Subgroups — C₅×#84111 #14412716

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	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×#5225	C₂	1	3	yes	maximal, complemented
7	C₂×C₅×#835	C₂	1	3	yes	maximal, complemented
8	C₅×#2898	—	3	1	no	maximal, Hall
9	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
10	C₃×C₅×2₋¹⁺⁴	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×#41	—	2	3	no	—
12	C₂×C₃×C₅×#41	C₂²	1	3	yes	—
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	—	2	1	no	—
15	C₂²×C₃×C₅×Q₈	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	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	—
21	C₂×C₅×#208	C₂²	1	3	yes	—
22	C₂²×C₅×C₃⋊C₈	C₂²	1	3	yes	—
23	C₅×#835	C₂²	1	3	yes	—
24	C₅×#835	C₂²	1	6	yes	—
25	C₅×#835	C₂²	1	3	yes	—
26	C₅×#832	C₂²	1	3	yes	—
27	C₅×#832	C₂²	1	1	yes	characteristic
28	#84111	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×2₋¹⁺⁴	D₃	1	1	yes	characteristic
30	C₂×C₅×#131	—	3	1	no	—
31	C₅×#520	—	3	1	no	—
32	C₅×#419	—	3	3	no	—
33	C₅×#417	—	3	3	no	—
34	C₅×#416	—	3	3	no	—
35	C₂×C₅×#103	—	3	3	no	—
36	C₃×C₅×#41	—	2	24	no	—
37	C₃×C₅×#41	—	2	6	no	—
38	C₃×C₅×#41	C₂×C₄	1	4	yes	—
39	C₃×C₅×#41	C₂×C₄	1	12	yes	complemented
40	C₃×C₅×#41	D₄	1	4	yes	—
41	C₂×C₃×C₅×Q₈	—	2	8	no	—
42	C₂×C₃×C₅×Q₈	—	2	3	no	—
43	C₂×C₃×C₅×Q₈	—	2	6	no	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	12	yes	complemented
45	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
46	C₂×C₃×C₅×Q₈	C₂³	1	3	yes	—
47	C₂×C₃×C₅×D₄	—	2	3	no	—
48	C₂×C₃×C₅×D₄	D₄	1	3	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	—	2	3	no	—
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×C₃×2₋¹⁺⁴	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	#5225	C₂×C₅	1	3	yes	complemented
69	C₂×#835	C₂×C₅	1	3	yes	complemented
70	C₅×2₋¹⁺⁴	—	2	4	no	—
71	C₅×2₋¹⁺⁴	Dic₃	1	8	yes	complemented
72	C₂×C₅×#41	—	2	3	no	—
73	C₂×C₅×#41	C₂×D₃	1	3	yes	—
74	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₅×Q₈	—	2	1	no	—
76	C₂²×C₅×Q₈	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	3	no	—
85	C₅×#103	—	3	6	no	—
86	C₅×#103	—	3	3	no	—
87	C₅×#102	—	3	1	no	—
88	C₅×#102	—	3	3	no	—
89	#2898	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	1	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
92	C₃×C₅×Q₈	—	2	12	no	—
93	C₃×C₅×Q₈	—	2	3	no	—
94	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
95	C₃×C₅×Q₈	C₂²×C₄	1	6	yes	—
96	C₃×C₅×D₄	—	2	12	no	—
97	C₃×C₅×D₄	—	2	1	no	—
98	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
99	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	—	2	12	no	—
101	C₂×C₃×C₄×C₅	—	2	3	no	—
102	C₂×C₃×C₄×C₅	—	2	12	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	6	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×Dic₃	—	2	1	no	—
108	C₂×C₅×Dic₃	—	2	3	no	—
109	C₂×C₅×Dic₃	—	8	3	no	—
110	C₅×C₃⋊C₈	—	2	1	no	—
111	C₅×C₃⋊C₈	—	2	3	no	—
112	C₃×2₋¹⁺⁴	—	2	4	no	—
113	C₃×2₋¹⁺⁴	C₄×C₅	1	8	yes	complemented
114	C₂×C₃×#41	—	2	3	no	—
115	C₂×C₃×#41	C₂²×C₅	1	3	yes	—
116	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₃×Q₈	—	2	1	no	—
118	C₂²×C₃×Q₈	C₂²×C₅	1	3	yes	—
119	#948	—	2	4	no	—
120	Q₈×Dic₃	—	2	1	no	—
121	D₄×Dic₃	—	2	3	no	—
122	#926	C₂²×C₅	1	3	yes	—
123	C₂×C₄⋊Dic₃	C₂²×C₅	1	3	yes	—
124	C₂×#208	C₂²×C₅	1	3	yes	—
125	C₂²×C₃⋊C₈	C₂²×C₅	1	3	yes	—
126	#835	C₂²×C₅	1	3	yes	—
127	#835	C₂²×C₅	1	6	yes	—
128	#835	C₂²×C₅	1	3	yes	—
129	#832	C₂²×C₅	1	3	yes	—
130	#832	C₂²×C₅	1	1	yes	characteristic
131	C₅×#41	—	2	24	no	—
132	C₅×#41	—	2	6	no	—
133	C₅×#41	C₂×Dic₃	1	4	yes	—
134	C₅×#41	C₂×Dic₃	1	12	yes	complemented
135	C₅×#41	#67	1	4	yes	—
136	C₂×C₅×Q₈	—	2	8	no	—
137	C₂×C₅×Q₈	—	2	3	no	—
138	C₂×C₅×Q₈	—	2	6	no	—
139	C₂×C₅×Q₈	C₂×Dic₃	1	12	yes	complemented
140	C₂×C₅×Q₈	#67	1	1	yes	characteristic
141	C₂×C₅×Q₈	C₂²×D₃	1	3	yes	—
142	C₂×C₅×D₄	—	2	3	no	—
143	C₂×C₅×D₄	#67	1	3	yes	—
144	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	—	2	3	no	—
146	C₂²×C₄×C₅	—	2	3	no	—
147	C₂²×C₄×C₅	—	6	3	no	—
148	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
149	C₅×M₁₆	—	6	6	no	—
150	C₂×C₅×C₈	—	3	1	no	—
151	C₂×C₅×C₈	—	3	3	no	—
152	C₂×C₅×C₈	—	6	6	no	—
153	C₅×C₄⋊C₄	—	3	3	no	—
154	C₅×C₄⋊C₄	—	3	1	no	—
155	C₅×C₄⋊C₄	—	6	3	no	—
156	C₅×C₂²⋊C₄	—	6	3	no	—
157	C₄²×C₅	—	6	3	no	—
158	C₂×2₋¹⁺⁴	C₅×D₃	1	1	yes	characteristic
159	C₂×#131	—	3	1	no	—
160	#520	—	3	1	no	—
161	#419	—	3	3	no	—
162	#417	—	3	3	no	—
163	#416	—	3	3	no	—
164	C₂×#103	—	3	3	no	—
165	C₂²×C₃×C₅	—	2	3	no	—
166	C₂²×C₃×C₅	—	2	3	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	4	1	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₃×C₄×C₅	—	2	6	no	—
173	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
174	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₅×Dic₃	—	4	3	no	—
177	C₅×Dic₃	—	4	1	no	—
178	C₃×#41	—	2	24	no	—
179	C₃×#41	—	2	6	no	—
180	C₃×#41	C₂×C₄×C₅	1	4	yes	—
181	C₃×#41	C₂×C₄×C₅	1	12	yes	complemented
182	C₃×#41	C₅×D₄	1	4	yes	—
183	C₂×C₃×Q₈	—	2	8	no	—
184	C₂×C₃×Q₈	—	2	3	no	—
185	C₂×C₃×Q₈	—	2	6	no	—
186	C₂×C₃×Q₈	C₂×C₄×C₅	1	12	yes	complemented
187	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
188	C₂×C₃×Q₈	C₂³×C₅	1	3	yes	—
189	C₂×C₃×D₄	—	2	3	no	—
190	C₂×C₃×D₄	C₅×D₄	1	3	yes	—
191	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	2	3	no	—
193	C₂²×C₃×C₄	—	2	3	no	—
194	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
195	C₂²×Dic₃	—	2	3	no	—
196	#217	—	2	3	no	—
197	C₄⋊Dic₃	—	2	3	no	—
198	C₄⋊Dic₃	C₂³×C₅	1	3	yes	—
199	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
200	C₄×Dic₃	—	2	3	no	—
201	#208	—	2	6	no	—
202	C₂×C₃⋊C₈	—	2	6	no	—
203	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
204	C₂×C₃⋊C₈	C₂³×C₅	1	3	yes	—
205	C₂³×C₅	—	2	1	no	—
206	C₂³×C₅	C₂×#67	1	3	yes	—
207	C₅×Q₈	—	2	12	no	—
208	C₅×Q₈	—	2	3	no	—
209	C₅×Q₈	#217	1	4	yes	—
210	C₅×Q₈	C₂²×Dic₃	1	6	yes	—
211	C₅×D₄	—	2	12	no	—
212	C₅×D₄	—	2	1	no	—
213	C₅×D₄	#217	1	12	yes	—
214	C₅×D₄	C₂²×Dic₃	1	2	yes	—
215	C₂×C₄×C₅	—	2	12	no	—
216	C₂×C₄×C₅	—	2	3	no	—
217	C₂×C₄×C₅	—	2	12	no	—
218	C₂×C₄×C₅	—	6	1	no	—
219	C₂×C₄×C₅	—	6	3	no	—
220	C₂×C₄×C₅	—	24	3	no	—
221	C₂×C₄×C₅	C₂²×Dic₃	1	6	yes	—
222	C₂×C₄×C₅	C₂×#67	1	3	yes	—
223	C₂×C₄×C₅	C₂×#67	1	6	yes	—
224	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
225	C₅×C₈	—	6	1	no	—
226	C₅×C₈	—	6	3	no	—
227	2₋¹⁺⁴	—	2	4	no	—
228	2₋¹⁺⁴	C₅×Dic₃	1	8	yes	complemented
229	C₂×#41	—	2	3	no	—
230	C₂×#41	C₂×C₅×D₃	1	3	yes	—
231	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	C₂×C₅×D₃	1	3	yes	—
234	#131	—	6	4	no	—
235	C₂×M₁₆	—	3	3	no	—
236	C₂²×C₈	—	3	3	no	—
237	C₄×Q₈	—	6	1	no	—
238	C₄×D₄	—	6	3	no	—
239	#117	—	3	3	no	—
240	C₂×C₄⋊C₄	—	3	3	no	—
241	#103	—	3	3	no	—
242	#103	—	3	6	no	—
243	#103	—	3	3	no	—
244	#102	—	3	1	no	—
245	#102	—	3	3	no	—
246	C₂×C₃×C₅	—	2	6	no	—
247	C₂×C₃×C₅	—	4	2	no	—
248	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₅	#577	1	1	yes	characteristic
250	C₂×C₃×C₅	#578	1	1	yes	characteristic
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
253	C₃×Q₈	—	2	12	no	—
254	C₃×Q₈	—	2	3	no	—
255	C₃×Q₈	C₅×C₂²⋊C₄	1	4	yes	—
256	C₃×Q₈	C₂²×C₄×C₅	1	6	yes	—
257	C₃×D₄	—	2	12	no	—
258	C₃×D₄	—	2	1	no	—
259	C₃×D₄	C₅×C₂²⋊C₄	1	12	yes	—
260	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
261	C₂×C₃×C₄	—	2	12	no	—
262	C₂×C₃×C₄	—	2	3	no	—
263	C₂×C₃×C₄	—	2	12	no	—
264	C₂×C₃×C₄	C₂²×C₄×C₅	1	6	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	6	yes	—
267	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
268	C₂×Dic₃	—	2	1	no	—
269	C₂×Dic₃	—	2	3	no	—
270	C₂×Dic₃	—	8	3	no	—
271	C₃⋊C₈	—	2	1	no	—
272	C₃⋊C₈	—	2	3	no	—
273	C₂²×C₅	—	2	3	no	—
274	C₂²×C₅	—	2	3	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	C₂×#217	1	6	yes	—
279	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
280	C₄×C₅	—	2	6	no	—
281	C₄×C₅	—	12	3	no	—
282	C₄×C₅	—	12	1	no	—
283	C₄×C₅	C₂×#217	1	6	yes	—
284	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
285	C₄×C₅	C₂²×#67	1	1	yes	characteristic
286	#41	—	2	24	no	—
287	#41	—	2	6	no	—
288	#41	C₂×C₅×Dic₃	1	4	yes	—
289	#41	C₂×C₅×Dic₃	1	12	yes	complemented
290	#41	C₅×#67	1	4	yes	—
291	C₂×Q₈	—	2	8	no	—
292	C₂×Q₈	—	2	3	no	—
293	C₂×Q₈	—	2	6	no	—
294	C₂×Q₈	C₂×C₅×Dic₃	1	12	yes	complemented
295	C₂×Q₈	C₅×#67	1	1	yes	characteristic
296	C₂×Q₈	C₂²×C₅×D₃	1	3	yes	—
297	C₂×D₄	—	2	3	no	—
298	C₂×D₄	C₅×#67	1	3	yes	—
299	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
300	C₂²×C₄	—	2	3	no	—
301	C₂²×C₄	—	2	3	no	—
302	C₂²×C₄	—	6	3	no	—
303	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
304	M₁₆	—	6	6	no	—
305	C₂×C₈	—	3	1	no	—
306	C₂×C₈	—	3	3	no	—
307	C₂×C₈	—	6	6	no	—
308	C₄⋊C₄	—	3	3	no	—
309	C₄⋊C₄	—	3	1	no	—
310	C₄⋊C₄	—	6	3	no	—
311	C₂²⋊C₄	—	6	3	no	—
312	C₄²	—	6	3	no	—
313	C₃×C₅	#2898	1	1	yes	characteristic, complemented, Hall
314	C₂²×C₃	—	2	3	no	—
315	C₂²×C₃	—	2	3	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	4	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	6	yes	—
320	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
321	C₃×C₄	—	2	6	no	—
322	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	6	yes	—
323	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
324	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
325	Dic₃	—	4	3	no	—
326	Dic₃	—	4	1	no	—
327	C₂×C₅	—	2	6	no	—
328	C₂×C₅	—	4	2	no	—
329	C₂×C₅	#5837	1	1	yes	characteristic
330	C₂×C₅	#5838	1	1	yes	characteristic
331	C₂×C₅	C₂²×#217	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	C₂×C₅×#67	1	3	yes	—
334	Q₈	—	2	12	no	—
335	Q₈	—	2	3	no	—
336	Q₈	C₅×#217	1	4	yes	—
337	Q₈	C₂²×C₅×Dic₃	1	6	yes	—
338	D₄	—	2	12	no	—
339	D₄	—	2	1	no	—
340	D₄	C₅×#217	1	12	yes	—
341	D₄	C₂²×C₅×Dic₃	1	2	yes	—
342	C₂×C₄	—	2	12	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	2	12	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	6	3	no	—
347	C₂×C₄	—	24	3	no	—
348	C₂×C₄	C₂²×C₅×Dic₃	1	6	yes	—
349	C₂×C₄	C₂×C₅×#67	1	3	yes	—
350	C₂×C₄	C₂×C₅×#67	1	6	yes	—
351	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
352	C₈	—	6	1	no	—
353	C₈	—	6	3	no	—
354	C₂×C₃	—	2	6	no	—
355	C₂×C₃	—	4	2	no	—
356	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₃	C₅×#577	1	1	yes	characteristic
358	C₂×C₃	C₅×#578	1	1	yes	characteristic
359	C₅	#84111	1	1	yes	characteristic, direct product factor, Sylow
360	C₂²	—	2	3	no	—
361	C₂²	—	2	3	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	C₂×C₅×#217	1	6	yes	—
366	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
367	C₄	—	2	6	no	—
368	C₄	—	12	3	no	—
369	C₄	—	12	1	no	—
370	C₄	C₂×C₅×#217	1	6	yes	—
371	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
372	C₄	C₂²×C₅×#67	1	1	yes	characteristic
373	C₃	C₅×#2898	1	1	yes	characteristic, complemented, Sylow
374	C₂	—	2	6	no	—
375	C₂	—	4	2	no	—
376	C₂	C₅×#5837	1	1	yes	characteristic
377	C₂	C₅×#5838	1	1	yes	characteristic
378	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×C₅×2₋¹⁺⁴	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×2₋¹⁺⁴	D₃
hypocenter	C₃	C₅×#2898
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×2₋¹⁺⁴

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×#5225	C₂	semidirect
7. C₂×C₅×#835	C₂	semidirect
10. C₃×C₅×2₋¹⁺⁴	C₄	semidirect
28. #84111	C₅	direct (N × H)
39. C₃×C₅×#41	C₂×C₄	semidirect
44. C₂×C₃×C₅×Q₈	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. #5225	C₂×C₅	semidirect
69. C₂×#835	C₂×C₅	semidirect
71. C₅×2₋¹⁺⁴	Dic₃	semidirect
113. C₃×2₋¹⁺⁴	C₄×C₅	semidirect
134. C₅×#41	C₂×Dic₃	semidirect
139. C₂×C₅×Q₈	C₂×Dic₃	semidirect
181. C₃×#41	C₂×C₄×C₅	semidirect
186. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
228. 2₋¹⁺⁴	C₅×Dic₃	semidirect
289. #41	C₂×C₅×Dic₃	semidirect
294. C₂×Q₈	C₂×C₅×Dic₃	semidirect
313. C₃×C₅	#2898	semidirect
359. C₅	#84111	direct (N × H)
373. C₃	C₅×#2898	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×2₋¹⁺⁴	2
C₅×#5827	2
C₂×C₅×#948	2
C₅×#5233	2
C₅×#5232	2
C₅×#5225	2
C₂×C₅×#835	2
C₅×#2898	3
#84111	5

Subgroups — C5×#84111 #14412716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#84111 #14412716