Subgroups — C₅×#70833 #14283205

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5479	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4470	C₂	1	2	yes	maximal
5	C₅×#4467	C₂	1	2	yes	maximal, complemented
6	C₅×#1509	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₅×#930	C₂²	1	1	yes	characteristic
9	C₅×#929	—	2	1	no	—
10	C₄×C₅×#67	—	2	1	no	—
11	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
12	C₅×#924	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	—	2	1	no	—
14	C₅×#876	—	2	1	no	—
15	C₅×#875	C₄	1	1	yes	characteristic, complemented
16	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic, complemented
17	C₅×#872	—	2	1	no	—
18	C₅×#870	C₄	1	1	yes	characteristic, complemented
19	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic, complemented
20	C₃×C₅×C₄⋊C₈	—	2	1	no	—
21	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₃×C₅×#97	—	2	1	no	—
23	C₅×C₃⋊#95	C₂²	1	2	yes	—
24	#70833	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#529	—	3	1	no	—
26	C₅×#432	D₃	1	1	yes	characteristic, complemented
27	C₄×C₅×C₄⋊C₄	—	3	1	no	—
28	C₅×#328	—	3	2	no	—
29	C₅×#327	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂×C₅×#67	—	2	1	no	—
34	C₂²×C₅×Dic₃	—	2	2	no	—
35	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×C₅×D₃	—	2	1	no	—
37	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
43	C₅×#217	—	2	1	no	—
44	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
45	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
46	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
47	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
48	C₅×C₄⋊Dic₃	—	2	4	no	—
49	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×Dic₃⋊C₄	—	2	1	no	—
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₄×C₅×Dic₃	—	4	2	no	—
57	#5479	C₂×C₅	1	1	yes	characteristic
58	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
59	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
60	#4470	C₂×C₅	1	2	yes	—
61	#4467	C₂×C₅	1	2	yes	complemented
62	C₅×#126	—	6	1	no	—
63	C₅×#125	—	3	1	no	—
64	C₅×#124	—	3	1	no	—
65	C₅×#123	—	6	1	no	—
66	C₅×C₂²⋊Q₈	—	3	1	no	—
67	C₅×#121	—	3	1	no	—
68	C₄×C₅×Q₈	—	3	1	no	—
69	C₄×C₅×D₄	—	3	1	no	—
70	C₄×C₅×D₄	—	6	1	no	—
71	C₅×#117	—	6	1	no	—
72	C₂×C₅×C₄⋊C₄	—	6	1	no	—
73	C₂×C₄²×C₅	—	6	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	2	1	no	—
76	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
77	C₅×#97	—	2	1	no	—
78	C₅×#95	—	3	2	no	—
79	#1509	—	3	1	no	Sylow
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₅×#67	—	4	1	no	—
93	C₅×#67	—	4	1	no	—
94	C₂×C₅×Dic₃	—	2	4	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₂×C₅×Dic₃	—	2	1	no	—
97	C₂×C₅×Dic₃	—	2	1	no	—
98	C₂×C₅×Dic₃	—	4	2	no	—
99	C₂×C₅×Dic₃	—	4	2	no	—
100	C₅×D₁₂	—	4	1	no	—
101	C₄×C₅×D₃	—	4	2	no	—
102	C₅×Dic₆	—	4	1	no	—
103	C₃×C₅×C₈	—	4	2	no	—
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
105	#930	C₂²×C₅	1	1	yes	characteristic
106	#929	—	2	1	no	—
107	C₄×#67	—	2	1	no	—
108	C₂×C₄⋊Dic₃	—	2	1	no	—
109	#924	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₄×Dic₃	—	2	1	no	—
111	#876	—	2	1	no	—
112	#875	C₄×C₅	1	1	yes	characteristic, complemented
113	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic, complemented
114	#872	—	2	1	no	—
115	#870	C₄×C₅	1	1	yes	characteristic, complemented
116	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic, complemented
117	C₃×C₄⋊C₈	—	2	1	no	—
118	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
119	C₃×#97	—	2	1	no	—
120	C₃⋊#95	C₂²×C₅	1	2	yes	—
121	C₂×C₅×Q₈	—	3	1	no	—
122	C₂×C₅×D₄	—	3	1	no	—
123	C₂×C₅×D₄	—	6	1	no	—
124	C₂²×C₄×C₅	—	6	2	no	—
125	C₂²×C₄×C₅	—	6	1	no	—
126	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
127	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₅×C₈	—	2	2	no	—
130	C₅×C₄⋊C₄	—	3	1	no	—
131	C₅×C₄⋊C₄	—	3	1	no	—
132	C₅×C₄⋊C₄	—	6	4	no	—
133	C₅×C₄⋊C₄	—	6	1	no	—
134	C₅×C₄⋊C₄	—	6	1	no	—
135	C₅×C₄⋊C₄	—	6	1	no	—
136	C₅×C₄⋊C₄	—	6	1	no	—
137	C₅×C₂²⋊C₄	—	6	1	no	—
138	C₅×C₂²⋊C₄	—	6	1	no	—
139	C₅×C₂²⋊C₄	—	6	1	no	—
140	C₅×C₂²⋊C₄	—	6	1	no	—
141	C₅×C₂²⋊C₄	—	6	1	no	—
142	C₄²×C₅	—	6	1	no	—
143	C₄²×C₅	—	12	2	no	—
144	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
145	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
146	C₄²×C₅	#67	1	1	yes	characteristic
147	C₄²×C₅	#67	1	1	yes	characteristic
148	#529	—	3	1	no	—
149	#432	C₅×D₃	1	1	yes	characteristic, complemented
150	C₄×C₄⋊C₄	—	3	1	no	—
151	#328	—	3	2	no	—
152	#327	—	3	2	no	—
153	C₂²×C₃×C₅	—	2	1	no	—
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂²×C₃×C₅	#137	1	1	yes	characteristic
158	C₂×C₅×D₃	—	4	1	no	—
159	C₂×C₅×D₃	—	4	1	no	—
160	C₂×C₅×D₃	—	4	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	#104	1	2	yes	—
167	C₅×Dic₃	—	4	4	no	—
168	C₅×Dic₃	—	4	1	no	—
169	C₅×Dic₃	—	4	1	no	—
170	C₅×Dic₃	—	4	1	no	—
171	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂×#67	—	2	1	no	—
175	C₂²×Dic₃	—	2	2	no	—
176	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂×C₄×D₃	—	2	1	no	—
178	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
179	C₂×C₃×C₈	—	2	2	no	—
180	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
181	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
182	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
183	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
184	#217	—	2	1	no	—
185	(C₂×D₃)⋊C₄	—	2	1	no	—
186	(C₂×D₃)⋊C₄	—	2	1	no	—
187	(C₂×D₃)⋊C₄	—	2	1	no	—
188	(C₂×D₃)⋊C₄	—	2	1	no	—
189	C₄⋊Dic₃	—	2	4	no	—
190	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
191	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
192	Dic₃⋊C₄	—	2	1	no	—
193	Dic₃⋊C₄	—	2	1	no	—
194	Dic₃⋊C₄	—	2	1	no	—
195	Dic₃⋊C₄	—	2	1	no	—
196	C₄×Dic₃	—	2	1	no	—
197	C₄×Dic₃	—	4	2	no	—
198	C₂³×C₅	—	6	1	no	—
199	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
200	C₅×Q₈	—	12	1	no	—
201	C₅×D₄	—	12	1	no	—
202	C₅×D₄	—	12	1	no	—
203	C₅×D₄	—	12	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	6	4	no	—
209	C₂×C₄×C₅	—	6	1	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	6	1	no	—
212	C₂×C₄×C₅	—	12	2	no	—
213	C₂×C₄×C₅	—	12	2	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	4	2	no	—
222	#126	—	6	1	no	—
223	#125	—	3	1	no	—
224	#124	—	3	1	no	—
225	#123	—	6	1	no	—
226	C₂²⋊Q₈	—	3	1	no	—
227	#121	—	3	1	no	—
228	C₄×Q₈	—	3	1	no	—
229	C₄×D₄	—	3	1	no	—
230	C₄×D₄	—	6	1	no	—
231	#117	—	6	1	no	—
232	C₂×C₄⋊C₄	—	6	1	no	—
233	C₂×C₄²	—	6	1	no	—
234	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄⋊C₈	—	2	1	no	—
236	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
237	#97	—	2	1	no	—
238	#95	—	3	2	no	—
239	C₂×C₃×C₅	—	2	1	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	#410	1	1	yes	characteristic
242	C₂×C₃×C₅	#417	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
244	C₅×D₃	—	8	1	no	—
245	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
246	C₂²×D₃	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	#67	—	4	1	no	—
258	#67	—	4	1	no	—
259	C₂×Dic₃	—	2	4	no	—
260	C₂×Dic₃	—	2	1	no	—
261	C₂×Dic₃	—	2	1	no	—
262	C₂×Dic₃	—	2	1	no	—
263	C₂×Dic₃	—	4	2	no	—
264	C₂×Dic₃	—	4	2	no	—
265	D₁₂	—	4	1	no	—
266	C₄×D₃	—	4	2	no	—
267	Dic₆	—	4	1	no	—
268	C₃×C₈	—	4	2	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	12	1	no	—
272	C₂²×C₅	—	12	1	no	—
273	C₂²×C₅	—	12	1	no	—
274	C₂²×C₅	#908	1	1	yes	characteristic
275	C₂²×C₅	#909	1	1	yes	characteristic
276	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	12	4	no	—
283	C₄×C₅	—	12	1	no	—
284	C₄×C₅	—	12	1	no	—
285	C₄×C₅	—	12	1	no	—
286	C₄×C₅	#825	1	2	yes	—
287	C₂×Q₈	—	3	1	no	—
288	C₂×D₄	—	3	1	no	—
289	C₂×D₄	—	6	1	no	—
290	C₂²×C₄	—	6	2	no	—
291	C₂²×C₄	—	6	1	no	—
292	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
293	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₂×C₈	—	2	2	no	—
296	C₄⋊C₄	—	3	1	no	—
297	C₄⋊C₄	—	3	1	no	—
298	C₄⋊C₄	—	6	4	no	—
299	C₄⋊C₄	—	6	1	no	—
300	C₄⋊C₄	—	6	1	no	—
301	C₄⋊C₄	—	6	1	no	—
302	C₄⋊C₄	—	6	1	no	—
303	C₂²⋊C₄	—	6	1	no	—
304	C₂²⋊C₄	—	6	1	no	—
305	C₂²⋊C₄	—	6	1	no	—
306	C₂²⋊C₄	—	6	1	no	—
307	C₂²⋊C₄	—	6	1	no	—
308	C₄²	—	6	1	no	—
309	C₄²	—	12	2	no	—
310	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
311	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
312	C₄²	C₅×#67	1	1	yes	characteristic
313	C₄²	C₅×#67	1	1	yes	characteristic
314	C₃×C₅	#1509	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂²×C₃	C₅×#137	1	1	yes	characteristic
320	C₂×D₃	—	4	1	no	—
321	C₂×D₃	—	4	1	no	—
322	C₂×D₃	—	4	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	C₅×#104	1	2	yes	—
329	Dic₃	—	4	4	no	—
330	Dic₃	—	4	1	no	—
331	Dic₃	—	4	1	no	—
332	Dic₃	—	4	1	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	2	1	no	—
335	C₂×C₅	—	24	1	no	—
336	C₂×C₅	#5006	1	1	yes	characteristic
337	C₂×C₅	#5133	1	1	yes	characteristic
338	C₂×C₅	C₂×#825	1	1	yes	characteristic
339	C₂³	—	6	1	no	—
340	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
341	Q₈	—	12	1	no	—
342	D₄	—	12	1	no	—
343	D₄	—	12	1	no	—
344	D₄	—	12	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	6	4	no	—
350	C₂×C₄	—	6	1	no	—
351	C₂×C₄	—	6	1	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	—	12	2	no	—
354	C₂×C₄	—	12	2	no	—
355	C₂×C₄	—	12	2	no	—
356	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	C₅×#410	1	1	yes	characteristic
366	C₂×C₃	C₅×#417	1	1	yes	characteristic
367	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
368	D₃	—	8	1	no	—
369	C₅	#70833	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	12	1	no	—
373	C₂²	—	12	1	no	—
374	C₂²	—	12	1	no	—
375	C₂²	C₅×#908	1	1	yes	characteristic
376	C₂²	C₅×#909	1	1	yes	characteristic
377	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	12	4	no	—
384	C₄	—	12	1	no	—
385	C₄	—	12	1	no	—
386	C₄	—	12	1	no	—
387	C₄	C₅×#825	1	2	yes	—
388	C₃	C₅×#1509	1	1	yes	characteristic, complemented, Sylow
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	24	1	no	—
392	C₂	C₅×#5006	1	1	yes	characteristic
393	C₂	C₅×#5133	1	1	yes	characteristic
394	C₂	C₂×C₅×#825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#432	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#930	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#432	D₃
hypocenter	C₃	C₅×#1509
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#432

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#432	C₂	semidirect
3. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
5. C₅×#4467	C₂	semidirect
15. C₅×#875	C₄	semidirect
16. C₄×C₅×D₁₂	C₄	semidirect
18. C₅×#870	C₄	semidirect
19. C₄×C₅×Dic₆	C₄	semidirect
24. #70833	C₅	direct (N × H)
26. C₅×#432	D₃	semidirect
58. C₃×#432	C₂×C₅	semidirect
59. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
61. #4467	C₂×C₅	semidirect
112. #875	C₄×C₅	semidirect
113. C₄×D₁₂	C₄×C₅	semidirect
115. #870	C₄×C₅	semidirect
116. C₄×Dic₆	C₄×C₅	semidirect
149. #432	C₅×D₃	semidirect
314. C₃×C₅	#1509	semidirect
369. C₅	#70833	direct (N × H)
388. C₃	C₅×#1509	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
C₃×C₅×#432	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4470	2
C₅×#4467	2
C₅×#1509	3
#70833	5

Subgroups — C5×#70833 #14283205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70833 #14283205