Subgroups — C₃×C₅×#2433 #14275467

Order 1920.

2696 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	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#127	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#120	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#392	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2433	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×D₄	—	2	8	no	—
11	C₂²×C₃×C₅×D₄	—	2	4	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	—	2	8	no	—
19	C₃×C₅×#121	—	2	4	no	—
20	C₃×C₅×#120	—	2	16	no	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
26	C₃×C₅×#95	C₂²	1	2	yes	complemented
27	C₃×#2433	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#127	C₂×C₃	1	2	yes	complemented
30	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₅×#120	C₂×C₃	1	4	yes	complemented
32	C₅×#392	C₂×C₃	1	4	yes	complemented
33	C₅×#390	C₂×C₃	1	2	yes	complemented
34	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃×C₅	—	2	8	no	—
36	C₂⁴×C₃×C₅	—	2	4	no	—
37	C₂⁴×C₃×C₅	—	2	8	no	—
38	C₂⁴×C₃×C₅	—	4	4	no	—
39	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
40	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×D₄	—	2	32	no	—
43	C₂×C₃×C₅×D₄	—	2	8	no	—
44	C₂×C₃×C₅×D₄	—	2	8	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	16	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	4	no	—
52	C₂×C₃×C₅×D₄	—	2	16	no	—
53	C₂×C₃×C₅×D₄	—	4	8	no	—
54	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
55	C₂²×C₃×C₄×C₅	—	2	4	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	4	yes	complemented
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	16	no	—
64	C₃×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
65	C₃×C₄²×C₅	—	2	4	no	—
66	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×C₃×#127	C₂×C₅	1	2	yes	complemented
68	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×C₃×#120	C₂×C₅	1	4	yes	complemented
70	C₃×#392	C₂×C₅	1	4	yes	complemented
71	C₃×#390	C₂×C₅	1	2	yes	complemented
72	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
74	C₂²×C₅×D₄	—	2	8	no	—
75	C₂²×C₅×D₄	—	2	4	no	—
76	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
77	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
78	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
79	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₂²×C₅×D₄	C₂²×C₃	1	8	yes	complemented
81	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₅×#127	—	2	8	no	—
83	C₅×#121	—	2	4	no	—
84	C₅×#120	—	2	16	no	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
89	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
90	C₅×#95	C₂²×C₃	1	2	yes	complemented
91	#2433	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³×C₃×C₅	—	2	2	no	—
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	16	no	—
95	C₂³×C₃×C₅	—	2	8	no	—
96	C₂³×C₃×C₅	—	2	4	no	—
97	C₂³×C₃×C₅	—	2	4	no	—
98	C₂³×C₃×C₅	—	2	8	no	—
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	4	no	—
101	C₂³×C₃×C₅	—	2	4	no	—
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	—	4	32	no	—
104	C₂³×C₃×C₅	—	4	8	no	—
105	C₂³×C₃×C₅	—	4	8	no	—
106	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
107	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
108	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
109	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
110	C₃×C₅×D₄	—	2	16	no	—
111	C₃×C₅×D₄	—	2	16	no	—
112	C₃×C₅×D₄	—	4	32	no	—
113	C₃×C₅×D₄	—	4	8	no	—
114	C₃×C₅×D₄	—	4	4	no	—
115	C₂×C₃×C₄×C₅	—	2	4	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
125	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
126	C₂²×C₃×D₄	—	2	8	no	—
127	C₂²×C₃×D₄	—	2	4	no	—
128	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
129	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
130	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
131	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₂²×C₃×D₄	C₂²×C₅	1	8	yes	complemented
133	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
134	C₃×#127	—	2	8	no	—
135	C₃×#121	—	2	4	no	—
136	C₃×#120	—	2	16	no	—
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
138	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
141	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
142	C₃×#95	C₂²×C₅	1	2	yes	complemented
143	C₂⁴×C₅	—	2	8	no	—
144	C₂⁴×C₅	—	2	4	no	—
145	C₂⁴×C₅	—	2	8	no	—
146	C₂⁴×C₅	—	4	4	no	—
147	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
148	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
149	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₅×D₄	—	2	32	no	—
151	C₂×C₅×D₄	—	2	8	no	—
152	C₂×C₅×D₄	—	2	8	no	—
153	C₂×C₅×D₄	—	2	4	no	—
154	C₂×C₅×D₄	—	2	16	no	—
155	C₂×C₅×D₄	—	2	4	no	—
156	C₂×C₅×D₄	—	2	4	no	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	2	4	no	—
160	C₂×C₅×D₄	—	2	16	no	—
161	C₂×C₅×D₄	—	4	8	no	—
162	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
163	C₂²×C₄×C₅	—	2	4	no	—
164	C₂²×C₄×C₅	C₃×D₄	1	4	yes	complemented
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₂²⋊C₄	—	2	4	no	—
171	C₅×C₂²⋊C₄	—	2	16	no	—
172	C₅×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
173	C₄²×C₅	—	2	4	no	—
174	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
175	C₂×#127	C₂×C₃×C₅	1	2	yes	complemented
176	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
177	C₂×#120	C₂×C₃×C₅	1	4	yes	complemented
178	#392	C₂×C₃×C₅	1	4	yes	complemented
179	#390	C₂×C₃×C₅	1	2	yes	complemented
180	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	2	no	—
183	C₂²×C₃×C₅	—	2	8	no	—
184	C₂²×C₃×C₅	—	2	8	no	—
185	C₂²×C₃×C₅	—	2	16	no	—
186	C₂²×C₃×C₅	—	4	32	no	—
187	C₂²×C₃×C₅	—	4	4	no	—
188	C₂²×C₃×C₅	—	4	4	no	—
189	C₂²×C₃×C₅	—	4	8	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	4	2	no	—
193	C₂²×C₃×C₅	—	4	8	no	—
194	C₂²×C₃×C₅	#127	1	4	yes	complemented
195	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
197	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
198	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
199	C₃×C₄×C₅	—	2	2	no	—
200	C₃×C₄×C₅	—	2	8	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	#120	1	4	yes	complemented
203	C₂⁴×C₃	—	2	8	no	—
204	C₂⁴×C₃	—	2	4	no	—
205	C₂⁴×C₃	—	2	8	no	—
206	C₂⁴×C₃	—	4	4	no	—
207	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
208	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
209	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
210	C₂×C₃×D₄	—	2	32	no	—
211	C₂×C₃×D₄	—	2	8	no	—
212	C₂×C₃×D₄	—	2	8	no	—
213	C₂×C₃×D₄	—	2	4	no	—
214	C₂×C₃×D₄	—	2	16	no	—
215	C₂×C₃×D₄	—	2	4	no	—
216	C₂×C₃×D₄	—	2	4	no	—
217	C₂×C₃×D₄	—	2	4	no	—
218	C₂×C₃×D₄	—	2	2	no	—
219	C₂×C₃×D₄	—	2	4	no	—
220	C₂×C₃×D₄	—	2	16	no	—
221	C₂×C₃×D₄	—	4	8	no	—
222	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
223	C₂²×C₃×C₄	—	2	4	no	—
224	C₂²×C₃×C₄	C₅×D₄	1	4	yes	complemented
225	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₂²⋊C₄	—	2	4	no	—
231	C₃×C₂²⋊C₄	—	2	16	no	—
232	C₃×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
233	C₃×C₄²	—	2	4	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	16	no	—
237	C₂³×C₅	—	2	8	no	—
238	C₂³×C₅	—	2	4	no	—
239	C₂³×C₅	—	2	4	no	—
240	C₂³×C₅	—	2	8	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	2	4	no	—
243	C₂³×C₅	—	2	4	no	—
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	—	4	32	no	—
246	C₂³×C₅	—	4	8	no	—
247	C₂³×C₅	—	4	8	no	—
248	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
249	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
250	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
251	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
252	C₅×D₄	—	2	16	no	—
253	C₅×D₄	—	2	16	no	—
254	C₅×D₄	—	4	32	no	—
255	C₅×D₄	—	4	8	no	—
256	C₅×D₄	—	4	4	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	4	no	—
260	C₂×C₄×C₅	—	2	8	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
264	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
265	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
266	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	complemented
267	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
268	C₂²×D₄	—	2	8	no	—
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
271	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
272	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
273	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
274	C₂²×D₄	C₂²×C₃×C₅	1	8	yes	complemented
275	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
276	#127	—	2	8	no	—
277	#121	—	2	4	no	—
278	#120	—	2	16	no	—
279	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
280	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	8	yes	complemented
282	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
283	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
284	#95	C₂²×C₃×C₅	1	2	yes	complemented
285	C₂×C₃×C₅	—	2	4	no	—
286	C₂×C₃×C₅	—	4	8	no	—
287	C₂×C₃×C₅	—	8	2	no	—
288	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
290	C₂×C₃×C₅	#535	1	1	yes	characteristic
291	C₂×C₃×C₅	D₄²	1	4	yes	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	16	no	—
295	C₂³×C₃	—	2	8	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	2	4	no	—
298	C₂³×C₃	—	2	8	no	—
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	—	2	4	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	2	4	no	—
303	C₂³×C₃	—	4	32	no	—
304	C₂³×C₃	—	4	8	no	—
305	C₂³×C₃	—	4	8	no	—
306	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
307	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
308	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
309	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
310	C₃×D₄	—	2	16	no	—
311	C₃×D₄	—	2	16	no	—
312	C₃×D₄	—	4	32	no	—
313	C₃×D₄	—	4	8	no	—
314	C₃×D₄	—	4	4	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	8	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	complemented
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	2	8	no	—
328	C₂²×C₅	—	2	8	no	—
329	C₂²×C₅	—	2	16	no	—
330	C₂²×C₅	—	4	32	no	—
331	C₂²×C₅	—	4	4	no	—
332	C₂²×C₅	—	4	4	no	—
333	C₂²×C₅	—	4	8	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	4	2	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	8	no	—
338	C₂²×C₅	C₃×#127	1	4	yes	complemented
339	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
340	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
341	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
342	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	2	8	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	C₃×#120	1	4	yes	complemented
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	8	no	—
350	C₂⁴	—	4	4	no	—
351	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
352	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
353	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
354	C₂×D₄	—	2	32	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	16	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	4	8	no	—
366	C₂×D₄	C₃×C₅×D₄	1	8	yes	complemented
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	C₃×C₅×D₄	1	4	yes	complemented
369	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
370	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
371	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
372	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
373	C₄⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
377	C₄²	—	2	4	no	—
378	C₃×C₅	#2433	1	1	yes	characteristic, direct product factor, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	8	no	—
382	C₂²×C₃	—	2	8	no	—
383	C₂²×C₃	—	2	16	no	—
384	C₂²×C₃	—	4	32	no	—
385	C₂²×C₃	—	4	4	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	4	8	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	—	4	8	no	—
392	C₂²×C₃	C₅×#127	1	4	yes	complemented
393	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
395	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
396	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	8	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	C₅×#120	1	4	yes	complemented
401	C₂×C₅	—	2	4	no	—
402	C₂×C₅	—	4	8	no	—
403	C₂×C₅	—	8	2	no	—
404	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
405	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
406	C₂×C₅	C₃×#535	1	1	yes	characteristic
407	C₂×C₅	C₃×D₄²	1	4	yes	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	16	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	8	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	4	32	no	—
420	C₂³	—	4	8	no	—
421	C₂³	—	4	8	no	—
422	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
423	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
424	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
425	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
426	D₄	—	2	16	no	—
427	D₄	—	2	16	no	—
428	D₄	—	4	32	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
438	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
439	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
440	C₂×C₄	C₂×C₃×C₅×D₄	1	8	yes	complemented
441	C₂×C₃	—	2	4	no	—
442	C₂×C₃	—	4	8	no	—
443	C₂×C₃	—	8	2	no	—
444	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
445	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
446	C₂×C₃	C₅×#535	1	1	yes	characteristic
447	C₂×C₃	C₅×D₄²	1	4	yes	—
448	C₅	C₃×#2433	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	16	no	—
454	C₂²	—	4	32	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	8	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	8	no	—
462	C₂²	C₃×C₅×#127	1	4	yes	complemented
463	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
464	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
465	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
466	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
467	C₄	—	2	2	no	—
468	C₄	—	2	8	no	—
469	C₄	—	4	2	no	—
470	C₄	C₃×C₅×#120	1	4	yes	complemented
471	C₃	C₅×#2433	1	1	yes	characteristic, direct product factor, Sylow
472	C₂	—	2	4	no	—
473	C₂	—	4	8	no	—
474	C₂	—	8	2	no	—
475	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
476	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
477	C₂	C₃×C₅×#535	1	1	yes	characteristic
478	C₂	C₃×C₅×D₄²	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×C₅×#120	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
8. C₅×#2433	C₃	direct (N × H)
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
24. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂×C₃×C₄²×C₅	C₂²	semidirect
26. C₃×C₅×#95	C₂²	semidirect
27. C₃×#2433	C₅	direct (N × H)
28. C₂³×C₅×D₄	C₂×C₃	semidirect
29. C₂×C₅×#127	C₂×C₃	semidirect
30. C₂×C₅×#121	C₂×C₃	semidirect
31. C₂×C₅×#120	C₂×C₃	semidirect
32. C₅×#392	C₂×C₃	semidirect
33. C₅×#390	C₂×C₃	semidirect
34. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
54. C₂×C₃×C₅×D₄	D₄	semidirect
56. C₂²×C₃×C₄×C₅	D₄	semidirect
64. C₃×C₅×C₂²⋊C₄	D₄	semidirect
66. C₂³×C₃×D₄	C₂×C₅	semidirect
67. C₂×C₃×#127	C₂×C₅	semidirect
68. C₂×C₃×#121	C₂×C₅	semidirect
69. C₂×C₃×#120	C₂×C₅	semidirect
70. C₃×#392	C₂×C₅	semidirect
71. C₃×#390	C₂×C₅	semidirect
72. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
79. C₂²×C₅×D₄	C₂²×C₃	semidirect
80. C₂²×C₅×D₄	C₂²×C₃	semidirect
85. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
87. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
88. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
89. C₂×C₄²×C₅	C₂²×C₃	semidirect
90. C₅×#95	C₂²×C₃	semidirect
91. #2433	C₃×C₅	direct (N × H)
124. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
131. C₂²×C₃×D₄	C₂²×C₅	semidirect
132. C₂²×C₃×D₄	C₂²×C₅	semidirect
137. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
139. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
140. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
141. C₂×C₃×C₄²	C₂²×C₅	semidirect
142. C₃×#95	C₂²×C₅	semidirect
162. C₂×C₅×D₄	C₃×D₄	semidirect
164. C₂²×C₄×C₅	C₃×D₄	semidirect
172. C₅×C₂²⋊C₄	C₃×D₄	semidirect
174. C₂³×D₄	C₂×C₃×C₅	semidirect
175. C₂×#127	C₂×C₃×C₅	semidirect
176. C₂×#121	C₂×C₃×C₅	semidirect
177. C₂×#120	C₂×C₃×C₅	semidirect
178. #392	C₂×C₃×C₅	semidirect
179. #390	C₂×C₃×C₅	semidirect
180. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
194. C₂²×C₃×C₅	#127	semidirect
202. C₃×C₄×C₅	#120	semidirect
222. C₂×C₃×D₄	C₅×D₄	semidirect
224. C₂²×C₃×C₄	C₅×D₄	semidirect
232. C₃×C₂²⋊C₄	C₅×D₄	semidirect
266. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
273. C₂²×D₄	C₂²×C₃×C₅	semidirect
274. C₂²×D₄	C₂²×C₃×C₅	semidirect
279. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
281. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
282. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
283. C₂×C₄²	C₂²×C₃×C₅	semidirect
284. #95	C₂²×C₃×C₅	semidirect
324. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
338. C₂²×C₅	C₃×#127	semidirect
346. C₄×C₅	C₃×#120	semidirect
366. C₂×D₄	C₃×C₅×D₄	semidirect
368. C₂²×C₄	C₃×C₅×D₄	semidirect
376. C₂²⋊C₄	C₃×C₅×D₄	semidirect
378. C₃×C₅	#2433	direct (N × H)
392. C₂²×C₃	C₅×#127	semidirect
400. C₃×C₄	C₅×#120	semidirect
440. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
448. C₅	C₃×#2433	direct (N × H)
462. C₂²	C₃×C₅×#127	semidirect
470. C₄	C₃×C₅×#120	semidirect
471. C₃	C₅×#2433	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×C₃×C₅×D₄	2
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2433	3
C₃×#2433	5

Subgroups — C3×C5×#2433 #14275467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2433 #14275467