Subgroups — C₂×C₂₃×#3268 #19208652

Order 5888.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3268	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₂₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#447	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	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
23	C₂×C₂₃×#135	—	2	8	no	—
24	C₂×C₂₃×#135	C₂²	1	8	yes	complemented
25	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#550	—	2	4	no	—
37	C₂₃×#550	C₂²	1	8	yes	complemented
38	C₂₃×#546	—	2	4	no	—
39	C₂₃×#546	C₂²	1	8	yes	complemented
40	C₂×C₂₃×#127	—	2	1	no	—
41	C₂×C₂₃×#127	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	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#121	—	2	1	no	—
46	C₂×C₂₃×#121	—	2	1	no	—
47	C₂×C₂₃×#121	—	2	1	no	—
48	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
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×#496	C₂²	1	8	yes	complemented
58	C₂₃×#468	C₂²	1	8	yes	complemented
59	C₂₃×#466	C₂²	1	8	yes	complemented
60	C₂₃×#464	C₂²	1	8	yes	complemented
61	C₂₃×#459	C₂²	1	8	yes	complemented
62	C₂₃×#452	C₂²	1	8	yes	complemented
63	C₂₃×#449	C₂²	1	8	yes	complemented
64	C₂₃×#449	C₂²	1	8	yes	complemented
65	C₂₃×#447	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×#102	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
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	2	no	—
82	C₂×#41×C₂₃	—	2	2	no	—
83	C₂×#41×C₂₃	—	2	4	no	—
84	C₂×#41×C₂₃	—	2	4	no	—
85	C₂×#41×C₂₃	—	2	4	no	—
86	C₂×#41×C₂₃	—	4	2	no	—
87	C₂×#41×C₂₃	—	4	2	no	—
88	C₂×#41×C₂₃	—	4	2	no	—
89	C₂×#41×C₂₃	C₂³	1	4	yes	—
90	C₂×#41×C₂₃	C₂³	1	4	yes	—
91	C₂×#41×C₂₃	C₂³	1	4	yes	complemented
92	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	—	2	4	no	—
95	C₂²×D₄×C₂₃	—	2	1	no	—
96	C₂²×D₄×C₂₃	—	2	1	no	—
97	C₂²×D₄×C₂₃	—	2	1	no	—
98	C₂²×D₄×C₂₃	—	2	1	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	—	2	1	no	—
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	—	4	2	no	—
106	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
107	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₂₃	—	2	1	no	—
113	C₂³×C₄×C₂₃	—	2	1	no	—
114	C₂³×C₄×C₂₃	—	2	1	no	—
115	C₂³×C₄×C₂₃	—	2	1	no	—
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂₃×AGL(1,ℤ/8)	—	2	32	no	—
119	C₂₃×#135	—	2	32	no	—
120	C₂×Q₁₆×C₂₃	—	2	4	no	—
121	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
122	C₂×SD₁₆×C₂₃	—	2	4	no	—
123	C₂×SD₁₆×C₂₃	—	2	4	no	—
124	C₂×SD₁₆×C₂₃	—	4	2	no	—
125	C₂×SD₁₆×C₂₃	D₄	1	8	yes	complemented
126	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
129	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
130	C₂×D₈×C₂₃	—	2	4	no	—
131	C₂×D₈×C₂₃	—	2	4	no	—
132	C₂×D₈×C₂₃	—	2	4	no	—
133	C₂×D₈×C₂₃	—	4	2	no	—
134	C₂×D₈×C₂₃	C₂³	1	4	yes	—
135	C₂×D₈×C₂₃	C₂³	1	4	yes	—
136	C₂×D₈×C₂₃	C₂³	1	4	yes	—
137	C₂×D₈×C₂₃	C₂³	1	4	yes	—
138	C₂×M₁₆×C₂₃	—	2	4	no	—
139	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
140	C₂²×C₈×C₂₃	—	2	4	no	—
141	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₂₃	C₂³	1	4	yes	complemented
146	C₂₃×#127	—	2	8	no	—
147	C₂₃×#127	—	2	2	no	—
148	C₂₃×#127	C₂³	1	4	yes	complemented
149	C₂₃×#124	—	2	2	no	—
150	C₂₃×#124	C₂³	1	4	yes	—
151	C₂₃×#123	—	2	8	no	—
152	C₂₃×C₂²⋊Q₈	—	2	2	no	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	8	no	—
158	C₂₃×#121	—	2	8	no	—
159	C₂₃×#121	—	2	8	no	—
160	C₂₃×#121	C₂³	1	4	yes	—
161	C₂₃×#121	C₂³	1	4	yes	—
162	C₂₃×#121	C₂³	1	4	yes	complemented
163	C₂₃×#120	—	2	8	no	—
164	C₄×Q₈×C₂₃	—	2	2	no	—
165	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
166	C₄×D₄×C₂₃	—	2	8	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	D₄	1	4	yes	—
169	C₄×D₄×C₂₃	C₂³	1	4	yes	—
170	C₄×D₄×C₂₃	C₂³	1	4	yes	—
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×#102	C₂³	1	4	yes	—
193	C₂₃×#102	C₂³	1	4	yes	—
194	C₂₃×#102	C₂³	1	4	yes	complemented
195	C₂₃×#102	C₂³	1	4	yes	complemented
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	1	no	—
202	C₂⁴×C₂₃	—	2	1	no	—
203	C₂⁴×C₂₃	—	2	4	no	—
204	C₂⁴×C₂₃	—	4	4	no	—
205	C₂⁴×C₂₃	—	4	4	no	—
206	C₂⁴×C₂₃	—	8	2	no	—
207	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
209	#41×C₂₃	—	2	8	no	—
210	#41×C₂₃	—	2	8	no	—
211	#41×C₂₃	—	2	8	no	—
212	#41×C₂₃	—	4	4	no	—
213	#41×C₂₃	—	4	4	no	—
214	#41×C₂₃	—	4	4	no	—
215	#41×C₂₃	—	4	8	no	—
216	#41×C₂₃	—	4	8	no	—
217	#41×C₂₃	—	4	8	no	—
218	C₂×Q₈×C₂₃	—	2	1	no	—
219	C₂×Q₈×C₂₃	—	2	1	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	C₂×D₄	1	4	yes	—
224	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₂₃	—	2	8	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	4	no	—
229	C₂×D₄×C₂₃	—	2	4	no	—
230	C₂×D₄×C₂₃	—	2	4	no	—
231	C₂×D₄×C₂₃	—	2	4	no	—
232	C₂×D₄×C₂₃	—	2	4	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	2	2	no	—
236	C₂×D₄×C₂₃	—	2	2	no	—
237	C₂×D₄×C₂₃	—	2	4	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	1	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	2	1	no	—
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	4	4	no	—
248	C₂×D₄×C₂₃	—	4	8	no	—
249	C₂×D₄×C₂₃	—	4	2	no	—
250	C₂×D₄×C₂₃	—	4	4	no	—
251	C₂×D₄×C₂₃	—	4	4	no	—
252	C₂×D₄×C₂₃	—	4	4	no	—
253	C₂×D₄×C₂₃	—	4	4	no	—
254	C₂×D₄×C₂₃	—	4	4	no	—
255	C₂×D₄×C₂₃	—	8	2	no	—
256	C₂×D₄×C₂₃	—	8	2	no	—
257	C₂×D₄×C₂₃	—	8	2	no	—
258	C₂×D₄×C₂₃	—	8	2	no	—
259	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
260	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
261	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₂₃	—	2	1	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	2	1	no	—
271	C₂²×C₄×C₂₃	—	2	1	no	—
272	C₂²×C₄×C₂₃	—	2	1	no	—
273	C₂²×C₄×C₂₃	—	2	4	no	—
274	C₂²×C₄×C₂₃	—	2	4	no	—
275	C₂²×C₄×C₂₃	—	2	4	no	—
276	C₂²×C₄×C₂₃	—	2	4	no	—
277	C₂²×C₄×C₂₃	—	4	4	no	—
278	C₂²×C₄×C₂₃	—	4	4	no	—
279	C₂²×C₄×C₂₃	—	4	4	no	—
280	C₂²×C₄×C₂₃	—	8	2	no	—
281	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	Q₁₆×C₂₃	—	2	8	no	—
291	SD₁₆×C₂₃	—	2	8	no	—
292	SD₁₆×C₂₃	—	2	8	no	—
293	SD₁₆×C₂₃	—	4	4	no	—
294	SD₁₆×C₂₃	C₂×D₄	1	16	yes	complemented
295	D₈×C₂₃	—	2	8	no	—
296	D₈×C₂₃	—	2	8	no	—
297	D₈×C₂₃	—	2	8	no	—
298	D₈×C₂₃	—	4	4	no	—
299	M₁₆×C₂₃	—	2	8	no	—
300	C₂×C₈×C₂₃	—	2	2	no	—
301	C₂×C₈×C₂₃	—	2	2	no	—
302	C₂×C₈×C₂₃	—	2	2	no	—
303	C₂×C₈×C₂₃	—	2	8	no	—
304	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
305	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
306	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₂₃	—	2	4	no	—
310	C₄⋊C₄×C₂₃	—	2	4	no	—
311	C₄⋊C₄×C₂₃	—	2	1	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
314	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	—	2	4	no	—
320	C₂²⋊C₄×C₂₃	—	2	4	no	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
325	C₄²×C₂₃	—	2	4	no	—
326	C₄²×C₂₃	C₂×D₄	1	2	yes	—
327	C₄²×C₂₃	C₂⁴	1	2	yes	—
328	C₂×#3268	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	2	no	—
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	4	no	—
332	C₂³×C₂₃	—	2	2	no	—
333	C₂³×C₂₃	—	2	2	no	—
334	C₂³×C₂₃	—	2	2	no	—
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	4	8	no	—
341	C₂³×C₂₃	—	4	8	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	4	2	no	—
344	C₂³×C₂₃	—	4	2	no	—
345	C₂³×C₂₃	—	4	2	no	—
346	C₂³×C₂₃	—	4	2	no	—
347	C₂³×C₂₃	—	4	2	no	—
348	C₂³×C₂₃	—	4	2	no	—
349	C₂³×C₂₃	—	4	2	no	—
350	C₂³×C₂₃	—	4	2	no	—
351	C₂³×C₂₃	—	4	2	no	—
352	C₂³×C₂₃	—	4	2	no	—
353	C₂³×C₂₃	—	8	4	no	—
354	C₂³×C₂₃	—	8	16	no	—
355	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
356	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₂₃	—	2	4	no	—
359	Q₈×C₂₃	—	2	2	no	—
360	Q₈×C₂₃	—	2	2	no	—
361	Q₈×C₂₃	—	2	2	no	—
362	Q₈×C₂₃	—	4	2	no	—
363	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
364	D₄×C₂₃	—	2	4	no	—
365	D₄×C₂₃	—	2	2	no	—
366	D₄×C₂₃	—	2	2	no	—
367	D₄×C₂₃	—	2	2	no	—
368	D₄×C₂₃	—	2	2	no	—
369	D₄×C₂₃	—	2	2	no	—
370	D₄×C₂₃	—	2	2	no	—
371	D₄×C₂₃	—	2	2	no	—
372	D₄×C₂₃	—	4	4	no	—
373	D₄×C₂₃	—	4	8	no	—
374	D₄×C₂₃	—	4	8	no	—
375	D₄×C₂₃	—	4	8	no	—
376	D₄×C₂₃	—	4	8	no	—
377	D₄×C₂₃	—	4	8	no	—
378	D₄×C₂₃	—	4	2	no	—
379	D₄×C₂₃	—	4	2	no	—
380	D₄×C₂₃	—	4	2	no	—
381	D₄×C₂₃	—	8	4	no	—
382	D₄×C₂₃	—	8	4	no	—
383	D₄×C₂₃	—	8	4	no	—
384	D₄×C₂₃	—	8	4	no	—
385	D₄×C₂₃	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	4	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	4	no	—
393	C₂×C₄×C₂₃	—	2	4	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	4	8	no	—
402	C₂×C₄×C₂₃	—	4	8	no	—
403	C₂×C₄×C₂₃	—	4	8	no	—
404	C₂×C₄×C₂₃	—	4	2	no	—
405	C₂×C₄×C₂₃	—	4	2	no	—
406	C₂×C₄×C₂₃	—	4	2	no	—
407	C₂×C₄×C₂₃	—	8	4	no	—
408	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
409	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
416	C₈×C₂₃	—	2	2	no	—
417	C₈×C₂₃	—	2	2	no	—
418	C₈×C₂₃	—	2	2	no	—
419	C₈×C₂₃	C₂²×D₄	1	4	yes	—
420	C₂²×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
421	C₂²×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
422	C₂×#550	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₂×#546	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#3268	C₂×C₂₃	1	16	yes	direct product factor
425	C₂×#496	C₂×C₂₃	1	1	yes	characteristic, complemented
426	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
427	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
428	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
429	C₂×#459	C₂×C₂₃	1	1	yes	characteristic, complemented
430	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
431	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
432	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
433	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
434	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
435	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	2	4	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	2	2	no	—
441	C₂²×C₂₃	—	2	2	no	—
442	C₂²×C₂₃	—	2	2	no	—
443	C₂²×C₂₃	—	4	4	no	—
444	C₂²×C₂₃	—	4	4	no	—
445	C₂²×C₂₃	—	4	8	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	4	2	no	—
449	C₂²×C₂₃	—	4	2	no	—
450	C₂²×C₂₃	—	4	2	no	—
451	C₂²×C₂₃	—	4	2	no	—
452	C₂²×C₂₃	—	4	2	no	—
453	C₂²×C₂₃	—	4	2	no	—
454	C₂²×C₂₃	—	4	2	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	2	no	—
457	C₂²×C₂₃	—	8	16	no	—
458	C₂²×C₂₃	—	8	4	no	—
459	C₂²×C₂₃	—	8	4	no	—
460	C₂²×C₂₃	—	8	4	no	—
461	C₂²×C₂₃	D₄²	1	2	yes	—
462	C₂²×C₂₃	#575	1	2	yes	—
463	C₂²×C₂₃	#576	1	2	yes	—
464	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	2	no	—
467	C₄×C₂₃	—	2	4	no	—
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	2	no	—
470	C₄×C₂₃	—	4	2	no	—
471	C₄×C₂₃	—	4	2	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	D₄²	1	2	yes	—
474	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
475	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
477	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
478	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×AGL(1,ℤ/8)	—	2	8	no	—
481	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	8	yes	complemented
482	C₂×#135	—	2	8	no	—
483	C₂×#135	C₂²×C₂₃	1	8	yes	complemented
484	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
486	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
487	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
490	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
491	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
492	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
493	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
494	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
495	#550	—	2	4	no	—
496	#550	C₂²×C₂₃	1	8	yes	complemented
497	#546	—	2	4	no	—
498	#546	C₂²×C₂₃	1	8	yes	complemented
499	C₂×#127	—	2	1	no	—
500	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
502	C₂×#123	—	2	1	no	—
503	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
504	C₂×#121	—	2	1	no	—
505	C₂×#121	—	2	1	no	—
506	C₂×#121	—	2	1	no	—
507	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
508	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
509	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂×#120	—	2	1	no	—
511	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	C₂×C₄×D₄	—	2	1	no	—
513	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
515	C₂²×C₂²⋊C₄	—	2	1	no	—
516	#496	C₂²×C₂₃	1	8	yes	complemented
517	#468	C₂²×C₂₃	1	8	yes	complemented
518	#466	C₂²×C₂₃	1	8	yes	complemented
519	#464	C₂²×C₂₃	1	8	yes	complemented
520	#459	C₂²×C₂₃	1	8	yes	complemented
521	#452	C₂²×C₂₃	1	8	yes	complemented
522	#449	C₂²×C₂₃	1	8	yes	complemented
523	#449	C₂²×C₂₃	1	8	yes	complemented
524	#447	C₂²×C₂₃	1	8	yes	complemented
525	#440	C₂²×C₂₃	1	8	yes	complemented
526	#435	C₂²×C₂₃	1	8	yes	complemented
527	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
531	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
532	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
533	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
534	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
535	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
537	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
538	C₂×C₂₃	—	4	2	no	—
539	C₂×C₂₃	—	4	2	no	—
540	C₂×C₂₃	—	4	4	no	—
541	C₂×C₂₃	—	8	2	no	—
542	C₂×C₂₃	—	8	2	no	—
543	C₂×C₂₃	—	8	2	no	—
544	C₂×C₂₃	#3268	1	4	yes	direct product factor
545	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
546	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
547	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
548	C₂⁵	—	2	1	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	2	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	—	2	4	no	—
553	C₂×#41	—	2	4	no	—
554	C₂×#41	—	2	4	no	—
555	C₂×#41	—	4	2	no	—
556	C₂×#41	—	4	2	no	—
557	C₂×#41	—	4	2	no	—
558	C₂×#41	C₂³×C₂₃	1	4	yes	—
559	C₂×#41	C₂³×C₂₃	1	4	yes	—
560	C₂×#41	C₂³×C₂₃	1	4	yes	complemented
561	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
563	C₂²×D₄	—	2	4	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	—	2	1	no	—
570	C₂²×D₄	—	2	1	no	—
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	—	2	2	no	—
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	4	2	no	—
575	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
576	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
580	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
581	C₂³×C₄	—	2	1	no	—
582	C₂³×C₄	—	2	1	no	—
583	C₂³×C₄	—	2	1	no	—
584	C₂³×C₄	—	2	1	no	—
585	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
587	AGL(1,ℤ/8)	—	2	32	no	—
588	#135	—	2	32	no	—
589	C₂×Q₁₆	—	2	4	no	—
590	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
591	C₂×SD₁₆	—	2	4	no	—
592	C₂×SD₁₆	—	2	4	no	—
593	C₂×SD₁₆	—	4	2	no	—
594	C₂×SD₁₆	D₄×C₂₃	1	8	yes	complemented
595	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
596	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
597	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
598	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
599	C₂×D₈	—	2	4	no	—
600	C₂×D₈	—	2	4	no	—
601	C₂×D₈	—	2	4	no	—
602	C₂×D₈	—	4	2	no	—
603	C₂×D₈	C₂³×C₂₃	1	4	yes	—
604	C₂×D₈	C₂³×C₂₃	1	4	yes	—
605	C₂×D₈	C₂³×C₂₃	1	4	yes	—
606	C₂×D₈	C₂³×C₂₃	1	4	yes	—
607	C₂×M₁₆	—	2	4	no	—
608	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
609	C₂²×C₈	—	2	4	no	—
610	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
611	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
612	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
613	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₂₃	1	4	yes	complemented
615	#127	—	2	8	no	—
616	#127	—	2	2	no	—
617	#127	C₂³×C₂₃	1	4	yes	complemented
618	#124	—	2	2	no	—
619	#124	C₂³×C₂₃	1	4	yes	—
620	#123	—	2	8	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	2	8	no	—
627	#121	—	2	8	no	—
628	#121	—	2	8	no	—
629	#121	C₂³×C₂₃	1	4	yes	—
630	#121	C₂³×C₂₃	1	4	yes	—
631	#121	C₂³×C₂₃	1	4	yes	complemented
632	#120	—	2	8	no	—
633	C₄×Q₈	—	2	2	no	—
634	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
635	C₄×D₄	—	2	8	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	D₄×C₂₃	1	4	yes	—
638	C₄×D₄	C₂³×C₂₃	1	4	yes	—
639	C₄×D₄	C₂³×C₂₃	1	4	yes	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	8	no	—
653	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
657	#107	C₂³×C₂₃	1	4	yes	complemented
658	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
659	#103	C₂³×C₂₃	1	4	yes	complemented
660	#103	C₂³×C₂₃	1	4	yes	complemented
661	#102	C₂³×C₂₃	1	4	yes	—
662	#102	C₂³×C₂₃	1	4	yes	—
663	#102	C₂³×C₂₃	1	4	yes	complemented
664	#102	C₂³×C₂₃	1	4	yes	complemented
665	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
667	#97	C₂³×C₂₃	1	4	yes	complemented
668	C₂₃	C₂×#3268	1	1	yes	characteristic, direct product factor, Sylow
669	C₂⁴	—	2	1	no	—
670	C₂⁴	—	2	1	no	—
671	C₂⁴	—	2	1	no	—
672	C₂⁴	—	2	1	no	—
673	C₂⁴	—	2	4	no	—
674	C₂⁴	—	4	4	no	—
675	C₂⁴	—	4	4	no	—
676	C₂⁴	—	8	2	no	—
677	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
679	#41	—	2	8	no	—
680	#41	—	2	8	no	—
681	#41	—	2	8	no	—
682	#41	—	4	4	no	—
683	#41	—	4	4	no	—
684	#41	—	4	4	no	—
685	#41	—	4	8	no	—
686	#41	—	4	8	no	—
687	#41	—	4	8	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
694	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	8	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	4	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	—	8	2	no	—
727	C₂×D₄	—	8	2	no	—
728	C₂×D₄	—	8	2	no	—
729	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
730	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
731	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
732	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
733	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
734	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	4	4	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	—	4	4	no	—
750	C₂²×C₄	—	8	2	no	—
751	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
752	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
760	Q₁₆	—	2	8	no	—
761	SD₁₆	—	2	8	no	—
762	SD₁₆	—	2	8	no	—
763	SD₁₆	—	4	4	no	—
764	SD₁₆	C₂×D₄×C₂₃	1	16	yes	complemented
765	D₈	—	2	8	no	—
766	D₈	—	2	8	no	—
767	D₈	—	2	8	no	—
768	D₈	—	4	4	no	—
769	M₁₆	—	2	8	no	—
770	C₂×C₈	—	2	2	no	—
771	C₂×C₈	—	2	2	no	—
772	C₂×C₈	—	2	2	no	—
773	C₂×C₈	—	2	8	no	—
774	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
775	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
776	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
777	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
778	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
784	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
785	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
794	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
795	C₄²	—	2	4	no	—
796	C₄²	C₂×D₄×C₂₃	1	2	yes	—
797	C₄²	C₂⁴×C₂₃	1	2	yes	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	4	2	no	—
814	C₂³	—	4	2	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	2	no	—
820	C₂³	—	4	2	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	8	4	no	—
823	C₂³	—	8	16	no	—
824	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
825	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
826	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	Q₈	—	2	2	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	4	2	no	—
832	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	8	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	8	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	8	4	no	—
851	D₄	—	8	4	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	4	no	—
854	D₄	C₂²×D₄×C₂₃	1	4	yes	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	8	4	no	—
877	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
878	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
880	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
882	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
883	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
884	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
885	C₈	—	2	2	no	—
886	C₈	—	2	2	no	—
887	C₈	—	2	2	no	—
888	C₈	C₂²×D₄×C₂₃	1	4	yes	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	4	4	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	8	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	8	16	no	—
911	C₂²	—	8	4	no	—
912	C₂²	—	8	4	no	—
913	C₂²	—	8	4	no	—
914	C₂²	D₄²×C₂₃	1	2	yes	—
915	C₂²	C₂₃×#575	1	2	yes	—
916	C₂²	C₂₃×#576	1	2	yes	—
917	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	D₄²×C₂₃	1	2	yes	—
927	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
928	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	—	8	2	no	—
935	C₂	C₂₃×#3268	1	4	yes	direct product factor
936	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
937	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
938	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₂₃×#135	C₂	semidirect
3. C₂×C₂₃×#550	C₂	semidirect
4. C₂×C₂₃×#546	C₂	semidirect
5. C₂₃×#3268	C₂	direct (N × H)
6. C₂×C₂₃×#496	C₂	semidirect
7. C₂×C₂₃×#468	C₂	semidirect
8. C₂×C₂₃×#466	C₂	semidirect
9. C₂×C₂₃×#464	C₂	semidirect
10. C₂×C₂₃×#459	C₂	semidirect
11. C₂×C₂₃×#452	C₂	semidirect
12. C₂×C₂₃×#449	C₂	semidirect
13. C₂×C₂₃×#449	C₂	semidirect
14. C₂×C₂₃×#447	C₂	semidirect
15. C₂×C₂₃×#440	C₂	semidirect
16. C₂×C₂₃×#435	C₂	semidirect
19. C₂²×#41×C₂₃	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₂₃×#135	C₂²	semidirect
25. C₂²×Q₁₆×C₂₃	C₂²	semidirect
28. C₂²×SD₁₆×C₂₃	C₂²	semidirect
29. C₂²×SD₁₆×C₂₃	C₂²	semidirect
35. C₂³×C₈×C₂₃	C₂²	semidirect
37. C₂₃×#550	C₂²	semidirect
39. C₂₃×#546	C₂²	semidirect
41. C₂×C₂₃×#127	C₂²	semidirect
50. C₂×C₂₃×#121	C₂²	semidirect
52. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
57. C₂₃×#496	C₂²	semidirect
58. C₂₃×#468	C₂²	semidirect
59. C₂₃×#466	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#459	C₂²	semidirect
62. C₂₃×#452	C₂²	semidirect
63. C₂₃×#449	C₂²	semidirect
64. C₂₃×#449	C₂²	semidirect
65. C₂₃×#447	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
74. C₂×C₂₃×#102	C₂²	semidirect
75. C₂×C₂₃×#102	C₂²	semidirect
77. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
78. C₂×C₂₃×#97	C₂²	semidirect
91. C₂×#41×C₂₃	C₂³	semidirect
121. C₂×Q₁₆×C₂₃	C₂³	semidirect
125. C₂×SD₁₆×C₂₃	D₄	semidirect
128. C₂×SD₁₆×C₂₃	C₂³	semidirect
129. C₂×SD₁₆×C₂₃	C₂³	semidirect
145. C₂²×C₈×C₂₃	C₂³	semidirect
148. C₂₃×#127	C₂³	semidirect
162. C₂₃×#121	C₂³	semidirect
165. 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
194. C₂₃×#102	C₂³	semidirect
195. C₂₃×#102	C₂³	semidirect
197. C₂₃×C₂²⋊C₈	C₂³	semidirect
198. C₂₃×#97	C₂³	semidirect
294. SD₁₆×C₂₃	C₂×D₄	semidirect
328. C₂×#3268	C₂₃	direct (N × H)
420. C₂²×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
421. C₂²×#135	C₂×C₂₃	semidirect
422. C₂×#550	C₂×C₂₃	semidirect
423. C₂×#546	C₂×C₂₃	semidirect
424. #3268	C₂×C₂₃	direct (N × H)
425. C₂×#496	C₂×C₂₃	semidirect
426. C₂×#468	C₂×C₂₃	semidirect
427. C₂×#466	C₂×C₂₃	semidirect
428. C₂×#464	C₂×C₂₃	semidirect
429. C₂×#459	C₂×C₂₃	semidirect
430. C₂×#452	C₂×C₂₃	semidirect
431. C₂×#449	C₂×C₂₃	semidirect
432. C₂×#449	C₂×C₂₃	semidirect
433. C₂×#447	C₂×C₂₃	semidirect
434. C₂×#440	C₂×C₂₃	semidirect
435. C₂×#435	C₂×C₂₃	semidirect
478. C₂²×#41	C₂²×C₂₃	semidirect
481. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
483. C₂×#135	C₂²×C₂₃	semidirect
484. C₂²×Q₁₆	C₂²×C₂₃	semidirect
487. C₂²×SD₁₆	C₂²×C₂₃	semidirect
488. C₂²×SD₁₆	C₂²×C₂₃	semidirect
494. C₂³×C₈	C₂²×C₂₃	semidirect
496. #550	C₂²×C₂₃	semidirect
498. #546	C₂²×C₂₃	semidirect
500. C₂×#127	C₂²×C₂₃	semidirect
509. C₂×#121	C₂²×C₂₃	semidirect
511. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
516. #496	C₂²×C₂₃	semidirect
517. #468	C₂²×C₂₃	semidirect
518. #466	C₂²×C₂₃	semidirect
519. #464	C₂²×C₂₃	semidirect
520. #459	C₂²×C₂₃	semidirect
521. #452	C₂²×C₂₃	semidirect
522. #449	C₂²×C₂₃	semidirect
523. #449	C₂²×C₂₃	semidirect
524. #447	C₂²×C₂₃	semidirect
525. #440	C₂²×C₂₃	semidirect
526. #435	C₂²×C₂₃	semidirect
527. C₂×#107	C₂²×C₂₃	semidirect
528. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
529. C₂×#103	C₂²×C₂₃	semidirect
530. C₂×#103	C₂²×C₂₃	semidirect
533. C₂×#102	C₂²×C₂₃	semidirect
534. C₂×#102	C₂²×C₂₃	semidirect
536. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
537. C₂×#97	C₂²×C₂₃	semidirect
544. C₂×C₂₃	#3268	direct (N × H)
560. C₂×#41	C₂³×C₂₃	semidirect
590. C₂×Q₁₆	C₂³×C₂₃	semidirect
594. C₂×SD₁₆	D₄×C₂₃	semidirect
597. C₂×SD₁₆	C₂³×C₂₃	semidirect
598. C₂×SD₁₆	C₂³×C₂₃	semidirect
614. C₂²×C₈	C₂³×C₂₃	semidirect
617. #127	C₂³×C₂₃	semidirect
631. #121	C₂³×C₂₃	semidirect
634. C₄×Q₈	C₂³×C₂₃	semidirect
657. #107	C₂³×C₂₃	semidirect
658. C₄⋊C₈	C₂³×C₂₃	semidirect
659. #103	C₂³×C₂₃	semidirect
660. #103	C₂³×C₂₃	semidirect
663. #102	C₂³×C₂₃	semidirect
664. #102	C₂³×C₂₃	semidirect
666. C₂²⋊C₈	C₂³×C₂₃	semidirect
667. #97	C₂³×C₂₃	semidirect
668. C₂₃	C₂×#3268	direct (N × H)
764. SD₁₆	C₂×D₄×C₂₃	semidirect
935. C₂	C₂₃×#3268	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×AGL(1,ℤ/8)	2
C₂²×C₂₃×#135	2
C₂×C₂₃×#550	2
C₂×C₂₃×#546	2
C₂₃×#3268	2
C₂×C₂₃×#496	2
C₂×C₂₃×#468	2
C₂×C₂₃×#466	2
C₂×C₂₃×#464	2
C₂×C₂₃×#459	2
C₂×C₂₃×#452	2
C₂×C₂₃×#449	2
C₂×C₂₃×#447	2
C₂×C₂₃×#440	2
C₂×C₂₃×#435	2
C₂×#3268	23

Subgroups — C2×C23×#3268 #19208652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3268 #19208652