Subgroups — C₂×C₂₃×#3323 #19208769

Order 5888.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3323	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×SD₁₆×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×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×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×#552	—	2	4	no	—
25	C₂₃×#552	C₂²	1	8	yes	complemented
26	C₂₃×#546	—	2	4	no	—
27	C₂₃×#546	C₂²	1	8	yes	—
28	C₂×C₂₃×#126	—	2	1	no	—
29	C₂×C₂₃×#125	—	2	1	no	—
30	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#123	—	2	1	no	—
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂₃×#121	—	2	1	no	—
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#120	—	2	1	no	—
40	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#117	—	2	1	no	—
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×#481	C₂²	1	8	yes	complemented
50	C₂₃×#478	C₂²	1	8	yes	complemented
51	C₂₃×#470	C₂²	1	8	yes	complemented
52	C₂₃×#468	C₂²	1	8	yes	complemented
53	C₂₃×#464	C₂²	1	8	yes	complemented
54	C₂₃×#452	C₂²	1	8	yes	complemented
55	C₂₃×#450	C₂²	1	8	yes	complemented
56	C₄×SD₁₆×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×#106	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#418	C₂²	1	8	yes	complemented
63	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×#103	C₂²	1	1	yes	characteristic, complemented
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
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×Q₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	—	2	4	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	2	no	—
89	C₂²×D₄×C₂₃	—	4	2	no	—
90	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
91	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	—	2	1	no	—
95	C₂³×C₄×C₂₃	—	2	1	no	—
96	C₂³×C₄×C₂₃	—	2	1	no	—
97	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×Q₁₆×C₂₃	—	4	2	no	—
100	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
101	C₂×SD₁₆×C₂₃	—	2	4	no	—
102	C₂×SD₁₆×C₂₃	—	4	2	no	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×M₁₆×C₂₃	—	4	2	no	—
106	C₂×M₁₆×C₂₃	—	4	2	no	—
107	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
108	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
109	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×#126	—	2	8	no	—
114	C₂₃×#125	—	2	8	no	—
115	C₂₃×#125	—	2	2	no	—
116	C₂₃×#125	C₂³	1	4	yes	complemented
117	C₂₃×#124	—	2	2	no	—
118	C₂₃×#124	C₂³	1	4	yes	—
119	C₂₃×#123	—	2	8	no	—
120	C₂₃×#123	—	2	8	no	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	2	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	8	no	—
129	C₂₃×#121	C₂³	1	4	yes	—
130	C₂₃×#120	—	2	8	no	—
131	C₄×Q₈×C₂₃	—	2	2	no	—
132	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
133	C₄×D₄×C₂₃	—	2	2	no	—
134	C₄×D₄×C₂₃	D₄	1	4	yes	—
135	C₄×D₄×C₂₃	C₂³	1	4	yes	—
136	C₄×D₄×C₂₃	C₂³	1	4	yes	—
137	C₂₃×#117	—	2	2	no	—
138	C₂₃×#117	—	2	8	no	—
139	C₂₃×#117	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₂₃	—	2	2	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	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	8	no	—
163	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₂₃	—	2	1	no	—
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×#106	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×#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×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	4	no	—
188	C₂⁴×C₂₃	—	4	4	no	—
189	C₂⁴×C₂₃	—	4	4	no	—
190	C₂⁴×C₂₃	—	8	2	no	—
191	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
193	#41×C₂₃	—	2	8	no	—
194	#41×C₂₃	—	4	4	no	—
195	#41×C₂₃	—	4	8	no	—
196	C₂×Q₈×C₂₃	—	2	1	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	—	2	2	no	—
201	C₂×Q₈×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
203	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
204	C₂×D₄×C₂₃	—	2	8	no	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	2	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	—	4	4	no	—
214	C₂×D₄×C₂₃	—	4	8	no	—
215	C₂×D₄×C₂₃	—	4	2	no	—
216	C₂×D₄×C₂₃	—	4	4	no	—
217	C₂×D₄×C₂₃	—	4	4	no	—
218	C₂×D₄×C₂₃	—	8	2	no	—
219	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
220	C₂×D₄×C₂₃	#41	1	4	yes	—
221	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	—	2	2	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	2	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	2	4	no	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	4	no	—
235	C₂²×C₄×C₂₃	—	2	4	no	—
236	C₂²×C₄×C₂₃	—	4	4	no	—
237	C₂²×C₄×C₂₃	—	4	4	no	—
238	C₂²×C₄×C₂₃	—	8	2	no	—
239	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₂₃	—	4	4	no	—
249	SD₁₆×C₂₃	—	2	8	no	—
250	SD₁₆×C₂₃	—	4	4	no	—
251	M₁₆×C₂₃	—	4	4	no	—
252	M₁₆×C₂₃	—	4	4	no	—
253	C₂×C₈×C₂₃	—	2	2	no	—
254	C₂×C₈×C₂₃	—	2	2	no	—
255	C₂×C₈×C₂₃	—	2	2	no	—
256	C₂×C₈×C₂₃	—	2	2	no	—
257	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	4	no	—
264	C₄⋊C₄×C₂₃	—	2	4	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
273	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²⋊C₄×C₂₃	—	2	4	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
286	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
287	C₄²×C₂₃	—	2	4	no	—
288	C₄²×C₂₃	—	2	4	no	—
289	C₄²×C₂₃	C₂×D₄	1	2	yes	—
290	C₄²×C₂₃	C₂⁴	1	2	yes	—
291	C₂×#3323	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	2	no	—
294	C₂³×C₂₃	—	2	4	no	—
295	C₂³×C₂₃	—	2	2	no	—
296	C₂³×C₂₃	—	2	2	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	4	8	no	—
302	C₂³×C₂₃	—	4	8	no	—
303	C₂³×C₂₃	—	4	2	no	—
304	C₂³×C₂₃	—	4	2	no	—
305	C₂³×C₂₃	—	4	2	no	—
306	C₂³×C₂₃	—	4	2	no	—
307	C₂³×C₂₃	—	4	2	no	—
308	C₂³×C₂₃	—	8	4	no	—
309	C₂³×C₂₃	—	8	16	no	—
310	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
311	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
312	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₂₃	—	2	2	no	—
314	Q₈×C₂₃	—	2	2	no	—
315	Q₈×C₂₃	—	2	2	no	—
316	Q₈×C₂₃	—	2	2	no	—
317	Q₈×C₂₃	—	4	2	no	—
318	Q₈×C₂₃	—	4	2	no	—
319	D₄×C₂₃	—	2	4	no	—
320	D₄×C₂₃	—	2	2	no	—
321	D₄×C₂₃	—	2	2	no	—
322	D₄×C₂₃	—	2	2	no	—
323	D₄×C₂₃	—	4	4	no	—
324	D₄×C₂₃	—	4	8	no	—
325	D₄×C₂₃	—	4	8	no	—
326	D₄×C₂₃	—	4	2	no	—
327	D₄×C₂₃	—	8	4	no	—
328	D₄×C₂₃	C₂×#41	1	4	yes	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	4	no	—
334	C₂×C₄×C₂₃	—	2	4	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
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	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	4	8	no	—
346	C₂×C₄×C₂₃	—	4	8	no	—
347	C₂×C₄×C₂₃	—	4	2	no	—
348	C₂×C₄×C₂₃	—	4	2	no	—
349	C₂×C₄×C₂₃	—	4	2	no	—
350	C₂×C₄×C₂₃	—	4	2	no	—
351	C₂×C₄×C₂₃	—	4	2	no	—
352	C₂×C₄×C₂₃	—	4	2	no	—
353	C₂×C₄×C₂₃	—	8	4	no	—
354	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
360	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
362	C₈×C₂₃	—	2	2	no	—
363	C₈×C₂₃	—	2	2	no	—
364	C₈×C₂₃	—	2	2	no	—
365	C₈×C₂₃	—	2	2	no	—
366	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
367	C₂×#546	C₂×C₂₃	1	1	yes	characteristic
368	#3323	C₂×C₂₃	1	16	yes	direct product factor
369	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂×#485	C₂×C₂₃	1	1	yes	characteristic, complemented
372	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂×#470	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
377	C₂×#450	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
380	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
381	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
382	C₂²×C₂₃	—	2	2	no	—
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	4	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	2	2	no	—
388	C₂²×C₂₃	—	2	2	no	—
389	C₂²×C₂₃	—	4	4	no	—
390	C₂²×C₂₃	—	4	4	no	—
391	C₂²×C₂₃	—	4	8	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	8	16	no	—
398	C₂²×C₂₃	—	8	4	no	—
399	C₂²×C₂₃	#546	1	2	yes	—
400	C₂²×C₂₃	#575	1	2	yes	—
401	C₂²×C₂₃	#577	1	2	yes	—
402	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₂₃	—	2	2	no	—
404	C₄×C₂₃	—	2	2	no	—
405	C₄×C₂₃	—	2	2	no	—
406	C₄×C₂₃	—	2	2	no	—
407	C₄×C₂₃	—	4	2	no	—
408	C₄×C₂₃	—	4	2	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	2	no	—
413	C₄×C₂₃	#546	1	2	yes	—
414	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
415	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
417	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
418	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
419	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
420	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
421	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
422	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
423	#552	—	2	4	no	—
424	#552	C₂²×C₂₃	1	8	yes	complemented
425	#546	—	2	4	no	—
426	#546	C₂²×C₂₃	1	8	yes	—
427	C₂×#126	—	2	1	no	—
428	C₂×#125	—	2	1	no	—
429	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#123	—	2	1	no	—
432	C₂×#123	—	2	1	no	—
433	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	C₂×#121	—	2	1	no	—
437	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#120	—	2	1	no	—
439	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#117	—	2	1	no	—
443	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
444	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	C₂²×C₂²⋊C₄	—	2	1	no	—
446	#488	C₂²×C₂₃	1	8	yes	complemented
447	#485	C₂²×C₂₃	1	8	yes	complemented
448	#481	C₂²×C₂₃	1	8	yes	complemented
449	#478	C₂²×C₂₃	1	8	yes	complemented
450	#470	C₂²×C₂₃	1	8	yes	complemented
451	#468	C₂²×C₂₃	1	8	yes	complemented
452	#464	C₂²×C₂₃	1	8	yes	complemented
453	#452	C₂²×C₂₃	1	8	yes	complemented
454	#450	C₂²×C₂₃	1	8	yes	complemented
455	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
456	#436	C₂²×C₂₃	1	8	yes	complemented
457	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#418	C₂²×C₂₃	1	8	yes	complemented
462	#417	C₂²×C₂₃	1	8	yes	complemented
463	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
464	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂×C₂₃	—	4	2	no	—
477	C₂×C₂₃	—	4	2	no	—
478	C₂×C₂₃	—	4	4	no	—
479	C₂×C₂₃	—	8	2	no	—
480	C₂×C₂₃	#3323	1	4	yes	direct product factor
481	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
482	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
483	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
484	C₂⁵	—	2	1	no	—
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	4	no	—
487	C₂×#41	—	4	2	no	—
488	C₂×#41	C₂³×C₂₃	1	4	yes	—
489	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	4	2	no	—
497	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
500	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×Q₁₆	—	4	2	no	—
507	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
508	C₂×SD₁₆	—	2	4	no	—
509	C₂×SD₁₆	—	4	2	no	—
510	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
511	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
512	C₂×M₁₆	—	4	2	no	—
513	C₂×M₁₆	—	4	2	no	—
514	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
515	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
516	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
520	#126	—	2	8	no	—
521	#125	—	2	8	no	—
522	#125	—	2	2	no	—
523	#125	C₂³×C₂₃	1	4	yes	complemented
524	#124	—	2	2	no	—
525	#124	C₂³×C₂₃	1	4	yes	—
526	#123	—	2	8	no	—
527	#123	—	2	8	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
532	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
533	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
534	#121	—	2	2	no	—
535	#121	—	2	8	no	—
536	#121	C₂³×C₂₃	1	4	yes	—
537	#120	—	2	8	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	D₄×C₂₃	1	4	yes	—
542	C₄×D₄	C₂³×C₂₃	1	4	yes	—
543	C₄×D₄	C₂³×C₂₃	1	4	yes	—
544	#117	—	2	2	no	—
545	#117	—	2	8	no	—
546	#117	C₂³×C₂₃	1	4	yes	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	8	no	—
570	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
571	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
572	C₂×C₄²	—	2	1	no	—
573	C₂×C₄²	—	2	1	no	—
574	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
575	#107	C₂³×C₂₃	1	4	yes	complemented
576	#106	C₂³×C₂₃	1	4	yes	complemented
577	#106	C₂³×C₂₃	1	4	yes	complemented
578	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
579	#103	C₂³×C₂₃	1	4	yes	complemented
580	#103	C₂³×C₂₃	1	4	yes	complemented
581	#103	C₂³×C₂₃	1	4	yes	complemented
582	#103	C₂³×C₂₃	1	4	yes	complemented
583	#102	C₂³×C₂₃	1	4	yes	—
584	#102	C₂³×C₂₃	1	4	yes	—
585	#102	C₂³×C₂₃	1	4	yes	—
586	#102	C₂³×C₂₃	1	4	yes	—
587	#102	C₂³×C₂₃	1	4	yes	—
588	#102	C₂³×C₂₃	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
590	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
591	C₄×C₈	C₂³×C₂₃	1	4	yes	complemented
592	C₂₃	C₂×#3323	1	1	yes	characteristic, direct product factor, Sylow
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	1	no	—
595	C₂⁴	—	2	4	no	—
596	C₂⁴	—	4	4	no	—
597	C₂⁴	—	4	4	no	—
598	C₂⁴	—	8	2	no	—
599	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
600	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
601	#41	—	2	8	no	—
602	#41	—	4	4	no	—
603	#41	—	4	8	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
611	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	4	4	no	—
622	C₂×D₄	—	4	8	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	4	4	no	—
626	C₂×D₄	—	8	2	no	—
627	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
628	C₂×D₄	#41×C₂₃	1	4	yes	—
629	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
630	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	8	2	no	—
647	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
652	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
656	Q₁₆	—	4	4	no	—
657	SD₁₆	—	2	8	no	—
658	SD₁₆	—	4	4	no	—
659	M₁₆	—	4	4	no	—
660	M₁₆	—	4	4	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	2	2	no	—
664	C₂×C₈	—	2	2	no	—
665	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
667	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
668	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
694	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
695	C₄²	—	2	4	no	—
696	C₄²	—	2	4	no	—
697	C₄²	C₂×D₄×C₂₃	1	2	yes	—
698	C₄²	C₂⁴×C₂₃	1	2	yes	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	4	8	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	8	4	no	—
716	C₂³	—	8	16	no	—
717	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
718	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
719	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	4	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	2	no	—
734	D₄	—	8	4	no	—
735	D₄	C₂×#41×C₂₃	1	4	yes	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	4	8	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	8	4	no	—
761	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
764	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
765	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
766	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
767	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
768	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
769	C₈	—	2	2	no	—
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₈	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	8	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	8	16	no	—
789	C₂²	—	8	4	no	—
790	C₂²	C₂₃×#546	1	2	yes	—
791	C₂²	C₂₃×#575	1	2	yes	—
792	C₂²	C₂₃×#577	1	2	yes	—
793	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
794	C₄	—	2	2	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	C₂₃×#546	1	2	yes	—
805	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
806	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
807	C₂	—	4	2	no	—
808	C₂	—	4	2	no	—
809	C₂	—	4	4	no	—
810	C₂	—	8	2	no	—
811	C₂	C₂₃×#3323	1	4	yes	direct product factor
812	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
813	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
814	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#546	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×#552	C₂	semidirect
3. C₂₃×#3323	C₂	direct (N × H)
4. C₂×C₂₃×#488	C₂	semidirect
5. C₂×C₂₃×#481	C₂	semidirect
6. C₂×C₂₃×#485	C₂	semidirect
7. C₂×C₂₃×#478	C₂	semidirect
8. C₂×C₂₃×#470	C₂	semidirect
9. C₂×C₂₃×#468	C₂	semidirect
10. C₂×C₂₃×#464	C₂	semidirect
11. C₂×C₂₃×#452	C₂	semidirect
12. C₂×C₂₃×#450	C₂	semidirect
13. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
14. C₂×C₂₃×#436	C₂	semidirect
15. C₂×C₂₃×#417	C₂	semidirect
16. C₂×C₂₃×#418	C₂	semidirect
19. C₂²×Q₁₆×C₂₃	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
25. C₂₃×#552	C₂²	semidirect
30. C₂×C₂₃×#125	C₂²	semidirect
36. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
47. C₂₃×#488	C₂²	semidirect
48. C₂₃×#485	C₂²	semidirect
49. C₂₃×#481	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#470	C₂²	semidirect
52. C₂₃×#468	C₂²	semidirect
53. C₂₃×#464	C₂²	semidirect
54. C₂₃×#452	C₂²	semidirect
55. C₂₃×#450	C₂²	semidirect
56. C₄×SD₁₆×C₂₃	C₂²	semidirect
57. C₂₃×#436	C₂²	semidirect
58. C₂×C₂₃×#107	C₂²	semidirect
59. C₂×C₂₃×#106	C₂²	semidirect
60. C₂×C₂₃×#106	C₂²	semidirect
61. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
62. C₂₃×#418	C₂²	semidirect
63. C₂₃×#417	C₂²	semidirect
64. C₂×C₂₃×#103	C₂²	semidirect
65. C₂×C₂₃×#103	C₂²	semidirect
66. C₂×C₂₃×#103	C₂²	semidirect
67. C₂×C₂₃×#103	C₂²	semidirect
75. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₄×C₈×C₂₃	C₂²	semidirect
100. C₂×Q₁₆×C₂₃	C₂³	semidirect
108. C₂×M₁₆×C₂₃	C₂³	semidirect
116. C₂₃×#125	C₂³	semidirect
126. C₂₃×C₂²⋊Q₈	C₂³	semidirect
132. C₄×Q₈×C₂₃	C₂³	semidirect
153. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
168. C₂₃×#107	C₂³	semidirect
169. C₂₃×#106	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
175. C₂₃×#103	C₂³	semidirect
183. C₂₃×C₂²⋊C₈	C₂³	semidirect
184. C₄×C₈×C₂₃	C₂³	semidirect
291. C₂×#3323	C₂₃	direct (N × H)
366. C₂×#552	C₂×C₂₃	semidirect
368. #3323	C₂×C₂₃	direct (N × H)
369. C₂×#488	C₂×C₂₃	semidirect
370. C₂×#481	C₂×C₂₃	semidirect
371. C₂×#485	C₂×C₂₃	semidirect
372. C₂×#478	C₂×C₂₃	semidirect
373. C₂×#470	C₂×C₂₃	semidirect
374. C₂×#468	C₂×C₂₃	semidirect
375. C₂×#464	C₂×C₂₃	semidirect
376. C₂×#452	C₂×C₂₃	semidirect
377. C₂×#450	C₂×C₂₃	semidirect
378. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
379. C₂×#436	C₂×C₂₃	semidirect
380. C₂×#417	C₂×C₂₃	semidirect
381. C₂×#418	C₂×C₂₃	semidirect
418. C₂²×Q₁₆	C₂²×C₂₃	semidirect
422. C₂²×M₁₆	C₂²×C₂₃	semidirect
424. #552	C₂²×C₂₃	semidirect
429. C₂×#125	C₂²×C₂₃	semidirect
435. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
439. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
444. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
446. #488	C₂²×C₂₃	semidirect
447. #485	C₂²×C₂₃	semidirect
448. #481	C₂²×C₂₃	semidirect
449. #478	C₂²×C₂₃	semidirect
450. #470	C₂²×C₂₃	semidirect
451. #468	C₂²×C₂₃	semidirect
452. #464	C₂²×C₂₃	semidirect
453. #452	C₂²×C₂₃	semidirect
454. #450	C₂²×C₂₃	semidirect
455. C₄×SD₁₆	C₂²×C₂₃	semidirect
456. #436	C₂²×C₂₃	semidirect
457. C₂×#107	C₂²×C₂₃	semidirect
458. C₂×#106	C₂²×C₂₃	semidirect
459. C₂×#106	C₂²×C₂₃	semidirect
460. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
461. #418	C₂²×C₂₃	semidirect
462. #417	C₂²×C₂₃	semidirect
463. C₂×#103	C₂²×C₂₃	semidirect
464. C₂×#103	C₂²×C₂₃	semidirect
465. C₂×#103	C₂²×C₂₃	semidirect
466. C₂×#103	C₂²×C₂₃	semidirect
474. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
475. C₂×C₄×C₈	C₂²×C₂₃	semidirect
480. C₂×C₂₃	#3323	direct (N × H)
507. C₂×Q₁₆	C₂³×C₂₃	semidirect
515. C₂×M₁₆	C₂³×C₂₃	semidirect
523. #125	C₂³×C₂₃	semidirect
533. C₂²⋊Q₈	C₂³×C₂₃	semidirect
539. C₄×Q₈	C₂³×C₂₃	semidirect
560. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
575. #107	C₂³×C₂₃	semidirect
576. #106	C₂³×C₂₃	semidirect
577. #106	C₂³×C₂₃	semidirect
578. C₄⋊C₈	C₂³×C₂₃	semidirect
579. #103	C₂³×C₂₃	semidirect
580. #103	C₂³×C₂₃	semidirect
581. #103	C₂³×C₂₃	semidirect
582. #103	C₂³×C₂₃	semidirect
590. C₂²⋊C₈	C₂³×C₂₃	semidirect
591. C₄×C₈	C₂³×C₂₃	semidirect
592. C₂₃	C₂×#3323	direct (N × H)
811. C₂	C₂₃×#3323	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×#552	2
C₂×C₂₃×#546	2
C₂₃×#3323	2
C₂×C₂₃×#488	2
C₂×C₂₃×#481	2
C₂×C₂₃×#485	2
C₂×C₂₃×#478	2
C₂×C₂₃×#470	2
C₂×C₂₃×#468	2
C₂×C₂₃×#464	2
C₂×C₂₃×#452	2
C₂×C₂₃×#450	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×C₂₃×#436	2
C₂×C₂₃×#417	2
C₂×C₂₃×#418	2
C₂×#3323	23

Subgroups — C2×C23×#3323 #19208769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3323 #19208769