Subgroups — C₂×C₂₃×#3266 #19208650

Order 5888.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#3266	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₂₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#137	—	2	8	no	—
22	C₂×C₂₃×#137	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₂₃	—	2	8	no	—
27	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
34	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₂₃	—	2	4	no	—
37	D₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
38	C₂₃×#546	—	2	4	no	—
39	C₂₃×#546	C₂²	1	8	yes	—
40	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#123	—	2	1	no	—
44	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
46	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂₃×#121	—	2	1	no	—
50	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#120	—	2	1	no	—
52	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₂₃	—	2	1	no	—
54	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
57	C₂₃×#497	C₂²	1	8	yes	complemented
58	C₂₃×#468	C₂²	1	8	yes	complemented
59	C₂₃×#467	C₂²	1	8	yes	complemented
60	C₂₃×#464	C₂²	1	8	yes	complemented
61	C₂₃×#461	C₂²	1	8	yes	complemented
62	C₂₃×#452	C₂²	1	8	yes	complemented
63	C₂₃×#451	C₂²	1	8	yes	complemented
64	C₂₃×#450	C₂²	1	8	yes	complemented
65	C₂₃×#448	C₂²	1	8	yes	complemented
66	C₂₃×#440	C₂²	1	8	yes	complemented
67	C₂₃×#435	C₂²	1	8	yes	complemented
68	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
79	C₂⁵×C₂₃	—	2	1	no	—
80	C₂×#41×C₂₃	—	2	2	no	—
81	C₂×#41×C₂₃	—	2	4	no	—
82	C₂×#41×C₂₃	—	4	2	no	—
83	C₂×#41×C₂₃	C₂³	1	4	yes	—
84	C₂²×Q₈×C₂₃	—	2	2	no	—
85	C₂²×Q₈×C₂₃	—	2	2	no	—
86	C₂²×Q₈×C₂₃	—	2	1	no	—
87	C₂²×Q₈×C₂₃	—	2	1	no	—
88	C₂²×Q₈×C₂₃	—	2	4	no	—
89	C₂²×Q₈×C₂₃	—	2	4	no	—
90	C₂²×Q₈×C₂₃	—	4	2	no	—
91	C₂²×Q₈×C₂₃	—	4	2	no	—
92	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
96	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₂₃	C₂³	1	4	yes	complemented
98	C₂²×D₄×C₂₃	—	2	4	no	—
99	C₂²×D₄×C₂₃	—	2	1	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	—	2	1	no	—
102	C₂²×D₄×C₂₃	—	2	2	no	—
103	C₂²×D₄×C₂₃	—	4	2	no	—
104	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	—	2	1	no	—
109	C₂³×C₄×C₂₃	—	2	1	no	—
110	C₂³×C₄×C₂₃	—	2	1	no	—
111	C₂³×C₄×C₂₃	—	2	1	no	—
112	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂₃×#137	—	2	32	no	—
115	C₂×Q₁₆×C₂₃	—	2	4	no	—
116	C₂×Q₁₆×C₂₃	—	2	4	no	—
117	C₂×Q₁₆×C₂₃	—	4	2	no	—
118	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
119	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
120	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
121	C₂×SD₁₆×C₂₃	—	2	4	no	—
122	C₂×SD₁₆×C₂₃	—	2	4	no	—
123	C₂×SD₁₆×C₂₃	—	2	4	no	—
124	C₂×SD₁₆×C₂₃	—	2	32	no	—
125	C₂×SD₁₆×C₂₃	—	2	4	no	—
126	C₂×SD₁₆×C₂₃	—	4	2	no	—
127	C₂×SD₁₆×C₂₃	D₄	1	8	yes	complemented
128	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
132	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
133	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
134	C₂×M₁₆×C₂₃	—	2	4	no	—
135	C₂×M₁₆×C₂₃	C₂³	1	4	yes	complemented
136	C₂²×C₈×C₂₃	—	2	4	no	—
137	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
139	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂₃×C₄⋊Q₈	—	2	8	no	—
143	C₂₃×C₄⋊Q₈	—	2	2	no	—
144	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
145	C₂₃×#124	—	2	2	no	—
146	C₂₃×#124	C₂³	1	4	yes	—
147	C₂₃×#123	—	2	8	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	8	no	—
152	C₂₃×C₂²⋊Q₈	—	2	8	no	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	8	no	—
158	C₂₃×#121	C₂³	1	4	yes	—
159	C₂₃×#120	—	2	8	no	—
160	C₄×Q₈×C₂₃	—	2	2	no	—
161	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
162	C₄×D₄×C₂₃	—	2	8	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	D₄	1	4	yes	—
165	C₄×D₄×C₂₃	C₂³	1	4	yes	—
166	C₄×D₄×C₂₃	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
170	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
172	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
173	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
184	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	—	2	1	no	—
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂₃×#107	C₂³	1	4	yes	complemented
189	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
190	C₂₃×#103	C₂³	1	4	yes	complemented
191	C₂₃×#103	C₂³	1	4	yes	complemented
192	C₂₃×#103	C₂³	1	4	yes	complemented
193	C₂₃×#103	C₂³	1	4	yes	complemented
194	C₂₃×#102	C₂³	1	4	yes	—
195	C₂₃×#102	C₂³	1	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
198	C₂₃×#97	C₂³	1	4	yes	complemented
199	C₂⁴×C₂₃	—	2	1	no	—
200	C₂⁴×C₂₃	—	2	1	no	—
201	C₂⁴×C₂₃	—	2	4	no	—
202	C₂⁴×C₂₃	—	4	4	no	—
203	C₂⁴×C₂₃	—	4	4	no	—
204	C₂⁴×C₂₃	—	8	2	no	—
205	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
207	#41×C₂₃	—	2	8	no	—
208	#41×C₂₃	—	4	4	no	—
209	#41×C₂₃	—	4	8	no	—
210	C₂×Q₈×C₂₃	—	2	1	no	—
211	C₂×Q₈×C₂₃	—	2	1	no	—
212	C₂×Q₈×C₂₃	—	2	4	no	—
213	C₂×Q₈×C₂₃	—	2	1	no	—
214	C₂×Q₈×C₂₃	—	2	1	no	—
215	C₂×Q₈×C₂₃	—	2	4	no	—
216	C₂×Q₈×C₂₃	—	2	2	no	—
217	C₂×Q₈×C₂₃	—	2	8	no	—
218	C₂×Q₈×C₂₃	—	2	8	no	—
219	C₂×Q₈×C₂₃	—	2	2	no	—
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	—	2	2	no	—
222	C₂×Q₈×C₂₃	—	2	2	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	2	2	no	—
225	C₂×Q₈×C₂₃	—	4	4	no	—
226	C₂×Q₈×C₂₃	—	4	4	no	—
227	C₂×Q₈×C₂₃	—	4	4	no	—
228	C₂×Q₈×C₂₃	—	4	4	no	—
229	C₂×Q₈×C₂₃	—	4	8	no	—
230	C₂×Q₈×C₂₃	—	4	8	no	—
231	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
232	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
236	C₂×D₄×C₂₃	—	2	4	no	—
237	C₂×D₄×C₂₃	—	2	8	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	4	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	4	4	no	—
247	C₂×D₄×C₂₃	—	4	8	no	—
248	C₂×D₄×C₂₃	—	4	4	no	—
249	C₂×D₄×C₂₃	—	4	4	no	—
250	C₂×D₄×C₂₃	—	8	2	no	—
251	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	—	2	4	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	1	no	—
265	C₂²×C₄×C₂₃	—	2	1	no	—
266	C₂²×C₄×C₂₃	—	2	1	no	—
267	C₂²×C₄×C₂₃	—	2	4	no	—
268	C₂²×C₄×C₂₃	—	2	4	no	—
269	C₂²×C₄×C₂₃	—	4	4	no	—
270	C₂²×C₄×C₂₃	—	4	4	no	—
271	C₂²×C₄×C₂₃	—	4	4	no	—
272	C₂²×C₄×C₂₃	—	8	2	no	—
273	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	Q₁₆×C₂₃	—	2	8	no	—
283	Q₁₆×C₂₃	—	2	8	no	—
284	Q₁₆×C₂₃	—	4	4	no	—
285	SD₁₆×C₂₃	—	2	8	no	—
286	SD₁₆×C₂₃	—	2	8	no	—
287	SD₁₆×C₂₃	—	2	8	no	—
288	SD₁₆×C₂₃	—	2	8	no	—
289	SD₁₆×C₂₃	—	4	4	no	—
290	SD₁₆×C₂₃	C₂×D₄	1	16	yes	complemented
291	M₁₆×C₂₃	—	2	8	no	—
292	C₂×C₈×C₂₃	—	2	2	no	—
293	C₂×C₈×C₂₃	—	2	2	no	—
294	C₂×C₈×C₂₃	—	2	2	no	—
295	C₂×C₈×C₂₃	—	2	8	no	—
296	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
297	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₂₃	—	2	4	no	—
302	C₄⋊C₄×C₂₃	—	2	4	no	—
303	C₄⋊C₄×C₂₃	—	2	4	no	—
304	C₄⋊C₄×C₂₃	—	2	4	no	—
305	C₄⋊C₄×C₂₃	—	2	4	no	—
306	C₄⋊C₄×C₂₃	—	2	4	no	—
307	C₄⋊C₄×C₂₃	—	2	1	no	—
308	C₄⋊C₄×C₂₃	—	2	1	no	—
309	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
310	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
312	C₂²⋊C₄×C₂₃	—	2	4	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	4	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	no	—
319	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
320	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
321	C₄²×C₂₃	—	2	4	no	—
322	C₄²×C₂₃	C₂×D₄	1	2	yes	—
323	C₄²×C₂₃	C₂⁴	1	2	yes	—
324	C₂×#3266	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂³×C₂₃	—	2	2	no	—
326	C₂³×C₂₃	—	2	2	no	—
327	C₂³×C₂₃	—	2	2	no	—
328	C₂³×C₂₃	—	2	4	no	—
329	C₂³×C₂₃	—	2	2	no	—
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	2	no	—
332	C₂³×C₂₃	—	2	2	no	—
333	C₂³×C₂₃	—	4	8	no	—
334	C₂³×C₂₃	—	4	2	no	—
335	C₂³×C₂₃	—	4	2	no	—
336	C₂³×C₂₃	—	4	2	no	—
337	C₂³×C₂₃	—	4	2	no	—
338	C₂³×C₂₃	—	4	8	no	—
339	C₂³×C₂₃	—	4	2	no	—
340	C₂³×C₂₃	—	8	4	no	—
341	C₂³×C₂₃	—	8	16	no	—
342	C₂³×C₂₃	#137	1	4	yes	complemented
343	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
344	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
345	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₂₃	—	2	4	no	—
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	2	2	no	—
351	Q₈×C₂₃	—	2	2	no	—
352	Q₈×C₂₃	—	2	2	no	—
353	Q₈×C₂₃	—	2	2	no	—
354	Q₈×C₂₃	—	4	8	no	—
355	Q₈×C₂₃	—	4	8	no	—
356	Q₈×C₂₃	—	4	2	no	—
357	Q₈×C₂₃	—	4	2	no	—
358	Q₈×C₂₃	—	4	2	no	—
359	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
360	D₄×C₂₃	—	2	8	no	—
361	D₄×C₂₃	—	2	4	no	—
362	D₄×C₂₃	—	2	2	no	—
363	D₄×C₂₃	—	2	2	no	—
364	D₄×C₂₃	—	2	2	no	—
365	D₄×C₂₃	—	4	8	no	—
366	D₄×C₂₃	—	4	8	no	—
367	D₄×C₂₃	—	4	2	no	—
368	D₄×C₂₃	—	8	4	no	—
369	D₄×C₂₃	C₂²×D₄	1	4	yes	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	4	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	4	no	—
377	C₂×C₄×C₂₃	—	2	4	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	4	8	no	—
388	C₂×C₄×C₂₃	—	4	8	no	—
389	C₂×C₄×C₂₃	—	4	8	no	—
390	C₂×C₄×C₂₃	—	4	2	no	—
391	C₂×C₄×C₂₃	—	4	2	no	—
392	C₂×C₄×C₂₃	—	4	2	no	—
393	C₂×C₄×C₂₃	—	4	2	no	—
394	C₂×C₄×C₂₃	—	4	2	no	—
395	C₂×C₄×C₂₃	—	8	4	no	—
396	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₂₃	—	2	2	no	—
405	C₈×C₂₃	—	2	2	no	—
406	C₈×C₂₃	—	2	2	no	—
407	C₈×C₂₃	C₂²×D₄	1	4	yes	—
408	C₂²×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
409	C₂³×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
410	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
411	C₂×#546	C₂×C₂₃	1	1	yes	characteristic
412	#3266	C₂×C₂₃	1	16	yes	direct product factor
413	C₂×#497	C₂×C₂₃	1	1	yes	characteristic, complemented
414	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
415	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
416	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
417	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
418	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
419	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
420	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₂×#450	C₂×C₂₃	1	1	yes	characteristic, complemented
422	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
424	C₂²×C₂₃	—	2	2	no	—
425	C₂²×C₂₃	—	2	8	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	2	2	no	—
428	C₂²×C₂₃	—	2	4	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	2	2	no	—
431	C₂²×C₂₃	—	4	4	no	—
432	C₂²×C₂₃	—	4	8	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	2	no	—
435	C₂²×C₂₃	—	4	2	no	—
436	C₂²×C₂₃	—	4	2	no	—
437	C₂²×C₂₃	—	4	2	no	—
438	C₂²×C₂₃	—	8	16	no	—
439	C₂²×C₂₃	—	8	4	no	—
440	C₂²×C₂₃	D₄²	1	2	yes	—
441	C₂²×C₂₃	C₂×#137	1	2	yes	—
442	C₂²×C₂₃	C₂×#137	1	4	yes	complemented
443	C₂²×C₂₃	#577	1	2	yes	—
444	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
445	C₄×C₂₃	—	2	2	no	—
446	C₄×C₂₃	—	2	2	no	—
447	C₄×C₂₃	—	2	4	no	—
448	C₄×C₂₃	—	2	2	no	—
449	C₄×C₂₃	—	2	2	no	—
450	C₄×C₂₃	—	4	2	no	—
451	C₄×C₂₃	—	4	2	no	—
452	C₄×C₂₃	—	4	2	no	—
453	C₄×C₂₃	—	4	2	no	—
454	C₄×C₂₃	—	4	2	no	—
455	C₄×C₂₃	D₄²	1	2	yes	—
456	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
457	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
459	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
460	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#137	—	2	8	no	—
463	C₂×#137	C₂²×C₂₃	1	8	yes	complemented
464	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂²×SD₁₆	—	2	8	no	—
468	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
469	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
470	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
471	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
472	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
473	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
474	C₂²×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
475	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
477	D₄×Q₈	—	2	4	no	—
478	D₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
479	#546	—	2	4	no	—
480	#546	C₂²×C₂₃	1	8	yes	—
481	C₂×C₄⋊Q₈	—	2	1	no	—
482	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#123	—	2	1	no	—
485	C₂×C₂²⋊Q₈	—	2	1	no	—
486	C₂×C₂²⋊Q₈	—	2	1	no	—
487	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
489	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
490	C₂×#121	—	2	1	no	—
491	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
492	C₂×#120	—	2	1	no	—
493	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
494	C₂×C₄×D₄	—	2	1	no	—
495	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
497	C₂²×C₂²⋊C₄	—	2	1	no	—
498	#497	C₂²×C₂₃	1	8	yes	complemented
499	#468	C₂²×C₂₃	1	8	yes	complemented
500	#467	C₂²×C₂₃	1	8	yes	complemented
501	#464	C₂²×C₂₃	1	8	yes	complemented
502	#461	C₂²×C₂₃	1	8	yes	complemented
503	#452	C₂²×C₂₃	1	8	yes	complemented
504	#451	C₂²×C₂₃	1	8	yes	complemented
505	#450	C₂²×C₂₃	1	8	yes	complemented
506	#448	C₂²×C₂₃	1	8	yes	complemented
507	#440	C₂²×C₂₃	1	8	yes	complemented
508	#435	C₂²×C₂₃	1	8	yes	complemented
509	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
514	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
516	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
520	C₂×C₂₃	—	2	4	no	—
521	C₂×C₂₃	—	4	2	no	—
522	C₂×C₂₃	—	4	4	no	—
523	C₂×C₂₃	—	8	2	no	—
524	C₂×C₂₃	#3266	1	4	yes	direct product factor
525	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
526	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
527	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
528	C₂⁵	—	2	1	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	4	no	—
531	C₂×#41	—	4	2	no	—
532	C₂×#41	C₂³×C₂₃	1	4	yes	—
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	—	2	2	no	—
536	C₂²×Q₈	—	2	2	no	—
537	C₂²×Q₈	—	2	4	no	—
538	C₂²×Q₈	—	2	4	no	—
539	C₂²×Q₈	—	4	2	no	—
540	C₂²×Q₈	—	4	2	no	—
541	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
545	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₂₃	1	4	yes	complemented
547	C₂²×D₄	—	2	4	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	2	no	—
552	C₂²×D₄	—	4	2	no	—
553	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
556	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
563	#137	—	2	32	no	—
564	C₂×Q₁₆	—	2	4	no	—
565	C₂×Q₁₆	—	2	4	no	—
566	C₂×Q₁₆	—	4	2	no	—
567	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
568	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
569	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
570	C₂×SD₁₆	—	2	4	no	—
571	C₂×SD₁₆	—	2	4	no	—
572	C₂×SD₁₆	—	2	4	no	—
573	C₂×SD₁₆	—	2	32	no	—
574	C₂×SD₁₆	—	2	4	no	—
575	C₂×SD₁₆	—	4	2	no	—
576	C₂×SD₁₆	D₄×C₂₃	1	8	yes	complemented
577	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
583	C₂×M₁₆	—	2	4	no	—
584	C₂×M₁₆	C₂³×C₂₃	1	4	yes	complemented
585	C₂²×C₈	—	2	4	no	—
586	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
587	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
588	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
589	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄⋊Q₈	—	2	8	no	—
592	C₄⋊Q₈	—	2	2	no	—
593	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
594	#124	—	2	2	no	—
595	#124	C₂³×C₂₃	1	4	yes	—
596	#123	—	2	8	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	8	no	—
601	C₂²⋊Q₈	—	2	8	no	—
602	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
603	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
605	#121	—	2	2	no	—
606	#121	—	2	8	no	—
607	#121	C₂³×C₂₃	1	4	yes	—
608	#120	—	2	8	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
611	C₄×D₄	—	2	8	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	D₄×C₂₃	1	4	yes	—
614	C₄×D₄	C₂³×C₂₃	1	4	yes	—
615	C₄×D₄	C₂³×C₂₃	1	4	yes	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	8	no	—
633	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
637	#107	C₂³×C₂₃	1	4	yes	complemented
638	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
639	#103	C₂³×C₂₃	1	4	yes	complemented
640	#103	C₂³×C₂₃	1	4	yes	complemented
641	#103	C₂³×C₂₃	1	4	yes	complemented
642	#103	C₂³×C₂₃	1	4	yes	complemented
643	#102	C₂³×C₂₃	1	4	yes	—
644	#102	C₂³×C₂₃	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
647	#97	C₂³×C₂₃	1	4	yes	complemented
648	C₂₃	C₂×#3266	1	1	yes	characteristic, direct product factor, Sylow
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	2	1	no	—
651	C₂⁴	—	2	4	no	—
652	C₂⁴	—	4	4	no	—
653	C₂⁴	—	4	4	no	—
654	C₂⁴	—	8	2	no	—
655	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
657	#41	—	2	8	no	—
658	#41	—	4	4	no	—
659	#41	—	4	8	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	8	no	—
668	C₂×Q₈	—	2	8	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	8	no	—
680	C₂×Q₈	—	4	8	no	—
681	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
682	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
685	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	8	2	no	—
701	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
702	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
703	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
704	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	4	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	8	2	no	—
723	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
728	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
732	Q₁₆	—	2	8	no	—
733	Q₁₆	—	2	8	no	—
734	Q₁₆	—	4	4	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	2	8	no	—
737	SD₁₆	—	2	8	no	—
738	SD₁₆	—	2	8	no	—
739	SD₁₆	—	4	4	no	—
740	SD₁₆	C₂×D₄×C₂₃	1	16	yes	complemented
741	M₁₆	—	2	8	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	2	no	—
745	C₂×C₈	—	2	8	no	—
746	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
747	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
749	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
750	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
760	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
770	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
771	C₄²	—	2	4	no	—
772	C₄²	C₂×D₄×C₂₃	1	2	yes	—
773	C₄²	C₂⁴×C₂₃	1	2	yes	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	4	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	8	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	2	no	—
786	C₂³	—	4	8	no	—
787	C₂³	—	4	2	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	4	no	—
790	C₂³	—	8	16	no	—
791	C₂³	C₂₃×#137	1	4	yes	complemented
792	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
793	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
794	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
795	Q₈	—	2	2	no	—
796	Q₈	—	2	4	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	4	8	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
809	D₄	—	2	8	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	4	no	—
814	D₄	—	4	8	no	—
815	D₄	—	4	8	no	—
816	D₄	—	4	2	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂²×D₄×C₂₃	1	4	yes	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	8	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	8	4	no	—
845	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
851	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
852	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	C₂²×D₄×C₂₃	1	4	yes	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	8	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	4	8	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	8	16	no	—
872	C₂²	—	8	4	no	—
873	C₂²	D₄²×C₂₃	1	2	yes	—
874	C₂²	C₂×C₂₃×#137	1	2	yes	—
875	C₂²	C₂×C₂₃×#137	1	4	yes	complemented
876	C₂²	C₂₃×#577	1	2	yes	—
877	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	4	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	D₄²×C₂₃	1	2	yes	—
889	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
890	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
891	C₂	—	2	4	no	—
892	C₂	—	4	2	no	—
893	C₂	—	4	4	no	—
894	C₂	—	8	2	no	—
895	C₂	C₂₃×#3266	1	4	yes	direct product factor
896	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
897	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
898	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. C₂²×C₂₃×#137	C₂	semidirect
2. C₂³×SD₁₆×C₂₃	C₂	semidirect
3. C₂×D₄×Q₈×C₂₃	C₂	semidirect
5. C₂₃×#3266	C₂	direct (N × H)
6. C₂×C₂₃×#497	C₂	semidirect
7. C₂×C₂₃×#468	C₂	semidirect
8. C₂×C₂₃×#467	C₂	semidirect
9. C₂×C₂₃×#464	C₂	semidirect
10. C₂×C₂₃×#461	C₂	semidirect
11. C₂×C₂₃×#452	C₂	semidirect
12. C₂×C₂₃×#451	C₂	semidirect
13. C₂×C₂₃×#448	C₂	semidirect
14. C₂×C₂₃×#450	C₂	semidirect
15. C₂×C₂₃×#440	C₂	semidirect
16. C₂×C₂₃×#435	C₂	semidirect
19. C₂³×Q₈×C₂₃	C₂²	semidirect
22. C₂×C₂₃×#137	C₂²	semidirect
23. C₂²×Q₁₆×C₂₃	C₂²	semidirect
24. C₂²×Q₁₆×C₂₃	C₂²	semidirect
25. C₂²×Q₁₆×C₂₃	C₂²	semidirect
33. C₂²×SD₁₆×C₂₃	C₂²	semidirect
34. C₂²×M₁₆×C₂₃	C₂²	semidirect
37. D₄×Q₈×C₂₃	C₂²	semidirect
41. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
48. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
57. C₂₃×#497	C₂²	semidirect
58. C₂₃×#468	C₂²	semidirect
59. C₂₃×#467	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#461	C₂²	semidirect
62. C₂₃×#452	C₂²	semidirect
63. C₂₃×#451	C₂²	semidirect
64. C₂₃×#450	C₂²	semidirect
65. C₂₃×#448	C₂²	semidirect
66. C₂₃×#440	C₂²	semidirect
67. C₂₃×#435	C₂²	semidirect
68. C₂×C₂₃×#107	C₂²	semidirect
69. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
70. C₂×C₂₃×#103	C₂²	semidirect
71. C₂×C₂₃×#103	C₂²	semidirect
72. C₂×C₂₃×#103	C₂²	semidirect
73. C₂×C₂₃×#103	C₂²	semidirect
77. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₂₃×#97	C₂²	semidirect
97. C₂²×Q₈×C₂₃	C₂³	semidirect
118. C₂×Q₁₆×C₂₃	C₂³	semidirect
119. C₂×Q₁₆×C₂₃	C₂³	semidirect
120. C₂×Q₁₆×C₂₃	C₂³	semidirect
127. C₂×SD₁₆×C₂₃	D₄	semidirect
135. C₂×M₁₆×C₂₃	C₂³	semidirect
144. C₂₃×C₄⋊Q₈	C₂³	semidirect
155. C₂₃×C₂²⋊Q₈	C₂³	semidirect
161. C₄×Q₈×C₂₃	C₂³	semidirect
188. C₂₃×#107	C₂³	semidirect
189. C₂₃×C₄⋊C₈	C₂³	semidirect
190. C₂₃×#103	C₂³	semidirect
191. C₂₃×#103	C₂³	semidirect
192. C₂₃×#103	C₂³	semidirect
193. C₂₃×#103	C₂³	semidirect
197. C₂₃×C₂²⋊C₈	C₂³	semidirect
198. C₂₃×#97	C₂³	semidirect
290. SD₁₆×C₂₃	C₂×D₄	semidirect
324. C₂×#3266	C₂₃	direct (N × H)
342. C₂³×C₂₃	#137	semidirect
408. C₂²×#137	C₂×C₂₃	semidirect
409. C₂³×SD₁₆	C₂×C₂₃	semidirect
410. C₂×D₄×Q₈	C₂×C₂₃	semidirect
412. #3266	C₂×C₂₃	direct (N × H)
413. C₂×#497	C₂×C₂₃	semidirect
414. C₂×#468	C₂×C₂₃	semidirect
415. C₂×#467	C₂×C₂₃	semidirect
416. C₂×#464	C₂×C₂₃	semidirect
417. C₂×#461	C₂×C₂₃	semidirect
418. C₂×#452	C₂×C₂₃	semidirect
419. C₂×#451	C₂×C₂₃	semidirect
420. C₂×#448	C₂×C₂₃	semidirect
421. C₂×#450	C₂×C₂₃	semidirect
422. C₂×#440	C₂×C₂₃	semidirect
423. C₂×#435	C₂×C₂₃	semidirect
442. C₂²×C₂₃	C₂×#137	semidirect
460. C₂³×Q₈	C₂²×C₂₃	semidirect
463. C₂×#137	C₂²×C₂₃	semidirect
464. C₂²×Q₁₆	C₂²×C₂₃	semidirect
465. C₂²×Q₁₆	C₂²×C₂₃	semidirect
466. C₂²×Q₁₆	C₂²×C₂₃	semidirect
474. C₂²×SD₁₆	C₂²×C₂₃	semidirect
475. C₂²×M₁₆	C₂²×C₂₃	semidirect
478. D₄×Q₈	C₂²×C₂₃	semidirect
482. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
489. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
493. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
498. #497	C₂²×C₂₃	semidirect
499. #468	C₂²×C₂₃	semidirect
500. #467	C₂²×C₂₃	semidirect
501. #464	C₂²×C₂₃	semidirect
502. #461	C₂²×C₂₃	semidirect
503. #452	C₂²×C₂₃	semidirect
504. #451	C₂²×C₂₃	semidirect
505. #450	C₂²×C₂₃	semidirect
506. #448	C₂²×C₂₃	semidirect
507. #440	C₂²×C₂₃	semidirect
508. #435	C₂²×C₂₃	semidirect
509. C₂×#107	C₂²×C₂₃	semidirect
510. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
511. C₂×#103	C₂²×C₂₃	semidirect
512. C₂×#103	C₂²×C₂₃	semidirect
513. C₂×#103	C₂²×C₂₃	semidirect
514. C₂×#103	C₂²×C₂₃	semidirect
518. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
519. C₂×#97	C₂²×C₂₃	semidirect
524. C₂×C₂₃	#3266	direct (N × H)
546. C₂²×Q₈	C₂³×C₂₃	semidirect
567. C₂×Q₁₆	C₂³×C₂₃	semidirect
568. C₂×Q₁₆	C₂³×C₂₃	semidirect
569. C₂×Q₁₆	C₂³×C₂₃	semidirect
576. C₂×SD₁₆	D₄×C₂₃	semidirect
584. C₂×M₁₆	C₂³×C₂₃	semidirect
593. C₄⋊Q₈	C₂³×C₂₃	semidirect
604. C₂²⋊Q₈	C₂³×C₂₃	semidirect
610. C₄×Q₈	C₂³×C₂₃	semidirect
637. #107	C₂³×C₂₃	semidirect
638. C₄⋊C₈	C₂³×C₂₃	semidirect
639. #103	C₂³×C₂₃	semidirect
640. #103	C₂³×C₂₃	semidirect
641. #103	C₂³×C₂₃	semidirect
642. #103	C₂³×C₂₃	semidirect
646. C₂²⋊C₈	C₂³×C₂₃	semidirect
647. #97	C₂³×C₂₃	semidirect
648. C₂₃	C₂×#3266	direct (N × H)
740. SD₁₆	C₂×D₄×C₂₃	semidirect
791. C₂³	C₂₃×#137	semidirect
875. C₂²	C₂×C₂₃×#137	semidirect
895. C₂	C₂₃×#3266	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂₃×#137	2
C₂³×SD₁₆×C₂₃	2
C₂×D₄×Q₈×C₂₃	2
C₂×C₂₃×#546	2
C₂₃×#3266	2
C₂×C₂₃×#497	2
C₂×C₂₃×#468	2
C₂×C₂₃×#467	2
C₂×C₂₃×#464	2
C₂×C₂₃×#461	2
C₂×C₂₃×#452	2
C₂×C₂₃×#451	2
C₂×C₂₃×#448	2
C₂×C₂₃×#450	2
C₂×C₂₃×#440	2
C₂×C₂₃×#435	2
C₂×#3266	23

Subgroups — C2×C23×#3266 #19208650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3266 #19208650