Subgroups — C₂×C₂₃×#1650 #19166128

Order 5888.

978 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1650	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×SD₁₆×C₂₃	—	2	1	no	—
10	C₂₃×#556	—	2	2	no	—
11	C₂₃×#556	—	2	2	no	—
12	C₂₃×#556	—	2	2	no	—
13	C₂₃×#556	C₂²	1	4	yes	—
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#126	—	2	2	no	—
17	C₂×C₂₃×#124	—	2	1	no	—
18	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#117	—	2	1	no	—
23	C₂₃×#500	—	2	2	no	—
24	C₂₃×#500	C₂²	1	4	yes	complemented
25	C₂₃×#475	—	2	2	no	—
26	C₂₃×#475	C₂²	1	4	yes	complemented
27	C₂₃×#461	—	2	2	no	—
28	C₂₃×#461	C₂²	1	4	yes	—
29	C₂×C₂₃×#107	—	2	2	no	—
30	C₂×C₂₃×#106	—	2	1	no	—
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#103	—	2	1	no	—
34	C₂×C₂₃×#103	—	2	1	no	—
35	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#332	C₂²	1	4	yes	complemented
37	C₂₃×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₂₃×D₄⋊C₈	C₂²	1	4	yes	—
39	C₂²×Q₈×C₂₃	—	2	1	no	—
40	C₂²×Q₈×C₂₃	—	2	1	no	—
41	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	—	2	1	no	—
44	C₂×SD₁₆×C₂₃	—	2	4	no	—
45	C₂×SD₁₆×C₂₃	—	4	4	no	—
46	C₂²×C₈×C₂₃	—	2	1	no	—
47	C₂²×C₈×C₂₃	—	2	1	no	—
48	C₂²×C₈×C₂₃	—	2	1	no	—
49	C₂₃×C₄⋊Q₈	—	2	1	no	—
50	C₂₃×C₄⋊Q₈	—	2	1	no	—
51	C₂₃×C₄⋊Q₈	—	2	1	no	—
52	C₂₃×C₄⋊Q₈	—	2	1	no	—
53	C₂₃×C₄⋊Q₈	—	2	1	no	—
54	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
55	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₂₃×#126	—	2	8	no	—
58	C₂₃×#126	—	2	8	no	—
59	C₂₃×#124	—	2	4	no	—
60	C₂₃×#124	—	2	4	no	—
61	C₂₃×C₂²⋊Q₈	—	2	4	no	—
62	C₂₃×C₂²⋊Q₈	—	2	4	no	—
63	C₄×Q₈×C₂₃	—	2	4	no	—
64	C₄×Q₈×C₂₃	—	2	4	no	—
65	C₄×Q₈×C₂₃	—	2	1	no	—
66	C₄×Q₈×C₂₃	—	2	1	no	—
67	C₄×Q₈×C₂₃	D₄	1	2	yes	—
68	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
69	C₄×D₄×C₂₃	—	2	1	no	—
70	C₄×D₄×C₂₃	—	2	1	no	—
71	C₄×D₄×C₂₃	D₄	1	2	yes	—
72	C₄×D₄×C₂₃	C₂³	1	2	yes	—
73	C₂₃×#117	—	2	4	no	—
74	C₂₃×#117	—	2	4	no	—
75	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
86	C₂×C₄²×C₂₃	—	2	2	no	—
87	C₂×C₄²×C₂₃	—	2	1	no	—
88	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×#107	—	2	8	no	—
90	C₂₃×#106	—	2	4	no	—
91	C₂₃×C₄⋊C₈	—	2	1	no	—
92	C₂₃×C₄⋊C₈	—	2	1	no	—
93	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
94	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
95	C₂₃×#103	—	2	4	no	—
96	C₂₃×#103	—	2	4	no	—
97	C₄×C₈×C₂₃	—	2	1	no	—
98	C₄×C₈×C₂₃	C₂³	1	2	yes	—
99	C₂⁴×C₂₃	—	2	1	no	—
100	C₂×Q₈×C₂₃	—	2	1	no	—
101	C₂×Q₈×C₂₃	—	2	2	no	—
102	C₂×Q₈×C₂₃	—	2	2	no	—
103	C₂×Q₈×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	—	2	2	no	—
105	C₂×Q₈×C₂₃	—	2	2	no	—
106	C₂×Q₈×C₂₃	—	4	1	no	—
107	C₂×Q₈×C₂₃	—	4	2	no	—
108	C₂×Q₈×C₂₃	—	4	2	no	—
109	C₂×Q₈×C₂₃	—	4	2	no	—
110	C₂×Q₈×C₂₃	—	4	2	no	—
111	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₂₃	—	2	1	no	—
113	C₂×D₄×C₂₃	—	2	2	no	—
114	C₂×D₄×C₂₃	—	2	2	no	—
115	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₂₃	—	2	1	no	—
117	C₂²×C₄×C₂₃	—	2	1	no	—
118	C₂²×C₄×C₂₃	—	2	1	no	—
119	C₂²×C₄×C₂₃	—	2	2	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	2	2	no	—
122	C₂²×C₄×C₂₃	—	4	2	no	—
123	C₂²×C₄×C₂₃	—	4	2	no	—
124	C₂²×C₄×C₂₃	—	4	1	no	—
125	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
128	SD₁₆×C₂₃	—	4	8	no	—
129	C₂×C₈×C₂₃	—	2	4	no	—
130	C₂×C₈×C₂₃	—	2	2	no	—
131	C₂×C₈×C₂₃	—	2	2	no	—
132	C₂×C₈×C₂₃	—	2	2	no	—
133	C₂×C₈×C₂₃	—	4	2	no	—
134	C₂×C₈×C₂₃	—	4	2	no	—
135	C₄⋊C₄×C₂₃	—	2	8	no	—
136	C₄⋊C₄×C₂₃	—	2	2	no	—
137	C₄⋊C₄×C₂₃	—	2	2	no	—
138	C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₄⋊C₄×C₂₃	—	2	1	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	—	2	2	no	—
142	C₄⋊C₄×C₂₃	—	2	2	no	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	2	2	no	—
145	C₄⋊C₄×C₂₃	—	4	1	no	—
146	C₄⋊C₄×C₂₃	—	4	1	no	—
147	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
150	C₂²⋊C₄×C₂₃	—	2	8	no	—
151	C₂²⋊C₄×C₂₃	—	2	8	no	—
152	C₂²⋊C₄×C₂₃	—	2	2	no	—
153	C₂²⋊C₄×C₂₃	—	2	2	no	—
154	C₄²×C₂₃	—	2	8	no	—
155	C₄²×C₂₃	—	2	2	no	—
156	C₄²×C₂₃	—	2	2	no	—
157	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
161	C₂×#1650	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₂₃	—	2	2	no	—
163	C₂³×C₂₃	—	4	2	no	—
164	C₂³×C₂₃	—	4	2	no	—
165	C₂³×C₂₃	—	4	2	no	—
166	C₂³×C₂₃	#120	1	1	yes	characteristic
167	Q₈×C₂₃	—	2	2	no	—
168	Q₈×C₂₃	—	2	2	no	—
169	Q₈×C₂₃	—	4	2	no	—
170	Q₈×C₂₃	—	4	2	no	—
171	Q₈×C₂₃	—	4	4	no	—
172	Q₈×C₂₃	—	4	2	no	—
173	Q₈×C₂₃	—	4	2	no	—
174	Q₈×C₂₃	—	4	2	no	—
175	Q₈×C₂₃	—	8	2	no	—
176	D₄×C₂₃	—	2	2	no	—
177	D₄×C₂₃	—	2	2	no	—
178	D₄×C₂₃	—	4	2	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	4	4	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	—	4	2	no	—
187	C₂×C₄×C₂₃	—	4	2	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	4	4	no	—
191	C₂×C₄×C₂₃	—	4	2	no	—
192	C₂×C₄×C₂₃	—	8	2	no	—
193	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
194	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
195	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
196	C₂×C₄×C₂₃	#135	1	2	yes	—
197	C₂×C₄×C₂₃	#135	1	2	yes	—
198	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₂₃	#137	1	2	yes	—
200	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₂₃	—	2	4	no	—
204	C₈×C₂₃	—	4	2	no	—
205	C₈×C₂₃	—	4	2	no	—
206	C₂×#556	C₂×C₂₃	1	1	yes	characteristic
207	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
208	C₂×#475	C₂×C₂₃	1	1	yes	characteristic, complemented
209	C₂×#461	C₂×C₂₃	1	1	yes	characteristic
210	#1650	C₂×C₂₃	1	8	yes	direct product factor
211	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
212	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
213	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
214	C₂²×C₂₃	—	4	2	no	—
215	C₂²×C₂₃	—	4	2	no	—
216	C₂²×C₂₃	—	4	2	no	—
217	C₂²×C₂₃	—	8	4	no	—
218	C₂²×C₂₃	#449	1	2	yes	—
219	C₂²×C₂₃	#452	1	2	yes	—
220	C₂²×C₂₃	#456	1	2	yes	—
221	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
222	C₄×C₂₃	—	2	1	no	—
223	C₄×C₂₃	—	2	1	no	—
224	C₄×C₂₃	—	4	4	no	—
225	C₄×C₂₃	—	4	2	no	—
226	C₄×C₂₃	—	4	2	no	—
227	C₄×C₂₃	—	4	2	no	—
228	C₄×C₂₃	—	8	2	no	—
229	C₄×C₂₃	#449	1	2	yes	—
230	C₄×C₂₃	#452	1	2	yes	—
231	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
232	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
233	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
235	C₂²×SD₁₆	—	2	1	no	—
236	#556	—	2	2	no	—
237	#556	—	2	2	no	—
238	#556	—	2	2	no	—
239	#556	C₂²×C₂₃	1	4	yes	—
240	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×#126	—	2	2	no	—
243	C₂×#124	—	2	1	no	—
244	C₂×C₂²⋊Q₈	—	2	1	no	—
245	C₂×C₄×Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
248	C₂×#117	—	2	1	no	—
249	#500	—	2	2	no	—
250	#500	C₂²×C₂₃	1	4	yes	complemented
251	#475	—	2	2	no	—
252	#475	C₂²×C₂₃	1	4	yes	complemented
253	#461	—	2	2	no	—
254	#461	C₂²×C₂₃	1	4	yes	—
255	C₂×#107	—	2	2	no	—
256	C₂×#106	—	2	1	no	—
257	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
259	C₂×#103	—	2	1	no	—
260	C₂×#103	—	2	1	no	—
261	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
262	#332	C₂²×C₂₃	1	4	yes	complemented
263	Q₈⋊C₈	C₂²×C₂₃	1	4	yes	complemented
264	D₄⋊C₈	C₂²×C₂₃	1	4	yes	—
265	C₂×C₂₃	—	8	2	no	—
266	C₂×C₂₃	#1650	1	4	yes	direct product factor
267	C₂×C₂₃	C₂×#449	1	1	yes	characteristic
268	C₂×C₂₃	C₂×#452	1	1	yes	characteristic
269	C₂×C₂₃	C₂×#456	1	1	yes	characteristic
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
273	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×SD₁₆	—	4	4	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
286	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
287	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
288	#126	—	2	8	no	—
289	#126	—	2	8	no	—
290	#124	—	2	4	no	—
291	#124	—	2	4	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	D₄×C₂₃	1	2	yes	—
299	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	D₄×C₂₃	1	2	yes	—
303	C₄×D₄	C₂³×C₂₃	1	2	yes	—
304	#117	—	2	4	no	—
305	#117	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
320	#107	—	2	8	no	—
321	#106	—	2	4	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
325	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
326	#103	—	2	4	no	—
327	#103	—	2	4	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	C₂³×C₂₃	1	2	yes	—
330	C₂₃	C₂×#1650	1	1	yes	characteristic, direct product factor, Sylow
331	C₂⁴	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	4	1	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
360	SD₁₆	—	4	8	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
380	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
381	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₄²	—	2	8	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
392	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂₃×#120	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	4	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	8	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	2	no	—
424	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
425	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
426	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
427	C₂×C₄	C₂₃×#135	1	2	yes	—
428	C₂×C₄	C₂₃×#135	1	2	yes	—
429	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
430	C₂×C₄	C₂₃×#137	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	4	no	—
441	C₂²	C₂₃×#449	1	2	yes	—
442	C₂²	C₂₃×#452	1	2	yes	—
443	C₂²	C₂₃×#456	1	2	yes	—
444	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	2	no	—
452	C₄	C₂₃×#449	1	2	yes	—
453	C₄	C₂₃×#452	1	2	yes	—
454	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
455	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
456	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
457	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
458	C₂	—	8	2	no	—
459	C₂	C₂₃×#1650	1	4	yes	direct product factor
460	C₂	C₂×C₂₃×#449	1	1	yes	characteristic
461	C₂	C₂×C₂₃×#452	1	1	yes	characteristic
462	C₂	C₂×C₂₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#500	C₂	semidirect
3. C₂×C₂₃×#475	C₂	semidirect
5. C₂₃×#1650	C₂	direct (N × H)
6. C₂×C₂₃×#332	C₂	semidirect
7. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
24. C₂₃×#500	C₂²	semidirect
26. C₂₃×#475	C₂²	semidirect
36. C₂₃×#332	C₂²	semidirect
37. C₂₃×Q₈⋊C₈	C₂²	semidirect
161. C₂×#1650	C₂₃	direct (N × H)
207. C₂×#500	C₂×C₂₃	semidirect
208. C₂×#475	C₂×C₂₃	semidirect
210. #1650	C₂×C₂₃	direct (N × H)
211. C₂×#332	C₂×C₂₃	semidirect
212. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
250. #500	C₂²×C₂₃	semidirect
252. #475	C₂²×C₂₃	semidirect
262. #332	C₂²×C₂₃	semidirect
263. Q₈⋊C₈	C₂²×C₂₃	semidirect
266. C₂×C₂₃	#1650	direct (N × H)
330. C₂₃	C₂×#1650	direct (N × H)
459. C₂	C₂₃×#1650	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#556	2
C₂×C₂₃×#500	2
C₂×C₂₃×#475	2
C₂×C₂₃×#461	2
C₂₃×#1650	2
C₂×C₂₃×#332	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂×#1650	23

Subgroups — C2×C23×#1650 #19166128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1650 #19166128