Subgroups — C₂₃×#25433 #19173059

Order 5888.

916 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3042	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2046	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2003	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1885	C₂	1	2	yes	maximal, complemented
11	C₂₃×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
17	C₂₃×#536	C₂²	1	2	yes	—
18	C₂×C₂₃×#124	C₂²	1	2	yes	—
19	C₂₃×#518	C₂²	1	2	yes	—
20	C₂₃×#495	—	2	4	no	—
21	C₂₃×#472	—	2	4	no	—
22	C₂₃×#470	—	2	2	no	—
23	C₂₃×#467	—	2	2	no	—
24	C₂₃×#463	—	2	4	no	—
25	C₂₃×#461	—	2	4	no	—
26	C₂₃×#442	—	2	2	no	—
27	C₄×D₈×C₂₃	—	2	2	no	—
28	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
29	C₂₃×#427	C₂²	1	1	yes	characteristic
30	C₂₃×#424	C₂²	1	2	yes	—
31	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
32	C₂₃×#419	C₂²	1	2	yes	—
33	C₂₃×#419	C₂²	1	2	yes	—
34	C₂₃×#418	C₂²	1	2	yes	—
35	C₂₃×#416	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#101	C₂²	1	2	yes	—
37	C₂×C₂₃×#100	C₂²	1	2	yes	—
38	C₂₃×#405	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#341	C₂²	1	1	yes	characteristic
41	C₂₃×#339	C₂²	1	1	yes	characteristic
42	C₂₃×#339	C₂²	1	2	yes	—
43	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
45	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
46	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
47	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
48	C₂×Q₁₆×C₂₃	—	2	1	no	—
49	C₂×Q₁₆×C₂₃	—	2	1	no	—
50	C₂×Q₁₆×C₂₃	—	2	2	no	—
51	C₂×Q₁₆×C₂₃	—	2	2	no	—
52	C₂×SD₁₆×C₂₃	—	2	2	no	—
53	C₂×SD₁₆×C₂₃	—	2	4	no	—
54	C₂×SD₁₆×C₂₃	—	2	4	no	—
55	C₂×SD₁₆×C₂₃	—	4	2	no	—
56	C₂×D₈×C₂₃	—	2	2	no	—
57	C₂×D₈×C₂₃	—	2	1	no	—
58	C₂×D₈×C₂₃	—	2	1	no	—
59	C₂×D₈×C₂₃	—	2	2	no	—
60	C₂×D₈×C₂₃	D₄	1	4	yes	—
61	C₂₃×#131	—	2	2	no	—
62	C₂₃×#131	—	2	2	no	—
63	C₂×M₁₆×C₂₃	—	2	1	no	—
64	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
66	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₃	—	2	1	no	—
68	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂₃×C₄⋊Q₈	—	2	2	no	—
71	C₂₃×#124	—	2	2	no	—
72	C₂₃×#124	—	2	4	no	—
73	C₂₃×#124	—	2	4	no	—
74	C₂₃×#123	—	4	2	no	—
75	C₂₃×C₂²⋊Q₈	—	2	4	no	—
76	C₄×D₄×C₂₃	—	2	4	no	—
77	C₄×D₄×C₂₃	—	2	4	no	—
78	C₂₃×#117	C₂³	1	1	yes	characteristic
79	C₂₃×#117	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
81	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
82	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×#108	—	2	2	no	—
84	C₂₃×#107	D₄	1	2	yes	—
85	C₂₃×#106	D₄	1	2	yes	—
86	C₂₃×C₄⋊C₈	—	2	4	no	—
87	C₂₃×#104	—	2	2	no	—
88	C₂₃×#103	—	2	4	no	—
89	C₂₃×#103	—	2	4	no	—
90	C₂₃×#103	D₄	1	2	yes	—
91	C₂₃×#102	—	2	4	no	—
92	C₂₃×#102	D₄	1	2	yes	—
93	C₂₃×#101	—	4	2	no	—
94	C₂₃×#100	—	2	4	no	—
95	C₂₃×#97	—	2	1	no	—
96	C₄×C₈×C₂₃	—	2	2	no	—
97	C₄×C₈×C₂₃	—	2	1	no	—
98	C₂⁴×C₂₃	—	2	2	no	—
99	#41×C₂₃	—	2	1	no	—
100	#41×C₂₃	—	2	1	no	—
101	#41×C₂₃	—	2	1	no	—
102	#41×C₂₃	—	2	1	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	—	2	2	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	2	2	no	—
109	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
110	C₂×D₄×C₂₃	—	2	1	no	—
111	C₂×D₄×C₂₃	—	2	2	no	—
112	C₂×D₄×C₂₃	—	2	2	no	—
113	C₂×D₄×C₂₃	—	2	2	no	—
114	C₂×D₄×C₂₃	—	2	2	no	—
115	C₂×D₄×C₂₃	—	2	2	no	—
116	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
117	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	—	2	1	no	—
119	C₂²×C₄×C₂₃	—	2	1	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	4	4	no	—
122	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
123	Q₁₆×C₂₃	—	4	2	no	—
124	Q₁₆×C₂₃	—	4	2	no	—
125	SD₁₆×C₂₃	—	4	8	no	—
126	SD₁₆×C₂₃	—	4	4	no	—
127	D₈×C₂₃	—	2	4	no	—
128	D₈×C₂₃	—	2	4	no	—
129	D₈×C₂₃	—	4	4	no	—
130	M₁₆×C₂₃	—	2	1	no	—
131	M₁₆×C₂₃	—	2	2	no	—
132	M₁₆×C₂₃	—	2	1	no	—
133	M₁₆×C₂₃	—	2	1	no	—
134	M₁₆×C₂₃	—	2	1	no	—
135	M₁₆×C₂₃	—	2	2	no	—
136	M₁₆×C₂₃	—	4	2	no	—
137	C₂×C₈×C₂₃	—	2	1	no	—
138	C₂×C₈×C₂₃	—	2	1	no	—
139	C₂×C₈×C₂₃	—	2	1	no	—
140	C₂×C₈×C₂₃	—	2	1	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	—	4	2	no	—
143	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₂₃	#41	1	2	yes	—
148	C₄⋊C₄×C₂₃	—	4	4	no	—
149	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
151	C₂²⋊C₄×C₂₃	—	2	1	no	—
152	C₂²⋊C₄×C₂₃	—	2	2	no	—
153	C₂²⋊C₄×C₂₃	—	4	4	no	—
154	C₂²⋊C₄×C₂₃	—	4	8	no	—
155	C₂²⋊C₄×C₂₃	—	4	4	no	—
156	C₄²×C₂₃	—	2	2	no	—
157	C₄²×C₂₃	—	2	1	no	—
158	C₄²×C₂₃	—	2	1	no	—
159	C₄²×C₂₃	#41	1	2	yes	—
160	#25433	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₂₃	—	2	1	no	—
162	C₂³×C₂₃	—	2	4	no	—
163	C₂³×C₂₃	—	4	2	no	—
164	C₂³×C₂₃	—	4	2	no	—
165	C₂³×C₂₃	—	8	4	no	—
166	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
167	Q₈×C₂₃	—	2	1	no	—
168	Q₈×C₂₃	—	2	1	no	—
169	Q₈×C₂₃	—	4	2	no	—
170	Q₈×C₂₃	—	4	2	no	—
171	Q₈×C₂₃	—	4	2	no	—
172	Q₈×C₂₃	—	4	2	no	—
173	D₄×C₂₃	—	2	4	no	—
174	D₄×C₂₃	—	2	1	no	—
175	D₄×C₂₃	—	2	1	no	—
176	D₄×C₂₃	—	2	4	no	—
177	D₄×C₂₃	—	4	1	no	—
178	D₄×C₂₃	—	4	1	no	—
179	D₄×C₂₃	—	4	2	no	—
180	D₄×C₂₃	—	4	2	no	—
181	C₂×C₄×C₂₃	—	2	4	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	1	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	4	2	no	—
186	C₂×C₄×C₂₃	—	4	1	no	—
187	C₂×C₄×C₂₃	—	4	1	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	4	2	no	—
191	C₂×C₄×C₂₃	—	16	4	no	—
192	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₈×C₂₃	—	2	2	no	—
199	C₈×C₂₃	—	4	1	no	—
200	C₈×C₂₃	—	4	2	no	—
201	C₈×C₂₃	—	4	1	no	—
202	C₈×C₂₃	#121	1	2	yes	—
203	C₈×C₂₃	#121	1	2	yes	—
204	C₂×#495	C₂×C₂₃	1	1	yes	characteristic, complemented
205	C₂×#472	C₂×C₂₃	1	1	yes	characteristic
206	#3059	C₂×C₂₃	1	1	yes	characteristic, complemented
207	#3042	C₂×C₂₃	1	2	yes	complemented
208	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
209	#2046	C₂×C₂₃	1	2	yes	complemented
210	#2003	C₂×C₂₃	1	2	yes	complemented
211	#1979	C₂×C₂₃	1	1	yes	characteristic, complemented
212	#1945	C₂×C₂₃	1	1	yes	characteristic, complemented
213	#1885	C₂×C₂₃	1	2	yes	complemented
214	#1764	C₂×C₂₃	1	1	yes	characteristic, complemented
215	C₂²×C₂₃	—	2	2	no	—
216	C₂²×C₂₃	—	4	1	no	—
217	C₂²×C₂₃	—	4	4	no	—
218	C₂²×C₂₃	—	4	2	no	—
219	C₂²×C₂₃	—	8	4	no	—
220	C₂²×C₂₃	—	8	4	no	—
221	C₂²×C₂₃	—	16	2	no	—
222	C₂²×C₂₃	#540	1	1	yes	characteristic
223	C₂²×C₂₃	D₄²	1	1	yes	characteristic
224	C₂²×C₂₃	#546	1	1	yes	characteristic
225	C₄×C₂₃	—	4	2	no	—
226	C₄×C₂₃	—	4	1	no	—
227	C₄×C₂₃	—	4	4	no	—
228	C₄×C₂₃	—	4	2	no	—
229	C₄×C₂₃	—	8	2	no	—
230	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
231	C₄×C₂₃	#532	1	1	yes	characteristic
232	C₄×C₂₃	D₄²	1	1	yes	characteristic
233	C₄×C₂₃	#550	1	1	yes	characteristic
234	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
235	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
236	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
237	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
238	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
239	#536	C₂²×C₂₃	1	2	yes	—
240	C₂×#124	C₂²×C₂₃	1	2	yes	—
241	#518	C₂²×C₂₃	1	2	yes	—
242	#495	—	2	4	no	—
243	#472	—	2	4	no	—
244	#470	—	2	2	no	—
245	#467	—	2	2	no	—
246	#463	—	2	4	no	—
247	#461	—	2	4	no	—
248	#442	—	2	2	no	—
249	C₄×D₈	—	2	2	no	—
250	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
251	#427	C₂²×C₂₃	1	1	yes	characteristic
252	#424	C₂²×C₂₃	1	2	yes	—
253	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
254	#419	C₂²×C₂₃	1	2	yes	—
255	#419	C₂²×C₂₃	1	2	yes	—
256	#418	C₂²×C₂₃	1	2	yes	—
257	#416	C₂²×C₂₃	1	1	yes	characteristic
258	C₂×#101	C₂²×C₂₃	1	2	yes	—
259	C₂×#100	C₂²×C₂₃	1	2	yes	—
260	#405	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
262	#341	C₂²×C₂₃	1	1	yes	characteristic
263	#339	C₂²×C₂₃	1	1	yes	characteristic
264	#339	C₂²×C₂₃	1	2	yes	—
265	C₂×C₂₃	—	2	1	no	—
266	C₂×C₂₃	—	2	1	no	—
267	C₂×C₂₃	—	8	1	no	—
268	C₂×C₂₃	—	8	4	no	—
269	C₂×C₂₃	#2428	1	1	yes	characteristic
270	C₂×C₂₃	#3290	1	2	yes	—
271	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
272	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
273	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
274	AGL(1,ℤ/8)	—	2	4	no	—
275	AGL(1,ℤ/8)	—	4	2	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	4	no	—
282	C₂×SD₁₆	—	2	4	no	—
283	C₂×SD₁₆	—	4	2	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	D₄×C₂₃	1	4	yes	—
289	#131	—	2	2	no	—
290	#131	—	2	2	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
293	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
294	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
298	C₄⋊Q₈	—	2	2	no	—
299	#124	—	2	4	no	—
300	#124	—	2	2	no	—
301	#124	—	2	4	no	—
302	#123	—	4	2	no	—
303	C₂²⋊Q₈	—	2	4	no	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	#117	C₂³×C₂₃	1	1	yes	characteristic
307	#117	C₂³×C₂₃	1	2	yes	—
308	C₂×C₂²⋊C₄	—	4	2	no	—
309	C₂×C₂²⋊C₄	—	4	2	no	—
310	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
311	#108	—	2	2	no	—
312	#107	D₄×C₂₃	1	2	yes	—
313	#106	D₄×C₂₃	1	2	yes	—
314	C₄⋊C₈	—	2	4	no	—
315	#104	—	2	2	no	—
316	#103	—	2	4	no	—
317	#103	—	2	4	no	—
318	#103	D₄×C₂₃	1	2	yes	—
319	#102	—	2	4	no	—
320	#102	D₄×C₂₃	1	2	yes	—
321	#101	—	4	2	no	—
322	#100	—	2	4	no	—
323	#97	—	2	1	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	—	2	1	no	—
326	C₂₃	#25433	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	—	2	2	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	1	no	—
331	#41	—	2	1	no	—
332	C₂×Q₈	—	2	2	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	C₂×D₄×C₂₃	1	1	yes	characteristic
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
346	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
352	Q₁₆	—	4	2	no	—
353	Q₁₆	—	4	2	no	—
354	SD₁₆	—	4	8	no	—
355	SD₁₆	—	4	4	no	—
356	D₈	—	2	4	no	—
357	D₈	—	2	4	no	—
358	D₈	—	4	4	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	1	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	4	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
373	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
376	C₂×C₈	#41×C₂₃	1	2	yes	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
379	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	8	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	#41×C₂₃	1	2	yes	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	4	no	—
394	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
395	Q₈	—	2	1	no	—
396	Q₈	—	2	1	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	1	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	16	4	no	—
420	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
425	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₈	C₂₃×#121	1	2	yes	—
431	C₈	C₂₃×#121	1	2	yes	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	16	2	no	—
439	C₂²	C₂₃×#540	1	1	yes	characteristic
440	C₂²	D₄²×C₂₃	1	1	yes	characteristic
441	C₂²	C₂₃×#546	1	1	yes	characteristic
442	C₄	—	4	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
448	C₄	C₂₃×#532	1	1	yes	characteristic
449	C₄	D₄²×C₂₃	1	1	yes	characteristic
450	C₄	C₂₃×#550	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	8	1	no	—
454	C₂	—	8	4	no	—
455	C₂	C₂₃×#2428	1	1	yes	characteristic
456	C₂	C₂₃×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#472	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#495	C₂	semidirect
3. C₂₃×#3059	C₂	semidirect
4. C₂₃×#3042	C₂	semidirect
5. C₂₃×#2948	C₂	semidirect
6. C₂₃×#2046	C₂	semidirect
7. C₂₃×#2003	C₂	semidirect
8. C₂₃×#1979	C₂	semidirect
9. C₂₃×#1945	C₂	semidirect
10. C₂₃×#1885	C₂	semidirect
11. C₂₃×#1764	C₂	semidirect
160. #25433	C₂₃	direct (N × H)
204. C₂×#495	C₂×C₂₃	semidirect
206. #3059	C₂×C₂₃	semidirect
207. #3042	C₂×C₂₃	semidirect
208. #2948	C₂×C₂₃	semidirect
209. #2046	C₂×C₂₃	semidirect
210. #2003	C₂×C₂₃	semidirect
211. #1979	C₂×C₂₃	semidirect
212. #1945	C₂×C₂₃	semidirect
213. #1885	C₂×C₂₃	semidirect
214. #1764	C₂×C₂₃	semidirect
326. C₂₃	#25433	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×#495	2
C₂×C₂₃×#472	2
C₂₃×#3059	2
C₂₃×#3042	2
C₂₃×#2948	2
C₂₃×#2046	2
C₂₃×#2003	2
C₂₃×#1979	2
C₂₃×#1945	2
C₂₃×#1885	2
C₂₃×#1764	2
#25433	23

Subgroups — C23×#25433 #19173059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25433 #19173059