Subgroups — C₅×#69494 #14297816

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	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#805	C₂	1	2	yes	maximal
4	C₅×#4924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4523	C₂	1	2	yes	maximal, complemented
6	C₅×#1806	—	3	1	no	maximal, Hall
7	C₂×C₅×#235	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₄×C₅×#67	—	2	1	no	—
12	C₄×C₅×#67	—	2	1	no	—
13	C₅×#926	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	2	yes	—
15	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic, complemented
16	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic, complemented
17	C₅×#872	—	2	1	no	—
18	C₄²×C₅×D₃	—	2	1	no	—
19	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic, complemented
20	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic, complemented
21	C₃×C₅×#95	—	2	1	no	—
22	C₅×#805	—	2	4	no	—
23	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
25	#69494	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₄×C₅×#41	—	3	1	no	—
27	C₅×#423	—	3	1	no	—
28	C₂×C₅×#104	—	3	2	no	—
29	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
30	C₅×#339	—	3	2	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	—	2	1	no	—
36	C₅×#235	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	D₄	1	2	yes	—
39	C₅×#235	Q₈	1	2	yes	—
40	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₄²×C₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	2	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₅×#217	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
57	C₅×Dic₃⋊C₄	—	2	1	no	—
58	C₅×Dic₃⋊C₄	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	1	no	—
60	C₄×C₅×Dic₃	—	2	1	no	—
61	C₄×C₅×Dic₃	—	2	1	no	—
62	C₅×#208	—	2	2	no	—
63	C₅×#208	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	—	2	2	no	—
65	C₄×#235	C₂×C₅	1	1	yes	characteristic
66	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#805	C₂×C₅	1	2	yes	—
68	#4924	C₂×C₅	1	1	yes	characteristic, complemented
69	#4523	C₂×C₅	1	2	yes	complemented
70	C₂×C₅×#41	—	3	1	no	—
71	C₂×C₅×M₁₆	—	3	2	no	—
72	C₄×C₅×Q₈	—	3	1	no	—
73	C₄×C₅×Q₈	—	3	1	no	—
74	C₄×C₅×D₄	—	3	1	no	—
75	C₄×C₅×D₄	—	3	1	no	—
76	C₄×C₅×D₄	—	6	1	no	—
77	C₄×C₅×D₄	—	6	1	no	—
78	C₅×#117	—	3	1	no	—
79	C₅×#117	—	6	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₅	—	6	1	no	—
82	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
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	—	2	1	no	—
88	#1806	—	3	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₅×D₃	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₅×#67	—	2	2	no	—
107	C₅×#67	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	1	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	2	1	no	—
111	C₅×D₁₂	—	2	1	no	—
112	C₅×D₁₂	C₄⋊C₄	1	2	yes	complemented
113	C₄×C₅×D₃	—	2	2	no	—
114	C₄×C₅×D₃	—	2	2	no	—
115	C₄×C₅×D₃	—	4	2	no	—
116	C₄×C₅×D₃	—	4	2	no	—
117	C₅×Dic₆	—	2	1	no	—
118	C₅×Dic₆	C₄⋊C₄	1	2	yes	complemented
119	C₅×C₃⋊C₈	—	4	2	no	—
120	C₂×#235	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	—	2	1	no	—
122	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
123	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
124	C₄×#67	—	2	1	no	—
125	C₄×#67	—	2	1	no	—
126	#926	C₂²×C₅	1	1	yes	characteristic
127	C₂×#208	C₂²×C₅	1	2	yes	—
128	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic, complemented
129	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic, complemented
130	#872	—	2	1	no	—
131	C₄²×D₃	—	2	1	no	—
132	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic, complemented
133	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic, complemented
134	C₃×#95	—	2	1	no	—
135	#805	—	2	4	no	—
136	C₄⋊(C₃⋊C₈)	—	2	1	no	—
137	C₄⋊(C₃⋊C₈)	—	2	1	no	—
138	C₅×#41	—	3	2	no	—
139	C₅×#41	—	3	2	no	—
140	C₅×#41	—	6	1	no	—
141	C₅×#41	—	6	1	no	—
142	C₂×C₅×Q₈	—	3	1	no	—
143	C₂×C₅×D₄	—	3	1	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	6	1	no	—
147	C₂²×C₄×C₅	—	6	1	no	—
148	C₂²×C₄×C₅	—	6	1	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	4	no	—
156	C₅×C₄⋊C₄	—	3	1	no	—
157	C₅×C₄⋊C₄	—	3	1	no	—
158	C₅×C₄⋊C₄	—	6	1	no	—
159	C₅×C₄⋊C₄	—	6	1	no	—
160	C₅×C₂²⋊C₄	—	6	1	no	—
161	C₅×C₂²⋊C₄	—	6	1	no	—
162	C₅×C₂²⋊C₄	—	6	1	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	2	no	—
165	C₄²×C₅	—	6	1	no	—
166	C₄²×C₅	—	6	1	no	—
167	C₄²×C₅	—	6	1	no	—
168	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
169	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
170	C₄²×C₅	D₁₂	1	1	yes	characteristic
171	C₄²×C₅	D₁₂	1	1	yes	characteristic
172	C₄×#41	—	3	1	no	—
173	#423	—	3	1	no	—
174	C₂×#104	—	3	2	no	—
175	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
176	#339	—	3	2	no	—
177	C₂²×C₃×C₅	—	2	1	no	—
178	C₂²×C₃×C₅	—	2	1	no	—
179	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	#121	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₅×D₃	—	2	2	no	—
183	C₂×C₅×D₃	—	4	1	no	—
184	C₂×C₅×D₃	—	4	1	no	—
185	C₃×C₄×C₅	—	2	1	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	2	1	no	—
188	C₃×C₄×C₅	—	4	4	no	—
189	C₃×C₄×C₅	#104	1	2	yes	complemented
190	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₃×C₄×C₅	#117	1	1	yes	characteristic
192	C₃×C₄×C₅	#121	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
194	C₅×Dic₃	—	2	2	no	—
195	C₅×Dic₃	—	4	1	no	—
196	C₅×Dic₃	—	4	1	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂×#67	—	2	1	no	—
202	#235	—	2	1	no	—
203	#235	—	2	1	no	—
204	#235	C₅×D₄	1	2	yes	—
205	#235	C₅×Q₈	1	2	yes	—
206	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄×D₃	—	2	1	no	—
208	C₂×C₄×D₃	—	2	1	no	—
209	C₂×C₄×D₃	—	2	1	no	—
210	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
211	C₃×C₄⋊C₄	—	2	4	no	—
212	C₃×C₄²	—	2	2	no	—
213	C₃×C₄²	—	2	2	no	—
214	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
215	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
216	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
217	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
218	#217	—	2	1	no	—
219	(C₂×D₃)⋊C₄	—	2	1	no	—
220	(C₂×D₃)⋊C₄	—	2	1	no	—
221	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
222	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
223	Dic₃⋊C₄	—	2	1	no	—
224	Dic₃⋊C₄	—	2	1	no	—
225	C₄×Dic₃	—	2	1	no	—
226	C₄×Dic₃	—	2	1	no	—
227	C₄×Dic₃	—	2	1	no	—
228	#208	—	2	2	no	—
229	#208	—	2	2	no	—
230	C₂×C₃⋊C₈	—	2	2	no	—
231	C₂³×C₅	—	6	1	no	—
232	C₂³×C₅	C₂×#67	1	1	yes	characteristic
233	C₅×Q₈	—	3	2	no	—
234	C₅×Q₈	—	6	1	no	—
235	C₅×D₄	—	3	2	no	—
236	C₅×D₄	—	6	2	no	—
237	C₅×D₄	—	6	2	no	—
238	C₅×D₄	—	6	1	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	—	6	2	no	—
246	C₂×C₄×C₅	—	6	2	no	—
247	C₂×C₄×C₅	—	6	1	no	—
248	C₂×C₄×C₅	—	6	1	no	—
249	C₂×C₄×C₅	—	12	2	no	—
250	C₂×C₄×C₅	—	12	2	no	—
251	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
257	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	#237	1	1	yes	characteristic
259	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₅	#239	1	1	yes	characteristic
261	C₅×C₈	—	12	2	no	—
262	C₂×#41	—	3	1	no	—
263	C₂×M₁₆	—	3	2	no	—
264	C₄×Q₈	—	3	1	no	—
265	C₄×Q₈	—	3	1	no	—
266	C₄×D₄	—	3	1	no	—
267	C₄×D₄	—	3	1	no	—
268	C₄×D₄	—	6	1	no	—
269	C₄×D₄	—	6	1	no	—
270	#117	—	3	1	no	—
271	#117	—	6	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄²	—	6	1	no	—
274	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
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	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	#380	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
284	C₂×C₃×C₅	#421	1	1	yes	characteristic
285	C₅×D₃	—	4	2	no	—
286	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂²×D₃	—	2	1	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	2	no	—
292	C₂×C₃×C₄	—	4	2	no	—
293	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
301	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
303	#67	—	2	2	no	—
304	#67	—	2	2	no	—
305	C₂×Dic₃	—	2	1	no	—
306	C₂×Dic₃	—	2	1	no	—
307	C₂×Dic₃	—	2	1	no	—
308	D₁₂	—	2	1	no	—
309	D₁₂	C₅×C₄⋊C₄	1	2	yes	complemented
310	C₄×D₃	—	2	2	no	—
311	C₄×D₃	—	2	2	no	—
312	C₄×D₃	—	4	2	no	—
313	C₄×D₃	—	4	2	no	—
314	Dic₆	—	2	1	no	—
315	Dic₆	C₅×C₄⋊C₄	1	2	yes	complemented
316	C₃⋊C₈	—	4	2	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	6	2	no	—
320	C₂²×C₅	—	12	1	no	—
321	C₂²×C₅	—	12	1	no	—
322	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
323	C₂²×C₅	#938	1	1	yes	characteristic
324	C₂²×C₅	#946	1	1	yes	characteristic
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	4	4	no	—
329	C₄×C₅	—	6	2	no	—
330	C₄×C₅	—	12	1	no	—
331	C₄×C₅	—	12	1	no	—
332	C₄×C₅	#805	1	2	yes	complemented
333	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
334	C₄×C₅	#892	1	1	yes	characteristic
335	C₄×C₅	#895	1	1	yes	characteristic
336	C₄×C₅	#897	1	1	yes	characteristic
337	#41	—	3	2	no	—
338	#41	—	3	2	no	—
339	#41	—	6	1	no	—
340	#41	—	6	1	no	—
341	C₂×Q₈	—	3	1	no	—
342	C₂×D₄	—	3	1	no	—
343	C₂×D₄	—	6	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	6	1	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	—	6	1	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	4	no	—
355	C₄⋊C₄	—	3	1	no	—
356	C₄⋊C₄	—	3	1	no	—
357	C₄⋊C₄	—	6	1	no	—
358	C₄⋊C₄	—	6	1	no	—
359	C₂²⋊C₄	—	6	1	no	—
360	C₂²⋊C₄	—	6	1	no	—
361	C₂²⋊C₄	—	6	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	6	1	no	—
365	C₄²	—	6	1	no	—
366	C₄²	—	6	1	no	—
367	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
368	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
369	C₄²	C₅×D₁₂	1	1	yes	characteristic
370	C₄²	C₅×D₁₂	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	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
375	C₂²×C₃	C₅×#121	1	1	yes	characteristic
376	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	4	1	no	—
379	C₂×D₃	—	4	1	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	4	4	no	—
384	C₃×C₄	C₅×#104	1	2	yes	complemented
385	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
386	C₃×C₄	C₅×#117	1	1	yes	characteristic
387	C₃×C₄	C₅×#121	1	1	yes	characteristic
388	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
389	Dic₃	—	2	2	no	—
390	Dic₃	—	4	1	no	—
391	Dic₃	—	4	1	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	—	12	2	no	—
395	C₂×C₅	C₂×#805	1	1	yes	characteristic
396	C₂×C₅	#4987	1	1	yes	characteristic
397	C₂×C₅	#5005	1	1	yes	characteristic
398	C₂³	—	6	1	no	—
399	C₂³	C₂×C₅×#67	1	1	yes	characteristic
400	Q₈	—	3	2	no	—
401	Q₈	—	6	1	no	—
402	D₄	—	3	2	no	—
403	D₄	—	6	2	no	—
404	D₄	—	6	2	no	—
405	D₄	—	6	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	6	1	no	—
412	C₂×C₄	—	6	2	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	—	6	1	no	—
415	C₂×C₄	—	6	1	no	—
416	C₂×C₄	—	12	2	no	—
417	C₂×C₄	—	12	2	no	—
418	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
419	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
420	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
421	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
422	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
423	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
424	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
425	C₂×C₄	C₅×#237	1	1	yes	characteristic
426	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
427	C₂×C₄	C₅×#239	1	1	yes	characteristic
428	C₈	—	12	2	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	C₅×#380	1	1	yes	characteristic
432	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
433	C₂×C₃	C₅×#421	1	1	yes	characteristic
434	D₃	—	4	2	no	—
435	C₅	#69494	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	6	2	no	—
439	C₂²	—	12	1	no	—
440	C₂²	—	12	1	no	—
441	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
442	C₂²	C₅×#938	1	1	yes	characteristic
443	C₂²	C₅×#946	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	6	2	no	—
449	C₄	—	12	1	no	—
450	C₄	—	12	1	no	—
451	C₄	C₅×#805	1	2	yes	complemented
452	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
453	C₄	C₅×#892	1	1	yes	characteristic
454	C₄	C₅×#895	1	1	yes	characteristic
455	C₄	C₅×#897	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	—	12	2	no	—
460	C₂	C₂×C₅×#805	1	1	yes	characteristic
461	C₂	C₅×#4987	1	1	yes	characteristic
462	C₂	C₅×#5005	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#1806
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₅×#4924	C₂	semidirect
5. C₅×#4523	C₂	semidirect
15. C₄×C₅×D₁₂	C₄	semidirect
16. C₄×C₅×D₁₂	C₄	semidirect
19. C₄×C₅×Dic₆	C₄	semidirect
20. C₄×C₅×Dic₆	C₄	semidirect
25. #69494	C₅	direct (N × H)
29. C₄×C₅×C₄⋊C₄	D₃	semidirect
66. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
68. #4924	C₂×C₅	semidirect
69. #4523	C₂×C₅	semidirect
112. C₅×D₁₂	C₄⋊C₄	semidirect
118. C₅×Dic₆	C₄⋊C₄	semidirect
128. C₄×D₁₂	C₄×C₅	semidirect
129. C₄×D₁₂	C₄×C₅	semidirect
132. C₄×Dic₆	C₄×C₅	semidirect
133. C₄×Dic₆	C₄×C₅	semidirect
175. C₄×C₄⋊C₄	C₅×D₃	semidirect
189. C₃×C₄×C₅	#104	semidirect
309. D₁₂	C₅×C₄⋊C₄	semidirect
315. Dic₆	C₅×C₄⋊C₄	semidirect
332. C₄×C₅	#805	semidirect
371. C₃×C₅	#1806	semidirect
384. C₃×C₄	C₅×#104	semidirect
435. C₅	#69494	direct (N × H)
451. C₄	C₅×#805	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
C₄×C₅×#235	2
C₃×C₄×C₅×C₄⋊C₄	2
C₂×C₅×#805	2
C₅×#4924	2
C₅×#4523	2
C₅×#1806	3
#69494	5

Subgroups — C5×#69494 #14297816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69494 #14297816