Subgroups — C₅×#84099 #14412629

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₅×#5827	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	3	yes	maximal, complemented
5	C₅×#5232	C₂	1	3	yes	maximal, complemented
6	C₅×#5215	C₂	1	3	yes	maximal, complemented
7	C₂×C₅×#832	C₂	1	3	yes	maximal, complemented
8	C₅×#2897	—	3	1	no	maximal, Hall
9	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
10	C₃×C₅×H(5,𝔽₂)	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×#41	—	2	1	no	—
12	C₂×C₃×C₅×#41	C₂²	1	3	yes	—
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	—	2	3	no	—
15	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
16	C₅×#948	—	2	4	no	—
17	C₅×Q₈×Dic₃	—	2	1	no	—
18	C₅×D₄×Dic₃	—	2	3	no	—
19	C₅×#926	C₂²	1	3	yes	complemented
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	complemented
21	C₂×C₅×#208	C₂²	1	3	yes	complemented
22	C₂²×C₅×C₃⋊C₈	C₂²	1	3	yes	complemented
23	C₅×#835	C₂²	1	3	yes	complemented
24	C₅×#835	C₂²	1	1	yes	characteristic, complemented
25	C₅×#832	C₂²	1	3	yes	complemented
26	C₅×#832	C₂²	1	6	yes	complemented
27	C₅×#832	C₂²	1	3	yes	complemented
28	#84099	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×H(5,𝔽₂)	D₃	1	1	yes	characteristic
30	C₂×C₅×#131	—	3	1	no	—
31	C₅×#520	—	3	1	no	—
32	C₅×#418	—	3	3	no	—
33	C₅×#417	—	3	3	no	—
34	C₅×#416	—	3	3	no	—
35	C₂×C₅×#102	—	3	3	no	—
36	C₂⁴×C₃×C₅	—	2	3	no	—
37	C₃×C₅×#41	—	2	8	no	—
38	C₃×C₅×#41	—	2	6	no	—
39	C₃×C₅×#41	C₂×C₄	1	4	yes	—
40	C₃×C₅×#41	C₂×C₄	1	12	yes	complemented
41	C₃×C₅×#41	D₄	1	4	yes	—
42	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×D₄	—	2	3	no	—
45	C₂×C₃×C₅×D₄	—	2	24	no	—
46	C₂×C₃×C₅×D₄	—	2	3	no	—
47	C₂×C₃×C₅×D₄	—	2	6	no	—
48	C₂×C₃×C₅×D₄	C₂×C₄	1	12	yes	complemented
49	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
50	C₂×C₃×C₅×D₄	C₂³	1	3	yes	—
51	C₂²×C₃×C₄×C₅	—	2	3	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
53	C₂²×C₅×Dic₃	—	2	3	no	—
54	C₅×#217	—	2	3	no	—
55	C₅×C₄⋊Dic₃	—	2	3	no	—
56	C₅×C₄⋊Dic₃	C₂³	1	3	yes	—
57	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
58	C₄×C₅×Dic₃	—	2	3	no	—
59	C₅×#208	—	2	6	no	—
60	C₂×C₅×C₃⋊C₈	—	2	6	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₃⋊C₈	C₂³	1	3	yes	—
63	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic
64	#5827	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×#948	C₂×C₅	1	1	yes	characteristic, complemented
66	#5233	C₂×C₅	1	3	yes	complemented
67	#5232	C₂×C₅	1	3	yes	complemented
68	#5215	C₂×C₅	1	3	yes	complemented
69	C₂×#832	C₂×C₅	1	3	yes	complemented
70	C₅×H(5,𝔽₂)	—	2	4	no	—
71	C₅×H(5,𝔽₂)	Dic₃	1	8	yes	complemented
72	C₂×C₅×#41	—	2	1	no	—
73	C₂×C₅×#41	C₂×D₃	1	3	yes	—
74	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₅×D₄	—	2	3	no	—
76	C₂²×C₅×D₄	C₂×D₃	1	3	yes	—
77	C₅×#131	—	6	4	no	—
78	C₂×C₅×M₁₆	—	3	3	no	—
79	C₂²×C₅×C₈	—	3	3	no	—
80	C₄×C₅×Q₈	—	6	1	no	—
81	C₄×C₅×D₄	—	6	3	no	—
82	C₅×#117	—	3	3	no	—
83	C₂×C₅×C₄⋊C₄	—	3	3	no	—
84	C₅×#103	—	3	1	no	—
85	C₅×#103	—	3	3	no	—
86	C₅×#102	—	3	3	no	—
87	C₅×#102	—	3	6	no	—
88	C₅×#102	—	3	3	no	—
89	#2897	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	3	no	—
91	C₂³×C₃×C₅	—	2	12	no	—
92	C₂³×C₃×C₅	—	8	3	no	—
93	C₂³×C₃×C₅	—	8	3	no	—
94	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
97	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
98	C₃×C₅×D₄	—	2	12	no	—
99	C₃×C₅×D₄	—	2	12	no	—
100	C₃×C₅×D₄	—	2	3	no	—
101	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
102	C₃×C₅×D₄	C₂²×C₄	1	6	yes	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	12	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	2	3	no	—
111	C₂×C₅×Dic₃	—	8	3	no	—
112	C₅×C₃⋊C₈	—	2	1	no	—
113	C₅×C₃⋊C₈	—	2	3	no	—
114	C₃×H(5,𝔽₂)	—	2	4	no	—
115	C₃×H(5,𝔽₂)	C₄×C₅	1	8	yes	complemented
116	C₂×C₃×#41	—	2	1	no	—
117	C₂×C₃×#41	C₂²×C₅	1	3	yes	—
118	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×D₄	—	2	3	no	—
120	C₂²×C₃×D₄	C₂²×C₅	1	3	yes	—
121	#948	—	2	4	no	—
122	Q₈×Dic₃	—	2	1	no	—
123	D₄×Dic₃	—	2	3	no	—
124	#926	C₂²×C₅	1	3	yes	complemented
125	C₂×C₄⋊Dic₃	C₂²×C₅	1	3	yes	complemented
126	C₂×#208	C₂²×C₅	1	3	yes	complemented
127	C₂²×C₃⋊C₈	C₂²×C₅	1	3	yes	complemented
128	#835	C₂²×C₅	1	3	yes	complemented
129	#835	C₂²×C₅	1	1	yes	characteristic, complemented
130	#832	C₂²×C₅	1	3	yes	complemented
131	#832	C₂²×C₅	1	6	yes	complemented
132	#832	C₂²×C₅	1	3	yes	complemented
133	C₂⁴×C₅	—	2	3	no	—
134	C₅×#41	—	2	8	no	—
135	C₅×#41	—	2	6	no	—
136	C₅×#41	C₂×Dic₃	1	4	yes	—
137	C₅×#41	C₂×Dic₃	1	12	yes	complemented
138	C₅×#41	#67	1	4	yes	—
139	C₂×C₅×Q₈	#67	1	1	yes	characteristic
140	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
141	C₂×C₅×D₄	—	2	3	no	—
142	C₂×C₅×D₄	—	2	24	no	—
143	C₂×C₅×D₄	—	2	3	no	—
144	C₂×C₅×D₄	—	2	6	no	—
145	C₂×C₅×D₄	C₂×Dic₃	1	12	yes	complemented
146	C₂×C₅×D₄	#67	1	3	yes	—
147	C₂×C₅×D₄	C₂²×D₃	1	3	yes	—
148	C₂²×C₄×C₅	—	2	3	no	—
149	C₂²×C₄×C₅	—	6	3	no	—
150	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
151	C₅×M₁₆	—	6	6	no	—
152	C₂×C₅×C₈	—	3	1	no	—
153	C₂×C₅×C₈	—	3	3	no	—
154	C₂×C₅×C₈	—	6	6	no	—
155	C₅×C₄⋊C₄	—	3	3	no	—
156	C₅×C₄⋊C₄	—	3	1	no	—
157	C₅×C₄⋊C₄	—	6	3	no	—
158	C₅×C₂²⋊C₄	—	6	3	no	—
159	C₄²×C₅	—	6	3	no	—
160	C₂×H(5,𝔽₂)	C₅×D₃	1	1	yes	characteristic
161	C₂×#131	—	3	1	no	—
162	#520	—	3	1	no	—
163	#418	—	3	3	no	—
164	#417	—	3	3	no	—
165	#416	—	3	3	no	—
166	C₂×#102	—	3	3	no	—
167	C₂²×C₃×C₅	—	2	3	no	—
168	C₂²×C₃×C₅	—	2	3	no	—
169	C₂²×C₃×C₅	—	2	6	no	—
170	C₂²×C₃×C₅	—	4	3	no	—
171	C₂²×C₃×C₅	—	4	3	no	—
172	C₂²×C₃×C₅	—	8	12	no	—
173	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
174	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₃×C₄×C₅	—	2	2	no	—
176	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
177	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₅×Dic₃	—	4	3	no	—
180	C₅×Dic₃	—	4	1	no	—
181	C₂⁴×C₃	—	2	3	no	—
182	C₃×#41	—	2	8	no	—
183	C₃×#41	—	2	6	no	—
184	C₃×#41	C₂×C₄×C₅	1	4	yes	—
185	C₃×#41	C₂×C₄×C₅	1	12	yes	complemented
186	C₃×#41	C₅×D₄	1	4	yes	—
187	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
188	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
189	C₂×C₃×D₄	—	2	3	no	—
190	C₂×C₃×D₄	—	2	24	no	—
191	C₂×C₃×D₄	—	2	3	no	—
192	C₂×C₃×D₄	—	2	6	no	—
193	C₂×C₃×D₄	C₂×C₄×C₅	1	12	yes	complemented
194	C₂×C₃×D₄	C₅×D₄	1	3	yes	—
195	C₂×C₃×D₄	C₂³×C₅	1	3	yes	—
196	C₂²×C₃×C₄	—	2	3	no	—
197	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
198	C₂²×Dic₃	—	2	3	no	—
199	#217	—	2	3	no	—
200	C₄⋊Dic₃	—	2	3	no	—
201	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
202	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
203	C₄×Dic₃	—	2	3	no	—
204	#208	—	2	6	no	—
205	C₂×C₃⋊C₈	—	2	6	no	—
206	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
207	C₂×C₃⋊C₈	C₂³×C₅	1	3	yes	—
208	C₂³×C₅	—	2	3	no	—
209	C₂³×C₅	—	2	12	no	—
210	C₂³×C₅	—	8	3	no	—
211	C₂³×C₅	—	8	3	no	—
212	C₂³×C₅	C₂×#67	1	3	yes	—
213	C₅×Q₈	—	2	1	no	—
214	C₅×Q₈	#217	1	4	yes	—
215	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
216	C₅×D₄	—	2	12	no	—
217	C₅×D₄	—	2	12	no	—
218	C₅×D₄	—	2	3	no	—
219	C₅×D₄	#217	1	12	yes	—
220	C₅×D₄	C₂²×Dic₃	1	6	yes	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	12	no	—
223	C₂×C₄×C₅	—	6	1	no	—
224	C₂×C₄×C₅	—	6	3	no	—
225	C₂×C₄×C₅	—	24	3	no	—
226	C₂×C₄×C₅	C₂²×Dic₃	1	6	yes	—
227	C₂×C₄×C₅	C₂×#67	1	3	yes	—
228	C₂×C₄×C₅	C₂×#67	1	6	yes	—
229	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
230	C₅×C₈	—	6	1	no	—
231	C₅×C₈	—	6	3	no	—
232	H(5,𝔽₂)	—	2	4	no	—
233	H(5,𝔽₂)	C₅×Dic₃	1	8	yes	complemented
234	C₂×#41	—	2	1	no	—
235	C₂×#41	C₂×C₅×D₃	1	3	yes	—
236	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
237	C₂²×D₄	—	2	3	no	—
238	C₂²×D₄	C₂×C₅×D₃	1	3	yes	—
239	#131	—	6	4	no	—
240	C₂×M₁₆	—	3	3	no	—
241	C₂²×C₈	—	3	3	no	—
242	C₄×Q₈	—	6	1	no	—
243	C₄×D₄	—	6	3	no	—
244	#117	—	3	3	no	—
245	C₂×C₄⋊C₄	—	3	3	no	—
246	#103	—	3	1	no	—
247	#103	—	3	3	no	—
248	#102	—	3	3	no	—
249	#102	—	3	6	no	—
250	#102	—	3	3	no	—
251	C₂×C₃×C₅	—	2	6	no	—
252	C₂×C₃×C₅	—	4	6	no	—
253	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₅	#576	1	1	yes	characteristic
255	C₂×C₃×C₅	#577	1	1	yes	characteristic
256	C₂³×C₃	—	2	3	no	—
257	C₂³×C₃	—	2	12	no	—
258	C₂³×C₃	—	8	3	no	—
259	C₂³×C₃	—	8	3	no	—
260	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
261	C₃×Q₈	—	2	1	no	—
262	C₃×Q₈	C₅×C₂²⋊C₄	1	4	yes	—
263	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
264	C₃×D₄	—	2	12	no	—
265	C₃×D₄	—	2	12	no	—
266	C₃×D₄	—	2	3	no	—
267	C₃×D₄	C₅×C₂²⋊C₄	1	12	yes	—
268	C₃×D₄	C₂²×C₄×C₅	1	6	yes	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	12	no	—
271	C₂×C₃×C₄	C₂²×C₄×C₅	1	6	yes	—
272	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
274	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
275	C₂×Dic₃	—	2	1	no	—
276	C₂×Dic₃	—	2	3	no	—
277	C₂×Dic₃	—	8	3	no	—
278	C₃⋊C₈	—	2	1	no	—
279	C₃⋊C₈	—	2	3	no	—
280	C₂²×C₅	—	2	3	no	—
281	C₂²×C₅	—	2	3	no	—
282	C₂²×C₅	—	2	6	no	—
283	C₂²×C₅	—	4	3	no	—
284	C₂²×C₅	—	4	3	no	—
285	C₂²×C₅	—	8	12	no	—
286	C₂²×C₅	C₂×#217	1	6	yes	—
287	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	12	3	no	—
290	C₄×C₅	—	12	1	no	—
291	C₄×C₅	C₂×#217	1	6	yes	—
292	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
293	C₄×C₅	C₂²×#67	1	1	yes	characteristic
294	C₂⁴	—	2	3	no	—
295	#41	—	2	8	no	—
296	#41	—	2	6	no	—
297	#41	C₂×C₅×Dic₃	1	4	yes	—
298	#41	C₂×C₅×Dic₃	1	12	yes	complemented
299	#41	C₅×#67	1	4	yes	—
300	C₂×Q₈	C₅×#67	1	1	yes	characteristic
301	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₂×D₄	—	2	3	no	—
303	C₂×D₄	—	2	24	no	—
304	C₂×D₄	—	2	3	no	—
305	C₂×D₄	—	2	6	no	—
306	C₂×D₄	C₂×C₅×Dic₃	1	12	yes	complemented
307	C₂×D₄	C₅×#67	1	3	yes	—
308	C₂×D₄	C₂²×C₅×D₃	1	3	yes	—
309	C₂²×C₄	—	2	3	no	—
310	C₂²×C₄	—	6	3	no	—
311	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
312	M₁₆	—	6	6	no	—
313	C₂×C₈	—	3	1	no	—
314	C₂×C₈	—	3	3	no	—
315	C₂×C₈	—	6	6	no	—
316	C₄⋊C₄	—	3	3	no	—
317	C₄⋊C₄	—	3	1	no	—
318	C₄⋊C₄	—	6	3	no	—
319	C₂²⋊C₄	—	6	3	no	—
320	C₄²	—	6	3	no	—
321	C₃×C₅	#2897	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	—	2	3	no	—
323	C₂²×C₃	—	2	3	no	—
324	C₂²×C₃	—	2	6	no	—
325	C₂²×C₃	—	4	3	no	—
326	C₂²×C₃	—	4	3	no	—
327	C₂²×C₃	—	8	12	no	—
328	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	6	yes	—
329	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	6	yes	—
332	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
333	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
334	Dic₃	—	4	3	no	—
335	Dic₃	—	4	1	no	—
336	C₂×C₅	—	2	6	no	—
337	C₂×C₅	—	4	6	no	—
338	C₂×C₅	#5835	1	1	yes	characteristic
339	C₂×C₅	#5836	1	1	yes	characteristic
340	C₂×C₅	C₂²×#217	1	1	yes	characteristic
341	C₂³	—	2	3	no	—
342	C₂³	—	2	12	no	—
343	C₂³	—	8	3	no	—
344	C₂³	—	8	3	no	—
345	C₂³	C₂×C₅×#67	1	3	yes	—
346	Q₈	—	2	1	no	—
347	Q₈	C₅×#217	1	4	yes	—
348	Q₈	C₂²×C₅×Dic₃	1	2	yes	—
349	D₄	—	2	12	no	—
350	D₄	—	2	12	no	—
351	D₄	—	2	3	no	—
352	D₄	C₅×#217	1	12	yes	—
353	D₄	C₂²×C₅×Dic₃	1	6	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	12	no	—
356	C₂×C₄	—	6	1	no	—
357	C₂×C₄	—	6	3	no	—
358	C₂×C₄	—	24	3	no	—
359	C₂×C₄	C₂²×C₅×Dic₃	1	6	yes	—
360	C₂×C₄	C₂×C₅×#67	1	3	yes	—
361	C₂×C₄	C₂×C₅×#67	1	6	yes	—
362	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
363	C₈	—	6	1	no	—
364	C₈	—	6	3	no	—
365	C₂×C₃	—	2	6	no	—
366	C₂×C₃	—	4	6	no	—
367	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₃	C₅×#576	1	1	yes	characteristic
369	C₂×C₃	C₅×#577	1	1	yes	characteristic
370	C₅	#84099	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	3	no	—
372	C₂²	—	2	3	no	—
373	C₂²	—	2	6	no	—
374	C₂²	—	4	3	no	—
375	C₂²	—	4	3	no	—
376	C₂²	—	8	12	no	—
377	C₂²	C₂×C₅×#217	1	6	yes	—
378	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	12	3	no	—
381	C₄	—	12	1	no	—
382	C₄	C₂×C₅×#217	1	6	yes	—
383	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
384	C₄	C₂²×C₅×#67	1	1	yes	characteristic
385	C₃	C₅×#2897	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	2	6	no	—
387	C₂	—	4	6	no	—
388	C₂	C₅×#5835	1	1	yes	characteristic
389	C₂	C₅×#5836	1	1	yes	characteristic
390	C₂	C₂²×C₅×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×H(5,𝔽₂)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×H(5,𝔽₂)	D₃
hypocenter	C₃	C₅×#2897
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
2. C₅×#5827	C₂	semidirect
3. C₂×C₅×#948	C₂	semidirect
4. C₅×#5233	C₂	semidirect
5. C₅×#5232	C₂	semidirect
6. C₅×#5215	C₂	semidirect
7. C₂×C₅×#832	C₂	semidirect
10. C₃×C₅×H(5,𝔽₂)	C₄	semidirect
19. C₅×#926	C₂²	semidirect
20. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
21. C₂×C₅×#208	C₂²	semidirect
22. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
23. C₅×#835	C₂²	semidirect
24. C₅×#835	C₂²	semidirect
25. C₅×#832	C₂²	semidirect
26. C₅×#832	C₂²	semidirect
27. C₅×#832	C₂²	semidirect
28. #84099	C₅	direct (N × H)
40. C₃×C₅×#41	C₂×C₄	semidirect
48. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
64. #5827	C₂×C₅	semidirect
65. C₂×#948	C₂×C₅	semidirect
66. #5233	C₂×C₅	semidirect
67. #5232	C₂×C₅	semidirect
68. #5215	C₂×C₅	semidirect
69. C₂×#832	C₂×C₅	semidirect
71. C₅×H(5,𝔽₂)	Dic₃	semidirect
115. C₃×H(5,𝔽₂)	C₄×C₅	semidirect
124. #926	C₂²×C₅	semidirect
125. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
126. C₂×#208	C₂²×C₅	semidirect
127. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
128. #835	C₂²×C₅	semidirect
129. #835	C₂²×C₅	semidirect
130. #832	C₂²×C₅	semidirect
131. #832	C₂²×C₅	semidirect
132. #832	C₂²×C₅	semidirect
137. C₅×#41	C₂×Dic₃	semidirect
145. C₂×C₅×D₄	C₂×Dic₃	semidirect
185. C₃×#41	C₂×C₄×C₅	semidirect
193. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
233. H(5,𝔽₂)	C₅×Dic₃	semidirect
298. #41	C₂×C₅×Dic₃	semidirect
306. C₂×D₄	C₂×C₅×Dic₃	semidirect
321. C₃×C₅	#2897	semidirect
370. C₅	#84099	direct (N × H)
385. C₃	C₅×#2897	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×H(5,𝔽₂)	2
C₅×#5827	2
C₂×C₅×#948	2
C₅×#5233	2
C₅×#5232	2
C₅×#5215	2
C₂×C₅×#832	2
C₅×#2897	3
#84099	5

Subgroups — C5×#84099 #14412629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#84099 #14412629