Subgroups — C₂×C₂₃×#3519 #19210397

Order 5888.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₂₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#546	C₂	1	4	yes	maximal, complemented
9	C₂×D₄²×C₂₃	C₂	1	2	yes	maximal, complemented
10	C₂×D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#540	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#538	C₂	1	4	yes	maximal, complemented
13	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#525	C₂	1	2	yes	maximal, complemented
16	C₂²×C₂₃×#121	C₂	1	2	yes	maximal, complemented
17	C₂×C₂₃×#518	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
20	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
21	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
23	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
24	C₂³×D₄×C₂₃	C₂²	1	4	yes	complemented
25	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	complemented
26	C₂₃×#555	C₂²	1	16	yes	complemented
27	C₂₃×#554	C₂²	1	16	yes	complemented
28	C₂₃×#553	C₂²	1	32	yes	complemented
29	C₂₃×#553	C₂²	1	32	yes	complemented
30	C₂₃×#550	C₂²	1	16	yes	complemented
31	C₂₃×#546	C₂²	1	64	yes	complemented
32	C₂₃×#546	C₂²	1	32	yes	complemented
33	D₄²×C₂₃	C₂²	1	16	yes	complemented
34	D₄²×C₂₃	C₂²	1	32	yes	complemented
35	C₂₃×#540	C₂²	1	32	yes	complemented
36	C₂₃×#538	C₂²	1	64	yes	complemented
37	C₂₃×#532	C₂²	1	16	yes	complemented
38	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₂₃×#127	C₂²	1	2	yes	complemented
41	C₂₃×#529	C₂²	1	16	yes	complemented
42	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
43	C₂×C₂₃×#126	C₂²	1	4	yes	complemented
44	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
46	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
48	C₂×C₂₃×#124	C₂²	1	4	yes	complemented
49	C₂₃×#525	C₂²	1	32	yes	complemented
50	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
51	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
52	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
53	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
54	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
59	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
60	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
61	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
62	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
63	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
64	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
65	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
66	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
67	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
68	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
69	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
70	C₂×C₂₃×#121	C₂²	1	32	yes	complemented
71	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
72	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
73	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
74	C₂₃×#518	C₂²	1	32	yes	complemented
75	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
85	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
86	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
89	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄×C₂₃	C₂²	1	16	yes	complemented
92	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
93	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
94	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
95	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
97	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
99	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₂₃	C₂³	1	2	yes	—
102	C₂⁵×C₂₃	C₂³	1	4	yes	—
103	C₂×#41×C₂₃	—	4	8	no	—
104	C₂×#41×C₂₃	—	4	8	no	—
105	C₂×#41×C₂₃	C₂³	1	16	yes	complemented
106	C₂×#41×C₂₃	C₂³	1	16	yes	complemented
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₂₃	—	2	8	no	—
110	C₂²×D₄×C₂₃	—	2	16	no	—
111	C₂²×D₄×C₂₃	—	4	8	no	—
112	C₂²×D₄×C₂₃	—	4	16	no	—
113	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
115	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
118	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
119	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
120	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
122	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
123	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
124	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
127	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₂₃	C₂³	1	16	yes	complemented
130	C₂²×D₄×C₂₃	C₂³	1	32	yes	complemented
131	C₂³×C₄×C₂₃	—	4	8	no	—
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
143	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
144	C₂³×C₄×C₂₃	C₂³	1	16	yes	complemented
145	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
146	C₂₃×#127	C₂³	1	8	yes	complemented
147	C₂₃×#127	C₂³	1	16	yes	complemented
148	C₂₃×#126	C₂³	1	32	yes	complemented
149	C₂₃×#126	C₂³	1	16	yes	complemented
150	C₂₃×#125	C₂³	1	8	yes	complemented
151	C₂₃×#125	C₂³	1	16	yes	complemented
152	C₂₃×#124	C₂³	1	32	yes	complemented
153	C₂₃×#124	C₂³	1	8	yes	complemented
154	C₂₃×#124	C₂³	1	16	yes	complemented
155	C₂₃×#123	C₂³	1	32	yes	complemented
156	C₂₃×#123	C₂³	1	32	yes	complemented
157	C₂₃×#123	C₂³	1	32	yes	complemented
158	C₂₃×#123	C₂³	1	16	yes	complemented
159	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
160	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
161	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
162	C₂₃×#121	C₂³	1	8	yes	—
163	C₂₃×#121	C₂³	1	16	yes	complemented
164	C₂₃×#121	C₂³	1	32	yes	complemented
165	C₂₃×#121	C₂³	1	32	yes	complemented
166	C₂₃×#121	C₂³	1	16	yes	complemented
167	C₂₃×#121	C₂³	1	16	yes	complemented
168	C₂₃×#121	C₂³	1	32	yes	complemented
169	C₂₃×#121	C₂³	1	16	yes	complemented
170	C₂₃×#121	C₂³	1	16	yes	complemented
171	C₂₃×#121	C₂³	1	16	yes	complemented
172	C₂₃×#121	C₂³	1	16	yes	complemented
173	C₂₃×#121	C₂³	1	32	yes	complemented
174	C₂₃×#121	C₂³	1	32	yes	complemented
175	C₂₃×#120	C₂³	1	32	yes	complemented
176	C₂₃×#120	C₂³	1	32	yes	complemented
177	C₂₃×#120	C₂³	1	32	yes	complemented
178	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
179	C₄×D₄×C₂₃	C₂³	1	8	yes	—
180	C₄×D₄×C₂₃	C₂³	1	16	yes	—
181	C₄×D₄×C₂₃	C₂³	1	8	yes	—
182	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
183	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
184	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
185	C₄×D₄×C₂₃	C₂³	1	32	yes	complemented
186	C₄×D₄×C₂₃	C₂³	1	32	yes	complemented
187	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
188	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
189	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
190	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
191	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
192	C₄×D₄×C₂₃	C₂³	1	32	yes	complemented
193	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
194	C₂₃×#117	C₂³	1	16	yes	complemented
195	C₂₃×#117	C₂³	1	16	yes	complemented
196	C₂₃×#117	C₂³	1	16	yes	complemented
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
211	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	complemented
212	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
228	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	complemented
229	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	complemented
230	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	complemented
231	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
236	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
237	C₂×C₄²×C₂₃	C₂³	1	8	yes	complemented
238	C₂⁴×C₂₃	—	2	8	no	—
239	C₂⁴×C₂₃	—	2	8	no	—
240	C₂⁴×C₂₃	—	2	16	no	—
241	C₂⁴×C₂₃	—	4	4	no	—
242	C₂⁴×C₂₃	—	4	8	no	—
243	C₂⁴×C₂₃	—	4	8	no	—
244	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
245	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
246	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
247	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
248	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
249	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₂₃	C₂⁴	1	16	yes	—
251	#41×C₂₃	—	4	32	no	—
252	#41×C₂₃	—	4	32	no	—
253	C₂×Q₈×C₂₃	—	2	4	no	—
254	C₂×Q₈×C₂₃	—	4	4	no	—
255	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
256	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
257	C₂×D₄×C₂₃	—	2	8	no	—
258	C₂×D₄×C₂₃	—	2	16	no	—
259	C₂×D₄×C₂₃	—	2	8	no	—
260	C₂×D₄×C₂₃	—	2	16	no	—
261	C₂×D₄×C₂₃	—	2	32	no	—
262	C₂×D₄×C₂₃	—	2	64	no	—
263	C₂×D₄×C₂₃	—	2	4	no	—
264	C₂×D₄×C₂₃	—	2	8	no	—
265	C₂×D₄×C₂₃	—	2	4	no	—
266	C₂×D₄×C₂₃	—	2	8	no	—
267	C₂×D₄×C₂₃	—	4	32	no	—
268	C₂×D₄×C₂₃	—	4	8	no	—
269	C₂×D₄×C₂₃	—	4	8	no	—
270	C₂×D₄×C₂₃	—	4	8	no	—
271	C₂×D₄×C₂₃	—	4	4	no	—
272	C₂×D₄×C₂₃	—	4	8	no	—
273	C₂×D₄×C₂₃	—	4	64	no	—
274	C₂×D₄×C₂₃	#41	1	8	yes	complemented
275	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
276	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
277	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
278	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
279	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
280	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
281	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
282	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
283	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
284	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
285	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
286	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
287	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
288	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₂₃	—	2	4	no	—
290	C₂²×C₄×C₂₃	—	2	4	no	—
291	C₂²×C₄×C₂₃	—	2	8	no	—
292	C₂²×C₄×C₂₃	—	2	4	no	—
293	C₂²×C₄×C₂₃	—	2	8	no	—
294	C₂²×C₄×C₂₃	—	2	8	no	—
295	C₂²×C₄×C₂₃	—	4	32	no	—
296	C₂²×C₄×C₂₃	—	4	4	no	—
297	C₂²×C₄×C₂₃	—	4	4	no	—
298	C₂²×C₄×C₂₃	—	4	4	no	—
299	C₂²×C₄×C₂₃	—	4	8	no	—
300	C₂²×C₄×C₂₃	—	4	8	no	—
301	C₂²×C₄×C₂₃	—	4	8	no	—
302	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
315	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
319	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
320	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
321	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
322	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
323	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
324	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
327	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
328	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
329	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
332	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
333	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
334	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
335	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
336	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
337	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
338	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
341	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
342	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
344	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
345	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
348	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
349	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
350	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
351	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
352	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
353	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
354	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
355	C₄²×C₂₃	C₂⁴	1	4	yes	—
356	C₄²×C₂₃	C₂⁴	1	4	yes	—
357	C₄²×C₂₃	C₂⁴	1	4	yes	—
358	C₄²×C₂₃	C₂⁴	1	4	yes	—
359	C₄²×C₂₃	C₂⁴	1	16	yes	—
360	C₄²×C₂₃	C₂⁴	1	8	yes	—
361	C₂×#3519	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	2	no	—
364	C₂³×C₂₃	—	2	4	no	—
365	C₂³×C₂₃	—	2	4	no	—
366	C₂³×C₂₃	—	2	4	no	—
367	C₂³×C₂₃	—	2	16	no	—
368	C₂³×C₂₃	—	2	4	no	—
369	C₂³×C₂₃	—	2	8	no	—
370	C₂³×C₂₃	—	2	4	no	—
371	C₂³×C₂₃	—	2	8	no	—
372	C₂³×C₂₃	—	2	8	no	—
373	C₂³×C₂₃	—	2	4	no	—
374	C₂³×C₂₃	—	2	4	no	—
375	C₂³×C₂₃	—	2	16	no	—
376	C₂³×C₂₃	—	2	4	no	—
377	C₂³×C₂₃	—	2	32	no	—
378	C₂³×C₂₃	—	4	8	no	—
379	C₂³×C₂₃	—	4	16	no	—
380	C₂³×C₂₃	—	4	16	no	—
381	C₂³×C₂₃	—	4	32	no	—
382	C₂³×C₂₃	—	8	32	no	—
383	C₂³×C₂₃	C₂×#41	1	8	yes	—
384	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
385	C₂³×C₂₃	C₂⁵	1	4	yes	—
386	C₂³×C₂₃	C₂⁵	1	4	yes	—
387	C₂³×C₂₃	C₂⁵	1	8	yes	—
388	C₂³×C₂₃	C₂⁵	1	4	yes	—
389	C₂³×C₂₃	C₂⁵	1	2	yes	—
390	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
391	Q₈×C₂₃	—	2	8	no	—
392	Q₈×C₂₃	—	4	8	no	—
393	D₄×C₂₃	—	2	16	no	—
394	D₄×C₂₃	—	2	32	no	—
395	D₄×C₂₃	—	2	16	no	—
396	D₄×C₂₃	—	2	32	no	—
397	D₄×C₂₃	—	2	8	no	—
398	D₄×C₂₃	—	2	16	no	—
399	D₄×C₂₃	—	2	8	no	—
400	D₄×C₂₃	—	2	16	no	—
401	D₄×C₂₃	—	4	16	no	—
402	D₄×C₂₃	—	4	16	no	—
403	D₄×C₂₃	—	4	16	no	—
404	D₄×C₂₃	—	4	8	no	—
405	D₄×C₂₃	—	4	16	no	—
406	D₄×C₂₃	C₂×#41	1	16	yes	complemented
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	4	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	2	no	—
411	C₂×C₄×C₂₃	—	2	4	no	—
412	C₂×C₄×C₂₃	—	2	4	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	8	no	—
415	C₂×C₄×C₂₃	—	2	4	no	—
416	C₂×C₄×C₂₃	—	2	8	no	—
417	C₂×C₄×C₂₃	—	2	4	no	—
418	C₂×C₄×C₂₃	—	2	8	no	—
419	C₂×C₄×C₂₃	—	2	16	no	—
420	C₂×C₄×C₂₃	—	2	8	no	—
421	C₂×C₄×C₂₃	—	2	16	no	—
422	C₂×C₄×C₂₃	—	2	16	no	—
423	C₂×C₄×C₂₃	—	4	8	no	—
424	C₂×C₄×C₂₃	—	4	8	no	—
425	C₂×C₄×C₂₃	—	4	8	no	—
426	C₂×C₄×C₂₃	—	4	16	no	—
427	C₂×C₄×C₂₃	—	4	16	no	—
428	C₂×C₄×C₂₃	—	4	16	no	—
429	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
430	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
431	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
432	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
433	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
434	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
435	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
436	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
437	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
438	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
439	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
440	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
441	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
442	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
443	#3519	C₂×C₂₃	1	32	yes	direct product factor
444	C₂×#555	C₂×C₂₃	1	1	yes	characteristic, complemented
445	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
446	C₂×#553	C₂×C₂₃	1	2	yes	complemented
447	C₂×#553	C₂×C₂₃	1	2	yes	complemented
448	C₂×#550	C₂×C₂₃	1	1	yes	characteristic, complemented
449	C₂×#546	C₂×C₂₃	1	4	yes	complemented
450	C₂×#546	C₂×C₂₃	1	2	yes	complemented
451	C₂×D₄²	C₂×C₂₃	1	1	yes	characteristic, complemented
452	C₂×D₄²	C₂×C₂₃	1	2	yes	complemented
453	C₂×#540	C₂×C₂₃	1	2	yes	complemented
454	C₂×#538	C₂×C₂₃	1	4	yes	complemented
455	C₂×#532	C₂×C₂₃	1	1	yes	characteristic, complemented
456	C₂×#529	C₂×C₂₃	1	1	yes	characteristic, complemented
457	C₂×#525	C₂×C₂₃	1	2	yes	complemented
458	C₂²×#121	C₂×C₂₃	1	2	yes	complemented
459	C₂×#518	C₂×C₂₃	1	2	yes	complemented
460	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
461	C₂²×C₂₃	—	2	2	no	—
462	C₂²×C₂₃	—	2	2	no	—
463	C₂²×C₂₃	—	2	4	no	—
464	C₂²×C₂₃	—	2	4	no	—
465	C₂²×C₂₃	—	2	8	no	—
466	C₂²×C₂₃	—	2	16	no	—
467	C₂²×C₂₃	—	2	4	no	—
468	C₂²×C₂₃	—	2	4	no	—
469	C₂²×C₂₃	—	2	8	no	—
470	C₂²×C₂₃	—	2	4	no	—
471	C₂²×C₂₃	—	2	8	no	—
472	C₂²×C₂₃	—	2	8	no	—
473	C₂²×C₂₃	—	2	4	no	—
474	C₂²×C₂₃	—	2	4	no	—
475	C₂²×C₂₃	—	2	4	no	—
476	C₂²×C₂₃	—	4	32	no	—
477	C₂²×C₂₃	—	4	8	no	—
478	C₂²×C₂₃	—	4	16	no	—
479	C₂²×C₂₃	—	4	8	no	—
480	C₂²×C₂₃	—	8	32	no	—
481	C₂²×C₂₃	C₂²×#41	1	8	yes	—
482	C₂²×C₂₃	C₂²×#41	1	2	yes	—
483	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
484	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
485	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
486	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
487	C₄×C₂₃	—	2	2	no	—
488	C₄×C₂₃	—	2	4	no	—
489	C₄×C₂₃	—	2	2	no	—
490	C₄×C₂₃	—	2	2	no	—
491	C₄×C₂₃	—	2	4	no	—
492	C₄×C₂₃	—	2	4	no	—
493	C₄×C₂₃	—	2	2	no	—
494	C₄×C₂₃	—	2	4	no	—
495	C₄×C₂₃	—	2	8	no	—
496	C₄×C₂₃	—	2	4	no	—
497	C₄×C₂₃	C₂²×#41	1	4	yes	—
498	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
499	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
500	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
501	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
502	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
503	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
504	C₂³×D₄	C₂²×C₂₃	1	4	yes	complemented
505	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	complemented
506	#555	C₂²×C₂₃	1	16	yes	complemented
507	#554	C₂²×C₂₃	1	16	yes	complemented
508	#553	C₂²×C₂₃	1	32	yes	complemented
509	#553	C₂²×C₂₃	1	32	yes	complemented
510	#550	C₂²×C₂₃	1	16	yes	complemented
511	#546	C₂²×C₂₃	1	64	yes	complemented
512	#546	C₂²×C₂₃	1	32	yes	complemented
513	D₄²	C₂²×C₂₃	1	16	yes	complemented
514	D₄²	C₂²×C₂₃	1	32	yes	complemented
515	#540	C₂²×C₂₃	1	32	yes	complemented
516	#538	C₂²×C₂₃	1	64	yes	complemented
517	#532	C₂²×C₂₃	1	16	yes	complemented
518	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
520	C₂×#127	C₂²×C₂₃	1	2	yes	complemented
521	#529	C₂²×C₂₃	1	16	yes	complemented
522	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
523	C₂×#126	C₂²×C₂₃	1	4	yes	complemented
524	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
526	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
528	C₂×#124	C₂²×C₂₃	1	4	yes	complemented
529	#525	C₂²×C₂₃	1	32	yes	complemented
530	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
531	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
532	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
533	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
534	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
535	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
536	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
537	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
538	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
539	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
540	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
541	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
542	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
543	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
544	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
545	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
546	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
547	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
548	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
549	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
550	C₂×#121	C₂²×C₂₃	1	32	yes	complemented
551	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
552	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
553	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
554	#518	C₂²×C₂₃	1	32	yes	complemented
555	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
556	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
557	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
558	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
559	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
560	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
561	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
562	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
563	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
564	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
565	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
566	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
567	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
568	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
569	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
571	C₂×C₄×D₄	C₂²×C₂₃	1	16	yes	complemented
572	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
573	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
574	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
575	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
576	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
577	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
578	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
579	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
580	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
581	C₂×C₂₃	—	2	4	no	—
582	C₂×C₂₃	—	2	8	no	—
583	C₂×C₂₃	—	4	4	no	—
584	C₂×C₂₃	—	4	8	no	—
585	C₂×C₂₃	—	4	4	no	—
586	C₂×C₂₃	#3519	1	4	yes	direct product factor
587	C₂×C₂₃	C₂³×#41	1	1	yes	characteristic
588	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂⁵	C₂³×C₂₃	1	2	yes	—
591	C₂⁵	C₂³×C₂₃	1	4	yes	—
592	C₂×#41	—	4	8	no	—
593	C₂×#41	—	4	8	no	—
594	C₂×#41	C₂³×C₂₃	1	16	yes	complemented
595	C₂×#41	C₂³×C₂₃	1	16	yes	complemented
596	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
598	C₂²×D₄	—	2	8	no	—
599	C₂²×D₄	—	2	16	no	—
600	C₂²×D₄	—	4	8	no	—
601	C₂²×D₄	—	4	16	no	—
602	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
604	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
605	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
606	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
607	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
608	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
609	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
611	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
612	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
613	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
614	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
615	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
616	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
617	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₂₃	1	16	yes	complemented
619	C₂²×D₄	C₂³×C₂₃	1	32	yes	complemented
620	C₂³×C₄	—	4	8	no	—
621	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
623	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
625	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
626	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
628	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
629	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
630	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
631	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
632	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
633	C₂³×C₄	C₂³×C₂₃	1	16	yes	complemented
634	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
635	#127	C₂³×C₂₃	1	8	yes	complemented
636	#127	C₂³×C₂₃	1	16	yes	complemented
637	#126	C₂³×C₂₃	1	16	yes	complemented
638	#126	C₂³×C₂₃	1	32	yes	complemented
639	#125	C₂³×C₂₃	1	8	yes	complemented
640	#125	C₂³×C₂₃	1	16	yes	complemented
641	#124	C₂³×C₂₃	1	8	yes	complemented
642	#124	C₂³×C₂₃	1	16	yes	complemented
643	#124	C₂³×C₂₃	1	32	yes	complemented
644	#123	C₂³×C₂₃	1	32	yes	complemented
645	#123	C₂³×C₂₃	1	16	yes	complemented
646	#123	C₂³×C₂₃	1	32	yes	complemented
647	#123	C₂³×C₂₃	1	32	yes	complemented
648	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
649	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
650	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
651	#121	C₂³×C₂₃	1	8	yes	—
652	#121	C₂³×C₂₃	1	16	yes	complemented
653	#121	C₂³×C₂₃	1	32	yes	complemented
654	#121	C₂³×C₂₃	1	32	yes	complemented
655	#121	C₂³×C₂₃	1	16	yes	complemented
656	#121	C₂³×C₂₃	1	16	yes	complemented
657	#121	C₂³×C₂₃	1	16	yes	complemented
658	#121	C₂³×C₂₃	1	16	yes	complemented
659	#121	C₂³×C₂₃	1	32	yes	complemented
660	#121	C₂³×C₂₃	1	32	yes	complemented
661	#121	C₂³×C₂₃	1	16	yes	complemented
662	#121	C₂³×C₂₃	1	16	yes	complemented
663	#121	C₂³×C₂₃	1	32	yes	complemented
664	#120	C₂³×C₂₃	1	32	yes	complemented
665	#120	C₂³×C₂₃	1	32	yes	complemented
666	#120	C₂³×C₂₃	1	32	yes	complemented
667	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
668	C₄×D₄	C₂³×C₂₃	1	8	yes	—
669	C₄×D₄	C₂³×C₂₃	1	8	yes	—
670	C₄×D₄	C₂³×C₂₃	1	16	yes	—
671	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
672	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
673	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
674	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
675	C₄×D₄	C₂³×C₂₃	1	32	yes	complemented
676	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
677	C₄×D₄	C₂³×C₂₃	1	32	yes	complemented
678	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
679	C₄×D₄	C₂³×C₂₃	1	32	yes	complemented
680	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
681	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
682	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
683	#117	C₂³×C₂₃	1	16	yes	complemented
684	#117	C₂³×C₂₃	1	16	yes	complemented
685	#117	C₂³×C₂₃	1	16	yes	complemented
686	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
692	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
698	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
700	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	complemented
701	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	complemented
718	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	complemented
719	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	complemented
720	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
722	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
723	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₂₃	1	8	yes	complemented
727	C₂₃	C₂×#3519	1	1	yes	characteristic, direct product factor, Sylow
728	C₂⁴	—	2	8	no	—
729	C₂⁴	—	2	8	no	—
730	C₂⁴	—	2	16	no	—
731	C₂⁴	—	4	4	no	—
732	C₂⁴	—	4	8	no	—
733	C₂⁴	—	4	8	no	—
734	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
735	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
736	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
737	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
738	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
739	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂⁴	C₂⁴×C₂₃	1	16	yes	—
741	#41	—	4	32	no	—
742	#41	—	4	32	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	4	4	no	—
745	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
746	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	2	16	no	—
749	C₂×D₄	—	2	8	no	—
750	C₂×D₄	—	2	16	no	—
751	C₂×D₄	—	2	32	no	—
752	C₂×D₄	—	2	64	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	8	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	2	8	no	—
757	C₂×D₄	—	4	32	no	—
758	C₂×D₄	—	4	8	no	—
759	C₂×D₄	—	4	8	no	—
760	C₂×D₄	—	4	8	no	—
761	C₂×D₄	—	4	4	no	—
762	C₂×D₄	—	4	8	no	—
763	C₂×D₄	—	4	64	no	—
764	C₂×D₄	#41×C₂₃	1	8	yes	complemented
765	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
766	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
767	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
768	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
769	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
770	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
771	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
772	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
773	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
774	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
775	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
776	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
777	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
778	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	8	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	8	no	—
784	C₂²×C₄	—	2	8	no	—
785	C₂²×C₄	—	4	32	no	—
786	C₂²×C₄	—	4	4	no	—
787	C₂²×C₄	—	4	4	no	—
788	C₂²×C₄	—	4	4	no	—
789	C₂²×C₄	—	4	8	no	—
790	C₂²×C₄	—	4	8	no	—
791	C₂²×C₄	—	4	8	no	—
792	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
799	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
802	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
803	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
804	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
806	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
807	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
808	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
809	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
810	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
811	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
812	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
813	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
814	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
817	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
818	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
819	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
820	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
821	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
822	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
823	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
824	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
825	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
826	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
827	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
828	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
829	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
830	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
831	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
832	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
834	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
835	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
836	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
837	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
838	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
839	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
840	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
841	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
842	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
843	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
844	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
845	C₄²	C₂⁴×C₂₃	1	4	yes	—
846	C₄²	C₂⁴×C₂₃	1	4	yes	—
847	C₄²	C₂⁴×C₂₃	1	4	yes	—
848	C₄²	C₂⁴×C₂₃	1	4	yes	—
849	C₄²	C₂⁴×C₂₃	1	16	yes	—
850	C₄²	C₂⁴×C₂₃	1	8	yes	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	4	no	—
856	C₂³	—	2	16	no	—
857	C₂³	—	2	4	no	—
858	C₂³	—	2	8	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	8	no	—
861	C₂³	—	2	8	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	2	16	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	2	32	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	16	no	—
869	C₂³	—	4	16	no	—
870	C₂³	—	4	32	no	—
871	C₂³	—	8	32	no	—
872	C₂³	C₂×#41×C₂₃	1	8	yes	—
873	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
874	C₂³	C₂⁵×C₂₃	1	4	yes	—
875	C₂³	C₂⁵×C₂₃	1	4	yes	—
876	C₂³	C₂⁵×C₂₃	1	8	yes	—
877	C₂³	C₂⁵×C₂₃	1	4	yes	—
878	C₂³	C₂⁵×C₂₃	1	2	yes	—
879	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	4	8	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	32	no	—
884	D₄	—	2	16	no	—
885	D₄	—	2	32	no	—
886	D₄	—	2	8	no	—
887	D₄	—	2	16	no	—
888	D₄	—	2	8	no	—
889	D₄	—	2	16	no	—
890	D₄	—	4	16	no	—
891	D₄	—	4	16	no	—
892	D₄	—	4	16	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	16	no	—
895	D₄	C₂×#41×C₂₃	1	16	yes	complemented
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	4	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	4	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	8	no	—
908	C₂×C₄	—	2	16	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	16	no	—
911	C₂×C₄	—	2	16	no	—
912	C₂×C₄	—	4	8	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	16	no	—
916	C₂×C₄	—	4	16	no	—
917	C₂×C₄	—	4	16	no	—
918	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
919	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
920	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
921	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
922	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
923	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
924	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
925	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
926	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
927	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
928	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
929	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
930	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
931	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
932	C₂²	—	2	8	no	—
933	C₂²	—	2	16	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	8	no	—
943	C₂²	—	2	8	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	4	32	no	—
948	C₂²	—	4	8	no	—
949	C₂²	—	4	8	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	8	32	no	—
952	C₂²	C₂²×#41×C₂₃	1	8	yes	—
953	C₂²	C₂²×#41×C₂₃	1	2	yes	—
954	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
955	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
956	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
957	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	4	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	4	no	—
966	C₄	—	2	8	no	—
967	C₄	—	2	4	no	—
968	C₄	C₂²×#41×C₂₃	1	4	yes	—
969	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	2	8	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	—	4	8	no	—
975	C₂	C₂₃×#3519	1	4	yes	direct product factor
976	C₂	C₂³×#41×C₂₃	1	1	yes	characteristic
977	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
978	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3519	C₂	direct (N × H)
2. C₂×C₂₃×#555	C₂	semidirect
3. C₂×C₂₃×#554	C₂	semidirect
4. C₂×C₂₃×#553	C₂	semidirect
5. C₂×C₂₃×#553	C₂	semidirect
6. C₂×C₂₃×#550	C₂	semidirect
7. C₂×C₂₃×#546	C₂	semidirect
8. C₂×C₂₃×#546	C₂	semidirect
9. C₂×D₄²×C₂₃	C₂	semidirect
10. C₂×D₄²×C₂₃	C₂	semidirect
11. C₂×C₂₃×#540	C₂	semidirect
12. C₂×C₂₃×#538	C₂	semidirect
13. C₂×C₂₃×#532	C₂	semidirect
14. C₂×C₂₃×#529	C₂	semidirect
15. C₂×C₂₃×#525	C₂	semidirect
16. C₂²×C₂₃×#121	C₂	semidirect
17. C₂×C₂₃×#518	C₂	semidirect
18. C₂²×C₄×D₄×C₂₃	C₂	semidirect
19. C₂²×#41×C₂₃	C₂²	semidirect
20. C₂²×#41×C₂₃	C₂²	semidirect
23. C₂³×D₄×C₂₃	C₂²	semidirect
24. C₂³×D₄×C₂₃	C₂²	semidirect
25. C₂⁴×C₄×C₂₃	C₂²	semidirect
26. C₂₃×#555	C₂²	semidirect
27. C₂₃×#554	C₂²	semidirect
28. C₂₃×#553	C₂²	semidirect
29. C₂₃×#553	C₂²	semidirect
30. C₂₃×#550	C₂²	semidirect
31. C₂₃×#546	C₂²	semidirect
32. C₂₃×#546	C₂²	semidirect
33. D₄²×C₂₃	C₂²	semidirect
34. D₄²×C₂₃	C₂²	semidirect
35. C₂₃×#540	C₂²	semidirect
36. C₂₃×#538	C₂²	semidirect
37. C₂₃×#532	C₂²	semidirect
38. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₂₃×#127	C₂²	semidirect
40. C₂×C₂₃×#127	C₂²	semidirect
41. C₂₃×#529	C₂²	semidirect
42. C₂×C₂₃×#126	C₂²	semidirect
43. C₂×C₂₃×#126	C₂²	semidirect
44. C₂×C₂₃×#125	C₂²	semidirect
45. C₂×C₂₃×#125	C₂²	semidirect
46. C₂×C₂₃×#124	C₂²	semidirect
47. C₂×C₂₃×#124	C₂²	semidirect
48. C₂×C₂₃×#124	C₂²	semidirect
49. C₂₃×#525	C₂²	semidirect
50. C₂×C₂₃×#123	C₂²	semidirect
51. C₂×C₂₃×#123	C₂²	semidirect
52. C₂×C₂₃×#123	C₂²	semidirect
53. C₂×C₂₃×#123	C₂²	semidirect
54. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₂₃×#121	C₂²	semidirect
59. C₂×C₂₃×#121	C₂²	semidirect
60. C₂×C₂₃×#121	C₂²	semidirect
61. C₂×C₂₃×#121	C₂²	semidirect
62. C₂×C₂₃×#121	C₂²	semidirect
63. C₂×C₂₃×#121	C₂²	semidirect
64. C₂×C₂₃×#121	C₂²	semidirect
65. C₂×C₂₃×#121	C₂²	semidirect
66. C₂×C₂₃×#121	C₂²	semidirect
67. C₂×C₂₃×#121	C₂²	semidirect
68. C₂×C₂₃×#121	C₂²	semidirect
69. C₂×C₂₃×#121	C₂²	semidirect
70. C₂×C₂₃×#121	C₂²	semidirect
71. C₂×C₂₃×#120	C₂²	semidirect
72. C₂×C₂₃×#120	C₂²	semidirect
73. C₂×C₂₃×#120	C₂²	semidirect
74. C₂₃×#518	C₂²	semidirect
75. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
79. C₂×C₄×D₄×C₂₃	C₂²	semidirect
80. C₂×C₄×D₄×C₂₃	C₂²	semidirect
81. C₂×C₄×D₄×C₂₃	C₂²	semidirect
82. C₂×C₄×D₄×C₂₃	C₂²	semidirect
83. C₂×C₄×D₄×C₂₃	C₂²	semidirect
84. C₂×C₄×D₄×C₂₃	C₂²	semidirect
85. C₂×C₄×D₄×C₂₃	C₂²	semidirect
86. C₂×C₄×D₄×C₂₃	C₂²	semidirect
87. C₂×C₄×D₄×C₂₃	C₂²	semidirect
88. C₂×C₄×D₄×C₂₃	C₂²	semidirect
89. C₂×C₄×D₄×C₂₃	C₂²	semidirect
90. C₂×C₄×D₄×C₂₃	C₂²	semidirect
91. C₂×C₄×D₄×C₂₃	C₂²	semidirect
92. C₂×C₂₃×#117	C₂²	semidirect
93. C₂×C₂₃×#117	C₂²	semidirect
94. C₂×C₂₃×#117	C₂²	semidirect
95. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
96. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
97. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
98. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
99. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
100. C₂²×C₄²×C₂₃	C₂²	semidirect
105. C₂×#41×C₂₃	C₂³	semidirect
106. C₂×#41×C₂₃	C₂³	semidirect
129. C₂²×D₄×C₂₃	C₂³	semidirect
130. C₂²×D₄×C₂₃	C₂³	semidirect
144. C₂³×C₄×C₂₃	C₂³	semidirect
145. C₂₃×C₄⋊Q₈	C₂³	semidirect
146. C₂₃×#127	C₂³	semidirect
147. C₂₃×#127	C₂³	semidirect
148. C₂₃×#126	C₂³	semidirect
149. C₂₃×#126	C₂³	semidirect
150. C₂₃×#125	C₂³	semidirect
151. C₂₃×#125	C₂³	semidirect
152. C₂₃×#124	C₂³	semidirect
153. C₂₃×#124	C₂³	semidirect
154. C₂₃×#124	C₂³	semidirect
155. C₂₃×#123	C₂³	semidirect
156. C₂₃×#123	C₂³	semidirect
157. C₂₃×#123	C₂³	semidirect
158. C₂₃×#123	C₂³	semidirect
159. C₂₃×C₂²⋊Q₈	C₂³	semidirect
160. C₂₃×C₂²⋊Q₈	C₂³	semidirect
161. C₂₃×C₂²⋊Q₈	C₂³	semidirect
163. C₂₃×#121	C₂³	semidirect
164. C₂₃×#121	C₂³	semidirect
165. C₂₃×#121	C₂³	semidirect
166. C₂₃×#121	C₂³	semidirect
167. C₂₃×#121	C₂³	semidirect
168. C₂₃×#121	C₂³	semidirect
169. C₂₃×#121	C₂³	semidirect
170. C₂₃×#121	C₂³	semidirect
171. C₂₃×#121	C₂³	semidirect
172. C₂₃×#121	C₂³	semidirect
173. C₂₃×#121	C₂³	semidirect
174. C₂₃×#121	C₂³	semidirect
175. C₂₃×#120	C₂³	semidirect
176. C₂₃×#120	C₂³	semidirect
177. C₂₃×#120	C₂³	semidirect
178. C₄×Q₈×C₂₃	C₂³	semidirect
182. C₄×D₄×C₂₃	C₂³	semidirect
183. C₄×D₄×C₂₃	C₂³	semidirect
184. C₄×D₄×C₂₃	C₂³	semidirect
185. C₄×D₄×C₂₃	C₂³	semidirect
186. C₄×D₄×C₂₃	C₂³	semidirect
187. C₄×D₄×C₂₃	C₂³	semidirect
188. C₄×D₄×C₂₃	C₂³	semidirect
189. C₄×D₄×C₂₃	C₂³	semidirect
190. C₄×D₄×C₂₃	C₂³	semidirect
191. C₄×D₄×C₂₃	C₂³	semidirect
192. C₄×D₄×C₂₃	C₂³	semidirect
193. C₄×D₄×C₂₃	C₂³	semidirect
194. C₂₃×#117	C₂³	semidirect
195. C₂₃×#117	C₂³	semidirect
196. C₂₃×#117	C₂³	semidirect
210. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
211. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
228. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
229. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
230. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
237. C₂×C₄²×C₂₃	C₂³	semidirect
274. C₂×D₄×C₂₃	#41	semidirect
361. C₂×#3519	C₂₃	direct (N × H)
406. D₄×C₂₃	C₂×#41	semidirect
443. #3519	C₂×C₂₃	direct (N × H)
444. C₂×#555	C₂×C₂₃	semidirect
445. C₂×#554	C₂×C₂₃	semidirect
446. C₂×#553	C₂×C₂₃	semidirect
447. C₂×#553	C₂×C₂₃	semidirect
448. C₂×#550	C₂×C₂₃	semidirect
449. C₂×#546	C₂×C₂₃	semidirect
450. C₂×#546	C₂×C₂₃	semidirect
451. C₂×D₄²	C₂×C₂₃	semidirect
452. C₂×D₄²	C₂×C₂₃	semidirect
453. C₂×#540	C₂×C₂₃	semidirect
454. C₂×#538	C₂×C₂₃	semidirect
455. C₂×#532	C₂×C₂₃	semidirect
456. C₂×#529	C₂×C₂₃	semidirect
457. C₂×#525	C₂×C₂₃	semidirect
458. C₂²×#121	C₂×C₂₃	semidirect
459. C₂×#518	C₂×C₂₃	semidirect
460. C₂²×C₄×D₄	C₂×C₂₃	semidirect
499. C₂²×#41	C₂²×C₂₃	semidirect
500. C₂²×#41	C₂²×C₂₃	semidirect
503. C₂³×D₄	C₂²×C₂₃	semidirect
504. C₂³×D₄	C₂²×C₂₃	semidirect
505. C₂⁴×C₄	C₂²×C₂₃	semidirect
506. #555	C₂²×C₂₃	semidirect
507. #554	C₂²×C₂₃	semidirect
508. #553	C₂²×C₂₃	semidirect
509. #553	C₂²×C₂₃	semidirect
510. #550	C₂²×C₂₃	semidirect
511. #546	C₂²×C₂₃	semidirect
512. #546	C₂²×C₂₃	semidirect
513. D₄²	C₂²×C₂₃	semidirect
514. D₄²	C₂²×C₂₃	semidirect
515. #540	C₂²×C₂₃	semidirect
516. #538	C₂²×C₂₃	semidirect
517. #532	C₂²×C₂₃	semidirect
518. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
519. C₂×#127	C₂²×C₂₃	semidirect
520. C₂×#127	C₂²×C₂₃	semidirect
521. #529	C₂²×C₂₃	semidirect
522. C₂×#126	C₂²×C₂₃	semidirect
523. C₂×#126	C₂²×C₂₃	semidirect
524. C₂×#125	C₂²×C₂₃	semidirect
525. C₂×#125	C₂²×C₂₃	semidirect
526. C₂×#124	C₂²×C₂₃	semidirect
527. C₂×#124	C₂²×C₂₃	semidirect
528. C₂×#124	C₂²×C₂₃	semidirect
529. #525	C₂²×C₂₃	semidirect
530. C₂×#123	C₂²×C₂₃	semidirect
531. C₂×#123	C₂²×C₂₃	semidirect
532. C₂×#123	C₂²×C₂₃	semidirect
533. C₂×#123	C₂²×C₂₃	semidirect
534. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
535. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
536. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
538. C₂×#121	C₂²×C₂₃	semidirect
539. C₂×#121	C₂²×C₂₃	semidirect
540. C₂×#121	C₂²×C₂₃	semidirect
541. C₂×#121	C₂²×C₂₃	semidirect
542. C₂×#121	C₂²×C₂₃	semidirect
543. C₂×#121	C₂²×C₂₃	semidirect
544. C₂×#121	C₂²×C₂₃	semidirect
545. C₂×#121	C₂²×C₂₃	semidirect
546. C₂×#121	C₂²×C₂₃	semidirect
547. C₂×#121	C₂²×C₂₃	semidirect
548. C₂×#121	C₂²×C₂₃	semidirect
549. C₂×#121	C₂²×C₂₃	semidirect
550. C₂×#121	C₂²×C₂₃	semidirect
551. C₂×#120	C₂²×C₂₃	semidirect
552. C₂×#120	C₂²×C₂₃	semidirect
553. C₂×#120	C₂²×C₂₃	semidirect
554. #518	C₂²×C₂₃	semidirect
555. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
559. C₂×C₄×D₄	C₂²×C₂₃	semidirect
560. C₂×C₄×D₄	C₂²×C₂₃	semidirect
561. C₂×C₄×D₄	C₂²×C₂₃	semidirect
562. C₂×C₄×D₄	C₂²×C₂₃	semidirect
563. C₂×C₄×D₄	C₂²×C₂₃	semidirect
564. C₂×C₄×D₄	C₂²×C₂₃	semidirect
565. C₂×C₄×D₄	C₂²×C₂₃	semidirect
566. C₂×C₄×D₄	C₂²×C₂₃	semidirect
567. C₂×C₄×D₄	C₂²×C₂₃	semidirect
568. C₂×C₄×D₄	C₂²×C₂₃	semidirect
569. C₂×C₄×D₄	C₂²×C₂₃	semidirect
570. C₂×C₄×D₄	C₂²×C₂₃	semidirect
571. C₂×C₄×D₄	C₂²×C₂₃	semidirect
572. C₂×#117	C₂²×C₂₃	semidirect
573. C₂×#117	C₂²×C₂₃	semidirect
574. C₂×#117	C₂²×C₂₃	semidirect
575. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
576. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
577. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
578. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
579. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
580. C₂²×C₄²	C₂²×C₂₃	semidirect
586. C₂×C₂₃	#3519	direct (N × H)
594. C₂×#41	C₂³×C₂₃	semidirect
595. C₂×#41	C₂³×C₂₃	semidirect
618. C₂²×D₄	C₂³×C₂₃	semidirect
619. C₂²×D₄	C₂³×C₂₃	semidirect
633. C₂³×C₄	C₂³×C₂₃	semidirect
634. C₄⋊Q₈	C₂³×C₂₃	semidirect
635. #127	C₂³×C₂₃	semidirect
636. #127	C₂³×C₂₃	semidirect
637. #126	C₂³×C₂₃	semidirect
638. #126	C₂³×C₂₃	semidirect
639. #125	C₂³×C₂₃	semidirect
640. #125	C₂³×C₂₃	semidirect
641. #124	C₂³×C₂₃	semidirect
642. #124	C₂³×C₂₃	semidirect
643. #124	C₂³×C₂₃	semidirect
644. #123	C₂³×C₂₃	semidirect
645. #123	C₂³×C₂₃	semidirect
646. #123	C₂³×C₂₃	semidirect
647. #123	C₂³×C₂₃	semidirect
648. C₂²⋊Q₈	C₂³×C₂₃	semidirect
649. C₂²⋊Q₈	C₂³×C₂₃	semidirect
650. C₂²⋊Q₈	C₂³×C₂₃	semidirect
652. #121	C₂³×C₂₃	semidirect
653. #121	C₂³×C₂₃	semidirect
654. #121	C₂³×C₂₃	semidirect
655. #121	C₂³×C₂₃	semidirect
656. #121	C₂³×C₂₃	semidirect
657. #121	C₂³×C₂₃	semidirect
658. #121	C₂³×C₂₃	semidirect
659. #121	C₂³×C₂₃	semidirect
660. #121	C₂³×C₂₃	semidirect
661. #121	C₂³×C₂₃	semidirect
662. #121	C₂³×C₂₃	semidirect
663. #121	C₂³×C₂₃	semidirect
664. #120	C₂³×C₂₃	semidirect
665. #120	C₂³×C₂₃	semidirect
666. #120	C₂³×C₂₃	semidirect
667. C₄×Q₈	C₂³×C₂₃	semidirect
671. C₄×D₄	C₂³×C₂₃	semidirect
672. C₄×D₄	C₂³×C₂₃	semidirect
673. C₄×D₄	C₂³×C₂₃	semidirect
674. C₄×D₄	C₂³×C₂₃	semidirect
675. C₄×D₄	C₂³×C₂₃	semidirect
676. C₄×D₄	C₂³×C₂₃	semidirect
677. C₄×D₄	C₂³×C₂₃	semidirect
678. C₄×D₄	C₂³×C₂₃	semidirect
679. C₄×D₄	C₂³×C₂₃	semidirect
680. C₄×D₄	C₂³×C₂₃	semidirect
681. C₄×D₄	C₂³×C₂₃	semidirect
682. C₄×D₄	C₂³×C₂₃	semidirect
683. #117	C₂³×C₂₃	semidirect
684. #117	C₂³×C₂₃	semidirect
685. #117	C₂³×C₂₃	semidirect
699. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
700. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
717. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
718. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
719. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
726. C₂×C₄²	C₂³×C₂₃	semidirect
727. C₂₃	C₂×#3519	direct (N × H)
764. C₂×D₄	#41×C₂₃	semidirect
895. D₄	C₂×#41×C₂₃	semidirect
975. C₂	C₂₃×#3519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3519	2
C₂×C₂₃×#555	2
C₂×C₂₃×#554	2
C₂×C₂₃×#553	2
C₂×C₂₃×#550	2
C₂×C₂₃×#546	2
C₂×D₄²×C₂₃	2
C₂×C₂₃×#540	2
C₂×C₂₃×#538	2
C₂×C₂₃×#532	2
C₂×C₂₃×#529	2
C₂×C₂₃×#525	2
C₂²×C₂₃×#121	2
C₂×C₂₃×#518	2
C₂²×C₄×D₄×C₂₃	2
C₂×#3519	23

Subgroups — C2×C23×#3519 #19210397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3519 #19210397