Subgroups — C₂×C₂₃×#3322 #19208768

Order 5888.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 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×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3322	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#480	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×#468	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×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#553	—	2	4	no	—
25	C₂₃×#553	C₂²	1	8	yes	complemented
26	C₂₃×#546	—	2	4	no	—
27	C₂₃×#546	C₂²	1	8	yes	complemented
28	C₂×C₂₃×#126	—	2	1	no	—
29	C₂×C₂₃×#125	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	—	2	1	no	—
35	C₂×C₂₃×#121	—	2	1	no	—
36	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₃×#120	—	2	1	no	—
40	C₂×C₄×D₄×C₂₃	—	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	C₂×C₂₃×#117	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×#488	C₂²	1	8	yes	complemented
48	C₂₃×#485	C₂²	1	8	yes	complemented
49	C₂₃×#480	C₂²	1	8	yes	complemented
50	C₂₃×#478	C₂²	1	8	yes	complemented
51	C₂₃×#469	C₂²	1	8	yes	complemented
52	C₂₃×#468	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	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
57	C₂₃×#436	C₂²	1	8	yes	complemented
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₂₃×#107	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	C₂₃×#417	C₂²	1	8	yes	complemented
64	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic
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×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₂₃	—	2	1	no	—
78	C₂×#41×C₂₃	—	2	2	no	—
79	C₂×#41×C₂₃	—	2	4	no	—
80	C₂×#41×C₂₃	—	4	2	no	—
81	C₂×#41×C₂₃	C₂³	1	4	yes	—
82	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	—	2	4	no	—
84	C₂²×D₄×C₂₃	—	2	1	no	—
85	C₂²×D₄×C₂₃	—	2	1	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	—	4	2	no	—
91	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
95	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	—	2	1	no	—
97	C₂³×C₄×C₂₃	—	2	1	no	—
98	C₂³×C₄×C₂₃	—	2	1	no	—
99	C₂³×C₄×C₂₃	—	2	1	no	—
100	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₂₃	—	4	2	no	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
104	C₂×D₈×C₂₃	—	2	4	no	—
105	C₂×D₈×C₂₃	—	4	2	no	—
106	C₂×D₈×C₂₃	C₂³	1	4	yes	—
107	C₂×D₈×C₂₃	C₂³	1	4	yes	—
108	C₂×M₁₆×C₂₃	—	4	2	no	—
109	C₂×M₁₆×C₂₃	—	4	2	no	—
110	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
112	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
116	C₂₃×#126	—	2	8	no	—
117	C₂₃×#125	—	2	2	no	—
118	C₂₃×#125	C₂³	1	4	yes	complemented
119	C₂₃×#124	—	2	2	no	—
120	C₂₃×#124	C₂³	1	4	yes	—
121	C₂₃×#123	—	2	8	no	—
122	C₂₃×#123	—	2	8	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×#121	—	2	8	no	—
126	C₂₃×#121	—	2	2	no	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	2	no	—
129	C₂₃×#121	—	2	8	no	—
130	C₂₃×#121	C₂³	1	4	yes	—
131	C₂₃×#121	C₂³	1	4	yes	—
132	C₂₃×#121	C₂³	1	4	yes	complemented
133	C₂₃×#120	—	2	8	no	—
134	C₄×D₄×C₂₃	—	2	8	no	—
135	C₄×D₄×C₂₃	—	2	2	no	—
136	C₄×D₄×C₂₃	—	2	2	no	—
137	C₄×D₄×C₂₃	D₄	1	4	yes	—
138	C₄×D₄×C₂₃	C₂³	1	4	yes	—
139	C₄×D₄×C₂₃	C₂³	1	4	yes	—
140	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
141	C₂₃×#117	—	2	2	no	—
142	C₂₃×#117	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
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	—	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	8	no	—
164	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₂₃	—	2	1	no	—
167	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	4	yes	complemented
169	C₂₃×#107	C₂³	1	4	yes	complemented
170	C₂₃×#106	C₂³	1	4	yes	complemented
171	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
172	C₂₃×#103	C₂³	1	4	yes	complemented
173	C₂₃×#103	C₂³	1	4	yes	complemented
174	C₂₃×#103	C₂³	1	4	yes	complemented
175	C₂₃×#102	C₂³	1	4	yes	—
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	complemented
182	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
184	C₄×C₈×C₂₃	C₂³	1	4	yes	complemented
185	C₂⁴×C₂₃	—	2	1	no	—
186	C₂⁴×C₂₃	—	2	1	no	—
187	C₂⁴×C₂₃	—	2	1	no	—
188	C₂⁴×C₂₃	—	2	4	no	—
189	C₂⁴×C₂₃	—	4	4	no	—
190	C₂⁴×C₂₃	—	4	4	no	—
191	C₂⁴×C₂₃	—	8	2	no	—
192	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
194	#41×C₂₃	—	2	8	no	—
195	#41×C₂₃	—	4	4	no	—
196	#41×C₂₃	—	4	8	no	—
197	C₂×Q₈×C₂₃	—	2	1	no	—
198	C₂×Q₈×C₂₃	—	2	2	no	—
199	C₂×Q₈×C₂₃	—	2	2	no	—
200	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
201	C₂×D₄×C₂₃	—	2	8	no	—
202	C₂×D₄×C₂₃	—	2	4	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	1	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	1	no	—
210	C₂×D₄×C₂₃	—	2	2	no	—
211	C₂×D₄×C₂₃	—	2	2	no	—
212	C₂×D₄×C₂₃	—	2	2	no	—
213	C₂×D₄×C₂₃	—	2	2	no	—
214	C₂×D₄×C₂₃	—	2	2	no	—
215	C₂×D₄×C₂₃	—	4	4	no	—
216	C₂×D₄×C₂₃	—	4	8	no	—
217	C₂×D₄×C₂₃	—	4	2	no	—
218	C₂×D₄×C₂₃	—	4	4	no	—
219	C₂×D₄×C₂₃	—	4	4	no	—
220	C₂×D₄×C₂₃	—	4	4	no	—
221	C₂×D₄×C₂₃	—	8	2	no	—
222	C₂×D₄×C₂₃	—	8	2	no	—
223	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
224	C₂×D₄×C₂₃	#41	1	4	yes	—
225	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₂₃	—	2	2	no	—
229	C₂²×C₄×C₂₃	—	2	2	no	—
230	C₂²×C₄×C₂₃	—	2	2	no	—
231	C₂²×C₄×C₂₃	—	2	2	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	4	no	—
238	C₂²×C₄×C₂₃	—	2	4	no	—
239	C₂²×C₄×C₂₃	—	2	4	no	—
240	C₂²×C₄×C₂₃	—	2	4	no	—
241	C₂²×C₄×C₂₃	—	4	4	no	—
242	C₂²×C₄×C₂₃	—	8	2	no	—
243	C₂²×C₄×C₂₃	—	8	2	no	—
244	C₂²×C₄×C₂₃	—	8	2	no	—
245	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₂₃	—	4	4	no	—
255	D₈×C₂₃	—	2	8	no	—
256	D₈×C₂₃	—	4	4	no	—
257	M₁₆×C₂₃	—	4	4	no	—
258	M₁₆×C₂₃	—	4	4	no	—
259	C₂×C₈×C₂₃	—	2	2	no	—
260	C₂×C₈×C₂₃	—	2	2	no	—
261	C₂×C₈×C₂₃	—	2	2	no	—
262	C₂×C₈×C₂₃	—	2	2	no	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	1	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
291	C₄²×C₂₃	—	2	4	no	—
292	C₄²×C₂₃	C₂×D₄	1	2	yes	—
293	C₄²×C₂₃	C₂⁴	1	2	yes	—
294	C₂×#3322	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₂₃	—	2	2	no	—
296	C₂³×C₂₃	—	2	2	no	—
297	C₂³×C₂₃	—	2	4	no	—
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	—	2	2	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	—	4	8	no	—
306	C₂³×C₂₃	—	4	8	no	—
307	C₂³×C₂₃	—	4	2	no	—
308	C₂³×C₂₃	—	4	2	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	2	no	—
315	C₂³×C₂₃	—	8	4	no	—
316	C₂³×C₂₃	—	8	16	no	—
317	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
318	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
319	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	Q₈×C₂₃	—	2	2	no	—
321	Q₈×C₂₃	—	2	2	no	—
322	Q₈×C₂₃	—	4	2	no	—
323	D₄×C₂₃	—	2	4	no	—
324	D₄×C₂₃	—	2	2	no	—
325	D₄×C₂₃	—	2	2	no	—
326	D₄×C₂₃	—	2	2	no	—
327	D₄×C₂₃	—	2	2	no	—
328	D₄×C₂₃	—	2	2	no	—
329	D₄×C₂₃	—	4	4	no	—
330	D₄×C₂₃	—	4	8	no	—
331	D₄×C₂₃	—	4	8	no	—
332	D₄×C₂₃	—	4	8	no	—
333	D₄×C₂₃	—	4	2	no	—
334	D₄×C₂₃	—	4	2	no	—
335	D₄×C₂₃	—	8	4	no	—
336	D₄×C₂₃	—	8	4	no	—
337	D₄×C₂₃	C₂×#41	1	4	yes	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	4	no	—
343	C₂×C₄×C₂₃	—	2	4	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	2	no	—
348	C₂×C₄×C₂₃	—	2	2	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	—	4	8	no	—
354	C₂×C₄×C₂₃	—	4	2	no	—
355	C₂×C₄×C₂₃	—	4	2	no	—
356	C₂×C₄×C₂₃	—	4	2	no	—
357	C₂×C₄×C₂₃	—	4	2	no	—
358	C₂×C₄×C₂₃	—	4	2	no	—
359	C₂×C₄×C₂₃	—	8	4	no	—
360	C₂×C₄×C₂₃	—	8	4	no	—
361	C₂×C₄×C₂₃	—	8	4	no	—
362	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
366	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
368	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
369	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
370	C₈×C₂₃	—	2	2	no	—
371	C₈×C₂₃	—	2	2	no	—
372	C₈×C₂₃	—	2	2	no	—
373	C₈×C₂₃	—	2	2	no	—
374	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂×#546	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#3322	C₂×C₂₃	1	16	yes	direct product factor
377	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂×#485	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
380	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
381	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
382	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
383	C₂×#463	C₂×C₂₃	1	1	yes	characteristic, complemented
384	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
385	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
386	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
388	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
389	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
390	C₂²×C₂₃	—	2	2	no	—
391	C₂²×C₂₃	—	2	2	no	—
392	C₂²×C₂₃	—	2	4	no	—
393	C₂²×C₂₃	—	2	2	no	—
394	C₂²×C₂₃	—	2	2	no	—
395	C₂²×C₂₃	—	2	2	no	—
396	C₂²×C₂₃	—	2	2	no	—
397	C₂²×C₂₃	—	4	4	no	—
398	C₂²×C₂₃	—	4	4	no	—
399	C₂²×C₂₃	—	4	8	no	—
400	C₂²×C₂₃	—	4	2	no	—
401	C₂²×C₂₃	—	4	2	no	—
402	C₂²×C₂₃	—	4	2	no	—
403	C₂²×C₂₃	—	4	2	no	—
404	C₂²×C₂₃	—	4	2	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	8	16	no	—
409	C₂²×C₂₃	—	8	4	no	—
410	C₂²×C₂₃	—	8	4	no	—
411	C₂²×C₂₃	#546	1	2	yes	—
412	C₂²×C₂₃	#575	1	2	yes	—
413	C₂²×C₂₃	#576	1	2	yes	—
414	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₂₃	—	2	2	no	—
416	C₄×C₂₃	—	2	2	no	—
417	C₄×C₂₃	—	2	2	no	—
418	C₄×C₂₃	—	2	2	no	—
419	C₄×C₂₃	—	4	2	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	#546	1	2	yes	—
425	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
426	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
428	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
429	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
431	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
433	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#553	—	2	4	no	—
435	#553	C₂²×C₂₃	1	8	yes	complemented
436	#546	—	2	4	no	—
437	#546	C₂²×C₂₃	1	8	yes	complemented
438	C₂×#126	—	2	1	no	—
439	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#123	—	2	1	no	—
442	C₂×#123	—	2	1	no	—
443	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#121	—	2	1	no	—
445	C₂×#121	—	2	1	no	—
446	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	C₂×#120	—	2	1	no	—
450	C₂×C₄×D₄	—	2	1	no	—
451	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
455	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	C₂²×C₂²⋊C₄	—	2	1	no	—
457	#488	C₂²×C₂₃	1	8	yes	complemented
458	#485	C₂²×C₂₃	1	8	yes	complemented
459	#480	C₂²×C₂₃	1	8	yes	complemented
460	#478	C₂²×C₂₃	1	8	yes	complemented
461	#469	C₂²×C₂₃	1	8	yes	complemented
462	#468	C₂²×C₂₃	1	8	yes	complemented
463	#463	C₂²×C₂₃	1	8	yes	complemented
464	#449	C₂²×C₂₃	1	8	yes	complemented
465	#447	C₂²×C₂₃	1	8	yes	complemented
466	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
467	#436	C₂²×C₂₃	1	8	yes	complemented
468	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
469	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
470	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	#418	C₂²×C₂₃	1	8	yes	complemented
473	#417	C₂²×C₂₃	1	8	yes	complemented
474	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
481	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
482	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
483	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
486	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	C₂×C₂₃	—	4	2	no	—
488	C₂×C₂₃	—	4	2	no	—
489	C₂×C₂₃	—	4	4	no	—
490	C₂×C₂₃	—	8	2	no	—
491	C₂×C₂₃	—	8	2	no	—
492	C₂×C₂₃	#3322	1	4	yes	direct product factor
493	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
494	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
495	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
496	C₂⁵	—	2	1	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	4	no	—
499	C₂×#41	—	4	2	no	—
500	C₂×#41	C₂³×C₂₃	1	4	yes	—
501	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×D₄	—	2	4	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	2	no	—
509	C₂²×D₄	—	4	2	no	—
510	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
514	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂×SD₁₆	—	4	2	no	—
522	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
523	C₂×D₈	—	2	4	no	—
524	C₂×D₈	—	4	2	no	—
525	C₂×D₈	C₂³×C₂₃	1	4	yes	—
526	C₂×D₈	C₂³×C₂₃	1	4	yes	—
527	C₂×M₁₆	—	4	2	no	—
528	C₂×M₁₆	—	4	2	no	—
529	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
530	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
531	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
535	#126	—	2	8	no	—
536	#125	—	2	2	no	—
537	#125	C₂³×C₂₃	1	4	yes	complemented
538	#124	—	2	2	no	—
539	#124	C₂³×C₂₃	1	4	yes	—
540	#123	—	2	8	no	—
541	#123	—	2	8	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
544	#121	—	2	8	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	8	no	—
549	#121	C₂³×C₂₃	1	4	yes	—
550	#121	C₂³×C₂₃	1	4	yes	—
551	#121	C₂³×C₂₃	1	4	yes	complemented
552	#120	—	2	8	no	—
553	C₄×D₄	—	2	8	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	D₄×C₂₃	1	4	yes	—
557	C₄×D₄	C₂³×C₂₃	1	4	yes	—
558	C₄×D₄	C₂³×C₂₃	1	4	yes	—
559	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
560	#117	—	2	2	no	—
561	#117	C₂³×C₂₃	1	4	yes	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	2	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	8	no	—
583	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
587	#107	C₂³×C₂₃	1	4	yes	complemented
588	#107	C₂³×C₂₃	1	4	yes	complemented
589	#106	C₂³×C₂₃	1	4	yes	complemented
590	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
591	#103	C₂³×C₂₃	1	4	yes	complemented
592	#103	C₂³×C₂₃	1	4	yes	complemented
593	#103	C₂³×C₂₃	1	4	yes	complemented
594	#102	C₂³×C₂₃	1	4	yes	—
595	#102	C₂³×C₂₃	1	4	yes	—
596	#102	C₂³×C₂₃	1	4	yes	—
597	#102	C₂³×C₂₃	1	4	yes	—
598	#102	C₂³×C₂₃	1	4	yes	—
599	#102	C₂³×C₂₃	1	4	yes	—
600	#102	C₂³×C₂₃	1	4	yes	complemented
601	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
603	C₄×C₈	C₂³×C₂₃	1	4	yes	complemented
604	C₂₃	C₂×#3322	1	1	yes	characteristic, direct product factor, Sylow
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	1	no	—
608	C₂⁴	—	2	4	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	4	4	no	—
611	C₂⁴	—	8	2	no	—
612	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
614	#41	—	2	8	no	—
615	#41	—	4	4	no	—
616	#41	—	4	8	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
621	C₂×D₄	—	2	8	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	4	4	no	—
641	C₂×D₄	—	8	2	no	—
642	C₂×D₄	—	8	2	no	—
643	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
644	C₂×D₄	#41×C₂₃	1	4	yes	—
645	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
646	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
647	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	8	2	no	—
663	C₂²×C₄	—	8	2	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
674	SD₁₆	—	4	4	no	—
675	D₈	—	2	8	no	—
676	D₈	—	4	4	no	—
677	M₁₆	—	4	4	no	—
678	M₁₆	—	4	4	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	2	2	no	—
682	C₂×C₈	—	2	2	no	—
683	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
684	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
685	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
686	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
696	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
710	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
711	C₄²	—	2	4	no	—
712	C₄²	C₂×D₄×C₂₃	1	2	yes	—
713	C₄²	C₂⁴×C₂₃	1	2	yes	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	4	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	4	8	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	8	4	no	—
735	C₂³	—	8	16	no	—
736	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
737	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
738	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	4	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	D₄	C₂×#41×C₂₃	1	4	yes	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
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	—	4	8	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
783	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
786	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
787	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
788	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	4	no	—
802	C₂²	—	4	8	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	16	no	—
812	C₂²	—	8	4	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₂₃×#546	1	2	yes	—
815	C₂²	C₂₃×#575	1	2	yes	—
816	C₂²	C₂₃×#576	1	2	yes	—
817	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	C₂₃×#546	1	2	yes	—
828	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
829	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂	—	4	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₂₃×#3322	1	4	yes	direct product factor
836	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
837	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
838	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×C₂₃×#546	C₂	semidirect
3. C₂₃×#3322	C₂	direct (N × H)
4. C₂×C₂₃×#488	C₂	semidirect
5. C₂×C₂₃×#485	C₂	semidirect
6. C₂×C₂₃×#480	C₂	semidirect
7. C₂×C₂₃×#478	C₂	semidirect
8. C₂×C₂₃×#469	C₂	semidirect
9. C₂×C₂₃×#468	C₂	semidirect
10. C₂×C₂₃×#463	C₂	semidirect
11. C₂×C₂₃×#449	C₂	semidirect
12. C₂×C₂₃×#447	C₂	semidirect
13. C₂×C₄×D₈×C₂₃	C₂	semidirect
14. C₂×C₂₃×#436	C₂	semidirect
15. C₂×C₂₃×#417	C₂	semidirect
16. C₂×C₂₃×#418	C₂	semidirect
19. C₂²×SD₁₆×C₂₃	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
25. C₂₃×#553	C₂²	semidirect
27. C₂₃×#546	C₂²	semidirect
29. C₂×C₂₃×#125	C₂²	semidirect
38. C₂×C₂₃×#121	C₂²	semidirect
43. C₂×C₄×D₄×C₂₃	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
47. C₂₃×#488	C₂²	semidirect
48. C₂₃×#485	C₂²	semidirect
49. C₂₃×#480	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#469	C₂²	semidirect
52. C₂₃×#468	C₂²	semidirect
53. C₂₃×#463	C₂²	semidirect
54. C₂₃×#449	C₂²	semidirect
55. C₂₃×#447	C₂²	semidirect
56. C₄×D₈×C₂₃	C₂²	semidirect
57. C₂₃×#436	C₂²	semidirect
58. C₂×C₂₃×#107	C₂²	semidirect
59. C₂×C₂₃×#107	C₂²	semidirect
60. C₂×C₂₃×#106	C₂²	semidirect
61. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
62. C₂₃×#418	C₂²	semidirect
63. C₂₃×#417	C₂²	semidirect
64. C₂×C₂₃×#103	C₂²	semidirect
65. C₂×C₂₃×#103	C₂²	semidirect
66. C₂×C₂₃×#103	C₂²	semidirect
73. C₂×C₂₃×#102	C₂²	semidirect
75. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₄×C₈×C₂₃	C₂²	semidirect
103. C₂×SD₁₆×C₂₃	C₂³	semidirect
111. C₂×M₁₆×C₂₃	C₂³	semidirect
118. C₂₃×#125	C₂³	semidirect
132. C₂₃×#121	C₂³	semidirect
140. C₄×D₄×C₂₃	C₂³	semidirect
153. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
168. C₂₃×#107	C₂³	semidirect
169. C₂₃×#107	C₂³	semidirect
170. C₂₃×#106	C₂³	semidirect
171. C₂₃×C₄⋊C₈	C₂³	semidirect
172. C₂₃×#103	C₂³	semidirect
173. C₂₃×#103	C₂³	semidirect
174. C₂₃×#103	C₂³	semidirect
181. C₂₃×#102	C₂³	semidirect
183. C₂₃×C₂²⋊C₈	C₂³	semidirect
184. C₄×C₈×C₂₃	C₂³	semidirect
294. C₂×#3322	C₂₃	direct (N × H)
374. C₂×#553	C₂×C₂₃	semidirect
375. C₂×#546	C₂×C₂₃	semidirect
376. #3322	C₂×C₂₃	direct (N × H)
377. C₂×#488	C₂×C₂₃	semidirect
378. C₂×#485	C₂×C₂₃	semidirect
379. C₂×#480	C₂×C₂₃	semidirect
380. C₂×#478	C₂×C₂₃	semidirect
381. C₂×#469	C₂×C₂₃	semidirect
382. C₂×#468	C₂×C₂₃	semidirect
383. C₂×#463	C₂×C₂₃	semidirect
384. C₂×#449	C₂×C₂₃	semidirect
385. C₂×#447	C₂×C₂₃	semidirect
386. C₂×C₄×D₈	C₂×C₂₃	semidirect
387. C₂×#436	C₂×C₂₃	semidirect
388. C₂×#417	C₂×C₂₃	semidirect
389. C₂×#418	C₂×C₂₃	semidirect
429. C₂²×SD₁₆	C₂²×C₂₃	semidirect
433. C₂²×M₁₆	C₂²×C₂₃	semidirect
435. #553	C₂²×C₂₃	semidirect
437. #546	C₂²×C₂₃	semidirect
439. C₂×#125	C₂²×C₂₃	semidirect
448. C₂×#121	C₂²×C₂₃	semidirect
453. C₂×C₄×D₄	C₂²×C₂₃	semidirect
455. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
457. #488	C₂²×C₂₃	semidirect
458. #485	C₂²×C₂₃	semidirect
459. #480	C₂²×C₂₃	semidirect
460. #478	C₂²×C₂₃	semidirect
461. #469	C₂²×C₂₃	semidirect
462. #468	C₂²×C₂₃	semidirect
463. #463	C₂²×C₂₃	semidirect
464. #449	C₂²×C₂₃	semidirect
465. #447	C₂²×C₂₃	semidirect
466. C₄×D₈	C₂²×C₂₃	semidirect
467. #436	C₂²×C₂₃	semidirect
468. C₂×#107	C₂²×C₂₃	semidirect
469. C₂×#107	C₂²×C₂₃	semidirect
470. C₂×#106	C₂²×C₂₃	semidirect
471. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
472. #418	C₂²×C₂₃	semidirect
473. #417	C₂²×C₂₃	semidirect
474. C₂×#103	C₂²×C₂₃	semidirect
475. C₂×#103	C₂²×C₂₃	semidirect
476. C₂×#103	C₂²×C₂₃	semidirect
483. C₂×#102	C₂²×C₂₃	semidirect
485. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
486. C₂×C₄×C₈	C₂²×C₂₃	semidirect
492. C₂×C₂₃	#3322	direct (N × H)
522. C₂×SD₁₆	C₂³×C₂₃	semidirect
530. C₂×M₁₆	C₂³×C₂₃	semidirect
537. #125	C₂³×C₂₃	semidirect
551. #121	C₂³×C₂₃	semidirect
559. C₄×D₄	C₂³×C₂₃	semidirect
572. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
587. #107	C₂³×C₂₃	semidirect
588. #107	C₂³×C₂₃	semidirect
589. #106	C₂³×C₂₃	semidirect
590. C₄⋊C₈	C₂³×C₂₃	semidirect
591. #103	C₂³×C₂₃	semidirect
592. #103	C₂³×C₂₃	semidirect
593. #103	C₂³×C₂₃	semidirect
600. #102	C₂³×C₂₃	semidirect
602. C₂²⋊C₈	C₂³×C₂₃	semidirect
603. C₄×C₈	C₂³×C₂₃	semidirect
604. C₂₃	C₂×#3322	direct (N × H)
835. C₂	C₂₃×#3322	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×#546	2
C₂₃×#3322	2
C₂×C₂₃×#488	2
C₂×C₂₃×#485	2
C₂×C₂₃×#480	2
C₂×C₂₃×#478	2
C₂×C₂₃×#469	2
C₂×C₂₃×#468	2
C₂×C₂₃×#463	2
C₂×C₂₃×#449	2
C₂×C₂₃×#447	2
C₂×C₄×D₈×C₂₃	2
C₂×C₂₃×#436	2
C₂×C₂₃×#417	2
C₂×C₂₃×#418	2
C₂×#3322	23

Subgroups — C2×C23×#3322 #19208768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3322 #19208768