Subgroups — C₂²×C₃×#2403 #72253974

Order 1536.

115796 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₂³×C₃×#120	C₂	1	4	yes	maximal, complemented
3	C₂×C₃×#2403	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₃×#392	C₂	1	4	yes	maximal, complemented
5	C₂²×C₃×#386	C₂	1	4	yes	maximal, complemented
6	C₂²×C₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#2403	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂⁷×C₃	C₂²	1	1	yes	characteristic
9	C₂⁷×C₃	C₂²	1	2	yes	complemented
10	C₂⁴×C₃×D₄	—	2	32	no	—
11	C₂⁴×C₃×D₄	—	2	64	no	—
12	C₂⁴×C₃×D₄	C₂²	1	4	yes	—
13	C₂⁴×C₃×D₄	C₂²	1	4	yes	complemented
14	C₂⁴×C₃×D₄	C₂²	1	4	yes	complemented
15	C₂⁴×C₃×D₄	C₂²	1	48	yes	complemented
16	C₂⁵×C₃×C₄	C₂²	1	2	yes	complemented
17	C₂²×C₃×#120	—	2	64	no	—
18	C₂²×C₃×#120	C₂²	1	96	yes	complemented
19	C₂³×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
20	C₂³×C₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
21	C₂³×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
22	C₃×#2403	C₂²	1	256	yes	direct product factor
23	C₂×C₃×#392	C₂²	1	96	yes	complemented
24	C₂×C₃×#386	C₂²	1	96	yes	complemented
25	C₂×C₃×#379	C₂²	1	24	yes	complemented
26	C₂²×C₃×#95	C₂²	1	4	yes	complemented
27	C₂⁵×D₄	C₂×C₃	1	2	yes	complemented
28	C₂³×#120	C₂×C₃	1	4	yes	complemented
29	C₂×#2403	C₂×C₃	1	48	yes	direct product factor
30	C₂²×#392	C₂×C₃	1	4	yes	complemented
31	C₂²×#386	C₂×C₃	1	4	yes	complemented
32	C₂²×#379	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁶×C₃	—	2	32	no	—
34	C₂⁶×C₃	—	2	16	no	—
35	C₂⁶×C₃	—	2	32	no	—
36	C₂⁶×C₃	—	2	32	no	—
37	C₂⁶×C₃	—	4	8	no	—
38	C₂⁶×C₃	—	4	16	no	—
39	C₂⁶×C₃	D₄	1	16	yes	complemented
40	C₂⁶×C₃	C₂³	1	1	yes	characteristic
41	C₂⁶×C₃	C₂³	1	4	yes	—
42	C₂⁶×C₃	C₂³	1	12	yes	—
43	C₂⁶×C₃	C₂³	1	2	yes	—
44	C₂⁶×C₃	C₂³	1	24	yes	complemented
45	C₂³×C₃×D₄	—	2	1024	no	—
46	C₂³×C₃×D₄	—	2	768	no	—
47	C₂³×C₃×D₄	—	2	32	no	—
48	C₂³×C₃×D₄	—	2	32	no	—
49	C₂³×C₃×D₄	—	2	32	no	—
50	C₂³×C₃×D₄	—	2	32	no	—
51	C₂³×C₃×D₄	—	2	32	no	—
52	C₂³×C₃×D₄	—	2	384	no	—
53	C₂³×C₃×D₄	—	2	64	no	—
54	C₂³×C₃×D₄	—	4	16	no	—
55	C₂³×C₃×D₄	D₄	1	64	yes	complemented
56	C₂³×C₃×D₄	C₂³	1	48	yes	—
57	C₂³×C₃×D₄	C₂³	1	48	yes	complemented
58	C₂³×C₃×D₄	C₂³	1	48	yes	complemented
59	C₂³×C₃×D₄	C₂³	1	128	yes	complemented
60	C₂⁴×C₃×C₄	—	2	32	no	—
61	C₂⁴×C₃×C₄	—	2	16	no	—
62	C₂⁴×C₃×C₄	C₂³	1	4	yes	—
63	C₂⁴×C₃×C₄	C₂³	1	4	yes	—
64	C₂⁴×C₃×C₄	C₂³	1	24	yes	complemented
65	C₂×C₃×#120	—	2	768	no	—
66	C₂×C₃×#120	C₂³	1	256	yes	complemented
67	C₂²×C₃×C₂²⋊C₄	—	2	64	no	—
68	C₂²×C₃×C₂²⋊C₄	—	2	32	no	—
69	C₂²×C₃×C₂²⋊C₄	—	4	8	no	—
70	C₂²×C₃×C₂²⋊C₄	C₂³	1	96	yes	complemented
71	C₂²×C₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
72	C₂²×C₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
73	C₃×#392	C₂³	1	256	yes	complemented
74	C₃×#386	C₂³	1	256	yes	complemented
75	C₃×#379	C₂³	1	64	yes	complemented
76	C₂×C₃×#95	C₂³	1	48	yes	complemented
77	C₂⁷	C₂²×C₃	1	1	yes	characteristic
78	C₂⁷	C₂²×C₃	1	2	yes	complemented
79	C₂⁴×D₄	—	2	32	no	—
80	C₂⁴×D₄	—	2	64	no	—
81	C₂⁴×D₄	C₂²×C₃	1	4	yes	—
82	C₂⁴×D₄	C₂²×C₃	1	4	yes	complemented
83	C₂⁴×D₄	C₂²×C₃	1	4	yes	complemented
84	C₂⁴×D₄	C₂²×C₃	1	48	yes	complemented
85	C₂⁵×C₄	C₂²×C₃	1	2	yes	complemented
86	C₂²×#120	—	2	64	no	—
87	C₂²×#120	C₂²×C₃	1	96	yes	complemented
88	C₂³×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
89	C₂³×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
90	C₂³×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
91	#2403	C₂²×C₃	1	256	yes	direct product factor
92	C₂×#392	C₂²×C₃	1	96	yes	complemented
93	C₂×#386	C₂²×C₃	1	96	yes	complemented
94	C₂×#379	C₂²×C₃	1	24	yes	complemented
95	C₂²×#95	C₂²×C₃	1	4	yes	complemented
96	C₂⁵×C₃	—	2	16	no	—
97	C₂⁵×C₃	—	2	16	no	—
98	C₂⁵×C₃	—	2	256	no	—
99	C₂⁵×C₃	—	2	256	no	—
100	C₂⁵×C₃	—	2	192	no	—
101	C₂⁵×C₃	—	2	16	no	—
102	C₂⁵×C₃	—	2	16	no	—
103	C₂⁵×C₃	—	2	16	no	—
104	C₂⁵×C₃	—	2	96	no	—
105	C₂⁵×C₃	—	2	32	no	—
106	C₂⁵×C₃	—	2	192	no	—
107	C₂⁵×C₃	—	2	32	no	—
108	C₂⁵×C₃	—	2	8	no	—
109	C₂⁵×C₃	—	2	192	no	—
110	C₂⁵×C₃	—	4	64	no	—
111	C₂⁵×C₃	—	4	48	no	—
112	C₂⁵×C₃	—	4	96	no	—
113	C₂⁵×C₃	—	4	256	no	—
114	C₂⁵×C₃	—	4	512	no	—
115	C₂⁵×C₃	—	4	128	no	—
116	C₂⁵×C₃	—	4	128	no	—
117	C₂⁵×C₃	C₂×D₄	1	8	yes	—
118	C₂⁵×C₃	C₂×D₄	1	16	yes	—
119	C₂⁵×C₃	C₂×D₄	1	32	yes	—
120	C₂⁵×C₃	C₂×D₄	1	32	yes	complemented
121	C₂⁵×C₃	C₂×D₄	1	96	yes	complemented
122	C₂⁵×C₃	C₂⁴	1	6	yes	—
123	C₂⁵×C₃	C₂⁴	1	24	yes	—
124	C₂⁵×C₃	C₂⁴	1	16	yes	—
125	C₂⁵×C₃	C₂⁴	1	12	yes	—
126	C₂⁵×C₃	C₂⁴	1	1	yes	characteristic
127	C₂⁵×C₃	C₂⁴	1	32	yes	complemented
128	C₂²×C₃×D₄	—	2	6144	no	—
129	C₂²×C₃×D₄	—	2	512	no	—
130	C₂²×C₃×D₄	—	2	512	no	—
131	C₂²×C₃×D₄	—	2	192	no	—
132	C₂²×C₃×D₄	—	2	192	no	—
133	C₂²×C₃×D₄	—	2	192	no	—
134	C₂²×C₃×D₄	—	2	192	no	—
135	C₂²×C₃×D₄	—	2	512	no	—
136	C₂²×C₃×D₄	—	2	1024	no	—
137	C₂²×C₃×D₄	—	2	384	no	—
138	C₂²×C₃×D₄	—	2	192	no	—
139	C₂²×C₃×D₄	—	4	96	no	—
140	C₂²×C₃×D₄	—	4	256	no	—
141	C₂²×C₃×D₄	C₂×D₄	1	384	yes	complemented
142	C₂²×C₃×D₄	C₂⁴	1	64	yes	—
143	C₂²×C₃×D₄	C₂⁴	1	64	yes	complemented
144	C₂²×C₃×D₄	C₂⁴	1	64	yes	complemented
145	C₂³×C₃×C₄	—	2	256	no	—
146	C₂³×C₃×C₄	—	2	16	no	—
147	C₂³×C₃×C₄	—	2	16	no	—
148	C₂³×C₃×C₄	—	2	96	no	—
149	C₂³×C₃×C₄	—	2	192	no	—
150	C₂³×C₃×C₄	—	2	32	no	—
151	C₂³×C₃×C₄	—	2	16	no	—
152	C₂³×C₃×C₄	C₂×D₄	1	32	yes	complemented
153	C₂³×C₃×C₄	C₂⁴	1	24	yes	—
154	C₂³×C₃×C₄	C₂⁴	1	24	yes	—
155	C₂³×C₃×C₄	C₂⁴	1	32	yes	complemented
156	C₃×#120	—	2	1024	no	—
157	C₂×C₃×C₂²⋊C₄	—	2	192	no	—
158	C₂×C₃×C₂²⋊C₄	—	2	384	no	—
159	C₂×C₃×C₂²⋊C₄	—	4	48	no	—
160	C₂×C₃×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
161	C₂×C₃×C₂²⋊C₄	C₂⁴	1	128	yes	complemented
162	C₂×C₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
163	C₃×#95	C₂⁴	1	64	yes	complemented
164	C₂⁶	—	2	32	no	—
165	C₂⁶	—	2	16	no	—
166	C₂⁶	—	2	32	no	—
167	C₂⁶	—	2	32	no	—
168	C₂⁶	—	4	8	no	—
169	C₂⁶	—	4	16	no	—
170	C₂⁶	C₃×D₄	1	16	yes	complemented
171	C₂⁶	C₂³×C₃	1	1	yes	characteristic
172	C₂⁶	C₂³×C₃	1	4	yes	—
173	C₂⁶	C₂³×C₃	1	12	yes	—
174	C₂⁶	C₂³×C₃	1	2	yes	—
175	C₂⁶	C₂³×C₃	1	24	yes	complemented
176	C₂³×D₄	—	2	1024	no	—
177	C₂³×D₄	—	2	32	no	—
178	C₂³×D₄	—	2	32	no	—
179	C₂³×D₄	—	2	32	no	—
180	C₂³×D₄	—	2	32	no	—
181	C₂³×D₄	—	2	384	no	—
182	C₂³×D₄	—	2	768	no	—
183	C₂³×D₄	—	2	64	no	—
184	C₂³×D₄	—	2	32	no	—
185	C₂³×D₄	—	4	16	no	—
186	C₂³×D₄	C₃×D₄	1	64	yes	complemented
187	C₂³×D₄	C₂³×C₃	1	48	yes	—
188	C₂³×D₄	C₂³×C₃	1	48	yes	complemented
189	C₂³×D₄	C₂³×C₃	1	48	yes	complemented
190	C₂³×D₄	C₂³×C₃	1	128	yes	complemented
191	C₂⁴×C₄	—	2	16	no	—
192	C₂⁴×C₄	—	2	32	no	—
193	C₂⁴×C₄	C₂³×C₃	1	4	yes	—
194	C₂⁴×C₄	C₂³×C₃	1	4	yes	—
195	C₂⁴×C₄	C₂³×C₃	1	24	yes	complemented
196	C₂×#120	—	2	768	no	—
197	C₂×#120	C₂³×C₃	1	256	yes	complemented
198	C₂²×C₂²⋊C₄	—	2	32	no	—
199	C₂²×C₂²⋊C₄	—	2	64	no	—
200	C₂²×C₂²⋊C₄	—	4	8	no	—
201	C₂²×C₂²⋊C₄	C₂³×C₃	1	96	yes	complemented
202	C₂²×C₂²⋊C₄	C₂³×C₃	1	48	yes	complemented
203	C₂²×C₂²⋊C₄	C₂³×C₃	1	24	yes	complemented
204	#392	C₂³×C₃	1	256	yes	complemented
205	#386	C₂³×C₃	1	256	yes	complemented
206	#379	C₂³×C₃	1	64	yes	complemented
207	C₂×#95	C₂³×C₃	1	48	yes	complemented
208	C₂⁴×C₃	—	2	64	no	—
209	C₂⁴×C₃	—	2	64	no	—
210	C₂⁴×C₃	—	2	256	no	—
211	C₂⁴×C₃	—	2	48	no	—
212	C₂⁴×C₃	—	2	48	no	—
213	C₂⁴×C₃	—	2	768	no	—
214	C₂⁴×C₃	—	2	64	no	—
215	C₂⁴×C₃	—	2	128	no	—
216	C₂⁴×C₃	—	2	768	no	—
217	C₂⁴×C₃	—	2	32	no	—
218	C₂⁴×C₃	—	2	256	no	—
219	C₂⁴×C₃	—	2	96	no	—
220	C₂⁴×C₃	—	2	128	no	—
221	C₂⁴×C₃	—	2	48	no	—
222	C₂⁴×C₃	—	2	48	no	—
223	C₂⁴×C₃	—	2	48	no	—
224	C₂⁴×C₃	—	2	64	no	—
225	C₂⁴×C₃	—	2	128	no	—
226	C₂⁴×C₃	—	2	24	no	—
227	C₂⁴×C₃	—	2	96	no	—
228	C₂⁴×C₃	—	2	128	no	—
229	C₂⁴×C₃	—	4	192	no	—
230	C₂⁴×C₃	—	4	32	no	—
231	C₂⁴×C₃	—	4	64	no	—
232	C₂⁴×C₃	—	4	1024	no	—
233	C₂⁴×C₃	—	4	768	no	—
234	C₂⁴×C₃	—	4	1536	no	—
235	C₂⁴×C₃	—	4	2048	no	—
236	C₂⁴×C₃	—	4	384	no	—
237	C₂⁴×C₃	—	4	64	no	—
238	C₂⁴×C₃	—	4	384	no	—
239	C₂⁴×C₃	—	4	64	no	—
240	C₂⁴×C₃	—	4	64	no	—
241	C₂⁴×C₃	—	4	128	no	—
242	C₂⁴×C₃	#120	1	128	yes	complemented
243	C₂⁴×C₃	C₂²×D₄	1	24	yes	—
244	C₂⁴×C₃	C₂²×D₄	1	96	yes	—
245	C₂⁴×C₃	C₂²×D₄	1	48	yes	—
246	C₂⁴×C₃	C₂²×D₄	1	4	yes	—
247	C₂⁴×C₃	C₂²×D₄	1	16	yes	—
248	C₂⁴×C₃	C₂²×D₄	1	96	yes	complemented
249	C₂⁴×C₃	C₂²×D₄	1	64	yes	complemented
250	C₂⁴×C₃	H(5,𝔽₂)	1	8	yes	—
251	C₂⁴×C₃	C₂⁵	1	4	yes	—
252	C₂⁴×C₃	C₂⁵	1	16	yes	—
253	C₂⁴×C₃	C₂⁵	1	8	yes	—
254	C₂⁴×C₃	C₂⁵	1	3	yes	—
255	C₂×C₃×D₄	—	2	4096	no	—
256	C₂×C₃×D₄	—	2	1536	no	—
257	C₂×C₃×D₄	—	2	1536	no	—
258	C₂×C₃×D₄	—	2	128	no	—
259	C₂×C₃×D₄	—	2	128	no	—
260	C₂×C₃×D₄	—	2	128	no	—
261	C₂×C₃×D₄	—	2	128	no	—
262	C₂×C₃×D₄	—	2	256	no	—
263	C₂×C₃×D₄	—	2	128	no	—
264	C₂×C₃×D₄	—	4	64	no	—
265	C₂×C₃×D₄	—	4	768	no	—
266	C₂×C₃×D₄	C₂²×D₄	1	256	yes	complemented
267	C₂²×C₃×C₄	—	2	768	no	—
268	C₂²×C₃×C₄	—	2	128	no	—
269	C₂²×C₃×C₄	—	2	48	no	—
270	C₂²×C₃×C₄	—	2	48	no	—
271	C₂²×C₃×C₄	—	2	64	no	—
272	C₂²×C₃×C₄	—	2	128	no	—
273	C₂²×C₃×C₄	—	2	96	no	—
274	C₂²×C₃×C₄	—	2	48	no	—
275	C₂²×C₃×C₄	—	4	64	no	—
276	C₂²×C₃×C₄	C₂²×D₄	1	96	yes	complemented
277	C₂²×C₃×C₄	C₂⁵	1	16	yes	—
278	C₂²×C₃×C₄	C₂⁵	1	16	yes	—
279	C₃×C₂²⋊C₄	—	2	128	no	—
280	C₃×C₂²⋊C₄	—	2	256	no	—
281	C₃×C₂²⋊C₄	—	4	32	no	—
282	C₂⁵	—	2	16	no	—
283	C₂⁵	—	2	16	no	—
284	C₂⁵	—	2	256	no	—
285	C₂⁵	—	2	256	no	—
286	C₂⁵	—	2	32	no	—
287	C₂⁵	—	2	192	no	—
288	C₂⁵	—	2	16	no	—
289	C₂⁵	—	2	16	no	—
290	C₂⁵	—	2	16	no	—
291	C₂⁵	—	2	96	no	—
292	C₂⁵	—	2	192	no	—
293	C₂⁵	—	2	8	no	—
294	C₂⁵	—	2	32	no	—
295	C₂⁵	—	2	192	no	—
296	C₂⁵	—	4	64	no	—
297	C₂⁵	—	4	48	no	—
298	C₂⁵	—	4	96	no	—
299	C₂⁵	—	4	256	no	—
300	C₂⁵	—	4	512	no	—
301	C₂⁵	—	4	128	no	—
302	C₂⁵	—	4	128	no	—
303	C₂⁵	C₂×C₃×D₄	1	8	yes	—
304	C₂⁵	C₂×C₃×D₄	1	32	yes	—
305	C₂⁵	C₂×C₃×D₄	1	16	yes	—
306	C₂⁵	C₂×C₃×D₄	1	32	yes	complemented
307	C₂⁵	C₂×C₃×D₄	1	96	yes	complemented
308	C₂⁵	C₂⁴×C₃	1	6	yes	—
309	C₂⁵	C₂⁴×C₃	1	24	yes	—
310	C₂⁵	C₂⁴×C₃	1	16	yes	—
311	C₂⁵	C₂⁴×C₃	1	12	yes	—
312	C₂⁵	C₂⁴×C₃	1	1	yes	characteristic
313	C₂⁵	C₂⁴×C₃	1	32	yes	complemented
314	C₂²×D₄	—	2	6144	no	—
315	C₂²×D₄	—	2	512	no	—
316	C₂²×D₄	—	2	512	no	—
317	C₂²×D₄	—	2	192	no	—
318	C₂²×D₄	—	2	192	no	—
319	C₂²×D₄	—	2	192	no	—
320	C₂²×D₄	—	2	192	no	—
321	C₂²×D₄	—	2	512	no	—
322	C₂²×D₄	—	2	1024	no	—
323	C₂²×D₄	—	2	384	no	—
324	C₂²×D₄	—	2	192	no	—
325	C₂²×D₄	—	4	96	no	—
326	C₂²×D₄	—	4	256	no	—
327	C₂²×D₄	C₂×C₃×D₄	1	384	yes	complemented
328	C₂²×D₄	C₂⁴×C₃	1	64	yes	—
329	C₂²×D₄	C₂⁴×C₃	1	64	yes	complemented
330	C₂²×D₄	C₂⁴×C₃	1	64	yes	complemented
331	C₂³×C₄	—	2	256	no	—
332	C₂³×C₄	—	2	16	no	—
333	C₂³×C₄	—	2	16	no	—
334	C₂³×C₄	—	2	96	no	—
335	C₂³×C₄	—	2	192	no	—
336	C₂³×C₄	—	2	32	no	—
337	C₂³×C₄	—	2	16	no	—
338	C₂³×C₄	C₂×C₃×D₄	1	32	yes	complemented
339	C₂³×C₄	C₂⁴×C₃	1	24	yes	—
340	C₂³×C₄	C₂⁴×C₃	1	24	yes	—
341	C₂³×C₄	C₂⁴×C₃	1	32	yes	complemented
342	#120	—	2	1024	no	—
343	C₂×C₂²⋊C₄	—	2	192	no	—
344	C₂×C₂²⋊C₄	—	2	384	no	—
345	C₂×C₂²⋊C₄	—	4	48	no	—
346	C₂×C₂²⋊C₄	C₂⁴×C₃	1	64	yes	complemented
347	C₂×C₂²⋊C₄	C₂⁴×C₃	1	128	yes	complemented
348	C₂×C₂²⋊C₄	C₂⁴×C₃	1	32	yes	complemented
349	#95	C₂⁴×C₃	1	64	yes	complemented
350	C₂³×C₃	—	2	16	no	—
351	C₂³×C₃	—	2	16	no	—
352	C₂³×C₃	—	2	512	no	—
353	C₂³×C₃	—	2	96	no	—
354	C₂³×C₃	—	2	96	no	—
355	C₂³×C₃	—	2	384	no	—
356	C₂³×C₃	—	2	256	no	—
357	C₂³×C₃	—	2	32	no	—
358	C₂³×C₃	—	2	16	no	—
359	C₂³×C₃	—	2	16	no	—
360	C₂³×C₃	—	2	16	no	—
361	C₂³×C₃	—	2	8	no	—
362	C₂³×C₃	—	2	32	no	—
363	C₂³×C₃	—	2	96	no	—
364	C₂³×C₃	—	2	192	no	—
365	C₂³×C₃	—	2	256	no	—
366	C₂³×C₃	—	2	48	no	—
367	C₂³×C₃	—	2	384	no	—
368	C₂³×C₃	—	4	64	no	—
369	C₂³×C₃	—	4	1536	no	—
370	C₂³×C₃	—	4	256	no	—
371	C₂³×C₃	—	4	512	no	—
372	C₂³×C₃	—	4	3072	no	—
373	C₂³×C₃	—	4	128	no	—
374	C₂³×C₃	—	4	128	no	—
375	C₂³×C₃	—	4	512	no	—
376	C₂³×C₃	—	4	96	no	—
377	C₂³×C₃	—	4	128	no	—
378	C₂³×C₃	—	4	96	no	—
379	C₂³×C₃	—	4	192	no	—
380	C₂³×C₃	—	4	96	no	—
381	C₂³×C₃	C₂×#120	1	32	yes	—
382	C₂³×C₃	C₂×#120	1	192	yes	complemented
383	C₂³×C₃	#534	1	16	yes	—
384	C₂³×C₃	D₄²	1	64	yes	—
385	C₂³×C₃	C₂³×D₄	1	8	yes	—
386	C₂³×C₃	C₂³×D₄	1	32	yes	—
387	C₂³×C₃	C₂³×D₄	1	16	yes	—
388	C₂³×C₃	C₂³×D₄	1	6	yes	—
389	C₂³×C₃	C₂³×D₄	1	24	yes	—
390	C₂³×C₃	C₂³×D₄	1	32	yes	complemented
391	C₂³×C₃	C₂×H(5,𝔽₂)	1	12	yes	—
392	C₂³×C₃	C₂⁶	1	1	yes	characteristic
393	C₃×D₄	—	2	512	no	—
394	C₃×D₄	—	2	512	no	—
395	C₃×D₄	—	4	256	no	—
396	C₂×C₃×C₄	—	2	256	no	—
397	C₂×C₃×C₄	—	2	16	no	—
398	C₂×C₃×C₄	—	2	16	no	—
399	C₂×C₃×C₄	—	2	192	no	—
400	C₂×C₃×C₄	—	2	32	no	—
401	C₂×C₃×C₄	—	2	16	no	—
402	C₂×C₃×C₄	—	4	96	no	—
403	C₂×C₃×C₄	C₂³×D₄	1	32	yes	complemented
404	C₂⁴	—	2	48	no	—
405	C₂⁴	—	2	48	no	—
406	C₂⁴	—	2	64	no	—
407	C₂⁴	—	2	64	no	—
408	C₂⁴	—	2	256	no	—
409	C₂⁴	—	2	768	no	—
410	C₂⁴	—	2	96	no	—
411	C₂⁴	—	2	128	no	—
412	C₂⁴	—	2	48	no	—
413	C₂⁴	—	2	48	no	—
414	C₂⁴	—	2	48	no	—
415	C₂⁴	—	2	64	no	—
416	C₂⁴	—	2	128	no	—
417	C₂⁴	—	2	24	no	—
418	C₂⁴	—	2	96	no	—
419	C₂⁴	—	2	64	no	—
420	C₂⁴	—	2	128	no	—
421	C₂⁴	—	2	768	no	—
422	C₂⁴	—	2	32	no	—
423	C₂⁴	—	2	256	no	—
424	C₂⁴	—	2	128	no	—
425	C₂⁴	—	4	192	no	—
426	C₂⁴	—	4	32	no	—
427	C₂⁴	—	4	64	no	—
428	C₂⁴	—	4	1024	no	—
429	C₂⁴	—	4	768	no	—
430	C₂⁴	—	4	1536	no	—
431	C₂⁴	—	4	384	no	—
432	C₂⁴	—	4	2048	no	—
433	C₂⁴	—	4	64	no	—
434	C₂⁴	—	4	384	no	—
435	C₂⁴	—	4	64	no	—
436	C₂⁴	—	4	128	no	—
437	C₂⁴	—	4	64	no	—
438	C₂⁴	C₃×#120	1	128	yes	complemented
439	C₂⁴	C₂²×C₃×D₄	1	24	yes	—
440	C₂⁴	C₂²×C₃×D₄	1	96	yes	—
441	C₂⁴	C₂²×C₃×D₄	1	48	yes	—
442	C₂⁴	C₂²×C₃×D₄	1	4	yes	—
443	C₂⁴	C₂²×C₃×D₄	1	16	yes	—
444	C₂⁴	C₂²×C₃×D₄	1	96	yes	complemented
445	C₂⁴	C₂²×C₃×D₄	1	64	yes	complemented
446	C₂⁴	C₃×H(5,𝔽₂)	1	8	yes	—
447	C₂⁴	C₂⁵×C₃	1	4	yes	—
448	C₂⁴	C₂⁵×C₃	1	16	yes	—
449	C₂⁴	C₂⁵×C₃	1	8	yes	—
450	C₂⁴	C₂⁵×C₃	1	3	yes	—
451	C₂×D₄	—	2	4096	no	—
452	C₂×D₄	—	2	1536	no	—
453	C₂×D₄	—	2	128	no	—
454	C₂×D₄	—	2	128	no	—
455	C₂×D₄	—	2	128	no	—
456	C₂×D₄	—	2	128	no	—
457	C₂×D₄	—	2	1536	no	—
458	C₂×D₄	—	2	256	no	—
459	C₂×D₄	—	2	128	no	—
460	C₂×D₄	—	4	64	no	—
461	C₂×D₄	—	4	768	no	—
462	C₂×D₄	C₂²×C₃×D₄	1	256	yes	complemented
463	C₂²×C₄	—	2	768	no	—
464	C₂²×C₄	—	2	48	no	—
465	C₂²×C₄	—	2	48	no	—
466	C₂²×C₄	—	2	64	no	—
467	C₂²×C₄	—	2	128	no	—
468	C₂²×C₄	—	2	128	no	—
469	C₂²×C₄	—	2	96	no	—
470	C₂²×C₄	—	2	48	no	—
471	C₂²×C₄	—	4	64	no	—
472	C₂²×C₄	C₂²×C₃×D₄	1	96	yes	complemented
473	C₂²×C₄	C₂⁵×C₃	1	16	yes	—
474	C₂²×C₄	C₂⁵×C₃	1	16	yes	—
475	C₂²⋊C₄	—	2	128	no	—
476	C₂²⋊C₄	—	2	256	no	—
477	C₂²⋊C₄	—	4	32	no	—
478	C₂²×C₃	—	2	384	no	—
479	C₂²×C₃	—	2	16	no	—
480	C₂²×C₃	—	2	16	no	—
481	C₂²×C₃	—	2	64	no	—
482	C₂²×C₃	—	2	16	no	—
483	C₂²×C₃	—	2	32	no	—
484	C₂²×C₃	—	2	8	no	—
485	C₂²×C₃	—	2	64	no	—
486	C₂²×C₃	—	4	256	no	—
487	C₂²×C₃	—	4	512	no	—
488	C₂²×C₃	—	4	96	no	—
489	C₂²×C₃	—	4	384	no	—
490	C₂²×C₃	—	4	16	no	—
491	C₂²×C₃	—	4	16	no	—
492	C₂²×C₃	—	4	32	no	—
493	C₂²×C₃	—	4	16	no	—
494	C₂²×C₃	#2403	1	64	yes	direct product factor
495	C₂²×C₃	C₂²×#120	1	24	yes	—
496	C₂²×C₃	C₂²×#120	1	32	yes	complemented
497	C₂²×C₃	C₂×#534	1	12	yes	—
498	C₂²×C₃	C₂×D₄²	1	48	yes	—
499	C₂²×C₃	C₂⁴×D₄	1	1	yes	characteristic
500	C₂²×C₃	C₂⁴×D₄	1	4	yes	—
501	C₂²×C₃	C₂²×H(5,𝔽₂)	1	2	yes	—
502	C₃×C₄	—	2	32	no	—
503	C₃×C₄	—	4	16	no	—
504	C₂³	—	2	96	no	—
505	C₂³	—	2	16	no	—
506	C₂³	—	2	16	no	—
507	C₂³	—	2	96	no	—
508	C₂³	—	2	512	no	—
509	C₂³	—	2	384	no	—
510	C₂³	—	2	256	no	—
511	C₂³	—	2	96	no	—
512	C₂³	—	2	192	no	—
513	C₂³	—	2	256	no	—
514	C₂³	—	2	32	no	—
515	C₂³	—	2	16	no	—
516	C₂³	—	2	16	no	—
517	C₂³	—	2	16	no	—
518	C₂³	—	2	8	no	—
519	C₂³	—	2	32	no	—
520	C₂³	—	2	48	no	—
521	C₂³	—	2	384	no	—
522	C₂³	—	4	64	no	—
523	C₂³	—	4	1536	no	—
524	C₂³	—	4	256	no	—
525	C₂³	—	4	512	no	—
526	C₂³	—	4	3072	no	—
527	C₂³	—	4	128	no	—
528	C₂³	—	4	96	no	—
529	C₂³	—	4	128	no	—
530	C₂³	—	4	96	no	—
531	C₂³	—	4	128	no	—
532	C₂³	—	4	512	no	—
533	C₂³	—	4	192	no	—
534	C₂³	—	4	96	no	—
535	C₂³	C₂×C₃×#120	1	32	yes	—
536	C₂³	C₂×C₃×#120	1	192	yes	complemented
537	C₂³	C₃×#534	1	16	yes	—
538	C₂³	C₃×D₄²	1	64	yes	—
539	C₂³	C₂³×C₃×D₄	1	8	yes	—
540	C₂³	C₂³×C₃×D₄	1	32	yes	—
541	C₂³	C₂³×C₃×D₄	1	16	yes	—
542	C₂³	C₂³×C₃×D₄	1	6	yes	—
543	C₂³	C₂³×C₃×D₄	1	24	yes	—
544	C₂³	C₂³×C₃×D₄	1	32	yes	complemented
545	C₂³	C₂×C₃×H(5,𝔽₂)	1	12	yes	—
546	C₂³	C₂⁶×C₃	1	1	yes	characteristic
547	D₄	—	2	512	no	—
548	D₄	—	2	512	no	—
549	D₄	—	4	256	no	—
550	C₂×C₄	—	2	256	no	—
551	C₂×C₄	—	2	192	no	—
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	16	no	—
554	C₂×C₄	—	2	32	no	—
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	4	96	no	—
557	C₂×C₄	C₂³×C₃×D₄	1	32	yes	complemented
558	C₂×C₃	—	2	32	no	—
559	C₂×C₃	—	4	8	no	—
560	C₂×C₃	—	4	32	no	—
561	C₂×C₃	C₂×#2403	1	24	yes	direct product factor
562	C₂×C₃	C₂³×#120	1	2	yes	—
563	C₂×C₃	C₂²×#534	1	1	yes	characteristic
564	C₂×C₃	C₂²×D₄²	1	4	yes	—
565	C₂²	—	2	384	no	—
566	C₂²	—	2	16	no	—
567	C₂²	—	2	16	no	—
568	C₂²	—	2	64	no	—
569	C₂²	—	2	16	no	—
570	C₂²	—	2	32	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	64	no	—
573	C₂²	—	4	256	no	—
574	C₂²	—	4	512	no	—
575	C₂²	—	4	96	no	—
576	C₂²	—	4	384	no	—
577	C₂²	—	4	16	no	—
578	C₂²	—	4	16	no	—
579	C₂²	—	4	32	no	—
580	C₂²	—	4	16	no	—
581	C₂²	C₃×#2403	1	64	yes	direct product factor
582	C₂²	C₂²×C₃×#120	1	24	yes	—
583	C₂²	C₂²×C₃×#120	1	32	yes	complemented
584	C₂²	C₂×C₃×#534	1	12	yes	—
585	C₂²	C₂×C₃×D₄²	1	48	yes	—
586	C₂²	C₂⁴×C₃×D₄	1	1	yes	characteristic
587	C₂²	C₂⁴×C₃×D₄	1	4	yes	—
588	C₂²	C₂²×C₃×H(5,𝔽₂)	1	2	yes	—
589	C₄	—	2	32	no	—
590	C₄	—	4	16	no	—
591	C₃	C₂²×#2403	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	32	no	—
593	C₂	—	4	8	no	—
594	C₂	—	4	32	no	—
595	C₂	C₂×C₃×#2403	1	24	yes	direct product factor
596	C₂	C₂³×C₃×#120	1	2	yes	—
597	C₂	C₂²×C₃×#534	1	1	yes	characteristic
598	C₂	C₂²×C₃×D₄²	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁵×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁶×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₃×D₄	C₂	semidirect
2. C₂³×C₃×#120	C₂	semidirect
3. C₂×C₃×#2403	C₂	direct (N × H)
4. C₂²×C₃×#392	C₂	semidirect
5. C₂²×C₃×#386	C₂	semidirect
6. C₂²×C₃×#379	C₂	semidirect
7. C₂²×#2403	C₃	direct (N × H)
9. C₂⁷×C₃	C₂²	semidirect
13. C₂⁴×C₃×D₄	C₂²	semidirect
14. C₂⁴×C₃×D₄	C₂²	semidirect
15. C₂⁴×C₃×D₄	C₂²	semidirect
16. C₂⁵×C₃×C₄	C₂²	semidirect
18. C₂²×C₃×#120	C₂²	semidirect
19. C₂³×C₃×C₂²⋊C₄	C₂²	semidirect
20. C₂³×C₃×C₂²⋊C₄	C₂²	semidirect
21. C₂³×C₃×C₂²⋊C₄	C₂²	semidirect
22. C₃×#2403	C₂²	direct (N × H)
23. C₂×C₃×#392	C₂²	semidirect
24. C₂×C₃×#386	C₂²	semidirect
25. C₂×C₃×#379	C₂²	semidirect
26. C₂²×C₃×#95	C₂²	semidirect
27. C₂⁵×D₄	C₂×C₃	semidirect
28. C₂³×#120	C₂×C₃	semidirect
29. C₂×#2403	C₂×C₃	direct (N × H)
30. C₂²×#392	C₂×C₃	semidirect
31. C₂²×#386	C₂×C₃	semidirect
32. C₂²×#379	C₂×C₃	semidirect
39. C₂⁶×C₃	D₄	semidirect
44. C₂⁶×C₃	C₂³	semidirect
55. C₂³×C₃×D₄	D₄	semidirect
57. C₂³×C₃×D₄	C₂³	semidirect
58. C₂³×C₃×D₄	C₂³	semidirect
59. C₂³×C₃×D₄	C₂³	semidirect
64. C₂⁴×C₃×C₄	C₂³	semidirect
66. C₂×C₃×#120	C₂³	semidirect
70. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
71. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
72. C₂²×C₃×C₂²⋊C₄	C₂³	semidirect
73. C₃×#392	C₂³	semidirect
74. C₃×#386	C₂³	semidirect
75. C₃×#379	C₂³	semidirect
76. C₂×C₃×#95	C₂³	semidirect
78. C₂⁷	C₂²×C₃	semidirect
82. C₂⁴×D₄	C₂²×C₃	semidirect
83. C₂⁴×D₄	C₂²×C₃	semidirect
84. C₂⁴×D₄	C₂²×C₃	semidirect
85. C₂⁵×C₄	C₂²×C₃	semidirect
87. C₂²×#120	C₂²×C₃	semidirect
88. C₂³×C₂²⋊C₄	C₂²×C₃	semidirect
89. C₂³×C₂²⋊C₄	C₂²×C₃	semidirect
90. C₂³×C₂²⋊C₄	C₂²×C₃	semidirect
91. #2403	C₂²×C₃	direct (N × H)
92. C₂×#392	C₂²×C₃	semidirect
93. C₂×#386	C₂²×C₃	semidirect
94. C₂×#379	C₂²×C₃	semidirect
95. C₂²×#95	C₂²×C₃	semidirect
120. C₂⁵×C₃	C₂×D₄	semidirect
121. C₂⁵×C₃	C₂×D₄	semidirect
127. C₂⁵×C₃	C₂⁴	semidirect
141. C₂²×C₃×D₄	C₂×D₄	semidirect
143. C₂²×C₃×D₄	C₂⁴	semidirect
144. C₂²×C₃×D₄	C₂⁴	semidirect
152. C₂³×C₃×C₄	C₂×D₄	semidirect
155. C₂³×C₃×C₄	C₂⁴	semidirect
160. C₂×C₃×C₂²⋊C₄	C₂⁴	semidirect
161. C₂×C₃×C₂²⋊C₄	C₂⁴	semidirect
162. C₂×C₃×C₂²⋊C₄	C₂⁴	semidirect
163. C₃×#95	C₂⁴	semidirect
170. C₂⁶	C₃×D₄	semidirect
175. C₂⁶	C₂³×C₃	semidirect
186. C₂³×D₄	C₃×D₄	semidirect
188. C₂³×D₄	C₂³×C₃	semidirect
189. C₂³×D₄	C₂³×C₃	semidirect
190. C₂³×D₄	C₂³×C₃	semidirect
195. C₂⁴×C₄	C₂³×C₃	semidirect
197. C₂×#120	C₂³×C₃	semidirect
201. C₂²×C₂²⋊C₄	C₂³×C₃	semidirect
202. C₂²×C₂²⋊C₄	C₂³×C₃	semidirect
203. C₂²×C₂²⋊C₄	C₂³×C₃	semidirect
204. #392	C₂³×C₃	semidirect
205. #386	C₂³×C₃	semidirect
206. #379	C₂³×C₃	semidirect
207. C₂×#95	C₂³×C₃	semidirect
242. C₂⁴×C₃	#120	semidirect
248. C₂⁴×C₃	C₂²×D₄	semidirect
249. C₂⁴×C₃	C₂²×D₄	semidirect
266. C₂×C₃×D₄	C₂²×D₄	semidirect
276. C₂²×C₃×C₄	C₂²×D₄	semidirect
306. C₂⁵	C₂×C₃×D₄	semidirect
307. C₂⁵	C₂×C₃×D₄	semidirect
313. C₂⁵	C₂⁴×C₃	semidirect
327. C₂²×D₄	C₂×C₃×D₄	semidirect
329. C₂²×D₄	C₂⁴×C₃	semidirect
330. C₂²×D₄	C₂⁴×C₃	semidirect
338. C₂³×C₄	C₂×C₃×D₄	semidirect
341. C₂³×C₄	C₂⁴×C₃	semidirect
346. C₂×C₂²⋊C₄	C₂⁴×C₃	semidirect
347. C₂×C₂²⋊C₄	C₂⁴×C₃	semidirect
348. C₂×C₂²⋊C₄	C₂⁴×C₃	semidirect
349. #95	C₂⁴×C₃	semidirect
382. C₂³×C₃	C₂×#120	semidirect
390. C₂³×C₃	C₂³×D₄	semidirect
403. C₂×C₃×C₄	C₂³×D₄	semidirect
438. C₂⁴	C₃×#120	semidirect
444. C₂⁴	C₂²×C₃×D₄	semidirect
445. C₂⁴	C₂²×C₃×D₄	semidirect
462. C₂×D₄	C₂²×C₃×D₄	semidirect
472. C₂²×C₄	C₂²×C₃×D₄	semidirect
494. C₂²×C₃	#2403	direct (N × H)
496. C₂²×C₃	C₂²×#120	semidirect
536. C₂³	C₂×C₃×#120	semidirect
544. C₂³	C₂³×C₃×D₄	semidirect
557. C₂×C₄	C₂³×C₃×D₄	semidirect
561. C₂×C₃	C₂×#2403	direct (N × H)
581. C₂²	C₃×#2403	direct (N × H)
583. C₂²	C₂²×C₃×#120	semidirect
591. C₃	C₂²×#2403	direct (N × H)
595. C₂	C₂×C₃×#2403	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃×D₄	2
C₂³×C₃×#120	2
C₂×C₃×#2403	2
C₂²×C₃×#392	2
C₂²×C₃×#386	2
C₂²×C₃×#379	2
C₂²×#2403	3

Subgroups — C22×C3×#2403 #72253974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#2403 #72253974