Subgroups — C₂₃×#36698 #19184324

Order 5888.

1484 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2844	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2838	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2836	C₂	1	4	yes	maximal, complemented
4	C₂₃×#2833	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2830	C₂	1	2	yes	maximal
6	C₂₃×#2822	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2820	C₂	1	2	yes	maximal
8	C₂₃×#2401	C₂	1	4	yes	maximal, complemented
9	C₂₃×#2399	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2396	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2395	C₂	1	2	yes	maximal
12	C₄×C₂₃×#125	C₂	1	2	yes	maximal, complemented
13	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
14	C₂×C₂₃×#125	C₂²	1	2	yes	—
15	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#117	C₂²	1	2	yes	—
20	C₂₃×#401	C₂²	1	4	yes	—
21	C₂₃×#400	C₂²	1	4	yes	—
22	C₂₃×#400	C₂²	1	4	yes	—
23	C₂₃×#400	C₂²	1	4	yes	—
24	C₂₃×#400	C₂²	1	4	yes	—
25	C₂₃×#400	C₂²	1	2	yes	—
26	C₂₃×#399	C₂²	1	4	yes	—
27	C₂₃×#399	C₂²	1	2	yes	—
28	C₂₃×#398	C₂²	1	2	yes	—
29	C₂₃×#398	C₂²	1	2	yes	—
30	C₂₃×#398	C₂²	1	4	yes	—
31	C₂₃×#398	C₂²	1	2	yes	—
32	C₂₃×#398	C₂²	1	4	yes	—
33	C₂₃×#398	C₂²	1	4	yes	—
34	C₂₃×#397	C₂²	1	4	yes	—
35	C₂₃×#397	C₂²	1	4	yes	—
36	C₂₃×#397	C₂²	1	4	yes	—
37	C₂₃×#397	C₂²	1	2	yes	—
38	C₂₃×#397	C₂²	1	4	yes	—
39	C₂₃×#396	C₂²	1	4	yes	—
40	C₂₃×#396	C₂²	1	4	yes	—
41	C₂₃×#396	C₂²	1	4	yes	—
42	C₂₃×#395	C₂²	1	4	yes	—
43	C₂₃×#395	C₂²	1	2	yes	—
44	C₂₃×#395	C₂²	1	2	yes	—
45	C₂₃×#395	C₂²	1	4	yes	—
46	C₂₃×#394	C₂²	1	4	yes	—
47	C₂₃×#393	C₂²	1	4	yes	—
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#390	C₂²	1	1	yes	characteristic
50	C₂₃×#389	C₂²	1	2	yes	—
51	C₂₃×#389	C₂²	1	2	yes	—
52	C₂₃×#388	C₂²	1	4	yes	—
53	C₂₃×#387	C₂²	1	4	yes	—
54	C₂₃×#387	C₂²	1	4	yes	—
55	C₂₃×#382	C₂²	1	1	yes	characteristic
56	C₂₃×#382	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
60	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
65	C₂₃×#376	C₂²	1	2	yes	—
66	C₄³×C₂₃	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
71	C₂₃×#125	—	2	8	no	—
72	C₂₃×#124	—	2	4	no	—
73	C₄×Q₈×C₂₃	—	4	4	no	—
74	C₄×Q₈×C₂₃	—	4	2	no	—
75	C₄×D₄×C₂₃	—	4	2	no	—
76	C₂₃×#117	—	4	4	no	—
77	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
101	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
104	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
106	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
108	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
109	C₂₃×#95	C₂³	1	4	yes	—
110	C₂₃×#95	C₂³	1	2	yes	—
111	C₂₃×#95	C₂³	1	2	yes	—
112	C₂₃×#95	C₂³	1	4	yes	—
113	C₂₃×#95	C₂³	1	4	yes	—
114	C₂₃×#95	C₂³	1	4	yes	—
115	C₂₃×#95	C₂³	1	4	yes	—
116	C₂₃×#95	C₂³	1	2	yes	—
117	C₂₃×#95	C₂³	1	2	yes	—
118	C₂₃×#95	C₂³	1	4	yes	—
119	C₂₃×#95	C₂³	1	4	yes	—
120	C₂₃×#95	C₂³	1	4	yes	—
121	C₂₃×#95	C₂³	1	4	yes	—
122	C₂₃×#95	C₂³	1	4	yes	—
123	C₂₃×#95	C₂³	1	4	yes	—
124	C₂₃×#95	C₂³	1	4	yes	—
125	C₂₃×#95	C₂³	1	4	yes	—
126	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
127	C₂×Q₈×C₂₃	—	2	2	no	—
128	C₂×Q₈×C₂₃	—	4	1	no	—
129	C₂×Q₈×C₂₃	—	4	2	no	—
130	C₂×Q₈×C₂₃	—	4	1	no	—
131	C₂×Q₈×C₂₃	—	4	4	no	—
132	C₂×D₄×C₂₃	—	2	2	no	—
133	C₂×D₄×C₂₃	—	4	1	no	—
134	C₂×D₄×C₂₃	—	4	1	no	—
135	C₂²×C₄×C₂₃	—	2	4	no	—
136	C₂²×C₄×C₂₃	—	2	8	no	—
137	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₂₃	—	2	8	no	—
150	C₄⋊C₄×C₂₃	—	2	4	no	—
151	C₄⋊C₄×C₂₃	—	2	4	no	—
152	C₄⋊C₄×C₂₃	—	2	8	no	—
153	C₄⋊C₄×C₂₃	—	4	2	no	—
154	C₄⋊C₄×C₂₃	—	4	2	no	—
155	C₄⋊C₄×C₂₃	—	4	4	no	—
156	C₄⋊C₄×C₂₃	—	4	4	no	—
157	C₄⋊C₄×C₂₃	—	4	4	no	—
158	C₄⋊C₄×C₂₃	—	4	4	no	—
159	C₄⋊C₄×C₂₃	—	4	2	no	—
160	C₄⋊C₄×C₂₃	—	4	2	no	—
161	C₄⋊C₄×C₂₃	—	4	1	no	—
162	C₄⋊C₄×C₂₃	—	4	1	no	—
163	C₄⋊C₄×C₂₃	—	4	2	no	—
164	C₄⋊C₄×C₂₃	—	4	2	no	—
165	C₄⋊C₄×C₂₃	—	4	4	no	—
166	C₂²⋊C₄×C₂₃	—	2	8	no	—
167	C₂²⋊C₄×C₂₃	—	4	4	no	—
168	C₂²⋊C₄×C₂₃	—	4	4	no	—
169	C₂²⋊C₄×C₂₃	—	4	4	no	—
170	C₂²⋊C₄×C₂₃	—	4	4	no	—
171	C₂²⋊C₄×C₂₃	—	4	4	no	—
172	C₂²⋊C₄×C₂₃	—	4	2	no	—
173	C₄²×C₂₃	—	2	8	no	—
174	C₄²×C₂₃	—	2	2	no	—
175	C₄²×C₂₃	—	2	4	no	—
176	C₄²×C₂₃	—	2	4	no	—
177	C₄²×C₂₃	—	2	8	no	—
178	C₄²×C₂₃	—	4	2	no	—
179	C₄²×C₂₃	—	4	1	no	—
180	C₄²×C₂₃	#41	1	4	yes	—
181	#36698	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₂₃	—	2	2	no	—
183	C₂³×C₂₃	—	2	2	no	—
184	C₂³×C₂₃	—	2	4	no	—
185	C₂³×C₂₃	—	2	4	no	—
186	C₂³×C₂₃	—	2	2	no	—
187	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
188	Q₈×C₂₃	—	4	4	no	—
189	Q₈×C₂₃	—	4	8	no	—
190	D₄×C₂₃	—	4	4	no	—
191	C₂×C₄×C₂₃	—	2	1	no	—
192	C₂×C₄×C₂₃	—	2	2	no	—
193	C₂×C₄×C₂₃	—	2	2	no	—
194	C₂×C₄×C₂₃	—	2	1	no	—
195	C₂×C₄×C₂₃	—	2	2	no	—
196	C₂×C₄×C₂₃	—	2	4	no	—
197	C₂×C₄×C₂₃	—	2	4	no	—
198	C₂×C₄×C₂₃	—	2	1	no	—
199	C₂×C₄×C₂₃	—	2	4	no	—
200	C₂×C₄×C₂₃	—	2	4	no	—
201	C₂×C₄×C₂₃	—	2	2	no	—
202	C₂×C₄×C₂₃	—	2	2	no	—
203	C₂×C₄×C₂₃	—	2	2	no	—
204	C₂×C₄×C₂₃	—	2	4	no	—
205	C₂×C₄×C₂₃	—	2	2	no	—
206	C₂×C₄×C₂₃	—	2	4	no	—
207	C₂×C₄×C₂₃	—	2	4	no	—
208	C₂×C₄×C₂₃	—	2	2	no	—
209	C₂×C₄×C₂₃	—	2	2	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	2	4	no	—
212	C₂×C₄×C₂₃	—	2	4	no	—
213	C₂×C₄×C₂₃	—	2	4	no	—
214	C₂×C₄×C₂₃	—	2	4	no	—
215	C₂×C₄×C₂₃	—	2	4	no	—
216	C₂×C₄×C₂₃	—	2	4	no	—
217	C₂×C₄×C₂₃	—	2	2	no	—
218	C₂×C₄×C₂₃	—	2	4	no	—
219	C₂×C₄×C₂₃	—	4	8	no	—
220	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
221	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
222	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
223	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
224	#2844	C₂×C₂₃	1	1	yes	characteristic, complemented
225	#2838	C₂×C₂₃	1	4	yes	complemented
226	#2836	C₂×C₂₃	1	4	yes	complemented
227	#2833	C₂×C₂₃	1	2	yes	complemented
228	#2830	C₂×C₂₃	1	2	yes	—
229	#2822	C₂×C₂₃	1	1	yes	characteristic, complemented
230	#2820	C₂×C₂₃	1	2	yes	—
231	#2401	C₂×C₂₃	1	4	yes	complemented
232	#2399	C₂×C₂₃	1	2	yes	complemented
233	#2396	C₂×C₂₃	1	4	yes	complemented
234	#2395	C₂×C₂₃	1	2	yes	—
235	C₄×#125	C₂×C₂₃	1	2	yes	complemented
236	C₄×#124	C₂×C₂₃	1	1	yes	characteristic
237	C₂²×C₂₃	—	4	2	no	—
238	C₂²×C₂₃	—	4	4	no	—
239	C₂²×C₂₃	—	4	2	no	—
240	C₂²×C₂₃	—	4	2	no	—
241	C₂²×C₂₃	—	4	4	no	—
242	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
243	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₂₃	#585	1	1	yes	characteristic
246	C₂²×C₂₃	#585	1	2	yes	—
247	C₄×C₂₃	—	2	2	no	—
248	C₄×C₂₃	—	2	4	no	—
249	C₄×C₂₃	—	4	4	no	—
250	C₄×C₂₃	—	4	2	no	—
251	C₄×C₂₃	—	4	4	no	—
252	C₄×C₂₃	—	4	2	no	—
253	C₄×C₂₃	—	4	1	no	—
254	C₄×C₂₃	—	4	4	no	—
255	C₄×C₂₃	—	4	2	no	—
256	C₄×C₂₃	—	4	2	no	—
257	C₄×C₂₃	—	4	4	no	—
258	C₄×C₂₃	#563	1	4	yes	—
259	C₂×#125	C₂²×C₂₃	1	2	yes	—
260	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
262	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
264	C₂×#117	C₂²×C₂₃	1	2	yes	—
265	#401	C₂²×C₂₃	1	4	yes	—
266	#400	C₂²×C₂₃	1	4	yes	—
267	#400	C₂²×C₂₃	1	4	yes	—
268	#400	C₂²×C₂₃	1	4	yes	—
269	#400	C₂²×C₂₃	1	2	yes	—
270	#400	C₂²×C₂₃	1	4	yes	—
271	#399	C₂²×C₂₃	1	4	yes	—
272	#399	C₂²×C₂₃	1	2	yes	—
273	#398	C₂²×C₂₃	1	2	yes	—
274	#398	C₂²×C₂₃	1	2	yes	—
275	#398	C₂²×C₂₃	1	4	yes	—
276	#398	C₂²×C₂₃	1	4	yes	—
277	#398	C₂²×C₂₃	1	2	yes	—
278	#398	C₂²×C₂₃	1	4	yes	—
279	#397	C₂²×C₂₃	1	4	yes	—
280	#397	C₂²×C₂₃	1	4	yes	—
281	#397	C₂²×C₂₃	1	4	yes	—
282	#397	C₂²×C₂₃	1	2	yes	—
283	#397	C₂²×C₂₃	1	4	yes	—
284	#396	C₂²×C₂₃	1	4	yes	—
285	#396	C₂²×C₂₃	1	4	yes	—
286	#396	C₂²×C₂₃	1	4	yes	—
287	#395	C₂²×C₂₃	1	4	yes	—
288	#395	C₂²×C₂₃	1	2	yes	—
289	#395	C₂²×C₂₃	1	2	yes	—
290	#395	C₂²×C₂₃	1	4	yes	—
291	#394	C₂²×C₂₃	1	4	yes	—
292	#393	C₂²×C₂₃	1	4	yes	—
293	#391	C₂²×C₂₃	1	1	yes	characteristic
294	#390	C₂²×C₂₃	1	1	yes	characteristic
295	#389	C₂²×C₂₃	1	2	yes	—
296	#389	C₂²×C₂₃	1	2	yes	—
297	#388	C₂²×C₂₃	1	4	yes	—
298	#387	C₂²×C₂₃	1	4	yes	—
299	#387	C₂²×C₂₃	1	4	yes	—
300	#382	C₂²×C₂₃	1	2	yes	—
301	#382	C₂²×C₂₃	1	1	yes	characteristic
302	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
303	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
305	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
308	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
310	#376	C₂²×C₂₃	1	2	yes	—
311	C₄³	C₂²×C₂₃	1	1	yes	characteristic
312	C₂×C₂₃	—	8	2	no	—
313	C₂×C₂₃	#3460	1	1	yes	characteristic
314	C₂×C₂₃	#3461	1	2	yes	—
315	C₂×C₂₃	C₂×#563	1	1	yes	characteristic
316	C₂×C₂₃	#3529	1	1	yes	characteristic
317	C₂×C₂₃	#3531	1	2	yes	—
318	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
319	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
322	#125	—	2	8	no	—
323	#124	—	2	4	no	—
324	C₄×Q₈	—	4	4	no	—
325	C₄×Q₈	—	4	2	no	—
326	C₄×D₄	—	4	2	no	—
327	#117	—	4	4	no	—
328	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
352	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
353	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
355	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
356	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
357	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
359	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
360	#95	C₂³×C₂₃	1	4	yes	—
361	#95	C₂³×C₂₃	1	2	yes	—
362	#95	C₂³×C₂₃	1	2	yes	—
363	#95	C₂³×C₂₃	1	4	yes	—
364	#95	C₂³×C₂₃	1	4	yes	—
365	#95	C₂³×C₂₃	1	4	yes	—
366	#95	C₂³×C₂₃	1	4	yes	—
367	#95	C₂³×C₂₃	1	2	yes	—
368	#95	C₂³×C₂₃	1	2	yes	—
369	#95	C₂³×C₂₃	1	4	yes	—
370	#95	C₂³×C₂₃	1	4	yes	—
371	#95	C₂³×C₂₃	1	4	yes	—
372	#95	C₂³×C₂₃	1	4	yes	—
373	#95	C₂³×C₂₃	1	4	yes	—
374	#95	C₂³×C₂₃	1	4	yes	—
375	#95	C₂³×C₂₃	1	4	yes	—
376	#95	C₂³×C₂₃	1	4	yes	—
377	C₂₃	#36698	1	1	yes	characteristic, direct product factor, Sylow
378	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	4	1	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₄²	—	2	8	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	4	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	8	no	—
430	C₄²	—	4	2	no	—
431	C₄²	—	4	1	no	—
432	C₄²	#41×C₂₃	1	4	yes	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	2	no	—
438	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
439	Q₈	—	4	4	no	—
440	Q₈	—	4	8	no	—
441	D₄	—	4	4	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
472	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
473	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
474	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	4	no	—
480	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
481	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
483	C₂²	C₂₃×#585	1	1	yes	characteristic
484	C₂²	C₂₃×#585	1	2	yes	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	C₂₃×#563	1	4	yes	—
497	C₂	—	8	2	no	—
498	C₂	C₂₃×#3460	1	1	yes	characteristic
499	C₂	C₂₃×#3461	1	2	yes	—
500	C₂	C₂×C₂₃×#563	1	1	yes	characteristic
501	C₂	C₂₃×#3529	1	1	yes	characteristic
502	C₂	C₂₃×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2844	C₂	semidirect
2. C₂₃×#2838	C₂	semidirect
3. C₂₃×#2836	C₂	semidirect
4. C₂₃×#2833	C₂	semidirect
6. C₂₃×#2822	C₂	semidirect
8. C₂₃×#2401	C₂	semidirect
9. C₂₃×#2399	C₂	semidirect
10. C₂₃×#2396	C₂	semidirect
12. C₄×C₂₃×#125	C₂	semidirect
181. #36698	C₂₃	direct (N × H)
224. #2844	C₂×C₂₃	semidirect
225. #2838	C₂×C₂₃	semidirect
226. #2836	C₂×C₂₃	semidirect
227. #2833	C₂×C₂₃	semidirect
229. #2822	C₂×C₂₃	semidirect
231. #2401	C₂×C₂₃	semidirect
232. #2399	C₂×C₂₃	semidirect
233. #2396	C₂×C₂₃	semidirect
235. C₄×#125	C₂×C₂₃	semidirect
377. C₂₃	#36698	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×#2844	2
C₂₃×#2838	2
C₂₃×#2836	2
C₂₃×#2833	2
C₂₃×#2830	2
C₂₃×#2822	2
C₂₃×#2820	2
C₂₃×#2401	2
C₂₃×#2399	2
C₂₃×#2396	2
C₂₃×#2395	2
C₄×C₂₃×#125	2
C₄×C₂₃×#124	2
#36698	23

Subgroups — C23×#36698 #19184324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36698 #19184324