Subgroups — C₂×C₂₃×#3120 #19208175

Order 5888.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#520	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3120	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic
11	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#541	—	2	4	no	—
23	C₂₃×#541	C₂²	1	8	yes	complemented
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	—	2	1	no	—
26	C₂×C₂₃×#126	—	2	1	no	—
27	C₂×C₂₃×#125	—	2	1	no	—
28	C₂×C₂₃×#125	—	2	1	no	—
29	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₃×#520	—	2	4	no	—
33	C₂₃×#520	C₂²	1	8	yes	—
34	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	—	2	1	no	—
39	C₂×C₄×D₄×C₂₃	—	2	1	no	—
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#117	—	2	1	no	—
43	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#484	C₂²	1	8	yes	complemented
47	C₂₃×#483	C₂²	1	8	yes	complemented
48	C₂₃×#479	C₂²	1	8	yes	complemented
49	C₂₃×#478	C₂²	1	8	yes	complemented
50	C₂₃×#462	C₂²	1	8	yes	complemented
51	C₂₃×#461	C₂²	1	8	yes	complemented
52	C₂₃×#452	C₂²	1	8	yes	—
53	C₂₃×#452	C₂²	1	8	yes	—
54	C₂₃×#441	C₂²	1	8	yes	complemented
55	C₂₃×#440	C₂²	1	8	yes	complemented
56	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
57	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
58	C₂₃×#433	C₂²	1	8	yes	complemented
59	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#103	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	2	4	no	—
78	C₂×#41×C₂₃	—	2	4	no	—
79	C₂×#41×C₂₃	—	2	2	no	—
80	C₂×#41×C₂₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	—	2	1	no	—
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	—	2	1	no	—
89	C₂³×C₄×C₂₃	—	2	1	no	—
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂×Q₁₆×C₂₃	—	2	4	no	—
92	C₂×Q₁₆×C₂₃	—	2	4	no	—
93	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
94	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₂₃	—	2	4	no	—
96	C₂×SD₁₆×C₂₃	—	2	4	no	—
97	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×C₄⋊Q₈	—	2	2	no	—
104	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₂₃×#126	—	2	8	no	—
106	C₂₃×#126	—	2	8	no	—
107	C₂₃×#125	—	2	8	no	—
108	C₂₃×#125	—	2	8	no	—
109	C₂₃×#125	—	2	2	no	—
110	C₂₃×#125	C₂³	1	4	yes	—
111	C₂₃×C₂²⋊Q₈	—	2	2	no	—
112	C₂₃×C₂²⋊Q₈	—	2	2	no	—
113	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₄×Q₈×C₂₃	—	2	2	no	—
116	C₄×Q₈×C₂₃	—	2	2	no	—
117	C₄×Q₈×C₂₃	—	2	2	no	—
118	C₄×Q₈×C₂₃	—	2	2	no	—
119	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
120	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
121	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
122	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
123	C₄×D₄×C₂₃	—	2	8	no	—
124	C₄×D₄×C₂₃	—	2	8	no	—
125	C₄×D₄×C₂₃	—	2	2	no	—
126	C₄×D₄×C₂₃	—	2	2	no	—
127	C₄×D₄×C₂₃	C₂³	1	4	yes	—
128	C₄×D₄×C₂₃	C₂³	1	4	yes	—
129	C₂₃×#117	—	2	8	no	—
130	C₂₃×#117	D₄	1	4	yes	—
131	C₂₃×#117	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
140	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
141	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
145	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₂₃	—	2	1	no	—
159	C₂×C₄²×C₂₃	—	2	1	no	—
160	C₂×C₄²×C₂₃	—	2	1	no	—
161	C₂×C₄²×C₂₃	—	2	1	no	—
162	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂₃×#107	C₂³	1	4	yes	—
165	C₂₃×#107	C₂³	1	4	yes	—
166	C₂₃×#106	C₂³	1	4	yes	—
167	C₂₃×#106	C₂³	1	4	yes	—
168	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
169	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#103	C₂³	1	4	yes	—
172	C₂₃×#103	C₂³	1	4	yes	—
173	C₂₃×#103	C₂³	1	4	yes	—
174	C₂₃×#103	C₂³	1	4	yes	—
175	C₂₃×#103	C₂³	1	4	yes	—
176	C₂₃×#102	C₂³	1	4	yes	—
177	C₂₃×#102	C₂³	1	4	yes	—
178	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₂₃×#97	C₂³	1	4	yes	—
181	C₄×C₈×C₂₃	C₂³	1	4	yes	—
182	C₂⁴×C₂₃	—	2	1	no	—
183	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
184	#41×C₂₃	—	2	16	no	—
185	#41×C₂₃	—	2	8	no	—
186	#41×C₂₃	—	2	8	no	—
187	C₂×Q₈×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	—	2	1	no	—
189	C₂×Q₈×C₂₃	—	2	1	no	—
190	C₂×Q₈×C₂₃	—	2	2	no	—
191	C₂×Q₈×C₂₃	—	2	2	no	—
192	C₂×Q₈×C₂₃	—	2	2	no	—
193	C₂×Q₈×C₂₃	—	2	2	no	—
194	C₂×Q₈×C₂₃	—	2	2	no	—
195	C₂×Q₈×C₂₃	#41	1	4	yes	—
196	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
199	C₂×D₄×C₂₃	—	2	8	no	—
200	C₂×D₄×C₂₃	—	2	4	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	2	no	—
203	C₂×D₄×C₂₃	#41	1	4	yes	—
204	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	—	2	8	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	2	4	no	—
208	C₂²×C₄×C₂₃	—	2	2	no	—
209	C₂²×C₄×C₂₃	—	2	2	no	—
210	C₂²×C₄×C₂₃	—	2	1	no	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	1	no	—
213	C₂²×C₄×C₂₃	—	2	1	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	4	no	—
217	C₂²×C₄×C₂₃	—	2	4	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	—	8	2	no	—
220	C₂²×C₄×C₂₃	—	8	2	no	—
221	C₂²×C₄×C₂₃	—	8	2	no	—
222	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₂₃	—	2	8	no	—
231	Q₁₆×C₂₃	—	2	8	no	—
232	SD₁₆×C₂₃	—	2	8	no	—
233	SD₁₆×C₂₃	—	2	8	no	—
234	C₂×C₈×C₂₃	—	2	2	no	—
235	C₂×C₈×C₂₃	—	2	2	no	—
236	C₂×C₈×C₂₃	—	2	2	no	—
237	C₂×C₈×C₂₃	—	2	2	no	—
238	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	1	no	—
256	C₄⋊C₄×C₂₃	—	2	1	no	—
257	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
258	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂²⋊C₄×C₂₃	—	2	4	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
268	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
269	C₄²×C₂₃	—	2	4	no	—
270	C₄²×C₂₃	—	2	4	no	—
271	C₄²×C₂₃	—	2	4	no	—
272	C₄²×C₂₃	—	2	4	no	—
273	C₄²×C₂₃	C₂×D₄	1	2	yes	—
274	C₄²×C₂₃	C₂×D₄	1	2	yes	—
275	C₄²×C₂₃	C₂⁴	1	2	yes	—
276	C₄²×C₂₃	C₂⁴	1	2	yes	—
277	C₂×#3120	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	4	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	4	2	no	—
284	C₂³×C₂₃	—	4	2	no	—
285	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₂₃	—	2	4	no	—
288	Q₈×C₂₃	—	2	2	no	—
289	Q₈×C₂₃	—	2	2	no	—
290	Q₈×C₂₃	—	2	2	no	—
291	Q₈×C₂₃	—	2	2	no	—
292	Q₈×C₂₃	—	2	2	no	—
293	Q₈×C₂₃	—	4	2	no	—
294	Q₈×C₂₃	—	4	2	no	—
295	Q₈×C₂₃	C₂×#41	1	4	yes	—
296	D₄×C₂₃	—	2	16	no	—
297	D₄×C₂₃	—	2	4	no	—
298	D₄×C₂₃	—	2	2	no	—
299	D₄×C₂₃	C₂×#41	1	4	yes	—
300	C₂×C₄×C₂₃	—	2	16	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	4	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	4	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	4	2	no	—
318	C₂×C₄×C₂₃	—	4	2	no	—
319	C₂×C₄×C₂₃	—	4	2	no	—
320	C₂×C₄×C₂₃	—	4	2	no	—
321	C₂×C₄×C₂₃	—	4	2	no	—
322	C₂×C₄×C₂₃	—	4	2	no	—
323	C₂×C₄×C₂₃	—	8	4	no	—
324	C₂×C₄×C₂₃	—	8	4	no	—
325	C₂×C₄×C₂₃	—	8	4	no	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
334	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
335	C₈×C₂₃	—	2	2	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	—	2	2	no	—
339	C₂×#541	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#520	C₂×C₂₃	1	1	yes	characteristic
341	#3120	C₂×C₂₃	1	16	yes	direct product factor
342	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂×#483	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
347	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
348	C₂×#452	C₂×C₂₃	1	1	yes	characteristic
349	C₂×#452	C₂×C₂₃	1	1	yes	characteristic
350	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	4	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	4	4	no	—
360	C₂²×C₂₃	—	4	8	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	#525	1	2	yes	—
364	C₂²×C₂₃	#577	1	2	yes	—
365	C₂²×C₂₃	#578	1	2	yes	—
366	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	—	2	4	no	—
369	C₄×C₂₃	—	2	2	no	—
370	C₄×C₂₃	—	2	2	no	—
371	C₄×C₂₃	—	2	2	no	—
372	C₄×C₂₃	—	2	2	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	—	4	2	no	—
376	C₄×C₂₃	—	4	2	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	—	4	2	no	—
379	C₄×C₂₃	#525	1	2	yes	—
380	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
381	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
382	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
383	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
384	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
385	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
386	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
387	#541	—	2	4	no	—
388	#541	C₂²×C₂₃	1	8	yes	complemented
389	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×#126	—	2	1	no	—
391	C₂×#126	—	2	1	no	—
392	C₂×#125	—	2	1	no	—
393	C₂×#125	—	2	1	no	—
394	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
397	#520	—	2	4	no	—
398	#520	C₂²×C₂₃	1	8	yes	—
399	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×C₄×D₄	—	2	1	no	—
404	C₂×C₄×D₄	—	2	1	no	—
405	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×#117	—	2	1	no	—
408	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	—	2	1	no	—
410	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
411	#484	C₂²×C₂₃	1	8	yes	complemented
412	#483	C₂²×C₂₃	1	8	yes	complemented
413	#479	C₂²×C₂₃	1	8	yes	complemented
414	#478	C₂²×C₂₃	1	8	yes	complemented
415	#462	C₂²×C₂₃	1	8	yes	complemented
416	#461	C₂²×C₂₃	1	8	yes	complemented
417	#452	C₂²×C₂₃	1	8	yes	—
418	#452	C₂²×C₂₃	1	8	yes	—
419	#441	C₂²×C₂₃	1	8	yes	complemented
420	#440	C₂²×C₂₃	1	8	yes	complemented
421	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
422	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
423	#433	C₂²×C₂₃	1	8	yes	complemented
424	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×C₂₃	—	4	2	no	—
443	C₂×C₂₃	—	4	4	no	—
444	C₂×C₂₃	#3120	1	4	yes	direct product factor
445	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
446	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
447	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
448	C₂×#41	—	2	4	no	—
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	2	no	—
451	C₂×#41	C₂³×C₂₃	1	4	yes	—
452	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×Q₁₆	—	2	4	no	—
463	C₂×Q₁₆	—	2	4	no	—
464	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
465	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
466	C₂×SD₁₆	—	2	4	no	—
467	C₂×SD₁₆	—	2	4	no	—
468	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
469	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
470	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
476	#126	—	2	8	no	—
477	#126	—	2	8	no	—
478	#125	—	2	8	no	—
479	#125	—	2	8	no	—
480	#125	—	2	2	no	—
481	#125	C₂³×C₂₃	1	4	yes	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
485	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
491	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
492	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
493	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
494	C₄×D₄	—	2	8	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	C₂³×C₂₃	1	4	yes	—
499	C₄×D₄	C₂³×C₂₃	1	4	yes	—
500	#117	—	2	8	no	—
501	#117	D₄×C₂₃	1	4	yes	—
502	#117	C₂³×C₂₃	1	4	yes	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	2	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	8	no	—
516	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
535	#107	C₂³×C₂₃	1	4	yes	—
536	#107	C₂³×C₂₃	1	4	yes	—
537	#106	C₂³×C₂₃	1	4	yes	—
538	#106	C₂³×C₂₃	1	4	yes	—
539	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
540	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
541	#103	C₂³×C₂₃	1	4	yes	—
542	#103	C₂³×C₂₃	1	4	yes	—
543	#103	C₂³×C₂₃	1	4	yes	—
544	#103	C₂³×C₂₃	1	4	yes	—
545	#103	C₂³×C₂₃	1	4	yes	—
546	#103	C₂³×C₂₃	1	4	yes	—
547	#102	C₂³×C₂₃	1	4	yes	—
548	#102	C₂³×C₂₃	1	4	yes	—
549	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
551	#97	C₂³×C₂₃	1	4	yes	—
552	C₄×C₈	C₂³×C₂₃	1	4	yes	—
553	C₂₃	C₂×#3120	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁴	—	2	1	no	—
555	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
556	#41	—	2	16	no	—
557	#41	—	2	8	no	—
558	#41	—	2	8	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	2	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	#41×C₂₃	1	4	yes	—
568	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
569	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
570	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
571	C₂×D₄	—	2	8	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	#41×C₂₃	1	4	yes	—
576	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
577	C₂²×C₄	—	2	8	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	—	8	2	no	—
593	C₂²×C₄	—	8	2	no	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
602	Q₁₆	—	2	8	no	—
603	Q₁₆	—	2	8	no	—
604	SD₁₆	—	2	8	no	—
605	SD₁₆	—	2	8	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
611	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
612	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
613	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
630	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
631	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
640	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	4	no	—
645	C₄²	C₂×D₄×C₂₃	1	2	yes	—
646	C₄²	C₂×D₄×C₂₃	1	2	yes	—
647	C₄²	C₂⁴×C₂₃	1	2	yes	—
648	C₄²	C₂⁴×C₂₃	1	2	yes	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
657	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	4	2	no	—
665	Q₈	—	4	2	no	—
666	Q₈	C₂×#41×C₂₃	1	4	yes	—
667	D₄	—	2	16	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	4	no	—
670	D₄	C₂×#41×C₂₃	1	4	yes	—
671	C₂×C₄	—	2	16	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
704	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
705	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	8	no	—
718	C₂²	C₂₃×#525	1	2	yes	—
719	C₂²	C₂₃×#577	1	2	yes	—
720	C₂²	C₂₃×#578	1	2	yes	—
721	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	4	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	2	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	C₂₃×#525	1	2	yes	—
735	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
736	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
737	C₂	—	4	2	no	—
738	C₂	—	4	4	no	—
739	C₂	C₂₃×#3120	1	4	yes	direct product factor
740	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
741	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
742	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#541	C₂	semidirect
3. C₂₃×#3120	C₂	direct (N × H)
4. C₂×C₂₃×#484	C₂	semidirect
5. C₂×C₂₃×#483	C₂	semidirect
6. C₂×C₂₃×#479	C₂	semidirect
7. C₂×C₂₃×#478	C₂	semidirect
8. C₂×C₂₃×#462	C₂	semidirect
9. C₂×C₂₃×#461	C₂	semidirect
12. C₂×C₂₃×#441	C₂	semidirect
13. C₂×C₂₃×#440	C₂	semidirect
14. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
15. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
16. C₂×C₂₃×#433	C₂	semidirect
23. C₂₃×#541	C₂²	semidirect
46. C₂₃×#484	C₂²	semidirect
47. C₂₃×#483	C₂²	semidirect
48. C₂₃×#479	C₂²	semidirect
49. C₂₃×#478	C₂²	semidirect
50. C₂₃×#462	C₂²	semidirect
51. C₂₃×#461	C₂²	semidirect
54. C₂₃×#441	C₂²	semidirect
55. C₂₃×#440	C₂²	semidirect
56. C₄×Q₁₆×C₂₃	C₂²	semidirect
57. C₄×SD₁₆×C₂₃	C₂²	semidirect
58. C₂₃×#433	C₂²	semidirect
277. C₂×#3120	C₂₃	direct (N × H)
339. C₂×#541	C₂×C₂₃	semidirect
341. #3120	C₂×C₂₃	direct (N × H)
342. C₂×#484	C₂×C₂₃	semidirect
343. C₂×#483	C₂×C₂₃	semidirect
344. C₂×#479	C₂×C₂₃	semidirect
345. C₂×#478	C₂×C₂₃	semidirect
346. C₂×#462	C₂×C₂₃	semidirect
347. C₂×#461	C₂×C₂₃	semidirect
350. C₂×#441	C₂×C₂₃	semidirect
351. C₂×#440	C₂×C₂₃	semidirect
352. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
353. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
354. C₂×#433	C₂×C₂₃	semidirect
388. #541	C₂²×C₂₃	semidirect
411. #484	C₂²×C₂₃	semidirect
412. #483	C₂²×C₂₃	semidirect
413. #479	C₂²×C₂₃	semidirect
414. #478	C₂²×C₂₃	semidirect
415. #462	C₂²×C₂₃	semidirect
416. #461	C₂²×C₂₃	semidirect
419. #441	C₂²×C₂₃	semidirect
420. #440	C₂²×C₂₃	semidirect
421. C₄×Q₁₆	C₂²×C₂₃	semidirect
422. C₄×SD₁₆	C₂²×C₂₃	semidirect
423. #433	C₂²×C₂₃	semidirect
444. C₂×C₂₃	#3120	direct (N × H)
553. C₂₃	C₂×#3120	direct (N × H)
739. C₂	C₂₃×#3120	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×#541	2
C₂×C₂₃×#520	2
C₂₃×#3120	2
C₂×C₂₃×#484	2
C₂×C₂₃×#483	2
C₂×C₂₃×#479	2
C₂×C₂₃×#478	2
C₂×C₂₃×#462	2
C₂×C₂₃×#461	2
C₂×C₂₃×#452	2
C₂×C₂₃×#441	2
C₂×C₂₃×#440	2
C₂×C₄×Q₁₆×C₂₃	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×C₂₃×#433	2
C₂×#3120	23

Subgroups — C2×C23×#3120 #19208175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3120 #19208175