Subgroups — C₄×C₅×#950 #14416209

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#216	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#215	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×#214	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#213	C₂	1	2	yes	maximal, complemented
9	C₅×#5002	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4998	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#135	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×C₄×C₅×D₄	—	2	2	no	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₃×C₅×#117	—	2	1	no	—
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	—	2	1	no	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₅×#950	C₄	1	8	yes	direct product factor
23	C₂×C₅×#216	C₂²	1	1	yes	characteristic
24	C₂×C₅×#215	C₂²	1	1	yes	characteristic
25	C₂×C₅×#214	C₂²	1	1	yes	characteristic
26	C₂×C₅×#213	C₂²	1	1	yes	characteristic
27	C₄×C₅×#67	—	2	2	no	—
28	C₅×#926	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×D₁₂	C₂²	1	2	yes	—
32	C₅×#872	—	2	1	no	—
33	C₄²×C₅×D₃	—	2	1	no	—
34	C₄×C₅×Dic₆	C₂²	1	2	yes	—
35	C₅×#835	C₂²	1	2	yes	—
36	C₅×#832	C₂²	1	2	yes	—
37	C₅×#810	C₂²	1	2	yes	—
38	C₅×#809	C₂²	1	2	yes	—
39	C₅×#808	C₂²	1	2	yes	—
40	C₅×#807	C₂²	1	2	yes	—
41	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
42	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
43	C₄×#950	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×#135	—	3	1	no	—
45	C₄×C₅×#41	—	3	1	no	—
46	C₄×C₅×#41	D₃	1	1	yes	characteristic, complemented
47	C₄×C₅×Q₁₆	—	3	2	no	—
48	C₄×C₅×SD₁₆	—	3	2	no	—
49	C₄×C₅×SD₁₆	—	3	2	no	—
50	C₄×C₅×D₈	—	3	2	no	—
51	C₅×#427	—	3	1	no	—
52	C₅×#416	—	3	1	no	—
53	C₅×#416	—	3	1	no	—
54	C₂×C₄×C₅×C₈	—	3	1	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₅×#67	—	2	1	no	—
65	C₅×#235	—	2	2	no	—
66	C₅×#235	C₂×C₄	1	4	yes	complemented
67	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	—	2	1	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₄²×C₅	—	2	1	no	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₃×C₄²×C₅	C₂³	1	2	yes	—
80	C₅×#217	—	2	1	no	—
81	C₅×#216	C₂×C₄	1	4	yes	complemented
82	C₅×#215	C₂×C₄	1	4	yes	complemented
83	C₅×#214	C₂×C₄	1	4	yes	complemented
84	C₅×#213	C₂×C₄	1	4	yes	complemented
85	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
87	C₅×Dic₃⋊C₄	—	2	2	no	—
88	C₄×C₅×Dic₃	—	2	2	no	—
89	C₄×C₅×Dic₃	—	2	1	no	—
90	C₂×C₅×C₃⋊C₈	—	2	2	no	—
91	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#950	C₂×C₅	1	1	yes	characteristic
97	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
98	#5233	C₂×C₅	1	1	yes	characteristic, complemented
99	C₄×#216	C₂×C₅	1	2	yes	complemented
100	C₄×#215	C₂×C₅	1	2	yes	complemented
101	C₄×#214	C₂×C₅	1	2	yes	complemented
102	C₄×#213	C₂×C₅	1	2	yes	complemented
103	#5002	C₂×C₅	1	1	yes	characteristic, complemented
104	#4998	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×C₅×#41	—	3	1	no	—
107	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
108	C₅×#135	—	3	8	no	—
109	C₂×C₅×Q₁₆	—	3	1	no	—
110	C₂×C₅×SD₁₆	—	3	1	no	—
111	C₂×C₅×SD₁₆	—	3	1	no	—
112	C₂×C₅×D₈	—	3	1	no	—
113	C₂²×C₅×C₈	—	3	1	no	—
114	C₂²×C₅×C₈	—	3	1	no	—
115	C₄×C₅×Q₈	—	3	2	no	—
116	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
117	C₄×C₅×D₄	—	2	2	no	—
118	C₄×C₅×D₄	—	3	2	no	—
119	C₄×C₅×D₄	—	6	2	no	—
120	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
121	C₅×#117	—	2	1	no	—
122	C₅×#117	—	3	1	no	—
123	C₅×#117	—	6	1	no	—
124	C₅×#117	C₂×D₃	1	1	yes	characteristic
125	C₂×C₄²×C₅	—	2	1	no	—
126	C₂×C₄²×C₅	—	6	1	no	—
127	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
128	C₅×#107	—	3	2	no	—
129	C₅×#106	—	3	2	no	—
130	C₅×#103	—	3	2	no	—
131	C₅×#103	—	3	2	no	—
132	C₅×#102	—	3	2	no	—
133	C₅×#102	—	3	2	no	—
134	C₄×C₅×C₈	—	3	2	no	—
135	C₄×C₅×C₈	—	3	2	no	—
136	C₄×#135	—	3	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₅×D₃	—	2	1	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	4	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	4	4	no	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	#41	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₅×#67	—	2	4	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₅×D₁₂	—	2	1	no	—
160	C₅×D₁₂	C₂²×C₄	1	2	yes	—
161	C₄×C₅×D₃	—	2	4	no	—
162	C₄×C₅×D₃	—	4	4	no	—
163	C₅×Dic₆	—	2	1	no	—
164	C₅×Dic₆	C₂²×C₄	1	2	yes	—
165	C₅×C₃⋊C₈	—	2	2	no	—
166	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
167	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
169	C₂×#235	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
171	C₃×C₄×D₄	—	2	2	no	—
172	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
173	C₃×#117	—	2	1	no	—
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄²	—	2	1	no	—
176	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
177	#950	C₄×C₅	1	8	yes	direct product factor
178	C₂×#216	C₂²×C₅	1	1	yes	characteristic
179	C₂×#215	C₂²×C₅	1	1	yes	characteristic
180	C₂×#214	C₂²×C₅	1	1	yes	characteristic
181	C₂×#213	C₂²×C₅	1	1	yes	characteristic
182	C₄×#67	—	2	2	no	—
183	#926	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
185	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	C₄×D₁₂	C₂²×C₅	1	2	yes	—
187	#872	—	2	1	no	—
188	C₄²×D₃	—	2	1	no	—
189	C₄×Dic₆	C₂²×C₅	1	2	yes	—
190	#835	C₂²×C₅	1	2	yes	—
191	#832	C₂²×C₅	1	2	yes	—
192	#810	C₂²×C₅	1	2	yes	—
193	#809	C₂²×C₅	1	2	yes	—
194	#808	C₂²×C₅	1	2	yes	—
195	#807	C₂²×C₅	1	2	yes	—
196	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
197	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	—	3	4	no	—
200	C₅×#41	—	6	2	no	—
201	C₅×#41	C₄×D₃	1	4	yes	complemented
202	C₂×C₅×Q₈	—	3	1	no	—
203	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	—	3	1	no	—
206	C₂×C₅×D₄	—	6	1	no	—
207	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	—	2	1	no	—
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	—	6	1	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	#67	1	2	yes	—
213	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₅×Q₁₆	—	3	4	no	—
215	C₅×SD₁₆	—	3	4	no	—
216	C₅×SD₁₆	—	3	4	no	—
217	C₅×D₈	—	3	4	no	—
218	C₂×C₅×C₈	—	3	4	no	—
219	C₂×C₅×C₈	—	3	1	no	—
220	C₂×C₅×C₈	—	3	1	no	—
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	—	6	2	no	—
223	C₅×C₄⋊C₄	—	2	2	no	—
224	C₅×C₄⋊C₄	—	3	2	no	—
225	C₅×C₄⋊C₄	—	6	2	no	—
226	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	6	1	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₄²×C₅	—	2	2	no	—
233	C₄²×C₅	—	6	1	no	—
234	C₄²×C₅	—	6	2	no	—
235	C₄²×C₅	#67	1	1	yes	characteristic
236	C₄²×C₅	#67	1	1	yes	characteristic
237	C₄²×C₅	C₂²×D₃	1	2	yes	—
238	C₂×#135	—	3	1	no	—
239	C₄×#41	—	3	1	no	—
240	C₄×#41	C₅×D₃	1	1	yes	characteristic, complemented
241	C₄×Q₁₆	—	3	2	no	—
242	C₄×SD₁₆	—	3	2	no	—
243	C₄×SD₁₆	—	3	2	no	—
244	C₄×D₈	—	3	2	no	—
245	#427	—	3	1	no	—
246	#416	—	3	1	no	—
247	#416	—	3	1	no	—
248	C₂×C₄×C₈	—	3	1	no	—
249	C₂²×C₃×C₅	—	2	2	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	—	4	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	4	2	no	—
259	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
260	C₃×C₄×C₅	#135	1	4	yes	complemented
261	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×Dic₃	—	2	2	no	—
264	C₅×Dic₃	—	4	2	no	—
265	C₃×#41	—	2	2	no	—
266	C₃×#41	C₂×C₄×C₅	1	4	yes	complemented
267	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×D₄	—	2	1	no	—
269	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂×#67	—	2	1	no	—
275	#235	—	2	2	no	—
276	#235	C₂×C₄×C₅	1	4	yes	complemented
277	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄×D₃	—	2	1	no	—
279	C₂×C₄×D₃	—	2	2	no	—
280	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
283	C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₄²	—	2	1	no	—
286	C₃×C₄²	—	2	2	no	—
287	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
288	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
289	C₃×C₄²	C₂³×C₅	1	2	yes	—
290	#217	—	2	1	no	—
291	#216	C₂×C₄×C₅	1	4	yes	complemented
292	#215	C₂×C₄×C₅	1	4	yes	complemented
293	#214	C₂×C₄×C₅	1	4	yes	complemented
294	#213	C₂×C₄×C₅	1	4	yes	complemented
295	(C₂×D₃)⋊C₄	—	2	2	no	—
296	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
297	Dic₃⋊C₄	—	2	2	no	—
298	C₄×Dic₃	—	2	2	no	—
299	C₄×Dic₃	—	2	1	no	—
300	C₂×C₃⋊C₈	—	2	2	no	—
301	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
302	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
303	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	—	6	1	no	—
307	C₂³×C₅	C₂×#67	1	1	yes	characteristic
308	C₅×Q₈	—	2	1	no	—
309	C₅×Q₈	—	3	2	no	—
310	C₅×Q₈	—	6	1	no	—
311	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
312	C₅×D₄	—	2	4	no	—
313	C₅×D₄	—	2	1	no	—
314	C₅×D₄	—	3	2	no	—
315	C₅×D₄	—	6	4	no	—
316	C₅×D₄	—	6	1	no	—
317	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	4	no	—
320	C₂×C₄×C₅	—	2	4	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	4	4	no	—
323	C₂×C₄×C₅	—	6	1	no	—
324	C₂×C₄×C₅	—	6	4	no	—
325	C₂×C₄×C₅	—	6	2	no	—
326	C₂×C₄×C₅	—	12	4	no	—
327	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
328	C₂×C₄×C₅	#235	1	2	yes	—
329	C₂×C₄×C₅	C₂×#67	1	2	yes	—
330	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×#67	1	2	yes	—
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	3	2	no	—
334	C₅×C₈	—	3	2	no	—
335	C₅×C₈	—	6	2	no	—
336	C₂×#41	—	3	1	no	—
337	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
338	#135	—	3	8	no	—
339	C₂×Q₁₆	—	3	1	no	—
340	C₂×SD₁₆	—	3	1	no	—
341	C₂×SD₁₆	—	3	1	no	—
342	C₂×D₈	—	3	1	no	—
343	C₂²×C₈	—	3	1	no	—
344	C₂²×C₈	—	3	1	no	—
345	C₄×Q₈	—	3	2	no	—
346	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	3	2	no	—
349	C₄×D₄	—	6	2	no	—
350	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
351	#117	—	2	1	no	—
352	#117	—	3	1	no	—
353	#117	—	6	1	no	—
354	#117	C₂×C₅×D₃	1	1	yes	characteristic
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	6	1	no	—
357	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
358	#107	—	3	2	no	—
359	#106	—	3	2	no	—
360	#103	—	3	2	no	—
361	#103	—	3	2	no	—
362	#102	—	3	2	no	—
363	#102	—	3	2	no	—
364	C₄×C₈	—	3	2	no	—
365	C₄×C₈	—	3	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
369	C₂×C₃×C₅	C₂×#135	1	2	yes	—
370	C₅×D₃	—	4	2	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×D₃	—	2	1	no	—
374	C₃×Q₈	—	2	1	no	—
375	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
376	C₃×D₄	—	2	4	no	—
377	C₃×D₄	—	2	1	no	—
378	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	4	no	—
381	C₂×C₃×C₄	—	2	4	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	4	4	no	—
384	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
385	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂×C₃×C₄	C₅×#41	1	2	yes	—
389	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
390	#67	—	2	4	no	—
391	C₂×Dic₃	—	2	1	no	—
392	C₂×Dic₃	—	2	2	no	—
393	D₁₂	—	2	1	no	—
394	D₁₂	C₂²×C₄×C₅	1	2	yes	—
395	C₄×D₃	—	2	4	no	—
396	C₄×D₃	—	4	4	no	—
397	Dic₆	—	2	1	no	—
398	Dic₆	C₂²×C₄×C₅	1	2	yes	—
399	C₃⋊C₈	—	2	2	no	—
400	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
401	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	6	2	no	—
406	C₂²×C₅	—	12	2	no	—
407	C₂²×C₅	C₄×#67	1	2	yes	—
408	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	2	2	no	—
411	C₄×C₅	—	4	2	no	—
412	C₄×C₅	—	6	2	no	—
413	C₄×C₅	—	12	2	no	—
414	C₄×C₅	C₄×#67	1	2	yes	—
415	C₄×C₅	#950	1	4	yes	direct product factor
416	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
417	C₄×C₅	C₂×#235	1	1	yes	characteristic
418	#41	—	2	2	no	—
419	#41	—	3	4	no	—
420	#41	—	6	2	no	—
421	#41	C₄×C₅×D₃	1	4	yes	complemented
422	C₂×Q₈	—	3	1	no	—
423	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	3	1	no	—
426	C₂×D₄	—	6	1	no	—
427	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	6	1	no	—
431	C₂²×C₄	—	6	2	no	—
432	C₂²×C₄	C₅×#67	1	2	yes	—
433	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
434	Q₁₆	—	3	4	no	—
435	SD₁₆	—	3	4	no	—
436	SD₁₆	—	3	4	no	—
437	D₈	—	3	4	no	—
438	C₂×C₈	—	3	4	no	—
439	C₂×C₈	—	3	1	no	—
440	C₂×C₈	—	3	1	no	—
441	C₂×C₈	—	3	2	no	—
442	C₂×C₈	—	6	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	3	2	no	—
445	C₄⋊C₄	—	6	2	no	—
446	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	6	1	no	—
450	C₂²⋊C₄	—	6	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	6	1	no	—
454	C₄²	—	6	2	no	—
455	C₄²	C₅×#67	1	1	yes	characteristic
456	C₄²	C₅×#67	1	1	yes	characteristic
457	C₄²	C₂²×C₅×D₃	1	2	yes	—
458	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
463	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
464	C₂×D₃	—	2	2	no	—
465	C₂×D₃	—	4	2	no	—
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	2	2	no	—
468	C₃×C₄	—	4	2	no	—
469	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
470	C₃×C₄	C₅×#135	1	4	yes	complemented
471	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
472	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
473	Dic₃	—	2	2	no	—
474	Dic₃	—	4	2	no	—
475	C₂×C₅	—	2	2	no	—
476	C₂×C₅	—	4	2	no	—
477	C₂×C₅	—	12	2	no	—
478	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
479	C₂×C₅	C₂×#950	1	2	yes	—
480	C₂³	—	2	1	no	—
481	C₂³	—	6	1	no	—
482	C₂³	C₂×C₅×#67	1	1	yes	characteristic
483	Q₈	—	2	1	no	—
484	Q₈	—	3	2	no	—
485	Q₈	—	6	1	no	—
486	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
487	D₄	—	2	4	no	—
488	D₄	—	2	1	no	—
489	D₄	—	3	2	no	—
490	D₄	—	6	4	no	—
491	D₄	—	6	1	no	—
492	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	6	1	no	—
499	C₂×C₄	—	6	4	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	12	4	no	—
502	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
503	C₂×C₄	C₅×#235	1	2	yes	—
504	C₂×C₄	C₂×C₅×#67	1	2	yes	—
505	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
506	C₂×C₄	C₂×C₅×#67	1	2	yes	—
507	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
508	C₈	—	3	2	no	—
509	C₈	—	3	2	no	—
510	C₈	—	6	2	no	—
511	C₂×C₃	—	2	2	no	—
512	C₂×C₃	—	4	2	no	—
513	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
514	C₂×C₃	C₂×C₅×#135	1	2	yes	—
515	D₃	—	4	2	no	—
516	C₅	C₄×#950	1	1	yes	characteristic, direct product factor, Sylow
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	6	2	no	—
521	C₂²	—	12	2	no	—
522	C₂²	C₄×C₅×#67	1	2	yes	—
523	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	6	2	no	—
528	C₄	—	12	2	no	—
529	C₄	C₄×C₅×#67	1	2	yes	—
530	C₄	C₅×#950	1	4	yes	direct product factor
531	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
532	C₄	C₂×C₅×#235	1	1	yes	characteristic
533	C₃	C₄×C₅×#135	1	1	yes	characteristic, complemented, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	—	12	2	no	—
537	C₂	C₂×C₄×C₅×#67	1	1	yes	characteristic
538	C₂	C₂×C₅×#950	1	2	yes	—

	subgroup	G/H
center	C₄²×C₅	#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₄×C₅×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
3. C₄×C₅×#235	C₂	semidirect
4. C₅×#5233	C₂	semidirect
5. C₄×C₅×#216	C₂	semidirect
6. C₄×C₅×#215	C₂	semidirect
7. C₄×C₅×#214	C₂	semidirect
8. C₄×C₅×#213	C₂	semidirect
9. C₅×#5002	C₂	semidirect
10. C₅×#4998	C₂	semidirect
11. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
22. C₅×#950	C₄	direct (N × H)
43. C₄×#950	C₅	direct (N × H)
46. C₄×C₅×#41	D₃	semidirect
56. C₃×C₅×#41	C₂×C₄	semidirect
66. C₅×#235	C₂×C₄	semidirect
81. C₅×#216	C₂×C₄	semidirect
82. C₅×#215	C₂×C₄	semidirect
83. C₅×#214	C₂×C₄	semidirect
84. C₅×#213	C₂×C₄	semidirect
91. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
95. C₃×C₄×#41	C₂×C₅	semidirect
97. C₄×#235	C₂×C₅	semidirect
98. #5233	C₂×C₅	semidirect
99. C₄×#216	C₂×C₅	semidirect
100. C₄×#215	C₂×C₅	semidirect
101. C₄×#214	C₂×C₅	semidirect
102. C₄×#213	C₂×C₅	semidirect
103. #5002	C₂×C₅	semidirect
104. #4998	C₂×C₅	semidirect
105. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
177. #950	C₄×C₅	direct (N × H)
201. C₅×#41	C₄×D₃	semidirect
240. C₄×#41	C₅×D₃	semidirect
260. C₃×C₄×C₅	#135	semidirect
266. C₃×#41	C₂×C₄×C₅	semidirect
276. #235	C₂×C₄×C₅	semidirect
291. #216	C₂×C₄×C₅	semidirect
292. #215	C₂×C₄×C₅	semidirect
293. #214	C₂×C₄×C₅	semidirect
294. #213	C₂×C₄×C₅	semidirect
301. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
415. C₄×C₅	#950	direct (N × H)
421. #41	C₄×C₅×D₃	semidirect
458. C₃×C₅	C₄×#135	semidirect
470. C₃×C₄	C₅×#135	semidirect
516. C₅	C₄×#950	direct (N × H)
530. C₄	C₅×#950	direct (N × H)
533. C₃	C₄×C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₂×C₅×#950	2
C₄×C₅×#235	2
C₅×#5233	2
C₄×C₅×#216	2
C₄×C₅×#215	2
C₄×C₅×#214	2
C₄×C₅×#213	2
C₅×#5002	2
C₅×#4998	2
C₂×C₄×C₅×C₃⋊C₈	2
C₄×C₅×#135	3
C₄×#950	5

Subgroups — C4×C5×#950 #14416209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#950 #14416209