Subgroups — D₂₃×#535 #15686701

Order 2944.

1896 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092986	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092985	C₂	1	2	yes	maximal, complemented
5	#13092984	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092983	C₂	1	4	yes	maximal, complemented
7	#13092982	C₂	1	4	yes	maximal, complemented
8	#13092981	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092980	C₂	1	2	yes	maximal, complemented
10	#127×D₂₃	C₂	1	2	yes	maximal, complemented
11	#124×D₂₃	C₂	1	2	yes	maximal, complemented
12	#121×D₂₃	C₂	1	4	yes	maximal, complemented
13	#120×D₂₃	C₂	1	4	yes	maximal, complemented
14	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×D₂₃	C₂²	1	2	yes	—
17	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
20	#41×D₂₃	—	2	8	no	—
21	C₂×#67292	C₂²	1	1	yes	characteristic, complemented
22	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#67290	C₂²	1	1	yes	characteristic, complemented
24	C₂×#67290	C₂²	1	2	yes	complemented
25	C₂×D₄×D₂₃	—	2	8	no	—
26	C₂×D₄×D₂₃	C₂²	1	2	yes	—
27	C₂×D₄×D₂₃	C₂²	1	2	yes	—
28	C₂×D₄×D₂₃	C₂²	1	2	yes	—
29	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₂₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×D₄×D₂₃	C₂²	1	8	yes	complemented
33	C₂×#67288	C₂²	1	2	yes	complemented
34	C₂×#67288	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₉₂	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
38	C₂₃×#127	C₂²	1	2	yes	complemented
39	C₂₃×#124	C₂²	1	2	yes	complemented
40	C₂₃×#121	C₂²	1	4	yes	complemented
41	C₂₃×#120	C₂²	1	4	yes	complemented
42	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
43	#10625124	C₂²	1	4	yes	complemented
44	#10625118	C₂²	1	2	yes	complemented
45	#10625111	C₂²	1	2	yes	complemented
46	#10625111	C₂²	1	8	yes	complemented
47	#10625111	C₂²	1	2	yes	complemented
48	#10625110	C₂²	1	8	yes	complemented
49	#10625109	C₂²	1	4	yes	complemented
50	#10625108	C₂²	1	8	yes	complemented
51	#10625108	C₂²	1	4	yes	complemented
52	#10625107	C₂²	1	2	yes	complemented
53	#10625101	C₂²	1	4	yes	complemented
54	#10625097	C₂²	1	1	yes	characteristic, complemented
55	#10625066	C₂²	1	4	yes	complemented
56	#10625063	C₂²	1	2	yes	complemented
57	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
58	#10625056	C₂²	1	8	yes	complemented
59	#10625055	C₂²	1	8	yes	complemented
60	#10625053	C₂²	1	8	yes	complemented
61	#10625053	C₂²	1	4	yes	complemented
62	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₂₃	C₂²	1	8	yes	complemented
64	#10625048	C₂²	1	2	yes	complemented
65	#10625046	C₂²	1	2	yes	complemented
66	#10625045	C₂²	1	2	yes	complemented
67	#10625043	C₂²	1	2	yes	complemented
68	C₄²×D₂₃	C₂²	1	2	yes	complemented
69	C₂⁴×C₂₃	C₂³	1	2	yes	—
70	C₂³×D₂₃	—	2	8	no	—
71	C₂³×D₂₃	—	4	8	no	—
72	C₂³×D₂₃	C₂³	1	4	yes	—
73	C₂³×D₂₃	C₂³	1	2	yes	—
74	C₂³×D₂₃	C₂³	1	1	yes	characteristic
75	C₂³×D₂₃	C₂³	1	2	yes	—
76	C₂³×D₂₃	C₂³	1	4	yes	—
77	#41×C₂₃	—	2	4	no	—
78	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
79	C₂×D₄×C₂₃	—	2	4	no	—
80	C₂×D₄×C₂₃	C₂³	1	2	yes	—
81	C₂×D₄×C₂₃	C₂³	1	2	yes	—
82	C₂×D₄×C₂₃	C₂³	1	2	yes	—
83	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
84	C₂×D₄×C₂₃	C₂³	1	8	yes	complemented
85	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₂³	1	2	yes	complemented
87	C₂×C₂²⋊D₂₃	—	2	8	no	—
88	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	complemented
93	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
94	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
95	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Dic₂₃	C₂³	1	2	yes	complemented
97	#67292	—	2	4	no	—
98	Q₈×D₂₃	—	2	4	no	—
99	#67290	—	2	8	no	—
100	#67290	—	2	4	no	—
101	D₄×D₂₃	—	2	8	no	—
102	D₄×D₂₃	—	2	8	no	—
103	D₄×D₂₃	—	2	8	no	—
104	D₄×D₂₃	—	2	4	no	—
105	D₄×D₂₃	—	2	8	no	—
106	D₄×D₂₃	—	2	8	no	—
107	D₄×D₂₃	—	4	16	no	—
108	#67288	—	2	4	no	—
109	#67288	—	2	8	no	—
110	C₂×D₉₂	—	2	4	no	—
111	C₂×D₉₂	C₂³	1	2	yes	—
112	C₂×D₉₂	C₂³	1	2	yes	—
113	C₂×D₉₂	C₂³	1	2	yes	—
114	C₂×D₉₂	C₂³	1	1	yes	characteristic, complemented
115	C₂×D₉₂	C₂³	1	8	yes	complemented
116	C₂×C₄×D₂₃	—	2	8	no	—
117	C₂×C₄×D₂₃	D₄	1	8	yes	complemented
118	C₂×C₄×D₂₃	C₂³	1	4	yes	—
119	C₂×C₄×D₂₃	C₂³	1	2	yes	—
120	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
122	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₂₃	C₂³	1	2	yes	complemented
125	C₂×C₄×D₂₃	C₂³	1	2	yes	complemented
126	C₂×Dic₄₆	C₂³	1	1	yes	characteristic, complemented
127	C₂×Dic₄₆	C₂³	1	2	yes	complemented
128	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
129	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
131	C₄²×C₂₃	C₂³	1	2	yes	complemented
132	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
133	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
134	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
136	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
137	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
138	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
139	C₄×Dic₂₃	C₂³	1	2	yes	complemented
140	C₄×Dic₂₃	C₂³	1	4	yes	complemented
141	C₂³×C₂₃	—	2	4	no	—
142	C₂³×C₂₃	—	4	4	no	—
143	C₂³×C₂₃	C₂⁴	1	4	yes	—
144	C₂³×C₂₃	C₂⁴	1	2	yes	—
145	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
146	C₂²×D₂₃	—	2	4	no	—
147	C₂²×D₂₃	—	2	4	no	—
148	C₂²×D₂₃	—	2	4	no	—
149	C₂²×D₂₃	—	2	8	no	—
150	C₂²×D₂₃	—	2	8	no	—
151	C₂²×D₂₃	—	2	8	no	—
152	C₂²×D₂₃	—	2	16	no	—
153	C₂²×D₂₃	—	4	8	no	—
154	C₂²×D₂₃	—	4	4	no	—
155	C₂²×D₂₃	—	4	32	no	—
156	C₂²×D₂₃	C₂×D₄	1	4	yes	—
157	C₂²×D₂₃	C₂⁴	1	4	yes	—
158	C₂²×D₂₃	C₂⁴	1	2	yes	—
159	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
160	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₂₃	—	2	2	no	—
162	D₄×C₂₃	—	2	4	no	—
163	D₄×C₂₃	—	2	4	no	—
164	D₄×C₂₃	—	2	4	no	—
165	D₄×C₂₃	—	2	2	no	—
166	D₄×C₂₃	—	4	8	no	—
167	C₂×C₄×C₂₃	—	2	4	no	—
168	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
169	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
170	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₂₃	—	2	4	no	—
174	C₂²⋊D₂₃	—	2	4	no	—
175	C₂²⋊D₂₃	—	2	4	no	—
176	C₂²⋊D₂₃	—	2	8	no	—
177	C₂²⋊D₂₃	—	2	8	no	—
178	C₂²⋊D₂₃	—	4	8	no	—
179	C₂²⋊D₂₃	—	4	8	no	—
180	C₂×Dic₂₃	—	2	4	no	—
181	C₂×Dic₂₃	C₂×D₄	1	4	yes	complemented
182	C₂×Dic₂₃	C₂⁴	1	4	yes	—
183	C₂×Dic₂₃	C₂⁴	1	2	yes	—
184	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
186	D₉₂	—	2	4	no	—
187	D₉₂	—	2	4	no	—
188	D₉₂	—	2	4	no	—
189	D₉₂	—	2	2	no	—
190	D₉₂	—	4	8	no	—
191	C₄×D₂₃	—	2	4	no	—
192	C₄×D₂₃	—	2	8	no	—
193	C₄×D₂₃	—	2	4	no	—
194	C₄×D₂₃	—	2	4	no	—
195	C₄×D₂₃	C₂×D₄	1	4	yes	—
196	C₄×D₂₃	C₂×D₄	1	4	yes	—
197	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
198	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
199	Dic₄₆	—	2	2	no	—
200	Dic₄₆	—	2	4	no	—
201	C₂×#535	—	23	1	no	maximal, Sylow
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	—	2	2	no	—
204	C₂²×C₂₃	—	2	4	no	—
205	C₂²×C₂₃	—	2	4	no	—
206	C₂²×C₂₃	—	2	8	no	—
207	C₂²×C₂₃	—	4	8	no	—
208	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
209	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
210	C₂×D₂₃	—	2	2	no	—
211	C₂×D₂₃	—	2	8	no	—
212	C₂×D₂₃	—	2	2	no	—
213	C₂×D₂₃	—	2	4	no	—
214	C₂×D₂₃	—	2	4	no	—
215	C₂×D₂₃	—	2	8	no	—
216	C₂×D₂₃	—	4	16	no	—
217	C₂×D₂₃	—	4	8	no	—
218	C₂×D₂₃	—	4	8	no	—
219	C₂×D₂₃	—	4	16	no	—
220	C₂×D₂₃	C₂²×D₄	1	2	yes	—
221	C₂×D₂₃	C₂²×D₄	1	2	yes	—
222	C₂×D₂₃	H(5,𝔽₂)	1	4	yes	—
223	C₄×C₂₃	—	2	2	no	—
224	C₄×C₂₃	—	2	4	no	—
225	C₄×C₂₃	C₂²×D₄	1	2	yes	—
226	C₄×C₂₃	C₂²×D₄	1	2	yes	—
227	Dic₂₃	—	2	2	no	—
228	Dic₂₃	—	2	4	no	—
229	Dic₂₃	C₂²×D₄	1	2	yes	—
230	Dic₂₃	C₂²×D₄	1	2	yes	—
231	C₂²×#41	—	23	1	no	—
232	C₂³×D₄	—	23	1	no	—
233	#535	—	23	1	no	—
234	#535	—	23	1	no	—
235	#535	—	23	2	no	—
236	#535	—	23	2	no	—
237	#535	—	23	4	no	—
238	#535	—	23	4	no	—
239	#535	—	23	1	no	—
240	#535	D₂₃	1	1	yes	characteristic, direct product factor
241	C₂×#127	—	23	2	no	—
242	C₂×#124	—	23	2	no	—
243	C₂×#121	—	23	4	no	—
244	C₂×#120	—	23	4	no	—
245	C₂×#117	—	23	1	no	—
246	C₂×C₂₃	—	2	2	no	—
247	C₂×C₂₃	—	4	4	no	—
248	C₂×C₂₃	—	4	2	no	—
249	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
250	C₂×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
251	D₂₃	—	2	2	no	—
252	D₂₃	—	4	2	no	—
253	D₂₃	—	4	4	no	—
254	D₂₃	#535	1	4	yes	direct product factor
255	C₂⁵	—	23	2	no	—
256	C₂×#41	—	23	1	no	—
257	C₂×#41	—	23	2	no	—
258	C₂×#41	—	23	1	no	—
259	C₂×#41	—	23	1	no	—
260	C₂×#41	—	23	2	no	—
261	C₂×#41	—	46	8	no	—
262	C₂×#41	C₂×D₂₃	1	1	yes	characteristic, complemented
263	C₂²×Q₈	—	23	1	no	—
264	C₂²×D₄	—	23	2	no	—
265	C₂²×D₄	—	23	2	no	—
266	C₂²×D₄	—	23	2	no	—
267	C₂²×D₄	—	23	2	no	—
268	C₂²×D₄	—	23	2	no	—
269	C₂²×D₄	—	23	2	no	—
270	C₂²×D₄	—	23	1	no	—
271	C₂²×D₄	—	23	8	no	—
272	C₂²×D₄	—	23	1	no	—
273	C₂²×D₄	—	46	8	no	—
274	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
275	C₂³×C₄	—	23	1	no	—
276	C₂³×C₄	—	23	2	no	—
277	#127	—	23	2	no	—
278	#127	—	23	8	no	—
279	#127	—	23	2	no	—
280	#127	—	23	2	no	—
281	#127	C₂×D₂₃	1	2	yes	complemented
282	#124	—	23	2	no	—
283	#124	—	23	2	no	—
284	#124	—	23	8	no	—
285	#124	—	23	2	no	—
286	#124	C₂×D₂₃	1	2	yes	complemented
287	#121	—	23	4	no	—
288	#121	—	23	8	no	—
289	#121	—	23	4	no	—
290	#121	—	23	4	no	—
291	#121	—	23	8	no	—
292	#121	C₂×D₂₃	1	4	yes	complemented
293	#120	—	23	4	no	—
294	#120	—	23	4	no	—
295	#120	—	23	8	no	—
296	#120	—	23	4	no	—
297	#120	—	23	8	no	—
298	#120	C₂×D₂₃	1	4	yes	complemented
299	#117	—	23	1	no	—
300	#117	—	23	2	no	—
301	#117	—	23	2	no	—
302	#117	—	23	2	no	—
303	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
304	C₂×C₄⋊C₄	—	23	2	no	—
305	C₂×C₂²⋊C₄	—	23	2	no	—
306	C₂×C₂²⋊C₄	—	23	8	no	—
307	C₂×C₄²	—	23	2	no	—
308	C₂₃	C₂×#535	1	1	yes	characteristic, complemented, Sylow
309	C₂⁴	—	23	1	no	—
310	C₂⁴	—	23	4	no	—
311	C₂⁴	—	23	2	no	—
312	C₂⁴	—	23	4	no	—
313	C₂⁴	—	23	2	no	—
314	C₂⁴	—	46	8	no	—
315	C₂⁴	—	92	8	no	—
316	C₂⁴	C₂²×D₂₃	1	2	yes	—
317	#41	—	2	4	no	—
318	#41	—	46	8	no	—
319	#41	—	46	8	no	—
320	#41	—	46	4	no	—
321	#41	—	46	4	no	—
322	#41	—	46	4	no	—
323	C₂×Q₈	—	23	2	no	—
324	C₂×Q₈	—	23	1	no	—
325	C₂×Q₈	—	46	4	no	—
326	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic, complemented
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	23	2	no	—
329	C₂×D₄	—	23	2	no	—
330	C₂×D₄	—	23	4	no	—
331	C₂×D₄	—	23	4	no	—
332	C₂×D₄	—	23	2	no	—
333	C₂×D₄	—	23	8	no	—
334	C₂×D₄	—	23	8	no	—
335	C₂×D₄	—	23	2	no	—
336	C₂×D₄	—	23	2	no	—
337	C₂×D₄	—	23	2	no	—
338	C₂×D₄	—	23	1	no	—
339	C₂×D₄	—	23	8	no	—
340	C₂×D₄	—	46	8	no	—
341	C₂×D₄	—	46	8	no	—
342	C₂×D₄	—	46	8	no	—
343	C₂×D₄	—	46	8	no	—
344	C₂×D₄	—	46	4	no	—
345	C₂×D₄	—	46	8	no	—
346	C₂×D₄	—	46	8	no	—
347	C₂×D₄	—	46	4	no	—
348	C₂×D₄	—	92	16	no	—
349	C₂×D₄	C₂²×D₂₃	1	2	yes	—
350	C₂×D₄	C₂²×D₂₃	1	2	yes	—
351	C₂×D₄	C₂²×D₂₃	1	2	yes	—
352	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic, complemented
353	C₂×D₄	C₂²×D₂₃	1	8	yes	complemented
354	C₂²×C₄	—	23	1	no	—
355	C₂²×C₄	—	23	8	no	—
356	C₂²×C₄	—	23	1	no	—
357	C₂²×C₄	—	23	1	no	—
358	C₂²×C₄	—	23	1	no	—
359	C₂²×C₄	—	23	1	no	—
360	C₂²×C₄	—	23	2	no	—
361	C₂²×C₄	—	23	4	no	—
362	C₂²×C₄	—	23	2	no	—
363	C₂²×C₄	—	23	2	no	—
364	C₂²×C₄	—	23	2	no	—
365	C₂²×C₄	—	46	8	no	—
366	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₂₃	1	2	yes	complemented
368	C₄⋊C₄	—	23	4	no	—
369	C₄⋊C₄	—	23	2	no	—
370	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
371	C₂²⋊C₄	—	23	2	no	—
372	C₂²⋊C₄	—	23	8	no	—
373	C₂²⋊C₄	—	23	4	no	—
374	C₂²⋊C₄	—	23	8	no	—
375	C₂²⋊C₄	—	23	8	no	—
376	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₂₃	1	8	yes	complemented
378	C₄²	—	23	4	no	—
379	C₄²	—	23	2	no	—
380	C₄²	C₂²×D₂₃	1	2	yes	complemented
381	C₂³	—	2	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	23	1	no	—
384	C₂³	—	23	4	no	—
385	C₂³	—	23	1	no	—
386	C₂³	—	23	4	no	—
387	C₂³	—	23	2	no	—
388	C₂³	—	46	4	no	—
389	C₂³	—	46	4	no	—
390	C₂³	—	46	8	no	—
391	C₂³	—	46	8	no	—
392	C₂³	—	46	8	no	—
393	C₂³	—	46	16	no	—
394	C₂³	—	46	4	no	—
395	C₂³	—	92	4	no	—
396	C₂³	—	92	8	no	—
397	C₂³	—	92	32	no	—
398	C₂³	C₂³×D₂₃	1	4	yes	—
399	C₂³	C₂³×D₂₃	1	2	yes	—
400	C₂³	C₂³×D₂₃	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	46	4	no	—
403	Q₈	—	46	2	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	8	no	—
409	D₄	—	46	4	no	—
410	D₄	—	46	8	no	—
411	D₄	—	46	8	no	—
412	D₄	—	46	4	no	—
413	D₄	—	46	4	no	—
414	D₄	—	46	4	no	—
415	D₄	—	46	4	no	—
416	D₄	—	46	4	no	—
417	D₄	—	46	2	no	—
418	D₄	—	92	8	no	—
419	D₄	—	92	8	no	—
420	D₄	—	92	8	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	23	4	no	—
423	C₂×C₄	—	23	1	no	—
424	C₂×C₄	—	23	1	no	—
425	C₂×C₄	—	23	4	no	—
426	C₂×C₄	—	23	4	no	—
427	C₂×C₄	—	23	4	no	—
428	C₂×C₄	—	23	4	no	—
429	C₂×C₄	—	23	4	no	—
430	C₂×C₄	—	23	2	no	—
431	C₂×C₄	—	46	4	no	—
432	C₂×C₄	—	46	4	no	—
433	C₂×C₄	—	46	8	no	—
434	C₂×C₄	—	46	4	no	—
435	C₂×C₄	—	46	4	no	—
436	C₂×C₄	D₄×D₂₃	1	4	yes	complemented
437	C₂×C₄	C₂³×D₂₃	1	4	yes	—
438	C₂×C₄	C₂³×D₂₃	1	2	yes	—
439	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	23	2	no	—
448	C₂²	—	23	4	no	—
449	C₂²	—	23	2	no	—
450	C₂²	—	46	8	no	—
451	C₂²	—	46	2	no	—
452	C₂²	—	46	2	no	—
453	C₂²	—	46	4	no	—
454	C₂²	—	46	4	no	—
455	C₂²	—	46	8	no	—
456	C₂²	—	92	8	no	—
457	C₂²	—	92	16	no	—
458	C₂²	—	92	8	no	—
459	C₂²	—	92	16	no	—
460	C₂²	C₂×D₄×D₂₃	1	2	yes	—
461	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	4	no	—
464	C₄	—	23	2	no	—
465	C₄	—	23	2	no	—
466	C₄	—	46	2	no	—
467	C₄	—	46	4	no	—
468	C₄	C₂×D₄×D₂₃	1	2	yes	—
469	C₄	C₂×D₄×D₂₃	1	2	yes	—
470	C₂	—	2	2	no	—
471	C₂	—	4	4	no	—
472	C₂	—	4	2	no	—
473	C₂	—	23	4	no	—
474	C₂	—	46	2	no	—
475	C₂	—	92	4	no	—
476	C₂	—	92	2	no	—
477	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
478	C₂	H(5,𝔽₂)×D₂₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#535	C₂
hypercenter	#535	D₂₃
hypocenter	C₂₃	C₂×#535
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₂₃	C₂	semidirect
2. C₂²×D₄×D₂₃	C₂	semidirect
3. #13092986	C₂	semidirect
4. #13092985	C₂	semidirect
5. #13092984	C₂	semidirect
6. #13092983	C₂	semidirect
7. #13092982	C₂	semidirect
8. #13092981	C₂	semidirect
9. #13092980	C₂	semidirect
10. #127×D₂₃	C₂	semidirect
11. #124×D₂₃	C₂	semidirect
12. #121×D₂₃	C₂	semidirect
13. #120×D₂₃	C₂	semidirect
14. #117×D₂₃	C₂	semidirect
15. C₂₃×#535	C₂	semidirect
17. C₂×#41×C₂₃	C₂²	semidirect
18. C₂²×D₄×C₂₃	C₂²	semidirect
19. C₂²×C₂²⋊D₂₃	C₂²	semidirect
21. C₂×#67292	C₂²	semidirect
22. C₂×Q₈×D₂₃	C₂²	semidirect
23. C₂×#67290	C₂²	semidirect
24. C₂×#67290	C₂²	semidirect
29. C₂×D₄×D₂₃	C₂²	semidirect
30. C₂×D₄×D₂₃	C₂²	semidirect
31. C₂×D₄×D₂₃	C₂²	semidirect
32. C₂×D₄×D₂₃	C₂²	semidirect
33. C₂×#67288	C₂²	semidirect
34. C₂×#67288	C₂²	semidirect
35. C₂²×D₉₂	C₂²	semidirect
37. C₂²×C₄×D₂₃	C₂²	semidirect
38. C₂₃×#127	C₂²	semidirect
39. C₂₃×#124	C₂²	semidirect
40. C₂₃×#121	C₂²	semidirect
41. C₂₃×#120	C₂²	semidirect
42. C₂₃×#117	C₂²	semidirect
43. #10625124	C₂²	semidirect
44. #10625118	C₂²	semidirect
45. #10625111	C₂²	semidirect
46. #10625111	C₂²	semidirect
47. #10625111	C₂²	semidirect
48. #10625110	C₂²	semidirect
49. #10625109	C₂²	semidirect
50. #10625108	C₂²	semidirect
51. #10625108	C₂²	semidirect
52. #10625107	C₂²	semidirect
53. #10625101	C₂²	semidirect
54. #10625097	C₂²	semidirect
55. #10625066	C₂²	semidirect
56. #10625063	C₂²	semidirect
57. C₄⋊C₄×D₂₃	C₂²	semidirect
58. #10625056	C₂²	semidirect
59. #10625055	C₂²	semidirect
60. #10625053	C₂²	semidirect
61. #10625053	C₂²	semidirect
63. C₂²⋊C₄×D₂₃	C₂²	semidirect
64. #10625048	C₂²	semidirect
65. #10625046	C₂²	semidirect
66. #10625045	C₂²	semidirect
67. #10625043	C₂²	semidirect
68. C₄²×D₂₃	C₂²	semidirect
78. C₂×Q₈×C₂₃	C₂³	semidirect
83. C₂×D₄×C₂₃	C₂³	semidirect
84. C₂×D₄×C₂₃	C₂³	semidirect
86. C₂²×C₄×C₂₃	C₂³	semidirect
92. C₂×C₂²⋊D₂₃	C₂³	semidirect
93. C₂×C₂²⋊D₂₃	C₂³	semidirect
94. C₂×C₂²⋊D₂₃	C₂³	semidirect
96. C₂²×Dic₂₃	C₂³	semidirect
114. C₂×D₉₂	C₂³	semidirect
115. C₂×D₉₂	C₂³	semidirect
117. C₂×C₄×D₂₃	D₄	semidirect
124. C₂×C₄×D₂₃	C₂³	semidirect
125. C₂×C₄×D₂₃	C₂³	semidirect
126. C₂×Dic₄₆	C₂³	semidirect
127. C₂×Dic₄₆	C₂³	semidirect
128. C₄⋊C₄×C₂₃	C₂³	semidirect
130. C₂²⋊C₄×C₂₃	C₂³	semidirect
131. C₄²×C₂₃	C₂³	semidirect
133. C₂²⋊Dic₂₃	C₂³	semidirect
135. (C₂×D₂₃)⋊C₄	C₂³	semidirect
136. (C₂×D₂₃)⋊C₄	C₂³	semidirect
137. C₄⋊Dic₂₃	C₂³	semidirect
138. Dic₂₃⋊C₄	C₂³	semidirect
139. C₄×Dic₂₃	C₂³	semidirect
140. C₄×Dic₂₃	C₂³	semidirect
168. C₂×C₄×C₂₃	C₂×D₄	semidirect
181. C₂×Dic₂₃	C₂×D₄	semidirect
197. C₄×D₂₃	C₂×D₄	semidirect
198. C₄×D₂₃	C₂×D₄	semidirect
240. #535	D₂₃	direct (N × H)
254. D₂₃	#535	direct (N × H)
262. C₂×#41	C₂×D₂₃	semidirect
274. C₂²×D₄	C₂×D₂₃	semidirect
281. #127	C₂×D₂₃	semidirect
286. #124	C₂×D₂₃	semidirect
292. #121	C₂×D₂₃	semidirect
298. #120	C₂×D₂₃	semidirect
303. #117	C₂×D₂₃	semidirect
308. C₂₃	C₂×#535	semidirect
326. C₂×Q₈	C₂²×D₂₃	semidirect
352. C₂×D₄	C₂²×D₂₃	semidirect
353. C₂×D₄	C₂²×D₂₃	semidirect
367. C₂²×C₄	C₂²×D₂₃	semidirect
370. C₄⋊C₄	C₂²×D₂₃	semidirect
377. C₂²⋊C₄	C₂²×D₂₃	semidirect
380. C₄²	C₂²×D₂₃	semidirect
436. C₂×C₄	D₄×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₃	2
C₂²×D₄×D₂₃	2
#13092986	2
#13092985	2
#13092984	2
#13092983	2
#13092982	2
#13092981	2
#13092980	2
#127×D₂₃	2
#124×D₂₃	2
#121×D₂₃	2
#120×D₂₃	2
#117×D₂₃	2
C₂₃×#535	2
C₂×#535	23

Subgroups — D23×#535 #15686701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#535 #15686701