Subgroups — C₅×#71646 #14297813

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 464 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
2	C₂×C₅×#837	C₂	1	2	yes	maximal
3	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4532	C₂	1	2	yes	maximal, complemented
6	C₅×#1806	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
9	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
10	C₃×C₄×C₅×D₄	—	2	1	no	—
11	C₃×C₄×C₅×D₄	—	2	1	no	—
12	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
13	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
14	C₃×C₅×#117	—	2	1	no	—
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
20	C₂×C₅×#208	C₂²	1	2	yes	—
21	C₅×#837	—	2	4	no	—
22	C₅×C₃⋊#95	—	2	1	no	—
23	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
25	#71646	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₄×C₅×#41	D₃	1	1	yes	characteristic
27	C₅×#423	—	3	1	no	—
28	C₂×C₅×#104	—	3	2	no	—
29	C₄×C₅×C₄⋊C₄	—	3	1	no	—
30	C₅×#339	—	3	2	no	—
31	C₃×C₅×#41	—	2	1	no	—
32	C₃×C₅×#41	—	2	1	no	—
33	C₃×C₅×#41	D₄	1	2	yes	—
34	C₃×C₅×#41	Q₈	1	2	yes	—
35	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₃×C₄²×C₅	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Dic₃	—	2	4	no	—
60	C₄×C₅×Dic₃	—	2	2	no	—
61	C₄×C₅×Dic₃	—	2	2	no	—
62	C₅×#208	—	2	2	no	—
63	C₅×#208	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	—	2	2	no	—
65	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
66	C₂×#837	C₂×C₅	1	2	yes	—
67	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
68	#4924	C₂×C₅	1	1	yes	characteristic, complemented
69	#4532	C₂×C₅	1	2	yes	complemented
70	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
71	C₂×C₅×M₁₆	—	3	2	no	—
72	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
73	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
77	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
78	C₅×#117	—	2	1	no	—
79	C₅×#117	C₂×D₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	—	6	1	no	—
81	C₂×C₄²×C₅	—	2	1	no	—
82	C₂×C₄²×C₅	—	3	2	no	—
83	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
84	C₅×C₄⋊C₈	—	6	1	no	—
85	C₅×C₄⋊C₈	—	6	1	no	—
86	C₅×#104	—	6	4	no	—
87	C₅×#95	—	6	1	no	—
88	#1806	—	3	1	no	Sylow
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	1	no	—
92	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	complemented
93	C₃×C₅×D₄	—	2	2	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₃×C₅×D₄	—	2	1	no	—
96	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	complemented
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
116	C₂×C₅×Dic₃	—	2	4	no	—
117	C₂×C₅×Dic₃	—	4	2	no	—
118	C₂×C₅×Dic₃	—	4	2	no	—
119	C₅×C₃⋊C₈	—	4	2	no	—
120	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
122	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
123	C₃×C₄×D₄	—	2	1	no	—
124	C₃×C₄×D₄	—	2	1	no	—
125	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic, complemented
126	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic, complemented
127	C₃×#117	—	2	1	no	—
128	C₃×#117	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄²	—	2	1	no	—
130	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₄⋊Dic₃	—	2	1	no	—
132	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
133	C₂×#208	C₂²×C₅	1	2	yes	—
134	#837	—	2	4	no	—
135	C₃⋊#95	—	2	1	no	—
136	C₄⋊(C₃⋊C₈)	—	2	1	no	—
137	C₄⋊(C₃⋊C₈)	—	2	1	no	—
138	C₅×#41	—	2	1	no	—
139	C₅×#41	—	2	1	no	—
140	C₅×#41	Dic₆	1	2	yes	—
141	C₅×#41	D₁₂	1	2	yes	—
142	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	6	2	no	—
149	C₂²×C₄×C₅	#67	1	1	yes	characteristic
150	C₂²×C₄×C₅	#67	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₅×M₁₆	—	6	2	no	—
153	C₅×M₁₆	—	6	2	no	—
154	C₂×C₅×C₈	—	6	2	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	6	4	no	—
158	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₅×C₂²⋊C₄	—	2	1	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	6	2	no	—
167	C₄²×C₅	—	6	2	no	—
168	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
169	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
170	C₄²×C₅	#67	1	1	yes	characteristic
171	C₄²×C₅	#67	1	1	yes	characteristic
172	C₄×#41	C₅×D₃	1	1	yes	characteristic
173	#423	—	3	1	no	—
174	C₂×#104	—	3	2	no	—
175	C₄×C₄⋊C₄	—	3	1	no	—
176	#339	—	3	2	no	—
177	C₂²×C₃×C₅	—	2	1	no	—
178	C₂²×C₃×C₅	—	2	1	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	4	1	no	—
181	C₂²×C₃×C₅	—	4	1	no	—
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	#121	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	2	1	no	—
188	C₃×C₄×C₅	—	2	1	no	—
189	C₃×C₄×C₅	—	4	1	no	—
190	C₃×C₄×C₅	—	4	1	no	—
191	C₃×C₄×C₅	#104	1	2	yes	complemented
192	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₃×C₄×C₅	#117	1	1	yes	characteristic
194	C₃×C₄×C₅	#121	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
196	C₅×Dic₃	—	4	4	no	—
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	C₅×D₄	1	2	yes	—
200	C₃×#41	C₅×Q₈	1	2	yes	—
201	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	2	no	—
211	C₃×C₄⋊C₄	—	2	1	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
214	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₃×C₂²⋊C₄	—	2	1	no	—
216	C₃×C₂²⋊C₄	—	2	1	no	—
217	C₃×C₂²⋊C₄	—	2	1	no	—
218	C₃×C₄²	—	2	1	no	—
219	C₃×C₄²	—	2	1	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
222	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
223	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
224	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
225	C₄⋊Dic₃	—	2	4	no	—
226	C₄×Dic₃	—	2	2	no	—
227	C₄×Dic₃	—	2	2	no	—
228	#208	—	2	2	no	—
229	#208	—	2	2	no	—
230	C₂×C₃⋊C₈	—	2	2	no	—
231	C₂³×C₅	—	2	1	no	—
232	C₂³×C₅	C₂×#67	1	1	yes	characteristic
233	C₅×Q₈	—	2	1	no	—
234	C₅×Q₈	C₄⋊Dic₃	1	2	yes	complemented
235	C₅×D₄	—	2	2	no	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	—	2	1	no	—
238	C₅×D₄	C₄⋊Dic₃	1	2	yes	complemented
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	6	4	no	—
249	C₂×C₄×C₅	—	12	2	no	—
250	C₂×C₄×C₅	—	12	2	no	—
251	C₂×C₄×C₅	#217	1	1	yes	characteristic
252	C₂×C₄×C₅	#217	1	1	yes	characteristic
253	C₂×C₄×C₅	#217	1	1	yes	characteristic
254	C₂×C₄×C₅	#217	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
257	C₂×C₄×C₅	#235	1	1	yes	characteristic
258	C₂×C₄×C₅	#235	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
261	C₅×C₈	—	12	2	no	—
262	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×M₁₆	—	3	2	no	—
264	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic, complemented
265	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic, complemented
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic, complemented
269	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic, complemented
270	#117	—	2	1	no	—
271	#117	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	6	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	3	2	no	—
275	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
276	C₄⋊C₈	—	6	1	no	—
277	C₄⋊C₈	—	6	1	no	—
278	#104	—	6	4	no	—
279	#95	—	6	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	—	4	2	no	—
283	C₂×C₃×C₅	#380	1	1	yes	characteristic
284	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
285	C₂×C₃×C₅	#421	1	1	yes	characteristic
286	C₂³×C₃	—	2	1	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
288	C₃×Q₈	—	2	1	no	—
289	C₃×Q₈	C₅×C₄⋊C₄	1	2	yes	complemented
290	C₃×D₄	—	2	2	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	—	2	1	no	—
293	C₃×D₄	C₅×C₄⋊C₄	1	2	yes	complemented
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	4	1	no	—
301	C₂×C₃×C₄	—	4	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
311	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
312	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
313	C₂×Dic₃	—	2	4	no	—
314	C₂×Dic₃	—	4	2	no	—
315	C₂×Dic₃	—	4	2	no	—
316	C₃⋊C₈	—	4	2	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	2	2	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	—	4	1	no	—
322	C₂²×C₅	#924	1	1	yes	characteristic
323	C₂²×C₅	#930	1	1	yes	characteristic
324	C₂²×C₅	C₂×#217	1	1	yes	characteristic
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	4	1	no	—
331	C₄×C₅	—	12	4	no	—
332	C₄×C₅	#837	1	2	yes	complemented
333	C₄×C₅	#924	1	1	yes	characteristic
334	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
335	C₄×C₅	#926	1	1	yes	characteristic
336	C₄×C₅	#930	1	1	yes	characteristic
337	#41	—	2	1	no	—
338	#41	—	2	1	no	—
339	#41	C₅×Dic₆	1	2	yes	—
340	#41	C₅×D₁₂	1	2	yes	—
341	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	6	2	no	—
348	C₂²×C₄	C₅×#67	1	1	yes	characteristic
349	C₂²×C₄	C₅×#67	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	M₁₆	—	6	2	no	—
352	M₁₆	—	6	2	no	—
353	C₂×C₈	—	6	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	6	4	no	—
357	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
358	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	6	2	no	—
366	C₄²	—	6	2	no	—
367	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
368	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
369	C₄²	C₅×#67	1	1	yes	characteristic
370	C₄²	C₅×#67	1	1	yes	characteristic
371	C₃×C₅	#1806	1	1	yes	characteristic, complemented, Hall
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	4	1	no	—
376	C₂²×C₃	—	4	1	no	—
377	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×C₃	C₅×#121	1	1	yes	characteristic
379	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	4	1	no	—
385	C₃×C₄	—	4	1	no	—
386	C₃×C₄	C₅×#104	1	2	yes	complemented
387	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
388	C₃×C₄	C₅×#117	1	1	yes	characteristic
389	C₃×C₄	C₅×#121	1	1	yes	characteristic
390	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
391	Dic₃	—	4	4	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	—	4	2	no	—
395	C₂×C₅	#5212	1	1	yes	characteristic
396	C₂×C₅	C₂×#837	1	1	yes	characteristic
397	C₂×C₅	#5236	1	1	yes	characteristic
398	C₂³	—	2	1	no	—
399	C₂³	C₂×C₅×#67	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₅×C₄⋊Dic₃	1	2	yes	complemented
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	C₅×C₄⋊Dic₃	1	2	yes	complemented
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	6	4	no	—
416	C₂×C₄	—	12	2	no	—
417	C₂×C₄	—	12	2	no	—
418	C₂×C₄	C₅×#217	1	1	yes	characteristic
419	C₂×C₄	C₅×#217	1	1	yes	characteristic
420	C₂×C₄	C₅×#217	1	1	yes	characteristic
421	C₂×C₄	C₅×#217	1	1	yes	characteristic
422	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
423	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
424	C₂×C₄	C₅×#235	1	1	yes	characteristic
425	C₂×C₄	C₅×#235	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
427	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
428	C₈	—	12	2	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	4	2	no	—
432	C₂×C₃	C₅×#380	1	1	yes	characteristic
433	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
434	C₂×C₃	C₅×#421	1	1	yes	characteristic
435	C₅	#71646	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₅×#924	1	1	yes	characteristic
442	C₂²	C₅×#930	1	1	yes	characteristic
443	C₂²	C₂×C₅×#217	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	12	4	no	—
451	C₄	C₅×#837	1	2	yes	complemented
452	C₄	C₅×#924	1	1	yes	characteristic
453	C₄	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
454	C₄	C₅×#926	1	1	yes	characteristic
455	C₄	C₅×#930	1	1	yes	characteristic
456	C₃	C₅×#1806	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	4	2	no	—
460	C₂	C₅×#5212	1	1	yes	characteristic
461	C₂	C₂×C₅×#837	1	1	yes	characteristic
462	C₂	C₅×#5236	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#1806
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
3. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
4. C₅×#4924	C₂	semidirect
5. C₅×#4532	C₂	semidirect
8. C₃×C₄×C₅×Q₈	C₄	semidirect
9. C₃×C₄×C₅×Q₈	C₄	semidirect
12. C₃×C₄×C₅×D₄	C₄	semidirect
13. C₃×C₄×C₅×D₄	C₄	semidirect
25. #71646	C₅	direct (N × H)
67. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
68. #4924	C₂×C₅	semidirect
69. #4532	C₂×C₅	semidirect
72. C₄×C₅×Q₈	Dic₃	semidirect
73. C₄×C₅×Q₈	Dic₃	semidirect
76. C₄×C₅×D₄	Dic₃	semidirect
77. C₄×C₅×D₄	Dic₃	semidirect
92. C₃×C₅×Q₈	C₄⋊C₄	semidirect
96. C₃×C₅×D₄	C₄⋊C₄	semidirect
121. C₃×C₄×Q₈	C₄×C₅	semidirect
122. C₃×C₄×Q₈	C₄×C₅	semidirect
125. C₃×C₄×D₄	C₄×C₅	semidirect
126. C₃×C₄×D₄	C₄×C₅	semidirect
191. C₃×C₄×C₅	#104	semidirect
234. C₅×Q₈	C₄⋊Dic₃	semidirect
238. C₅×D₄	C₄⋊Dic₃	semidirect
264. C₄×Q₈	C₅×Dic₃	semidirect
265. C₄×Q₈	C₅×Dic₃	semidirect
268. C₄×D₄	C₅×Dic₃	semidirect
269. C₄×D₄	C₅×Dic₃	semidirect
289. C₃×Q₈	C₅×C₄⋊C₄	semidirect
293. C₃×D₄	C₅×C₄⋊C₄	semidirect
332. C₄×C₅	#837	semidirect
371. C₃×C₅	#1806	semidirect
386. C₃×C₄	C₅×#104	semidirect
401. Q₈	C₅×C₄⋊Dic₃	semidirect
405. D₄	C₅×C₄⋊Dic₃	semidirect
435. C₅	#71646	direct (N × H)
451. C₄	C₅×#837	semidirect
456. C₃	C₅×#1806	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×#837	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4924	2
C₅×#4532	2
C₅×#1806	3
#71646	5

Subgroups — C5×#71646 #14297813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71646 #14297813