Subgroups — C₂₃×#60372 #19207998

Order 5888.

5126 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#576	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3012	C₂	1	6	yes	maximal, complemented
5	C₂₃×#3008	C₂	1	6	yes	maximal, complemented
6	C₂₃×#3006	C₂	1	3	yes	maximal, complemented
7	C₂₃×#3003	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3002	C₂	1	3	yes	maximal, complemented
9	C₂×C₂₃×#447	C₂	1	3	yes	maximal, complemented
10	C₂₃×#2897	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×H(5,𝔽₂)	—	2	16	no	—
13	C₂×C₂₃×H(5,𝔽₂)	—	2	3	no	—
14	C₂×C₂₃×H(5,𝔽₂)	—	2	1	no	—
15	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	6	yes	complemented
17	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#41×C₂₃	—	2	1	no	—
19	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₂₃	C₂²	1	3	yes	complemented
21	C₂³×D₄×C₂₃	—	2	3	no	—
22	C₂³×D₄×C₂₃	C₂²	1	3	yes	complemented
23	C₂₃×#576	—	2	16	no	—
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
26	C₂×C₂₃×#135	C₂²	1	6	yes	complemented
27	C₂²×D₈×C₂₃	C₂²	1	6	yes	complemented
28	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
29	C₂₃×#550	—	2	1	no	—
30	C₂₃×#548	—	2	1	no	—
31	C₂₃×#546	—	2	3	no	—
32	D₄²×C₂₃	—	2	3	no	—
33	C₂₃×#537	C₂²	1	3	yes	complemented
34	C₂₃×#535	C₂²	1	3	yes	complemented
35	C₂₃×#525	C₂²	1	3	yes	complemented
36	C₂×C₂₃×#121	C₂²	1	3	yes	complemented
37	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#452	C₂²	1	6	yes	complemented
39	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#450	C₂²	1	3	yes	complemented
41	C₂₃×#450	C₂²	1	6	yes	complemented
42	C₂₃×#449	C₂²	1	6	yes	complemented
43	C₂₃×#449	C₂²	1	12	yes	complemented
44	C₂₃×#448	C₂²	1	3	yes	complemented
45	C₂₃×#447	C₂²	1	3	yes	complemented
46	C₂₃×#447	C₂²	1	6	yes	complemented
47	C₂₃×#447	C₂²	1	12	yes	complemented
48	C₂₃×#447	C₂²	1	6	yes	complemented
49	C₂₃×#418	C₂²	1	6	yes	complemented
50	C₂₃×#417	C₂²	1	6	yes	complemented
51	C₂₃×#416	C₂²	1	6	yes	complemented
52	C₂×C₂₃×#102	C₂²	1	6	yes	complemented
53	C₂₃×#408	C₂²	1	6	yes	complemented
54	C₂₃×#407	C₂²	1	3	yes	complemented
55	C₂×C₂₃×C₂²⋊C₈	C₂²	1	3	yes	complemented
56	C₂⁵×C₂₃	—	2	3	no	—
57	C₂₃×H(5,𝔽₂)	—	2	16	no	—
58	C₂₃×H(5,𝔽₂)	—	2	48	no	—
59	C₂₃×H(5,𝔽₂)	—	2	8	no	—
60	C₂₃×H(5,𝔽₂)	—	2	24	no	—
61	C₂₃×H(5,𝔽₂)	—	2	24	no	—
62	C₂₃×H(5,𝔽₂)	—	2	8	no	—
63	C₂₃×H(5,𝔽₂)	D₄	1	16	yes	complemented
64	C₂×#41×C₂₃	—	2	16	no	—
65	C₂×#41×C₂₃	—	2	8	no	—
66	C₂×#41×C₂₃	—	2	24	no	—
67	C₂×#41×C₂₃	—	2	2	no	—
68	C₂×#41×C₂₃	—	2	6	no	—
69	C₂×#41×C₂₃	—	2	1	no	—
70	C₂×#41×C₂₃	—	2	3	no	—
71	C₂×#41×C₂₃	—	2	3	no	—
72	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
73	C₂×#41×C₂₃	D₄	1	3	yes	—
74	C₂×#41×C₂₃	C₂³	1	6	yes	—
75	C₂×#41×C₂₃	C₂³	1	6	yes	—
76	C₂×#41×C₂₃	C₂³	1	3	yes	—
77	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×#41×C₂₃	C₂³	1	3	yes	complemented
79	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₂₃	—	2	48	no	—
82	C₂²×D₄×C₂₃	—	2	3	no	—
83	C₂²×D₄×C₂₃	—	2	6	no	—
84	C₂²×D₄×C₂₃	—	2	12	no	—
85	C₂²×D₄×C₂₃	—	2	6	no	—
86	C₂²×D₄×C₂₃	—	2	24	no	—
87	C₂²×D₄×C₂₃	—	2	3	no	—
88	C₂²×D₄×C₂₃	—	2	3	no	—
89	C₂²×D₄×C₂₃	—	2	3	no	—
90	C₂²×D₄×C₂₃	—	2	3	no	—
91	C₂²×D₄×C₂₃	—	2	3	no	—
92	C₂²×D₄×C₂₃	D₄	1	3	yes	—
93	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
94	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
95	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
96	C₂²×D₄×C₂₃	C₂³	1	3	yes	complemented
97	C₂³×C₄×C₂₃	—	2	3	no	—
98	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
99	C₂₃×AGL(1,ℤ/8)	—	2	24	no	—
100	C₂₃×AGL(1,ℤ/8)	—	2	24	no	—
101	C₂₃×#135	—	2	24	no	—
102	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	complemented
103	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	complemented
104	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	complemented
105	C₂×D₈×C₂₃	—	2	24	no	—
106	C₂×D₈×C₂₃	C₂³	1	6	yes	complemented
107	C₂×D₈×C₂₃	C₂³	1	12	yes	complemented
108	C₂₃×#131	—	2	8	no	—
109	C₂×M₁₆×C₂₃	C₂³	1	6	yes	complemented
110	C₂²×C₈×C₂₃	C₂³	1	6	yes	complemented
111	C₂₃×#127	—	2	3	no	—
112	C₂₃×#124	—	2	3	no	—
113	C₂₃×#123	—	2	3	no	—
114	C₂₃×C₂²⋊Q₈	—	2	3	no	—
115	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₂²⋊Q₈	C₂³	1	3	yes	complemented
117	C₂₃×#121	—	2	3	no	—
118	C₂₃×#121	—	2	6	no	—
119	C₂₃×#121	—	2	3	no	—
120	C₂₃×#121	—	2	3	no	—
121	C₂₃×#121	C₂³	1	3	yes	—
122	C₂₃×#121	C₂³	1	6	yes	complemented
123	C₂₃×#121	C₂³	1	3	yes	complemented
124	C₂₃×#120	—	2	3	no	—
125	C₂₃×#120	—	2	6	no	—
126	C₄×Q₈×C₂₃	—	2	1	no	—
127	C₄×D₄×C₂₃	—	2	3	no	—
128	C₄×D₄×C₂₃	—	2	3	no	—
129	C₄×D₄×C₂₃	—	2	3	no	—
130	C₂₃×#117	C₂³	1	3	yes	complemented
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	complemented
132	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
133	C₂₃×#103	C₂³	1	2	yes	complemented
134	C₂₃×#103	C₂³	1	6	yes	complemented
135	C₂₃×#102	C₂³	1	6	yes	complemented
136	C₂₃×#102	C₂³	1	12	yes	complemented
137	C₂₃×#102	C₂³	1	6	yes	complemented
138	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
139	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
140	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	complemented
141	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	complemented
142	C₂⁴×C₂₃	—	2	24	no	—
143	C₂⁴×C₂₃	—	2	3	no	—
144	C₂⁴×C₂₃	—	2	6	no	—
145	C₂⁴×C₂₃	—	2	6	no	—
146	C₂⁴×C₂₃	—	2	3	no	—
147	C₂⁴×C₂₃	—	8	6	no	—
148	C₂⁴×C₂₃	—	8	6	no	—
149	C₂⁴×C₂₃	C₂×D₄	1	3	yes	—
150	#41×C₂₃	—	2	24	no	—
151	#41×C₂₃	—	2	48	no	—
152	#41×C₂₃	—	2	24	no	—
153	#41×C₂₃	—	2	16	no	—
154	#41×C₂₃	—	2	4	no	—
155	#41×C₂₃	—	2	12	no	—
156	#41×C₂₃	—	2	12	no	—
157	#41×C₂₃	—	2	12	no	—
158	#41×C₂₃	—	2	12	no	—
159	#41×C₂₃	—	2	12	no	—
160	#41×C₂₃	—	2	12	no	—
161	#41×C₂₃	—	4	4	no	—
162	#41×C₂₃	C₂×D₄	1	8	yes	—
163	#41×C₂₃	C₂×D₄	1	24	yes	complemented
164	C₂×Q₈×C₂₃	—	2	4	no	—
165	C₂×Q₈×C₂₃	—	2	4	no	—
166	C₂×Q₈×C₂₃	—	2	1	no	—
167	C₂×Q₈×C₂₃	C₂×D₄	1	3	yes	—
168	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
169	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
170	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
171	C₂×D₄×C₂₃	—	2	24	no	—
172	C₂×D₄×C₂₃	—	2	24	no	—
173	C₂×D₄×C₂₃	—	2	96	no	—
174	C₂×D₄×C₂₃	—	2	24	no	—
175	C₂×D₄×C₂₃	—	2	48	no	—
176	C₂×D₄×C₂₃	—	2	24	no	—
177	C₂×D₄×C₂₃	—	2	6	no	—
178	C₂×D₄×C₂₃	—	2	6	no	—
179	C₂×D₄×C₂₃	—	2	12	no	—
180	C₂×D₄×C₂₃	—	2	48	no	—
181	C₂×D₄×C₂₃	—	2	12	no	—
182	C₂×D₄×C₂₃	—	2	24	no	—
183	C₂×D₄×C₂₃	—	2	3	no	—
184	C₂×D₄×C₂₃	—	2	3	no	—
185	C₂×D₄×C₂₃	—	2	3	no	—
186	C₂×D₄×C₂₃	—	2	6	no	—
187	C₂×D₄×C₂₃	—	2	6	no	—
188	C₂×D₄×C₂₃	—	2	3	no	—
189	C₂×D₄×C₂₃	—	2	6	no	—
190	C₂×D₄×C₂₃	—	2	12	no	—
191	C₂×D₄×C₂₃	—	2	12	no	—
192	C₂×D₄×C₂₃	—	2	3	no	—
193	C₂×D₄×C₂₃	—	4	12	no	—
194	C₂×D₄×C₂₃	—	8	6	no	—
195	C₂×D₄×C₂₃	C₂×D₄	1	6	yes	—
196	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
197	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
198	C₂×D₄×C₂₃	C₂×D₄	1	24	yes	complemented
199	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
200	C₂×D₄×C₂₃	C₂⁴	1	6	yes	—
201	C₂²×C₄×C₂₃	—	2	24	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	6	no	—
204	C₂²×C₄×C₂₃	—	2	6	no	—
205	C₂²×C₄×C₂₃	—	2	12	no	—
206	C₂²×C₄×C₂₃	—	2	3	no	—
207	C₂²×C₄×C₂₃	—	2	3	no	—
208	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
209	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
211	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
214	Q₁₆×C₂₃	—	2	4	no	—
215	SD₁₆×C₂₃	—	2	12	no	—
216	SD₁₆×C₂₃	—	2	12	no	—
217	D₈×C₂₃	—	2	12	no	—
218	D₈×C₂₃	—	2	24	no	—
219	M₁₆×C₂₃	—	2	12	no	—
220	C₂×C₈×C₂₃	—	2	12	no	—
221	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
222	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
223	C₄⋊C₄×C₂₃	—	2	3	no	—
224	C₄⋊C₄×C₂₃	—	2	1	no	—
225	C₄⋊C₄×C₂₃	—	2	3	no	—
226	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
227	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²⋊C₄×C₂₃	—	2	3	no	—
229	C₂²⋊C₄×C₂₃	—	2	1	no	—
230	C₂²⋊C₄×C₂₃	—	2	3	no	—
231	C₂²⋊C₄×C₂₃	—	2	3	no	—
232	C₂²⋊C₄×C₂₃	—	2	6	no	—
233	C₂²⋊C₄×C₂₃	—	2	3	no	—
234	C₄²×C₂₃	—	2	3	no	—
235	#60372	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂³×C₂₃	—	2	12	no	—
237	C₂³×C₂₃	—	2	24	no	—
238	C₂³×C₂₃	—	2	6	no	—
239	C₂³×C₂₃	—	2	6	no	—
240	C₂³×C₂₃	—	2	6	no	—
241	C₂³×C₂₃	—	2	24	no	—
242	C₂³×C₂₃	—	2	3	no	—
243	C₂³×C₂₃	—	4	3	no	—
244	C₂³×C₂₃	—	4	6	no	—
245	C₂³×C₂₃	—	4	6	no	—
246	C₂³×C₂₃	—	4	6	no	—
247	C₂³×C₂₃	—	8	6	no	—
248	C₂³×C₂₃	—	8	6	no	—
249	C₂³×C₂₃	—	8	6	no	—
250	C₂³×C₂₃	—	8	6	no	—
251	C₂³×C₂₃	—	8	3	no	—
252	C₂³×C₂₃	—	8	3	no	—
253	C₂³×C₂₃	—	8	48	no	—
254	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
255	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
256	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
257	Q₈×C₂₃	—	2	4	no	—
258	Q₈×C₂₃	—	2	6	no	—
259	Q₈×C₂₃	—	2	2	no	—
260	Q₈×C₂₃	—	2	2	no	—
261	Q₈×C₂₃	#120	1	4	yes	—
262	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
263	D₄×C₂₃	—	2	24	no	—
264	D₄×C₂₃	—	2	24	no	—
265	D₄×C₂₃	—	2	12	no	—
266	D₄×C₂₃	—	2	24	no	—
267	D₄×C₂₃	—	2	12	no	—
268	D₄×C₂₃	—	2	6	no	—
269	D₄×C₂₃	—	2	24	no	—
270	D₄×C₂₃	—	2	6	no	—
271	D₄×C₂₃	—	2	6	no	—
272	D₄×C₂₃	—	4	6	no	—
273	D₄×C₂₃	—	4	6	no	—
274	D₄×C₂₃	—	4	6	no	—
275	D₄×C₂₃	—	8	3	no	—
276	D₄×C₂₃	—	8	6	no	—
277	D₄×C₂₃	#120	1	12	yes	—
278	D₄×C₂₃	C₂²×D₄	1	12	yes	—
279	C₂×C₄×C₂₃	—	2	4	no	—
280	C₂×C₄×C₂₃	—	2	24	no	—
281	C₂×C₄×C₂₃	—	2	6	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	6	no	—
284	C₂×C₄×C₂₃	—	2	24	no	—
285	C₂×C₄×C₂₃	—	2	6	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	6	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	3	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	4	6	no	—
292	C₂×C₄×C₂₃	—	8	3	no	—
293	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
294	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
296	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
297	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
298	C₈×C₂₃	—	2	2	no	—
299	C₈×C₂₃	—	2	6	no	—
300	C₂²×H(5,𝔽₂)	C₂×C₂₃	1	1	yes	characteristic, complemented
301	C₂×#576	C₂×C₂₃	1	2	yes	complemented
302	#3488	C₂×C₂₃	1	1	yes	characteristic, complemented
303	#3012	C₂×C₂₃	1	6	yes	complemented
304	#3008	C₂×C₂₃	1	6	yes	complemented
305	#3006	C₂×C₂₃	1	3	yes	complemented
306	#3003	C₂×C₂₃	1	3	yes	complemented
307	#3002	C₂×C₂₃	1	3	yes	complemented
308	C₂×#447	C₂×C₂₃	1	3	yes	complemented
309	#2897	C₂×C₂₃	1	2	yes	complemented
310	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
311	C₂²×C₂₃	—	2	1	no	—
312	C₂²×C₂₃	—	2	3	no	—
313	C₂²×C₂₃	—	2	1	no	—
314	C₂²×C₂₃	—	2	3	no	—
315	C₂²×C₂₃	—	2	3	no	—
316	C₂²×C₂₃	—	2	3	no	—
317	C₂²×C₂₃	—	2	12	no	—
318	C₂²×C₂₃	—	2	3	no	—
319	C₂²×C₂₃	—	4	12	no	—
320	C₂²×C₂₃	—	4	24	no	—
321	C₂²×C₂₃	—	4	6	no	—
322	C₂²×C₂₃	—	4	6	no	—
323	C₂²×C₂₃	—	4	3	no	—
324	C₂²×C₂₃	—	4	3	no	—
325	C₂²×C₂₃	—	4	3	no	—
326	C₂²×C₂₃	—	8	24	no	—
327	C₂²×C₂₃	—	8	24	no	—
328	C₂²×C₂₃	—	16	6	no	—
329	C₂²×C₂₃	C₂×#120	1	6	yes	—
330	C₂²×C₂₃	#576	1	2	yes	complemented
331	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₂₃	—	2	4	no	—
333	C₄×C₂₃	—	2	3	no	—
334	C₄×C₂₃	—	2	1	no	—
335	C₄×C₂₃	—	4	1	no	—
336	C₄×C₂₃	—	4	1	no	—
337	C₄×C₂₃	—	4	3	no	—
338	C₄×C₂₃	C₂×#120	1	6	yes	—
339	C₄×C₂₃	C₂³×D₄	1	2	yes	—
340	C₂×H(5,𝔽₂)	—	2	16	no	—
341	C₂×H(5,𝔽₂)	—	2	3	no	—
342	C₂×H(5,𝔽₂)	—	2	1	no	—
343	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
344	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	6	yes	complemented
345	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic, complemented
346	C₂²×#41	—	2	1	no	—
347	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
348	C₂²×#41	C₂²×C₂₃	1	3	yes	complemented
349	C₂³×D₄	—	2	3	no	—
350	C₂³×D₄	C₂²×C₂₃	1	3	yes	complemented
351	#576	—	2	16	no	—
352	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	6	yes	complemented
353	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	6	yes	complemented
354	C₂×#135	C₂²×C₂₃	1	6	yes	complemented
355	C₂²×D₈	C₂²×C₂₃	1	6	yes	complemented
356	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
357	#550	—	2	1	no	—
358	#548	—	2	1	no	—
359	#546	—	2	3	no	—
360	D₄²	—	2	3	no	—
361	#537	C₂²×C₂₃	1	3	yes	complemented
362	#535	C₂²×C₂₃	1	3	yes	complemented
363	#525	C₂²×C₂₃	1	3	yes	complemented
364	C₂×#121	C₂²×C₂₃	1	3	yes	complemented
365	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
366	#452	C₂²×C₂₃	1	6	yes	complemented
367	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
368	#450	C₂²×C₂₃	1	3	yes	complemented
369	#450	C₂²×C₂₃	1	6	yes	complemented
370	#449	C₂²×C₂₃	1	6	yes	complemented
371	#449	C₂²×C₂₃	1	12	yes	complemented
372	#448	C₂²×C₂₃	1	3	yes	complemented
373	#447	C₂²×C₂₃	1	3	yes	complemented
374	#447	C₂²×C₂₃	1	6	yes	complemented
375	#447	C₂²×C₂₃	1	12	yes	complemented
376	#447	C₂²×C₂₃	1	6	yes	complemented
377	#418	C₂²×C₂₃	1	6	yes	complemented
378	#417	C₂²×C₂₃	1	6	yes	complemented
379	#416	C₂²×C₂₃	1	6	yes	complemented
380	C₂×#102	C₂²×C₂₃	1	6	yes	complemented
381	#408	C₂²×C₂₃	1	6	yes	complemented
382	#407	C₂²×C₂₃	1	3	yes	complemented
383	C₂×C₂²⋊C₈	C₂²×C₂₃	1	3	yes	complemented
384	C₂×C₂₃	—	2	2	no	—
385	C₂×C₂₃	—	2	6	no	—
386	C₂×C₂₃	—	4	3	no	—
387	C₂×C₂₃	—	4	12	no	—
388	C₂×C₂₃	—	8	3	no	—
389	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
390	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
391	C₂×C₂₃	#3585	1	1	yes	characteristic
392	C₂⁵	—	2	3	no	—
393	H(5,𝔽₂)	—	2	16	no	—
394	H(5,𝔽₂)	—	2	48	no	—
395	H(5,𝔽₂)	—	2	8	no	—
396	H(5,𝔽₂)	—	2	24	no	—
397	H(5,𝔽₂)	—	2	24	no	—
398	H(5,𝔽₂)	—	2	8	no	—
399	H(5,𝔽₂)	D₄×C₂₃	1	16	yes	complemented
400	C₂×#41	—	2	16	no	—
401	C₂×#41	—	2	8	no	—
402	C₂×#41	—	2	24	no	—
403	C₂×#41	—	2	2	no	—
404	C₂×#41	—	2	6	no	—
405	C₂×#41	—	2	1	no	—
406	C₂×#41	—	2	3	no	—
407	C₂×#41	—	2	3	no	—
408	C₂×#41	D₄×C₂₃	1	3	yes	—
409	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
410	C₂×#41	C₂³×C₂₃	1	6	yes	—
411	C₂×#41	C₂³×C₂₃	1	6	yes	—
412	C₂×#41	C₂³×C₂₃	1	3	yes	—
413	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
414	C₂×#41	C₂³×C₂₃	1	3	yes	complemented
415	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
417	C₂²×D₄	—	2	48	no	—
418	C₂²×D₄	—	2	3	no	—
419	C₂²×D₄	—	2	6	no	—
420	C₂²×D₄	—	2	12	no	—
421	C₂²×D₄	—	2	6	no	—
422	C₂²×D₄	—	2	24	no	—
423	C₂²×D₄	—	2	3	no	—
424	C₂²×D₄	—	2	3	no	—
425	C₂²×D₄	—	2	3	no	—
426	C₂²×D₄	—	2	3	no	—
427	C₂²×D₄	—	2	3	no	—
428	C₂²×D₄	D₄×C₂₃	1	3	yes	—
429	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
430	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
431	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
432	C₂²×D₄	C₂³×C₂₃	1	3	yes	complemented
433	C₂³×C₄	—	2	3	no	—
434	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
435	AGL(1,ℤ/8)	—	2	24	no	—
436	AGL(1,ℤ/8)	—	2	24	no	—
437	#135	—	2	24	no	—
438	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	complemented
439	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	complemented
440	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	complemented
441	C₂×D₈	—	2	24	no	—
442	C₂×D₈	C₂³×C₂₃	1	6	yes	complemented
443	C₂×D₈	C₂³×C₂₃	1	12	yes	complemented
444	#131	—	2	8	no	—
445	C₂×M₁₆	C₂³×C₂₃	1	6	yes	complemented
446	C₂²×C₈	C₂³×C₂₃	1	6	yes	complemented
447	#127	—	2	3	no	—
448	#124	—	2	3	no	—
449	#123	—	2	3	no	—
450	C₂²⋊Q₈	—	2	3	no	—
451	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
452	C₂²⋊Q₈	C₂³×C₂₃	1	3	yes	complemented
453	#121	—	2	6	no	—
454	#121	—	2	3	no	—
455	#121	—	2	3	no	—
456	#121	—	2	3	no	—
457	#121	C₂³×C₂₃	1	3	yes	—
458	#121	C₂³×C₂₃	1	6	yes	complemented
459	#121	C₂³×C₂₃	1	3	yes	complemented
460	#120	—	2	3	no	—
461	#120	—	2	6	no	—
462	C₄×Q₈	—	2	1	no	—
463	C₄×D₄	—	2	3	no	—
464	C₄×D₄	—	2	3	no	—
465	C₄×D₄	—	2	3	no	—
466	#117	C₂³×C₂₃	1	3	yes	complemented
467	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	complemented
468	C₂×C₂²⋊C₄	—	2	3	no	—
469	#103	C₂³×C₂₃	1	2	yes	complemented
470	#103	C₂³×C₂₃	1	6	yes	complemented
471	#102	C₂³×C₂₃	1	6	yes	complemented
472	#102	C₂³×C₂₃	1	12	yes	complemented
473	#102	C₂³×C₂₃	1	6	yes	complemented
474	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
476	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	complemented
477	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	complemented
478	C₂₃	#60372	1	1	yes	characteristic, direct product factor, Sylow
479	C₂⁴	—	2	24	no	—
480	C₂⁴	—	2	3	no	—
481	C₂⁴	—	2	6	no	—
482	C₂⁴	—	2	6	no	—
483	C₂⁴	—	2	3	no	—
484	C₂⁴	—	8	6	no	—
485	C₂⁴	—	8	6	no	—
486	C₂⁴	C₂×D₄×C₂₃	1	3	yes	—
487	#41	—	2	24	no	—
488	#41	—	2	48	no	—
489	#41	—	2	24	no	—
490	#41	—	2	16	no	—
491	#41	—	2	4	no	—
492	#41	—	2	12	no	—
493	#41	—	2	12	no	—
494	#41	—	2	12	no	—
495	#41	—	2	12	no	—
496	#41	—	2	12	no	—
497	#41	—	2	12	no	—
498	#41	—	4	4	no	—
499	#41	C₂×D₄×C₂₃	1	8	yes	—
500	#41	C₂×D₄×C₂₃	1	24	yes	complemented
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	C₂×D₄×C₂₃	1	3	yes	—
505	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
506	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
507	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
508	C₂×D₄	—	2	24	no	—
509	C₂×D₄	—	2	24	no	—
510	C₂×D₄	—	2	96	no	—
511	C₂×D₄	—	2	24	no	—
512	C₂×D₄	—	2	48	no	—
513	C₂×D₄	—	2	24	no	—
514	C₂×D₄	—	2	6	no	—
515	C₂×D₄	—	2	6	no	—
516	C₂×D₄	—	2	12	no	—
517	C₂×D₄	—	2	48	no	—
518	C₂×D₄	—	2	12	no	—
519	C₂×D₄	—	2	24	no	—
520	C₂×D₄	—	2	3	no	—
521	C₂×D₄	—	2	3	no	—
522	C₂×D₄	—	2	3	no	—
523	C₂×D₄	—	2	6	no	—
524	C₂×D₄	—	2	6	no	—
525	C₂×D₄	—	2	3	no	—
526	C₂×D₄	—	2	6	no	—
527	C₂×D₄	—	2	12	no	—
528	C₂×D₄	—	2	12	no	—
529	C₂×D₄	—	2	3	no	—
530	C₂×D₄	—	4	12	no	—
531	C₂×D₄	—	8	6	no	—
532	C₂×D₄	C₂×D₄×C₂₃	1	6	yes	—
533	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
534	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
535	C₂×D₄	C₂×D₄×C₂₃	1	24	yes	complemented
536	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
537	C₂×D₄	C₂⁴×C₂₃	1	6	yes	—
538	C₂²×C₄	—	2	24	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	6	no	—
541	C₂²×C₄	—	2	6	no	—
542	C₂²×C₄	—	2	12	no	—
543	C₂²×C₄	—	2	3	no	—
544	C₂²×C₄	—	2	3	no	—
545	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
546	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
547	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
548	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
550	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
551	Q₁₆	—	2	4	no	—
552	SD₁₆	—	2	12	no	—
553	SD₁₆	—	2	12	no	—
554	D₈	—	2	12	no	—
555	D₈	—	2	24	no	—
556	M₁₆	—	2	12	no	—
557	C₂×C₈	—	2	12	no	—
558	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
559	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
560	C₄⋊C₄	—	2	3	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	3	no	—
563	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
564	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
565	C₂²⋊C₄	—	2	3	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	3	no	—
568	C₂²⋊C₄	—	2	3	no	—
569	C₂²⋊C₄	—	2	6	no	—
570	C₂²⋊C₄	—	2	3	no	—
571	C₄²	—	2	3	no	—
572	C₂³	—	2	12	no	—
573	C₂³	—	2	24	no	—
574	C₂³	—	2	6	no	—
575	C₂³	—	2	6	no	—
576	C₂³	—	2	6	no	—
577	C₂³	—	2	24	no	—
578	C₂³	—	2	3	no	—
579	C₂³	—	4	3	no	—
580	C₂³	—	4	6	no	—
581	C₂³	—	4	6	no	—
582	C₂³	—	4	6	no	—
583	C₂³	—	8	6	no	—
584	C₂³	—	8	6	no	—
585	C₂³	—	8	6	no	—
586	C₂³	—	8	6	no	—
587	C₂³	—	8	3	no	—
588	C₂³	—	8	3	no	—
589	C₂³	—	8	48	no	—
590	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
591	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
592	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
593	Q₈	—	2	4	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	6	no	—
596	Q₈	—	2	2	no	—
597	Q₈	C₂₃×#120	1	4	yes	—
598	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
599	D₄	—	2	24	no	—
600	D₄	—	2	24	no	—
601	D₄	—	2	12	no	—
602	D₄	—	2	24	no	—
603	D₄	—	2	12	no	—
604	D₄	—	2	6	no	—
605	D₄	—	2	6	no	—
606	D₄	—	2	6	no	—
607	D₄	—	2	24	no	—
608	D₄	—	4	6	no	—
609	D₄	—	4	6	no	—
610	D₄	—	4	6	no	—
611	D₄	—	8	6	no	—
612	D₄	—	8	3	no	—
613	D₄	C₂₃×#120	1	12	yes	—
614	D₄	C₂²×D₄×C₂₃	1	12	yes	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	24	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	6	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	6	no	—
621	C₂×C₄	—	2	6	no	—
622	C₂×C₄	—	2	24	no	—
623	C₂×C₄	—	2	6	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	3	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	4	6	no	—
628	C₂×C₄	—	8	3	no	—
629	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
630	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
631	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
632	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
633	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
634	C₈	—	2	2	no	—
635	C₈	—	2	6	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	3	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	3	no	—
640	C₂²	—	2	3	no	—
641	C₂²	—	2	12	no	—
642	C₂²	—	2	3	no	—
643	C₂²	—	2	3	no	—
644	C₂²	—	4	12	no	—
645	C₂²	—	4	24	no	—
646	C₂²	—	4	6	no	—
647	C₂²	—	4	6	no	—
648	C₂²	—	4	3	no	—
649	C₂²	—	4	3	no	—
650	C₂²	—	4	3	no	—
651	C₂²	—	8	24	no	—
652	C₂²	—	8	24	no	—
653	C₂²	—	16	6	no	—
654	C₂²	C₂×C₂₃×#120	1	6	yes	—
655	C₂²	C₂₃×#576	1	2	yes	complemented
656	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	3	no	—
659	C₄	—	2	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	3	no	—
662	C₄	—	4	1	no	—
663	C₄	C₂×C₂₃×#120	1	6	yes	—
664	C₄	C₂³×D₄×C₂₃	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	2	6	no	—
667	C₂	—	4	3	no	—
668	C₂	—	4	12	no	—
669	C₂	—	8	3	no	—
670	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
671	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
672	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₂₃×#576	C₂	semidirect
3. C₂₃×#3488	C₂	semidirect
4. C₂₃×#3012	C₂	semidirect
5. C₂₃×#3008	C₂	semidirect
6. C₂₃×#3006	C₂	semidirect
7. C₂₃×#3003	C₂	semidirect
8. C₂₃×#3002	C₂	semidirect
9. C₂×C₂₃×#447	C₂	semidirect
10. C₂₃×#2897	C₂	semidirect
11. C₂₃×#2880	C₂	semidirect
16. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×#41×C₂₃	C₂²	semidirect
22. C₂³×D₄×C₂₃	C₂²	semidirect
24. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₂₃×#135	C₂²	semidirect
27. C₂²×D₈×C₂₃	C₂²	semidirect
28. C₂×C₂₃×#131	C₂²	semidirect
33. C₂₃×#537	C₂²	semidirect
34. C₂₃×#535	C₂²	semidirect
35. C₂₃×#525	C₂²	semidirect
36. C₂×C₂₃×#121	C₂²	semidirect
37. C₂₃×#520	C₂²	semidirect
38. C₂₃×#452	C₂²	semidirect
39. C₂₃×#451	C₂²	semidirect
40. C₂₃×#450	C₂²	semidirect
41. C₂₃×#450	C₂²	semidirect
42. C₂₃×#449	C₂²	semidirect
43. C₂₃×#449	C₂²	semidirect
44. C₂₃×#448	C₂²	semidirect
45. C₂₃×#447	C₂²	semidirect
46. C₂₃×#447	C₂²	semidirect
47. C₂₃×#447	C₂²	semidirect
48. C₂₃×#447	C₂²	semidirect
49. C₂₃×#418	C₂²	semidirect
50. C₂₃×#417	C₂²	semidirect
51. C₂₃×#416	C₂²	semidirect
52. C₂×C₂₃×#102	C₂²	semidirect
53. C₂₃×#408	C₂²	semidirect
54. C₂₃×#407	C₂²	semidirect
55. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
63. C₂₃×H(5,𝔽₂)	D₄	semidirect
78. C₂×#41×C₂₃	C₂³	semidirect
96. C₂²×D₄×C₂₃	C₂³	semidirect
102. C₂×Q₁₆×C₂₃	C₂³	semidirect
103. C₂×SD₁₆×C₂₃	C₂³	semidirect
104. C₂×SD₁₆×C₂₃	C₂³	semidirect
106. C₂×D₈×C₂₃	C₂³	semidirect
107. C₂×D₈×C₂₃	C₂³	semidirect
109. C₂×M₁₆×C₂₃	C₂³	semidirect
110. C₂²×C₈×C₂₃	C₂³	semidirect
116. C₂₃×C₂²⋊Q₈	C₂³	semidirect
122. C₂₃×#121	C₂³	semidirect
123. C₂₃×#121	C₂³	semidirect
130. C₂₃×#117	C₂³	semidirect
131. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
133. C₂₃×#103	C₂³	semidirect
134. C₂₃×#103	C₂³	semidirect
135. C₂₃×#102	C₂³	semidirect
136. C₂₃×#102	C₂³	semidirect
137. C₂₃×#102	C₂³	semidirect
140. C₂₃×C₂²⋊C₈	C₂³	semidirect
141. C₂₃×C₂²⋊C₈	C₂³	semidirect
163. #41×C₂₃	C₂×D₄	semidirect
198. C₂×D₄×C₂₃	C₂×D₄	semidirect
235. #60372	C₂₃	direct (N × H)
300. C₂²×H(5,𝔽₂)	C₂×C₂₃	semidirect
301. C₂×#576	C₂×C₂₃	semidirect
302. #3488	C₂×C₂₃	semidirect
303. #3012	C₂×C₂₃	semidirect
304. #3008	C₂×C₂₃	semidirect
305. #3006	C₂×C₂₃	semidirect
306. #3003	C₂×C₂₃	semidirect
307. #3002	C₂×C₂₃	semidirect
308. C₂×#447	C₂×C₂₃	semidirect
309. #2897	C₂×C₂₃	semidirect
310. #2880	C₂×C₂₃	semidirect
330. C₂²×C₂₃	#576	semidirect
344. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
345. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
348. C₂²×#41	C₂²×C₂₃	semidirect
350. C₂³×D₄	C₂²×C₂₃	semidirect
352. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
353. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
354. C₂×#135	C₂²×C₂₃	semidirect
355. C₂²×D₈	C₂²×C₂₃	semidirect
356. C₂×#131	C₂²×C₂₃	semidirect
361. #537	C₂²×C₂₃	semidirect
362. #535	C₂²×C₂₃	semidirect
363. #525	C₂²×C₂₃	semidirect
364. C₂×#121	C₂²×C₂₃	semidirect
365. #520	C₂²×C₂₃	semidirect
366. #452	C₂²×C₂₃	semidirect
367. #451	C₂²×C₂₃	semidirect
368. #450	C₂²×C₂₃	semidirect
369. #450	C₂²×C₂₃	semidirect
370. #449	C₂²×C₂₃	semidirect
371. #449	C₂²×C₂₃	semidirect
372. #448	C₂²×C₂₃	semidirect
373. #447	C₂²×C₂₃	semidirect
374. #447	C₂²×C₂₃	semidirect
375. #447	C₂²×C₂₃	semidirect
376. #447	C₂²×C₂₃	semidirect
377. #418	C₂²×C₂₃	semidirect
378. #417	C₂²×C₂₃	semidirect
379. #416	C₂²×C₂₃	semidirect
380. C₂×#102	C₂²×C₂₃	semidirect
381. #408	C₂²×C₂₃	semidirect
382. #407	C₂²×C₂₃	semidirect
383. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
399. H(5,𝔽₂)	D₄×C₂₃	semidirect
414. C₂×#41	C₂³×C₂₃	semidirect
432. C₂²×D₄	C₂³×C₂₃	semidirect
438. C₂×Q₁₆	C₂³×C₂₃	semidirect
439. C₂×SD₁₆	C₂³×C₂₃	semidirect
440. C₂×SD₁₆	C₂³×C₂₃	semidirect
442. C₂×D₈	C₂³×C₂₃	semidirect
443. C₂×D₈	C₂³×C₂₃	semidirect
445. C₂×M₁₆	C₂³×C₂₃	semidirect
446. C₂²×C₈	C₂³×C₂₃	semidirect
452. C₂²⋊Q₈	C₂³×C₂₃	semidirect
458. #121	C₂³×C₂₃	semidirect
459. #121	C₂³×C₂₃	semidirect
466. #117	C₂³×C₂₃	semidirect
467. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
469. #103	C₂³×C₂₃	semidirect
470. #103	C₂³×C₂₃	semidirect
471. #102	C₂³×C₂₃	semidirect
472. #102	C₂³×C₂₃	semidirect
473. #102	C₂³×C₂₃	semidirect
476. C₂²⋊C₈	C₂³×C₂₃	semidirect
477. C₂²⋊C₈	C₂³×C₂₃	semidirect
478. C₂₃	#60372	direct (N × H)
500. #41	C₂×D₄×C₂₃	semidirect
535. C₂×D₄	C₂×D₄×C₂₃	semidirect
655. C₂²	C₂₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×H(5,𝔽₂)	2
C₂×C₂₃×#576	2
C₂₃×#3488	2
C₂₃×#3012	2
C₂₃×#3008	2
C₂₃×#3006	2
C₂₃×#3003	2
C₂₃×#3002	2
C₂×C₂₃×#447	2
C₂₃×#2897	2
C₂₃×#2880	2
#60372	23

Subgroups — C23×#60372 #19207998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60372 #19207998