Subgroups — C₂×C₂₃×#3263 #19208540

Order 5888.

1882 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#542	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3263	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#475	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#476	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂₃×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#463	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#542	—	2	8	no	—
17	C₂₃×#542	C₂²	1	16	yes	complemented
18	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₂₃×#126	—	2	2	no	—
20	C₂×C₂₃×#124	—	2	2	no	—
21	C₂×C₂₃×#124	C₂²	1	2	yes	—
22	C₂×C₂₃×#123	—	2	2	no	—
23	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₂₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂₃×#476	C₂²	1	16	yes	complemented
30	C₂₃×#475	C₂²	1	16	yes	complemented
31	C₂₃×#470	C₂²	1	8	yes	complemented
32	C₂₃×#469	C₂²	1	8	yes	—
33	C₂₃×#465	C₂²	1	16	yes	complemented
34	C₂₃×#464	C₂²	1	16	yes	complemented
35	C₂₃×#463	C₂²	1	16	yes	complemented
36	C₂×C₂₃×#106	C₂²	1	2	yes	—
37	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
39	C₂₃×#424	C₂²	1	8	yes	complemented
40	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₂₃×#103	C₂²	1	2	yes	—
43	C₂×C₂₃×#103	C₂²	1	2	yes	—
44	C₂×C₂₃×#102	C₂²	1	2	yes	—
45	C₂×C₂₃×#102	C₂²	1	2	yes	—
46	C₂²×Q₈×C₂₃	—	2	2	no	—
47	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₂₃	—	2	2	no	—
49	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₂₃	—	2	2	no	—
51	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₂₃	—	4	2	no	—
53	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
54	C₂×SD₁₆×C₂₃	—	4	4	no	—
55	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
56	C₂×D₈×C₂₃	—	4	2	no	—
57	C₂×D₈×C₂₃	C₂³	1	4	yes	—
58	C₂×M₁₆×C₂₃	—	4	2	no	—
59	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
60	C₂²×C₈×C₂₃	—	4	2	no	—
61	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
65	C₂₃×C₄⋊Q₈	—	2	4	no	—
66	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₂₃×#126	—	2	16	no	—
68	C₂₃×#124	—	2	16	no	—
69	C₂₃×#124	—	2	4	no	—
70	C₂₃×#124	C₂³	1	8	yes	—
71	C₂₃×#123	—	2	16	no	—
72	C₂₃×C₂²⋊Q₈	—	2	4	no	—
73	C₂₃×C₂²⋊Q₈	—	2	16	no	—
74	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
75	C₂₃×#121	—	2	4	no	—
76	C₂₃×#121	C₂³	1	8	yes	—
77	C₄×Q₈×C₂₃	—	2	4	no	—
78	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
79	C₄×D₄×C₂₃	—	2	4	no	—
80	C₄×D₄×C₂₃	C₂³	1	8	yes	—
81	C₂₃×#117	D₄	1	4	yes	—
82	C₂₃×#117	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₂₃	—	2	2	no	—
97	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
98	C₂₃×#106	C₂³	1	8	yes	—
99	C₂₃×#106	C₂³	1	4	yes	—
100	C₂₃×#106	C₂³	1	4	yes	—
101	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
103	C₂₃×#103	C₂³	1	8	yes	—
104	C₂₃×#103	C₂³	1	8	yes	—
105	C₂₃×#102	C₂³	1	8	yes	—
106	C₂₃×#102	C₂³	1	8	yes	—
107	C₂⁴×C₂₃	—	2	2	no	—
108	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₂₃	—	2	2	no	—
110	C₂×Q₈×C₂₃	—	2	8	no	—
111	C₂×Q₈×C₂₃	—	2	4	no	—
112	C₂×Q₈×C₂₃	—	2	4	no	—
113	C₂×Q₈×C₂₃	—	8	4	no	—
114	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
115	C₂×D₄×C₂₃	—	2	8	no	—
116	C₂×D₄×C₂₃	—	2	2	no	—
117	C₂×D₄×C₂₃	—	2	4	no	—
118	C₂×D₄×C₂₃	—	2	4	no	—
119	C₂×D₄×C₂₃	—	8	4	no	—
120	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₂₃	—	2	2	no	—
122	C₂²×C₄×C₂₃	—	2	2	no	—
123	C₂²×C₄×C₂₃	—	2	2	no	—
124	C₂²×C₄×C₂₃	—	2	2	no	—
125	C₂²×C₄×C₂₃	—	2	2	no	—
126	C₂²×C₄×C₂₃	—	2	8	no	—
127	C₂²×C₄×C₂₃	—	8	4	no	—
128	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
134	Q₁₆×C₂₃	—	4	4	no	—
135	SD₁₆×C₂₃	—	4	8	no	—
136	D₈×C₂₃	—	4	4	no	—
137	M₁₆×C₂₃	—	4	4	no	—
138	C₂×C₈×C₂₃	—	2	4	no	—
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	4	4	no	—
142	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
143	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
144	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
145	C₄⋊C₄×C₂₃	—	2	8	no	—
146	C₄⋊C₄×C₂₃	—	2	8	no	—
147	C₄⋊C₄×C₂₃	—	2	8	no	—
148	C₄⋊C₄×C₂₃	—	2	2	no	—
149	C₄⋊C₄×C₂₃	—	2	2	no	—
150	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
151	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₂₃	—	2	8	no	—
154	C₂²⋊C₄×C₂₃	—	2	8	no	—
155	C₂²⋊C₄×C₂₃	—	2	8	no	—
156	C₂²⋊C₄×C₂₃	—	2	8	no	—
157	C₂²⋊C₄×C₂₃	—	2	8	no	—
158	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
159	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
160	C₄²×C₂₃	—	2	8	no	—
161	C₄²×C₂₃	C₂×D₄	1	4	yes	—
162	C₄²×C₂₃	C₂⁴	1	4	yes	—
163	C₂×#3263	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₂₃	—	2	2	no	—
165	C₂³×C₂₃	—	2	4	no	—
166	C₂³×C₂₃	—	2	4	no	—
167	C₂³×C₂₃	—	4	4	no	—
168	C₂³×C₂₃	—	4	4	no	—
169	C₂³×C₂₃	—	4	4	no	—
170	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
171	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₂₃	—	2	4	no	—
173	Q₈×C₂₃	—	2	4	no	—
174	Q₈×C₂₃	—	4	4	no	—
175	Q₈×C₂₃	—	8	8	no	—
176	D₄×C₂₃	—	2	4	no	—
177	D₄×C₂₃	—	2	4	no	—
178	D₄×C₂₃	—	4	4	no	—
179	D₄×C₂₃	—	8	8	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	4	no	—
182	C₂×C₄×C₂₃	—	2	4	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	4	no	—
187	C₂×C₄×C₂₃	—	2	4	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	4	4	no	—
190	C₂×C₄×C₂₃	—	4	4	no	—
191	C₂×C₄×C₂₃	—	4	4	no	—
192	C₂×C₄×C₂₃	—	8	8	no	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
199	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
200	C₈×C₂₃	—	2	4	no	—
201	C₈×C₂₃	—	2	2	no	—
202	C₈×C₂₃	—	2	2	no	—
203	C₂×#542	C₂×C₂₃	1	2	yes	complemented
204	#3263	C₂×C₂₃	1	16	yes	direct product factor
205	C₂×#475	C₂×C₂₃	1	2	yes	complemented
206	C₂×#476	C₂×C₂₃	1	2	yes	complemented
207	C₂×#470	C₂×C₂₃	1	1	yes	characteristic, complemented
208	C₂×#469	C₂×C₂₃	1	1	yes	characteristic
209	C₂×#465	C₂×C₂₃	1	2	yes	complemented
210	C₂×#464	C₂×C₂₃	1	2	yes	complemented
211	C₂×#463	C₂×C₂₃	1	2	yes	complemented
212	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
213	C₂²×C₂₃	—	2	2	no	—
214	C₂²×C₂₃	—	2	4	no	—
215	C₂²×C₂₃	—	4	4	no	—
216	C₂²×C₂₃	—	4	4	no	—
217	C₂²×C₂₃	—	4	4	no	—
218	C₂²×C₂₃	—	4	4	no	—
219	C₂²×C₂₃	—	8	8	no	—
220	C₂²×C₂₃	#537	1	2	yes	—
221	C₂²×C₂₃	#577	1	4	yes	—
222	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₂₃	—	2	2	no	—
224	C₄×C₂₃	—	2	4	no	—
225	C₄×C₂₃	—	2	4	no	—
226	C₄×C₂₃	—	4	4	no	—
227	C₄×C₂₃	—	4	4	no	—
228	C₄×C₂₃	—	4	4	no	—
229	C₄×C₂₃	#537	1	2	yes	—
230	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
232	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
233	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
234	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
235	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
237	#542	—	2	8	no	—
238	#542	C₂²×C₂₃	1	16	yes	complemented
239	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
240	C₂×#126	—	2	2	no	—
241	C₂×#124	—	2	2	no	—
242	C₂×#124	C₂²×C₂₃	1	2	yes	—
243	C₂×#123	—	2	2	no	—
244	C₂×C₂²⋊Q₈	—	2	2	no	—
245	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
246	C₂×#121	C₂²×C₂₃	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
249	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
250	#476	C₂²×C₂₃	1	16	yes	complemented
251	#475	C₂²×C₂₃	1	16	yes	complemented
252	#470	C₂²×C₂₃	1	8	yes	complemented
253	#469	C₂²×C₂₃	1	8	yes	—
254	#465	C₂²×C₂₃	1	16	yes	complemented
255	#464	C₂²×C₂₃	1	16	yes	complemented
256	#463	C₂²×C₂₃	1	16	yes	complemented
257	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
258	C₂×#106	C₂²×C₂₃	1	2	yes	—
259	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
260	#424	C₂²×C₂₃	1	8	yes	complemented
261	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
262	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
263	C₂×#103	C₂²×C₂₃	1	2	yes	—
264	C₂×#103	C₂²×C₂₃	1	2	yes	—
265	C₂×#102	C₂²×C₂₃	1	2	yes	—
266	C₂×#102	C₂²×C₂₃	1	2	yes	—
267	C₂×C₂₃	—	4	2	no	—
268	C₂×C₂₃	—	8	4	no	—
269	C₂×C₂₃	#3263	1	4	yes	direct product factor
270	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
271	C₂×C₂₃	C₂×#577	1	2	yes	—
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
278	C₂×Q₁₆	—	4	2	no	—
279	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
280	C₂×SD₁₆	—	4	4	no	—
281	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
282	C₂×D₈	—	4	2	no	—
283	C₂×D₈	C₂³×C₂₃	1	4	yes	—
284	C₂×M₁₆	—	4	2	no	—
285	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
286	C₂²×C₈	—	4	2	no	—
287	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
291	C₄⋊Q₈	—	2	4	no	—
292	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
293	#126	—	2	16	no	—
294	#124	—	2	16	no	—
295	#124	—	2	4	no	—
296	#124	C₂³×C₂₃	1	8	yes	—
297	#123	—	2	16	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	16	no	—
300	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
301	#121	—	2	4	no	—
302	#121	C₂³×C₂₃	1	8	yes	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	C₂³×C₂₃	1	8	yes	—
307	#117	D₄×C₂₃	1	4	yes	—
308	#117	C₂³×C₂₃	1	4	yes	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
324	#106	C₂³×C₂₃	1	8	yes	—
325	#106	C₂³×C₂₃	1	4	yes	—
326	#106	C₂³×C₂₃	1	4	yes	—
327	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
328	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
329	#103	C₂³×C₂₃	1	8	yes	—
330	#103	C₂³×C₂₃	1	8	yes	—
331	#102	C₂³×C₂₃	1	8	yes	—
332	#102	C₂³×C₂₃	1	8	yes	—
333	C₂₃	C₂×#3263	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁴	—	2	2	no	—
335	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	8	4	no	—
341	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	8	4	no	—
347	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	8	4	no	—
355	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
361	Q₁₆	—	4	4	no	—
362	SD₁₆	—	4	8	no	—
363	D₈	—	4	4	no	—
364	M₁₆	—	4	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	4	no	—
369	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
370	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
371	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
378	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
386	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
387	C₄²	—	2	8	no	—
388	C₄²	C₂×D₄×C₂₃	1	4	yes	—
389	C₄²	C₂⁴×C₂₃	1	4	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
397	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	4	no	—
400	Q₈	—	4	4	no	—
401	Q₈	—	8	8	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	8	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
420	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
423	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
424	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
425	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	8	8	no	—
436	C₂²	C₂₃×#537	1	2	yes	—
437	C₂²	C₂₃×#577	1	4	yes	—
438	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	4	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	C₂₃×#537	1	2	yes	—
446	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
447	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
448	C₂	—	4	2	no	—
449	C₂	—	8	4	no	—
450	C₂	C₂₃×#3263	1	4	yes	direct product factor
451	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
452	C₂	C₂×C₂₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#542	C₂	semidirect
2. C₂₃×#3263	C₂	direct (N × H)
3. C₂×C₂₃×#475	C₂	semidirect
4. C₂×C₂₃×#476	C₂	semidirect
5. C₂×C₂₃×#470	C₂	semidirect
7. C₂×C₂₃×#465	C₂	semidirect
8. C₂×C₂₃×#464	C₂	semidirect
9. C₂×C₂₃×#463	C₂	semidirect
10. C₂×C₂₃×#424	C₂	semidirect
17. C₂₃×#542	C₂²	semidirect
29. C₂₃×#476	C₂²	semidirect
30. C₂₃×#475	C₂²	semidirect
31. C₂₃×#470	C₂²	semidirect
33. C₂₃×#465	C₂²	semidirect
34. C₂₃×#464	C₂²	semidirect
35. C₂₃×#463	C₂²	semidirect
39. C₂₃×#424	C₂²	semidirect
163. C₂×#3263	C₂₃	direct (N × H)
203. C₂×#542	C₂×C₂₃	semidirect
204. #3263	C₂×C₂₃	direct (N × H)
205. C₂×#475	C₂×C₂₃	semidirect
206. C₂×#476	C₂×C₂₃	semidirect
207. C₂×#470	C₂×C₂₃	semidirect
209. C₂×#465	C₂×C₂₃	semidirect
210. C₂×#464	C₂×C₂₃	semidirect
211. C₂×#463	C₂×C₂₃	semidirect
212. C₂×#424	C₂×C₂₃	semidirect
238. #542	C₂²×C₂₃	semidirect
250. #476	C₂²×C₂₃	semidirect
251. #475	C₂²×C₂₃	semidirect
252. #470	C₂²×C₂₃	semidirect
254. #465	C₂²×C₂₃	semidirect
255. #464	C₂²×C₂₃	semidirect
256. #463	C₂²×C₂₃	semidirect
260. #424	C₂²×C₂₃	semidirect
269. C₂×C₂₃	#3263	direct (N × H)
333. C₂₃	C₂×#3263	direct (N × H)
450. C₂	C₂₃×#3263	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×#542	2
C₂₃×#3263	2
C₂×C₂₃×#475	2
C₂×C₂₃×#476	2
C₂×C₂₃×#470	2
C₂×C₂₃×#469	2
C₂×C₂₃×#465	2
C₂×C₂₃×#464	2
C₂×C₂₃×#463	2
C₂×C₂₃×#424	2
C₂×#3263	23

Subgroups — C2×C23×#3263 #19208540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3263 #19208540