Subgroups — C₂×C₂₃×#3346 #19208864

Order 5888.

1942 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×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3346	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#554	—	2	4	no	—
21	C₂₃×#554	C₂²	1	8	yes	complemented
22	C₂₃×#553	—	2	4	no	—
23	C₂₃×#553	C₂²	1	8	yes	—
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	—	2	1	no	—
26	C₂×C₂₃×#125	—	2	1	no	—
27	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#123	—	2	1	no	—
29	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
31	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#121	—	2	1	no	—
34	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	—	2	1	no	—
38	C₂×C₄×D₄×C₂₃	—	2	1	no	—
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#501	C₂²	1	8	yes	complemented
46	C₂₃×#485	C₂²	1	8	yes	complemented
47	C₂₃×#484	C₂²	1	8	yes	complemented
48	C₂₃×#481	C₂²	1	8	yes	complemented
49	C₂₃×#480	C₂²	1	8	yes	complemented
50	C₂₃×#479	C₂²	1	8	yes	complemented
51	C₂₃×#474	C₂²	1	8	yes	complemented
52	C₂₃×#468	C₂²	1	8	yes	complemented
53	C₂₃×#465	C₂²	1	8	yes	complemented
54	C₂₃×#440	C₂²	1	8	yes	complemented
55	C₂₃×#435	C₂²	1	8	yes	complemented
56	C₂₃×#428	C₂²	1	8	yes	complemented
57	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#107	C₂²	1	8	yes	complemented
64	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	—	2	1	no	—
78	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	—	2	1	no	—
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×SD₁₆×C₂₃	—	2	4	no	—
90	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂×M₁₆×C₂₃	—	2	4	no	—
92	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₂₃	—	2	4	no	—
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂₃×C₄⋊Q₈	—	2	2	no	—
100	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₂₃×#126	—	2	8	no	—
102	C₂₃×#125	—	2	8	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	C₂³	1	4	yes	—
105	C₂₃×#123	—	2	8	no	—
106	C₂₃×C₂²⋊Q₈	—	2	2	no	—
107	C₂₃×C₂²⋊Q₈	—	2	2	no	—
108	C₂₃×C₂²⋊Q₈	—	2	8	no	—
109	C₂₃×C₂²⋊Q₈	—	2	8	no	—
110	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
111	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
112	C₂₃×#121	—	2	8	no	—
113	C₂₃×#121	—	2	2	no	—
114	C₂₃×#121	—	2	2	no	—
115	C₂₃×#121	C₂³	1	4	yes	—
116	C₂₃×#121	C₂³	1	4	yes	—
117	C₄×Q₈×C₂₃	—	2	2	no	—
118	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
119	C₄×D₄×C₂₃	—	2	8	no	—
120	C₄×D₄×C₂₃	—	2	8	no	—
121	C₄×D₄×C₂₃	—	2	2	no	—
122	C₄×D₄×C₂₃	D₄	1	4	yes	—
123	C₄×D₄×C₂₃	C₂³	1	4	yes	—
124	C₄×D₄×C₂₃	C₂³	1	4	yes	—
125	C₂₃×#117	—	2	2	no	—
126	C₂₃×#117	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
128	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
129	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
130	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
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	1	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
157	C₂×C₄²×C₂₃	—	2	1	no	—
158	C₂×C₄²×C₂₃	—	2	1	no	—
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#107	C₂³	1	4	yes	—
161	C₂₃×#107	C₂³	1	4	yes	—
162	C₂₃×#107	C₂³	1	4	yes	—
163	C₂₃×#107	C₂³	1	4	yes	—
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×#106	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×#102	C₂³	1	4	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×#102	C₂³	1	4	yes	—
176	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₂₃×#97	C₂³	1	4	yes	—
179	C₂⁴×C₂₃	—	2	1	no	—
180	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	4	no	—
184	C₂×Q₈×C₂₃	—	2	2	no	—
185	C₂×Q₈×C₂₃	—	2	2	no	—
186	C₂×Q₈×C₂₃	—	8	2	no	—
187	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
188	C₂×D₄×C₂₃	—	2	4	no	—
189	C₂×D₄×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	4	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	4	4	no	—
195	C₂×D₄×C₂₃	—	8	2	no	—
196	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
197	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₂₃	—	2	2	no	—
199	C₂²×C₄×C₂₃	—	2	2	no	—
200	C₂²×C₄×C₂₃	—	2	2	no	—
201	C₂²×C₄×C₂₃	—	2	2	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	2	1	no	—
208	C₂²×C₄×C₂₃	—	2	1	no	—
209	C₂²×C₄×C₂₃	—	2	4	no	—
210	C₂²×C₄×C₂₃	—	2	4	no	—
211	C₂²×C₄×C₂₃	—	2	4	no	—
212	C₂²×C₄×C₂₃	—	2	4	no	—
213	C₂²×C₄×C₂₃	—	8	2	no	—
214	C₂²×C₄×C₂₃	—	8	2	no	—
215	C₂²×C₄×C₂₃	—	8	2	no	—
216	C₂²×C₄×C₂₃	—	8	2	no	—
217	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	SD₁₆×C₂₃	—	2	8	no	—
227	M₁₆×C₂₃	—	2	8	no	—
228	C₂×C₈×C₂₃	—	2	2	no	—
229	C₂×C₈×C₂₃	—	2	2	no	—
230	C₂×C₈×C₂₃	—	2	2	no	—
231	C₂×C₈×C₂₃	—	2	8	no	—
232	C₂×C₈×C₂₃	#41	1	4	yes	—
233	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
234	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	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	1	no	—
252	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	4	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
266	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
267	C₄²×C₂₃	—	2	4	no	—
268	C₄²×C₂₃	—	2	4	no	—
269	C₄²×C₂₃	C₂×D₄	1	2	yes	—
270	C₄²×C₂₃	C₂⁴	1	2	yes	—
271	C₂×#3346	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	4	2	no	—
279	C₂³×C₂₃	—	4	2	no	—
280	C₂³×C₂₃	—	4	2	no	—
281	C₂³×C₂₃	#137	1	4	yes	—
282	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
283	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
284	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₂₃	—	2	2	no	—
286	Q₈×C₂₃	—	2	2	no	—
287	Q₈×C₂₃	—	4	2	no	—
288	Q₈×C₂₃	—	8	4	no	—
289	D₄×C₂₃	—	2	8	no	—
290	D₄×C₂₃	—	2	2	no	—
291	D₄×C₂₃	—	2	2	no	—
292	D₄×C₂₃	—	4	8	no	—
293	D₄×C₂₃	—	4	2	no	—
294	D₄×C₂₃	—	8	4	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	4	no	—
300	C₂×C₄×C₂₃	—	2	4	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	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	2	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	—	4	2	no	—
313	C₂×C₄×C₂₃	—	4	2	no	—
314	C₂×C₄×C₂₃	—	4	2	no	—
315	C₂×C₄×C₂₃	—	4	2	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	2	no	—
318	C₂×C₄×C₂₃	—	4	2	no	—
319	C₂×C₄×C₂₃	—	8	4	no	—
320	C₂×C₄×C₂₃	—	8	4	no	—
321	C₂×C₄×C₂₃	—	8	4	no	—
322	C₂×C₄×C₂₃	—	8	4	no	—
323	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
329	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
330	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
331	C₈×C₂₃	—	2	2	no	—
332	C₈×C₂₃	—	2	2	no	—
333	C₈×C₂₃	—	2	2	no	—
334	C₈×C₂₃	C₂×#41	1	4	yes	—
335	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
336	C₂×#553	C₂×C₂₃	1	1	yes	characteristic
337	#3346	C₂×C₂₃	1	16	yes	direct product factor
338	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#484	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
341	C₂×#485	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂×#474	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
347	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
348	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂²×C₂₃	—	2	8	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	4	4	no	—
358	C₂²×C₂₃	—	4	2	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	8	4	no	—
362	C₂²×C₂₃	#547	1	2	yes	—
363	C₂²×C₂₃	C₂×#137	1	4	yes	—
364	C₂²×C₂₃	C₂×#137	1	2	yes	—
365	C₂²×C₂₃	#576	1	2	yes	—
366	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	—	2	2	no	—
369	C₄×C₂₃	—	2	2	no	—
370	C₄×C₂₃	—	2	2	no	—
371	C₄×C₂₃	—	4	2	no	—
372	C₄×C₂₃	—	4	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	#547	1	2	yes	—
379	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
380	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
381	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
382	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
383	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
384	#554	—	2	4	no	—
385	#554	C₂²×C₂₃	1	8	yes	complemented
386	#553	—	2	4	no	—
387	#553	C₂²×C₂₃	1	8	yes	—
388	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#126	—	2	1	no	—
390	C₂×#125	—	2	1	no	—
391	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×#123	—	2	1	no	—
393	C₂×C₂²⋊Q₈	—	2	1	no	—
394	C₂×C₂²⋊Q₈	—	2	1	no	—
395	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×#121	—	2	1	no	—
398	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₄×D₄	—	2	1	no	—
402	C₂×C₄×D₄	—	2	1	no	—
403	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
409	#501	C₂²×C₂₃	1	8	yes	complemented
410	#485	C₂²×C₂₃	1	8	yes	complemented
411	#484	C₂²×C₂₃	1	8	yes	complemented
412	#481	C₂²×C₂₃	1	8	yes	complemented
413	#480	C₂²×C₂₃	1	8	yes	complemented
414	#479	C₂²×C₂₃	1	8	yes	complemented
415	#474	C₂²×C₂₃	1	8	yes	complemented
416	#468	C₂²×C₂₃	1	8	yes	complemented
417	#465	C₂²×C₂₃	1	8	yes	complemented
418	#440	C₂²×C₂₃	1	8	yes	complemented
419	#435	C₂²×C₂₃	1	8	yes	complemented
420	#428	C₂²×C₂₃	1	8	yes	complemented
421	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#107	C₂²×C₂₃	1	8	yes	complemented
428	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄⋊C₈	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×#102	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×C₂₃	—	2	4	no	—
442	C₂×C₂₃	—	4	2	no	—
443	C₂×C₂₃	—	8	2	no	—
444	C₂×C₂₃	#3346	1	4	yes	direct product factor
445	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
446	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
447	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
453	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
460	C₂×SD₁₆	—	2	4	no	—
461	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
462	C₂×M₁₆	—	2	4	no	—
463	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
464	C₂²×C₈	—	2	4	no	—
465	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
467	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₄⋊Q₈	—	2	2	no	—
471	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
472	#126	—	2	8	no	—
473	#125	—	2	8	no	—
474	#125	—	2	2	no	—
475	#125	C₂³×C₂₃	1	4	yes	—
476	#123	—	2	8	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	—	2	8	no	—
481	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
482	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
483	#121	—	2	8	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	C₂³×C₂₃	1	4	yes	—
487	#121	C₂³×C₂₃	1	4	yes	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	8	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	D₄×C₂₃	1	4	yes	—
494	C₄×D₄	C₂³×C₂₃	1	4	yes	—
495	C₄×D₄	C₂³×C₂₃	1	4	yes	—
496	#117	—	2	2	no	—
497	#117	C₂³×C₂₃	1	4	yes	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	2	no	—
502	C₂×C₄⋊C₄	—	2	2	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	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	D₄×C₂₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₂₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	#107	C₂³×C₂₃	1	4	yes	—
532	#107	C₂³×C₂₃	1	4	yes	—
533	#107	C₂³×C₂₃	1	4	yes	—
534	#107	C₂³×C₂₃	1	4	yes	—
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	#106	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	#102	C₂³×C₂₃	1	4	yes	—
545	#102	C₂³×C₂₃	1	4	yes	—
546	#102	C₂³×C₂₃	1	4	yes	—
547	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
549	#97	C₂³×C₂₃	1	4	yes	—
550	C₂₃	C₂×#3346	1	1	yes	characteristic, direct product factor, Sylow
551	C₂⁴	—	2	1	no	—
552	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
553	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	8	2	no	—
559	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	8	2	no	—
568	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
569	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	8	2	no	—
586	C₂²×C₄	—	8	2	no	—
587	C₂²×C₄	—	8	2	no	—
588	C₂²×C₄	—	8	2	no	—
589	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	SD₁₆	—	2	8	no	—
599	M₁₆	—	2	8	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	2	no	—
602	C₂×C₈	—	2	2	no	—
603	C₂×C₈	—	2	8	no	—
604	C₂×C₈	#41×C₂₃	1	4	yes	—
605	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
606	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
607	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
608	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	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	1	no	—
624	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
625	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
638	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	C₂×D₄×C₂₃	1	2	yes	—
642	C₄²	C₂⁴×C₂₃	1	2	yes	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	C₂₃×#137	1	4	yes	—
653	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
654	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
655	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	D₄	—	2	8	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	8	no	—
664	D₄	—	4	2	no	—
665	D₄	—	8	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	4	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	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
696	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
697	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
699	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
700	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
701	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	2	no	—
704	C₈	—	2	2	no	—
705	C₈	C₂×#41×C₂₃	1	4	yes	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	8	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	8	4	no	—
717	C₂²	C₂₃×#547	1	2	yes	—
718	C₂²	C₂×C₂₃×#137	1	4	yes	—
719	C₂²	C₂×C₂₃×#137	1	2	yes	—
720	C₂²	C₂₃×#576	1	2	yes	—
721	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	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	C₂₃×#547	1	2	yes	—
734	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
735	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂	—	2	4	no	—
737	C₂	—	4	2	no	—
738	C₂	—	8	2	no	—
739	C₂	C₂₃×#3346	1	4	yes	direct product factor
740	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
741	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
742	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#553	C₂
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×#554	C₂	semidirect
3. C₂₃×#3346	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#484	C₂	semidirect
6. C₂×C₂₃×#481	C₂	semidirect
7. C₂×C₂₃×#485	C₂	semidirect
8. C₂×C₂₃×#480	C₂	semidirect
9. C₂×C₂₃×#479	C₂	semidirect
10. C₂×C₂₃×#474	C₂	semidirect
11. C₂×C₂₃×#468	C₂	semidirect
12. C₂×C₂₃×#465	C₂	semidirect
13. C₂×C₂₃×#440	C₂	semidirect
14. C₂×C₂₃×#435	C₂	semidirect
15. C₂×C₂₃×#428	C₂	semidirect
16. C₂²×C₂₃×#107	C₂	semidirect
21. C₂₃×#554	C₂²	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#485	C₂²	semidirect
47. C₂₃×#484	C₂²	semidirect
48. C₂₃×#481	C₂²	semidirect
49. C₂₃×#480	C₂²	semidirect
50. C₂₃×#479	C₂²	semidirect
51. C₂₃×#474	C₂²	semidirect
52. C₂₃×#468	C₂²	semidirect
53. C₂₃×#465	C₂²	semidirect
54. C₂₃×#440	C₂²	semidirect
55. C₂₃×#435	C₂²	semidirect
56. C₂₃×#428	C₂²	semidirect
63. C₂×C₂₃×#107	C₂²	semidirect
271. C₂×#3346	C₂₃	direct (N × H)
335. C₂×#554	C₂×C₂₃	semidirect
337. #3346	C₂×C₂₃	direct (N × H)
338. C₂×#501	C₂×C₂₃	semidirect
339. C₂×#484	C₂×C₂₃	semidirect
340. C₂×#481	C₂×C₂₃	semidirect
341. C₂×#485	C₂×C₂₃	semidirect
342. C₂×#480	C₂×C₂₃	semidirect
343. C₂×#479	C₂×C₂₃	semidirect
344. C₂×#474	C₂×C₂₃	semidirect
345. C₂×#468	C₂×C₂₃	semidirect
346. C₂×#465	C₂×C₂₃	semidirect
347. C₂×#440	C₂×C₂₃	semidirect
348. C₂×#435	C₂×C₂₃	semidirect
349. C₂×#428	C₂×C₂₃	semidirect
350. C₂²×#107	C₂×C₂₃	semidirect
385. #554	C₂²×C₂₃	semidirect
409. #501	C₂²×C₂₃	semidirect
410. #485	C₂²×C₂₃	semidirect
411. #484	C₂²×C₂₃	semidirect
412. #481	C₂²×C₂₃	semidirect
413. #480	C₂²×C₂₃	semidirect
414. #479	C₂²×C₂₃	semidirect
415. #474	C₂²×C₂₃	semidirect
416. #468	C₂²×C₂₃	semidirect
417. #465	C₂²×C₂₃	semidirect
418. #440	C₂²×C₂₃	semidirect
419. #435	C₂²×C₂₃	semidirect
420. #428	C₂²×C₂₃	semidirect
427. C₂×#107	C₂²×C₂₃	semidirect
444. C₂×C₂₃	#3346	direct (N × H)
550. C₂₃	C₂×#3346	direct (N × H)
739. C₂	C₂₃×#3346	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×#554	2
C₂×C₂₃×#553	2
C₂₃×#3346	2
C₂×C₂₃×#501	2
C₂×C₂₃×#484	2
C₂×C₂₃×#481	2
C₂×C₂₃×#485	2
C₂×C₂₃×#480	2
C₂×C₂₃×#479	2
C₂×C₂₃×#474	2
C₂×C₂₃×#468	2
C₂×C₂₃×#465	2
C₂×C₂₃×#440	2
C₂×C₂₃×#435	2
C₂×C₂₃×#428	2
C₂²×C₂₃×#107	2
C₂×#3346	23

Subgroups — C2×C23×#3346 #19208864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3346 #19208864