃	semidirect
381. C₂×#546	C₂×C₂₃	semidirect
382. #3306	C₂×C₂₃	direct (N × H)
383. C₂×#489	C₂×C₂₃	semidirect
384. C₂×#481	C₂×C₂₃	semidirect
385. C₂×#483	C₂×C₂₃	semidirect
386. C₂×#476	C₂×C₂₃	semidirect
387. C₂×#469	C₂×C₂₃	semidirect
388. C₂×#465	C₂×C₂₃	semidirect
389. C₂×#463	C₂×C₂₃	semidirect
390. C₂×#449	C₂×C₂₃	semidirect
391. C₂×#447	C₂×C₂₃	semidirect
392. C₂×#442	C₂×C₂₃	semidirect
393. C₂×#435	C₂×C₂₃	semidirect
394. C₂×#417	C₂×C₂₃	semidirect
395. C₂²×#102	C₂×C₂₃	semidirect
436. C₂²×SD₁₆	C₂²×C₂₃	semidirect
439. C₂²×M₁₆	C₂²×C₂₃	semidirect
442. #547	C₂²×C₂₃	semidirect
444. #546	C₂²×C₂₃	semidirect
445. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
455. C₂×#121	C₂²×C₂₃	semidirect
459. C₂×C₄×D₄	C₂²×C₂₃	semidirect
461. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
463. #489	C₂²×C₂₃	semidirect
464. #483	C₂²×C₂₃	semidirect
465. #481	C₂²×C₂₃	semidirect
466. #476	C₂²×C₂₃	semidirect
467. #469	C₂²×C₂₃	semidirect
468. #465	C₂²×C₂₃	semidirect
469. #463	C₂²×C₂₃	semidirect
470. #449	C₂²×C₂₃	semidirect
471. #447	C₂²×C₂₃	semidirect
472. #442	C₂²×C₂₃	semidirect
473. #435	C₂²×C₂₃	semidirect
474. C₂×#106	C₂²×C₂₃	semidirect
475. C₂×#106	C₂²×C₂₃	semidirect
476. C₂×#106	C₂²×C₂₃	semidirect
477. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
478. #417	C₂²×C₂₃	semidirect
479. C₂×#103	C₂²×C₂₃	semidirect
480. C₂×#103	C₂²×C₂₃	semidirect
481. C₂×#103	C₂²×C₂₃	semidirect
488. C₂×#102	C₂²×C₂₃	semidirect
489. C₂×#102	C₂²×C₂₃	semidirect
491. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
492. C₂×#97	C₂²×C₂₃	semidirect
498. C₂×C₂₃	#3306	direct (N × H)
532. C₂×SD₁₆	C₂³×C₂₃	semidirect
538. C₂×M₁₆	C₂³×C₂₃	semidirect
546. C₄⋊Q₈	C₂³×C₂₃	semidirect
561. #121	C₂³×C₂₃	semidirect
568. C₄×D₄	C₂³×C₂₃	semidirect
581. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
594. #106	C₂³×C₂₃	semidirect
595. #106	C₂³×C₂₃	semidirect
596. #106	C₂³×C₂₃	semidirect
597. C₄⋊C₈	C₂³×C₂₃	semidirect
598. #103	C₂³×C₂₃	semidirect
599. #103	C₂³×C₂₃	semidirect
600. #103	C₂³×C₂₃	semidirect
607. #102	C₂³×C₂₃	semidirect
609. C₂²⋊C₈	C₂³×C₂₃	semidirect
610. #97	C₂³×C₂₃	semidirect
611. C₂₃	C₂×#3306	direct (N × H)
654. C₂×D₄	#41×C₂₃	semidirect
767. D₄	C₂×#41×C₂₃	semidirect
847. C₂	C₂₃×#3306	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×#547	2
C₂×C₂₃×#546	2
C₂₃×#3306	2
C₂×C₂₃×#489	2
C₂×C₂₃×#481	2
C₂×C₂₃×#483	2
C₂×C₂₃×#476	2
C₂×C₂₃×#469	2
C₂×C₂₃×#465	2
C₂×C₂₃×#463	2
C₂×C₂₃×#449	2
C₂×C₂₃×#447	2
C₂×C₂₃×#442	2
C₂×C₂₃×#435	2
C₂×C₂₃×#417	2
C₂²×C₂₃×#102	2
C₂×#3306	23

Subgroups — C2×C23×#3306 #19208751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3306 #19208751