Subgroups — C₅×#68277 #14282872

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5596	C₂	1	1	yes	maximal, characteristic
2	C₅×#4718	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4649	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1502	—	3	1	no	maximal, Hall
9	C₂×C₅×#237	—	2	1	no	—
10	C₃×C₅×#121	C₂²	1	1	yes	characteristic
11	C₅×#940	C₄	1	1	yes	characteristic, complemented
12	C₅×#939	—	2	1	no	—
13	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic, complemented
14	C₅×#930	C₂²	1	1	yes	characteristic
15	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
16	C₂×C₄×C₅×Dic₃	—	2	1	no	—
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₅×#893	C₄	1	1	yes	characteristic, complemented
19	C₅×#888	C₄	1	1	yes	characteristic, complemented
20	C₅×#885	—	2	1	no	—
21	C₅×#67⋊C₄	—	2	1	no	—
22	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	1	yes	characteristic
24	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
25	C₅×#830	C₂²	1	1	yes	characteristic
26	C₅×Dic₃⋊C₈	—	2	1	no	—
27	C₅×C₈×Dic₃	—	2	1	no	—
28	#68277	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#532	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₄×C₅×C₄⋊C₄	—	3	1	no	—
32	C₅×#327	—	3	1	no	—
33	C₅×#327	—	3	1	no	—
34	C₅×#327	—	3	1	no	—
35	C₅×#327	D₃	1	1	yes	characteristic, complemented
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	C₂³	1	1	yes	characteristic
40	C₂×C₅×#67	—	2	1	no	—
41	C₂×C₅×#67	—	2	1	no	—
42	C₂×C₅×#67	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
47	C₅×#237	—	4	2	no	—
48	C₅×#237	—	4	2	no	—
49	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	—	2	1	no	—
51	C₂×C₅×Dic₆	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
55	C₅×#217	—	2	1	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₅×Dic₃⋊C₄	—	2	4	no	—
60	C₅×Dic₃⋊C₄	—	2	1	no	—
61	C₄×C₅×Dic₃	—	4	2	no	—
62	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
65	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	#5596	C₂×C₅	1	1	yes	characteristic
68	#4718	C₂×C₅	1	1	yes	characteristic, complemented
69	#4649	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#327	C₂×C₅	1	1	yes	characteristic, complemented
71	#4537	C₂×C₅	1	1	yes	characteristic, complemented
72	#4470	C₂×C₅	1	1	yes	characteristic, complemented
73	#4451	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₅×#41	—	6	1	no	—
75	C₅×C₄⋊Q₈	—	3	1	no	—
76	C₅×#127	—	3	1	no	—
77	C₅×#124	—	6	1	no	—
78	C₅×#121	—	3	1	no	—
79	C₅×#121	—	6	1	no	—
80	C₅×#121	C₂×D₃	1	1	yes	characteristic
81	C₄×C₅×D₄	—	3	1	no	—
82	C₄×C₅×D₄	—	3	1	no	—
83	C₄×C₅×D₄	—	6	1	no	—
84	C₂×C₅×C₄⋊C₄	—	6	1	no	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×C₄²×C₅	—	6	1	no	—
87	C₅×C₄⋊C₈	—	6	1	no	—
88	C₅×C₂²⋊C₈	—	3	1	no	—
89	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
90	C₄×C₅×C₈	—	6	1	no	—
91	C₅×#95	—	3	1	no	—
92	C₅×#95	C₂×D₃	1	1	yes	characteristic
93	#1502	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	1	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	1	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₃×C₅×D₄	—	4	1	no	—
99	C₃×C₅×D₄	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₅×#67	—	4	1	no	—
108	C₅×#67	—	4	1	no	—
109	C₅×#67	—	4	2	no	—
110	C₅×#67	—	4	2	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₂×C₅×Dic₃	—	4	2	no	—
117	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₅×Dic₃	D₈	1	2	yes	—
122	C₂×C₅×Dic₃	SD₁₆	1	2	yes	—
123	C₅×D₁₂	—	4	1	no	—
124	C₄×C₅×D₃	—	4	2	no	—
125	C₅×Dic₆	—	4	2	no	—
126	C₃×C₅×C₈	—	4	1	no	—
127	C₅×C₃⋊C₈	—	4	1	no	—
128	C₂×#237	—	2	1	no	—
129	C₃×#121	C₂²×C₅	1	1	yes	characteristic
130	#940	C₄×C₅	1	1	yes	characteristic, complemented
131	#939	—	2	1	no	—
132	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic, complemented
133	#930	C₂²×C₅	1	1	yes	characteristic
134	C₂×Dic₃⋊C₄	—	2	1	no	—
135	C₂×C₄×Dic₃	—	2	1	no	—
136	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
137	#893	C₄×C₅	1	1	yes	characteristic, complemented
138	#888	C₄×C₅	1	1	yes	characteristic, complemented
139	#885	—	2	1	no	—
140	#67⋊C₄	—	2	1	no	—
141	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
142	C₃×#95	C₂²×C₅	1	1	yes	characteristic
143	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
144	#830	C₂²×C₅	1	1	yes	characteristic
145	Dic₃⋊C₈	—	2	1	no	—
146	C₈×Dic₃	—	2	1	no	—
147	C₅×#41	—	12	2	no	—
148	C₅×#41	—	12	2	no	—
149	C₂×C₅×Q₈	—	6	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	3	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂×C₅×D₄	—	6	1	no	—
155	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	6	1	no	—
165	C₅×C₄⋊C₄	—	3	1	no	—
166	C₅×C₄⋊C₄	—	6	1	no	—
167	C₅×C₄⋊C₄	—	6	4	no	—
168	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	6	1	no	—
171	C₅×C₂²⋊C₄	—	6	1	no	—
172	C₅×C₂²⋊C₄	—	6	1	no	—
173	C₄²×C₅	—	3	1	no	—
174	C₄²×C₅	—	3	1	no	—
175	C₄²×C₅	—	3	1	no	—
176	C₄²×C₅	—	3	1	no	—
177	C₄²×C₅	—	12	2	no	—
178	#532	—	3	1	no	—
179	#431	—	3	1	no	—
180	C₄×C₄⋊C₄	—	3	1	no	—
181	#327	—	3	1	no	—
182	#327	—	3	1	no	—
183	#327	—	3	1	no	—
184	#327	C₅×D₃	1	1	yes	characteristic, complemented
185	C₂²×C₃×C₅	—	2	1	no	—
186	C₂²×C₃×C₅	—	2	1	no	—
187	C₂²×C₃×C₅	—	4	1	no	—
188	C₂²×C₃×C₅	—	4	1	no	—
189	C₂²×C₃×C₅	—	4	1	no	—
190	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
193	C₂×C₅×D₃	—	4	1	no	—
194	C₂×C₅×D₃	—	4	1	no	—
195	C₂×C₅×D₃	—	4	1	no	—
196	C₃×C₄×C₅	—	2	1	no	—
197	C₃×C₄×C₅	—	2	1	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	—	4	1	no	—
200	C₅×Dic₃	—	2	1	no	—
201	C₅×Dic₃	—	4	2	no	—
202	C₅×Dic₃	—	4	1	no	—
203	C₅×Dic₃	#102	1	2	yes	—
204	C₅×Dic₃	#102	1	2	yes	—
205	C₅×Dic₃	#104	1	2	yes	—
206	C₂×C₃×D₄	—	2	1	no	—
207	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂×#67	—	2	1	no	—
211	C₂×#67	—	2	1	no	—
212	C₂×#67	—	2	1	no	—
213	C₂²×Dic₃	—	2	1	no	—
214	C₂²×Dic₃	—	2	1	no	—
215	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
216	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
217	#237	—	4	2	no	—
218	#237	—	4	2	no	—
219	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄×D₃	—	2	1	no	—
221	C₂×Dic₆	—	2	1	no	—
222	C₂×C₃×C₈	—	2	1	no	—
223	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
224	C₃×C₂²⋊C₄	—	2	1	no	—
225	#217	—	2	1	no	—
226	(C₂×D₃)⋊C₄	—	2	1	no	—
227	(C₂×D₃)⋊C₄	—	2	1	no	—
228	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
229	Dic₃⋊C₄	—	2	4	no	—
230	Dic₃⋊C₄	—	2	1	no	—
231	C₄×Dic₃	—	4	2	no	—
232	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
233	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
234	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
235	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂³×C₅	—	2	1	no	—
238	C₂³×C₅	—	6	1	no	—
239	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
240	C₅×Q₈	—	12	2	no	—
241	C₅×D₄	—	4	1	no	—
242	C₅×D₄	—	4	1	no	—
243	C₅×D₄	—	4	1	no	—
244	C₅×D₄	—	12	1	no	—
245	C₅×D₄	—	12	2	no	—
246	C₅×D₄	—	12	2	no	—
247	C₅×D₄	—	12	1	no	—
248	C₅×D₄	—	12	1	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	3	1	no	—
252	C₂×C₄×C₅	—	3	1	no	—
253	C₂×C₄×C₅	—	3	1	no	—
254	C₂×C₄×C₅	—	3	2	no	—
255	C₂×C₄×C₅	—	3	2	no	—
256	C₂×C₄×C₅	—	3	1	no	—
257	C₂×C₄×C₅	—	4	1	no	—
258	C₂×C₄×C₅	—	4	1	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	6	2	no	—
262	C₂×C₄×C₅	—	6	1	no	—
263	C₂×C₄×C₅	—	12	2	no	—
264	C₂×C₄×C₅	—	12	2	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	—	12	1	no	—
267	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
268	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	12	1	no	—
271	C₂×#41	—	6	1	no	—
272	C₄⋊Q₈	—	3	1	no	—
273	#127	—	3	1	no	—
274	#124	—	6	1	no	—
275	#121	—	3	1	no	—
276	#121	—	6	1	no	—
277	#121	C₂×C₅×D₃	1	1	yes	characteristic
278	C₄×D₄	—	3	1	no	—
279	C₄×D₄	—	3	1	no	—
280	C₄×D₄	—	6	1	no	—
281	C₂×C₄⋊C₄	—	6	1	no	—
282	C₂×C₄²	—	3	1	no	—
283	C₂×C₄²	—	6	1	no	—
284	C₄⋊C₈	—	6	1	no	—
285	C₂²⋊C₈	—	3	1	no	—
286	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
287	C₄×C₈	—	6	1	no	—
288	#95	—	3	1	no	—
289	#95	C₂×C₅×D₃	1	1	yes	characteristic
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	—	2	1	no	—
292	C₂×C₃×C₅	—	8	1	no	—
293	C₂×C₃×C₅	#410	1	1	yes	characteristic
294	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
295	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
296	C₅×D₃	—	8	1	no	—
297	C₂³×C₃	—	2	1	no	—
298	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂²×D₃	—	2	1	no	—
300	C₃×D₄	—	4	1	no	—
301	C₃×D₄	—	4	1	no	—
302	C₃×D₄	—	4	1	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	4	1	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	#67	—	4	1	no	—
311	#67	—	4	1	no	—
312	#67	—	4	2	no	—
313	#67	—	4	2	no	—
314	C₂×Dic₃	—	2	2	no	—
315	C₂×Dic₃	—	2	2	no	—
316	C₂×Dic₃	—	2	1	no	—
317	C₂×Dic₃	—	4	1	no	—
318	C₂×Dic₃	—	4	1	no	—
319	C₂×Dic₃	—	4	2	no	—
320	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
324	C₂×Dic₃	C₅×D₈	1	2	yes	—
325	C₂×Dic₃	C₅×SD₁₆	1	2	yes	—
326	D₁₂	—	4	1	no	—
327	C₄×D₃	—	4	2	no	—
328	Dic₆	—	4	2	no	—
329	C₃×C₈	—	4	1	no	—
330	C₃⋊C₈	—	4	1	no	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	4	1	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	—	4	1	no	—
336	C₂²×C₅	—	12	1	no	—
337	C₂²×C₅	—	12	1	no	—
338	C₂²×C₅	—	12	1	no	—
339	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
341	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	3	2	no	—
345	C₄×C₅	—	3	2	no	—
346	C₄×C₅	—	3	2	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	—	4	1	no	—
349	C₄×C₅	—	6	1	no	—
350	C₄×C₅	—	12	2	no	—
351	C₄×C₅	—	12	1	no	—
352	#41	—	12	2	no	—
353	#41	—	12	2	no	—
354	C₂×Q₈	—	6	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	3	1	no	—
357	C₂×D₄	—	6	1	no	—
358	C₂×D₄	—	6	1	no	—
359	C₂×D₄	—	6	1	no	—
360	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	3	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	6	1	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	6	1	no	—
370	C₄⋊C₄	—	3	1	no	—
371	C₄⋊C₄	—	6	1	no	—
372	C₄⋊C₄	—	6	4	no	—
373	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	6	1	no	—
376	C₂²⋊C₄	—	6	1	no	—
377	C₂²⋊C₄	—	6	1	no	—
378	C₄²	—	3	1	no	—
379	C₄²	—	3	1	no	—
380	C₄²	—	3	1	no	—
381	C₄²	—	3	1	no	—
382	C₄²	—	12	2	no	—
383	C₃×C₅	#1502	1	1	yes	characteristic, complemented, Hall
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	1	no	—
386	C₂²×C₃	—	4	1	no	—
387	C₂²×C₃	—	4	1	no	—
388	C₂²×C₃	—	4	1	no	—
389	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
391	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
392	C₂×D₃	—	4	1	no	—
393	C₂×D₃	—	4	1	no	—
394	C₂×D₃	—	4	1	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	4	2	no	—
398	C₃×C₄	—	4	1	no	—
399	Dic₃	—	2	1	no	—
400	Dic₃	—	4	2	no	—
401	Dic₃	—	4	1	no	—
402	Dic₃	C₅×#102	1	2	yes	—
403	Dic₃	C₅×#102	1	2	yes	—
404	Dic₃	C₅×#104	1	2	yes	—
405	C₂×C₅	—	2	1	no	—
406	C₂×C₅	—	2	1	no	—
407	C₂×C₅	—	8	1	no	—
408	C₂×C₅	—	24	1	no	—
409	C₂×C₅	#4740	1	1	yes	characteristic
410	C₂×C₅	D₃×#102	1	1	yes	characteristic
411	C₂×C₅	D₃×#104	1	1	yes	characteristic
412	C₂³	—	2	1	no	—
413	C₂³	—	6	1	no	—
414	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
415	Q₈	—	12	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	D₄	—	12	1	no	—
420	D₄	—	12	2	no	—
421	D₄	—	12	2	no	—
422	D₄	—	12	1	no	—
423	D₄	—	12	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	3	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	6	2	no	—
437	C₂×C₄	—	6	1	no	—
438	C₂×C₄	—	12	2	no	—
439	C₂×C₄	—	12	2	no	—
440	C₂×C₄	—	12	1	no	—
441	C₂×C₄	—	12	1	no	—
442	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
443	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
444	C₈	—	4	1	no	—
445	C₈	—	12	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	8	1	no	—
449	C₂×C₃	C₅×#410	1	1	yes	characteristic
450	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
451	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
452	D₃	—	8	1	no	—
453	C₅	#68277	1	1	yes	characteristic, direct product factor, Sylow
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	12	1	no	—
460	C₂²	—	12	1	no	—
461	C₂²	—	12	1	no	—
462	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
464	C₂²	C₅×D₃×SD₁₆	1	1	yes	characteristic
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	3	2	no	—
468	C₄	—	3	2	no	—
469	C₄	—	3	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	1	no	—
472	C₄	—	6	1	no	—
473	C₄	—	12	2	no	—
474	C₄	—	12	1	no	—
475	C₃	C₅×#1502	1	1	yes	characteristic, complemented, Sylow
476	C₂	—	2	1	no	—
477	C₂	—	2	1	no	—
478	C₂	—	8	1	no	—
479	C₂	—	24	1	no	—
480	C₂	C₅×#4740	1	1	yes	characteristic
481	C₂	C₅×D₃×#102	1	1	yes	characteristic
482	C₂	C₅×D₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#327	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5596	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#327	D₃
hypocenter	C₃	C₅×#1502
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#327

Complements

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

N	H ≅ G/N	type
2. C₅×#4718	C₂	semidirect
3. C₅×#4649	C₂	semidirect
4. C₃×C₅×#327	C₂	semidirect
5. C₅×#4537	C₂	semidirect
6. C₅×#4470	C₂	semidirect
7. C₅×#4451	C₂	semidirect
11. C₅×#940	C₄	semidirect
13. C₅×D₄×Dic₃	C₄	semidirect
18. C₅×#893	C₄	semidirect
19. C₅×#888	C₄	semidirect
28. #68277	C₅	direct (N × H)
35. C₅×#327	D₃	semidirect
68. #4718	C₂×C₅	semidirect
69. #4649	C₂×C₅	semidirect
70. C₃×#327	C₂×C₅	semidirect
71. #4537	C₂×C₅	semidirect
72. #4470	C₂×C₅	semidirect
73. #4451	C₂×C₅	semidirect
130. #940	C₄×C₅	semidirect
132. D₄×Dic₃	C₄×C₅	semidirect
137. #893	C₄×C₅	semidirect
138. #888	C₄×C₅	semidirect
184. #327	C₅×D₃	semidirect
383. C₃×C₅	#1502	semidirect
453. C₅	#68277	direct (N × H)
475. C₃	C₅×#1502	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5596	2
C₅×#4718	2
C₅×#4649	2
C₃×C₅×#327	2
C₅×#4537	2
C₅×#4470	2
C₅×#4451	2
C₅×#1502	3
#68277	5

Subgroups — C5×#68277 #14282872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68277 #14282872