Subgroups — C₅×#81059 #14430228

Order 1920.

776 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	C₅×#5728	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5091	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5007	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4860	C₂	1	2	yes	maximal, complemented
7	C₅×#4857	C₂	1	2	yes	maximal, complemented
8	C₅×#4851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4772	C₂	1	2	yes	maximal
11	C₅×#4763	C₂	1	2	yes	maximal, complemented
12	C₅×#3076	—	3	1	no	maximal, Hall
13	C₂×C₅×#237	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#946	—	2	1	no	—
17	C₅×Q₈×Dic₃	—	2	1	no	—
18	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₄×C₅×#67	—	2	1	no	—
20	C₂×C₄×C₅×Dic₃	—	2	1	no	—
21	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
22	C₅×#897	—	2	1	no	—
23	C₅×#892	C₂²	1	2	yes	—
24	C₅×#892	C₂²	1	1	yes	characteristic
25	C₅×#890	C₂²	1	2	yes	—
26	C₅×#887	—	2	1	no	—
27	C₅×#887	C₂²	1	1	yes	characteristic
28	C₅×#67⋊C₄	—	2	1	no	—
29	C₅×#877	—	2	1	no	—
30	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
31	C₅×#869	C₂²	1	1	yes	characteristic
32	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
33	C₃×C₅×#106	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₅×#832	C₂²	1	2	yes	—
37	C₅×#817	C₂²	1	2	yes	—
38	C₅×#816	C₂²	1	2	yes	—
39	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
40	C₅×#810	C₂²	1	2	yes	—
41	C₅×#807	C₂²	1	2	yes	—
42	C₅×#807	C₂²	1	2	yes	—
43	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
44	#81059	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	—	3	1	no	—
46	C₄×C₅×#41	—	3	1	no	—
47	C₅×#479	—	3	2	no	—
48	C₅×#478	—	3	2	no	—
49	C₅×#477	—	3	1	no	—
50	C₅×#476	D₃	1	1	yes	characteristic, complemented
51	C₅×#475	—	3	1	no	—
52	C₅×#474	—	3	1	no	—
53	C₅×#427	—	3	2	no	—
54	C₂×C₅×C₄⋊C₈	—	3	1	no	—
55	C₅×#416	—	3	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂×C₅×#67	—	2	1	no	—
60	C₂²×C₅×Dic₃	—	2	1	no	—
61	C₂²×C₅×Dic₃	—	2	1	no	—
62	C₅×#237	—	2	2	no	—
63	C₅×#237	Q₈	1	4	yes	complemented
64	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₂×C₅×Dic₆	—	2	1	no	—
68	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#217	—	2	1	no	—
76	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	2	1	no	—
79	C₅×C₄⋊Dic₃	—	2	2	no	—
80	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
82	C₅×Dic₃⋊C₄	—	2	1	no	—
83	C₅×Dic₃⋊C₄	—	2	1	no	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₄×C₅×Dic₃	—	2	1	no	—
86	C₄×C₅×Dic₃	—	2	1	no	—
87	C₄×C₅×Dic₃	—	2	1	no	—
88	C₄×C₅×Dic₃	—	2	2	no	—
89	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
93	C₅×D₃×C₈	—	2	4	no	—
94	#5728	C₂×C₅	1	1	yes	characteristic, complemented
95	C₄×#237	C₂×C₅	1	1	yes	characteristic
96	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
97	#5091	C₂×C₅	1	1	yes	characteristic, complemented
98	#5007	C₂×C₅	1	1	yes	characteristic, complemented
99	#4860	C₂×C₅	1	2	yes	complemented
100	#4857	C₂×C₅	1	2	yes	complemented
101	#4851	C₂×C₅	1	1	yes	characteristic, complemented
102	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
103	#4772	C₂×C₅	1	2	yes	—
104	#4763	C₂×C₅	1	2	yes	complemented
105	C₂×C₅×#41	—	3	1	no	—
106	C₂²×C₅×C₈	—	3	2	no	—
107	C₅×C₄⋊Q₈	—	3	1	no	—
108	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
109	C₅×#125	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	6	1	no	—
111	C₅×C₂²⋊Q₈	—	6	1	no	—
112	C₄×C₅×Q₈	—	3	1	no	—
113	C₄×C₅×Q₈	—	3	1	no	—
114	C₄×C₅×Q₈	—	6	1	no	—
115	C₄×C₅×Q₈	—	6	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	6	1	no	—
118	C₄×C₅×D₄	—	6	1	no	—
119	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
120	C₅×#117	—	3	2	no	—
121	C₅×#117	—	3	1	no	—
122	C₅×#117	—	6	1	no	—
123	C₂×C₄²×C₅	—	3	1	no	—
124	C₂×C₄²×C₅	—	6	1	no	—
125	C₅×#107	—	3	2	no	—
126	C₅×#107	—	3	2	no	—
127	C₅×#106	—	3	2	no	—
128	C₅×#106	C₂×D₃	1	2	yes	—
129	C₅×C₄⋊C₈	—	3	2	no	—
130	C₅×C₄⋊C₈	—	3	1	no	—
131	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
132	C₅×#103	—	3	2	no	—
133	C₅×#103	—	3	2	no	—
134	C₅×#102	—	3	2	no	—
135	C₅×#102	C₂×D₃	1	2	yes	—
136	#3076	—	3	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×#67	—	2	4	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	—	2	4	no	—
151	C₂×C₅×Dic₃	—	2	1	no	—
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₂×C₅×Dic₃	—	4	2	no	—
154	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
157	C₄×C₅×D₃	—	2	2	no	—
158	C₄×C₅×D₃	—	4	1	no	—
159	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
160	C₄×C₅×D₃	#41	1	2	yes	—
161	C₅×Dic₆	—	2	1	no	—
162	C₅×Dic₆	—	4	2	no	—
163	C₅×Dic₆	C₂×Q₈	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₅×C₃⋊C₈	—	2	2	no	—
166	C₂×#237	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
169	#946	—	2	1	no	—
170	Q₈×Dic₃	—	2	1	no	—
171	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
172	C₄×#67	—	2	1	no	—
173	C₂×C₄×Dic₃	—	2	1	no	—
174	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
175	#897	—	2	1	no	—
176	#892	C₂²×C₅	1	2	yes	—
177	#892	C₂²×C₅	1	1	yes	characteristic
178	#890	C₂²×C₅	1	2	yes	—
179	#887	—	2	1	no	—
180	#887	C₂²×C₅	1	1	yes	characteristic
181	#67⋊C₄	—	2	1	no	—
182	#877	—	2	1	no	—
183	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
184	#869	C₂²×C₅	1	1	yes	characteristic
185	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
186	C₃×#106	C₂²×C₅	1	2	yes	—
187	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	C₃×#102	C₂²×C₅	1	2	yes	—
189	#832	C₂²×C₅	1	2	yes	—
190	#817	C₂²×C₅	1	2	yes	—
191	#816	C₂²×C₅	1	2	yes	—
192	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
193	#810	C₂²×C₅	1	2	yes	—
194	#807	C₂²×C₅	1	2	yes	—
195	#807	C₂²×C₅	1	2	yes	—
196	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
197	C₅×#41	—	3	4	no	—
198	C₅×#41	—	6	2	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	—	3	1	no	—
201	C₂×C₅×Q₈	—	6	1	no	—
202	C₂×C₅×D₄	—	6	1	no	—
203	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	—	6	1	no	—
210	C₂×C₅×C₈	—	3	2	no	—
211	C₂×C₅×C₈	—	6	4	no	—
212	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	3	1	no	—
215	C₅×C₄⋊C₄	—	3	2	no	—
216	C₅×C₄⋊C₄	—	6	1	no	—
217	C₅×C₄⋊C₄	—	6	2	no	—
218	C₅×C₄⋊C₄	—	6	2	no	—
219	C₅×C₄⋊C₄	—	6	1	no	—
220	C₅×C₄⋊C₄	—	6	1	no	—
221	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	6	1	no	—
225	C₅×C₂²⋊C₄	—	6	2	no	—
226	C₅×C₂²⋊C₄	—	6	1	no	—
227	C₄²×C₅	—	3	1	no	—
228	C₄²×C₅	—	3	1	no	—
229	C₄²×C₅	—	3	1	no	—
230	C₄²×C₅	—	6	1	no	—
231	C₄²×C₅	—	6	1	no	—
232	C₄²×C₅	—	6	2	no	—
233	C₄²×C₅	—	6	1	no	—
234	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
235	#533	—	3	1	no	—
236	C₄×#41	—	3	1	no	—
237	#479	—	3	2	no	—
238	#478	—	3	2	no	—
239	#477	—	3	1	no	—
240	#476	C₅×D₃	1	1	yes	characteristic, complemented
241	#475	—	3	1	no	—
242	#474	—	3	1	no	—
243	#427	—	3	2	no	—
244	C₂×C₄⋊C₈	—	3	1	no	—
245	#416	—	3	2	no	—
246	C₂²×C₃×C₅	—	2	2	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	—	4	1	no	—
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	1	no	—
251	C₂×C₅×D₃	—	2	1	no	—
252	C₂×C₅×D₃	C₂²⋊Q₈	1	2	yes	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	—	4	2	no	—
256	C₃×C₄×C₅	#135	1	2	yes	—
257	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
258	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₅×Dic₃	—	2	2	no	—
260	C₅×Dic₃	—	2	1	no	—
261	C₅×Dic₃	—	2	1	no	—
262	C₅×Dic₃	—	4	2	no	—
263	C₅×Dic₃	—	4	1	no	—
264	C₅×Dic₃	C₂²⋊Q₈	1	2	yes	—
265	C₂×C₃×Q₈	—	2	1	no	—
266	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂×#67	—	2	1	no	—
269	C₂²×Dic₃	—	2	1	no	—
270	C₂²×Dic₃	—	2	1	no	—
271	#237	—	2	2	no	—
272	#237	C₅×Q₈	1	4	yes	complemented
273	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
274	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
276	C₂×Dic₆	—	2	1	no	—
277	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
284	#217	—	2	1	no	—
285	(C₂×D₃)⋊C₄	—	2	1	no	—
286	(C₂×D₃)⋊C₄	—	2	2	no	—
287	C₄⋊Dic₃	—	2	1	no	—
288	C₄⋊Dic₃	—	2	2	no	—
289	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
290	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
291	Dic₃⋊C₄	—	2	1	no	—
292	Dic₃⋊C₄	—	2	1	no	—
293	Dic₃⋊C₄	—	2	2	no	—
294	C₄×Dic₃	—	2	1	no	—
295	C₄×Dic₃	—	2	1	no	—
296	C₄×Dic₃	—	2	1	no	—
297	C₄×Dic₃	—	2	2	no	—
298	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
299	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
300	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
301	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
302	D₃×C₈	—	2	4	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	3	1	no	—
305	C₅×Q₈	—	3	2	no	—
306	C₅×Q₈	—	4	2	no	—
307	C₅×Q₈	—	6	1	no	—
308	C₅×Q₈	—	12	2	no	—
309	C₅×D₄	—	2	1	no	—
310	C₅×D₄	—	6	4	no	—
311	C₅×D₄	D₃×Q₈	1	2	yes	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	3	1	no	—
315	C₂×C₄×C₅	—	3	2	no	—
316	C₂×C₄×C₅	—	3	2	no	—
317	C₂×C₄×C₅	—	3	1	no	—
318	C₂×C₄×C₅	—	3	1	no	—
319	C₂×C₄×C₅	—	4	2	no	—
320	C₂×C₄×C₅	—	6	4	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	6	1	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	12	1	no	—
326	C₂×C₄×C₅	—	12	2	no	—
327	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	6	2	no	—
332	C₂×#41	—	3	1	no	—
333	C₂²×C₈	—	3	2	no	—
334	C₄⋊Q₈	—	3	1	no	—
335	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
336	#125	—	3	2	no	—
337	C₂²⋊Q₈	—	6	1	no	—
338	C₂²⋊Q₈	—	6	1	no	—
339	C₄×Q₈	—	3	1	no	—
340	C₄×Q₈	—	3	1	no	—
341	C₄×Q₈	—	6	1	no	—
342	C₄×Q₈	—	6	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	—	6	1	no	—
345	C₄×D₄	—	6	1	no	—
346	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
347	#117	—	3	1	no	—
348	#117	—	3	2	no	—
349	#117	—	6	1	no	—
350	C₂×C₄²	—	3	1	no	—
351	C₂×C₄²	—	6	1	no	—
352	#107	—	3	2	no	—
353	#107	—	3	2	no	—
354	#106	—	3	2	no	—
355	#106	C₂×C₅×D₃	1	2	yes	—
356	C₄⋊C₈	—	3	2	no	—
357	C₄⋊C₈	—	3	1	no	—
358	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
359	#103	—	3	2	no	—
360	#103	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	C₂×C₅×D₃	1	2	yes	—
363	C₂×C₃×C₅	—	4	2	no	—
364	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
366	C₂×C₃×C₅	#575	1	1	yes	characteristic
367	C₅×D₃	—	2	2	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
370	C₃×Q₈	—	4	2	no	—
371	C₃×D₄	—	2	1	no	—
372	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	4	2	no	—
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
379	#67	—	2	4	no	—
380	C₂×Dic₃	—	2	1	no	—
381	C₂×Dic₃	—	2	4	no	—
382	C₂×Dic₃	—	2	1	no	—
383	C₂×Dic₃	—	2	2	no	—
384	C₂×Dic₃	—	4	2	no	—
385	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
388	C₄×D₃	—	2	2	no	—
389	C₄×D₃	—	4	1	no	—
390	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
391	C₄×D₃	C₅×#41	1	2	yes	—
392	Dic₆	—	2	1	no	—
393	Dic₆	—	4	2	no	—
394	Dic₆	C₂×C₅×Q₈	1	2	yes	—
395	C₃×C₈	—	2	2	no	—
396	C₃⋊C₈	—	2	2	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	3	2	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	6	1	no	—
402	C₂²×C₅	—	6	1	no	—
403	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	3	2	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	6	1	no	—
409	C₄×C₅	—	6	1	no	—
410	C₄×C₅	—	6	2	no	—
411	C₄×C₅	—	12	2	no	—
412	C₄×C₅	—	12	1	no	—
413	C₄×C₅	#916	1	2	yes	—
414	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
415	C₄×C₅	D₃×#41	1	1	yes	characteristic
416	#41	—	3	4	no	—
417	#41	—	6	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	3	1	no	—
420	C₂×Q₈	—	6	1	no	—
421	C₂×D₄	—	6	1	no	—
422	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	3	1	no	—
425	C₂²×C₄	—	3	1	no	—
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	6	1	no	—
428	C₂²×C₄	—	6	1	no	—
429	C₂×C₈	—	3	2	no	—
430	C₂×C₈	—	6	4	no	—
431	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	3	2	no	—
434	C₄⋊C₄	—	3	1	no	—
435	C₄⋊C₄	—	6	1	no	—
436	C₄⋊C₄	—	6	2	no	—
437	C₄⋊C₄	—	6	2	no	—
438	C₄⋊C₄	—	6	1	no	—
439	C₄⋊C₄	—	6	1	no	—
440	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
441	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	6	1	no	—
444	C₂²⋊C₄	—	6	2	no	—
445	C₂²⋊C₄	—	6	1	no	—
446	C₄²	—	3	1	no	—
447	C₄²	—	3	1	no	—
448	C₄²	—	3	1	no	—
449	C₄²	—	6	1	no	—
450	C₄²	—	6	1	no	—
451	C₄²	—	6	2	no	—
452	C₄²	—	6	1	no	—
453	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×D₃	—	2	1	no	—
460	C₂×D₃	—	2	1	no	—
461	C₂×D₃	C₅×C₂²⋊Q₈	1	2	yes	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	4	1	no	—
464	C₃×C₄	—	4	2	no	—
465	C₃×C₄	C₅×#135	1	2	yes	—
466	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
467	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
468	Dic₃	—	2	2	no	—
469	Dic₃	—	2	1	no	—
470	Dic₃	—	2	1	no	—
471	Dic₃	—	4	2	no	—
472	Dic₃	—	4	1	no	—
473	Dic₃	C₅×C₂²⋊Q₈	1	2	yes	—
474	C₂×C₅	—	4	2	no	—
475	C₂×C₅	—	6	2	no	—
476	C₂×C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic
477	C₂×C₅	C₂×#916	1	1	yes	characteristic
478	C₂×C₅	#5773	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	3	1	no	—
481	Q₈	—	3	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	6	1	no	—
484	Q₈	—	12	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	6	4	no	—
487	D₄	C₅×D₃×Q₈	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	3	1	no	—
491	C₂×C₄	—	3	2	no	—
492	C₂×C₄	—	3	2	no	—
493	C₂×C₄	—	3	1	no	—
494	C₂×C₄	—	3	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	6	4	no	—
497	C₂×C₄	—	6	1	no	—
498	C₂×C₄	—	6	2	no	—
499	C₂×C₄	—	6	1	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	12	1	no	—
502	C₂×C₄	—	12	2	no	—
503	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
504	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
505	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	6	2	no	—
508	C₂×C₃	—	4	2	no	—
509	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
510	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
511	C₂×C₃	C₅×#575	1	1	yes	characteristic
512	D₃	—	2	2	no	—
513	C₅	#81059	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	3	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	6	1	no	—
519	C₂²	—	6	1	no	—
520	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
521	C₄	—	2	1	no	—
522	C₄	—	3	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	2	no	—
525	C₄	—	6	1	no	—
526	C₄	—	6	1	no	—
527	C₄	—	6	2	no	—
528	C₄	—	12	2	no	—
529	C₄	—	12	1	no	—
530	C₄	C₅×#916	1	2	yes	—
531	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
532	C₄	C₅×D₃×#41	1	1	yes	characteristic
533	C₃	C₅×#3076	1	1	yes	characteristic, complemented, Sylow
534	C₂	—	4	2	no	—
535	C₂	—	6	2	no	—
536	C₂	C₅×D₃×C₂²⋊Q₈	1	1	yes	characteristic
537	C₂	C₂×C₅×#916	1	1	yes	characteristic
538	C₂	C₅×#5773	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#476	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#237	C₂²
hypercenter	C₅×#476	D₃
hypocenter	C₃	C₅×#3076
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#476

Complements

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

N	H ≅ G/N	type
1. C₅×#5728	C₂	semidirect
3. C₃×C₅×#476	C₂	semidirect
4. C₅×#5091	C₂	semidirect
5. C₅×#5007	C₂	semidirect
6. C₅×#4860	C₂	semidirect
7. C₅×#4857	C₂	semidirect
8. C₅×#4851	C₂	semidirect
9. C₅×D₃×C₄⋊C₈	C₂	semidirect
11. C₅×#4763	C₂	semidirect
44. #81059	C₅	direct (N × H)
50. C₅×#476	D₃	semidirect
63. C₅×#237	Q₈	semidirect
94. #5728	C₂×C₅	semidirect
96. C₃×#476	C₂×C₅	semidirect
97. #5091	C₂×C₅	semidirect
98. #5007	C₂×C₅	semidirect
99. #4860	C₂×C₅	semidirect
100. #4857	C₂×C₅	semidirect
101. #4851	C₂×C₅	semidirect
102. D₃×C₄⋊C₈	C₂×C₅	semidirect
104. #4763	C₂×C₅	semidirect
240. #476	C₅×D₃	semidirect
272. #237	C₅×Q₈	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	#81059	direct (N × H)
533. C₃	C₅×#3076	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5728	2
C₄×C₅×#237	2
C₃×C₅×#476	2
C₅×#5091	2
C₅×#5007	2
C₅×#4860	2
C₅×#4857	2
C₅×#4851	2
C₅×D₃×C₄⋊C₈	2
C₅×#4772	2
C₅×#4763	2
C₅×#3076	3
#81059	5

Subgroups — C5×#81059 #14430228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81059 #14430228