Subgroups — C₂×C₅×#1962 #11943927

Order 1280.

1878 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	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#104	C₂	1	4	yes	maximal, complemented
4	C₂×C₄³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1962	C₂	1	8	yes	maximal, direct product factor
6	C₂²×C₅×#41	C₂²	1	2	yes	—
7	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
8	C₅×#532	—	2	2	no	—
9	C₅×#532	—	2	2	no	—
10	C₅×#532	C₄	1	4	yes	complemented
11	C₅×#532	C₂²	1	4	yes	—
12	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
13	C₂×C₅×#127	C₄	1	1	yes	characteristic, complemented
14	C₂×C₅×#124	C₄	1	2	yes	complemented
15	C₂×C₅×#121	—	2	2	no	—
16	C₂×C₄×C₅×D₄	—	2	2	no	—
17	C₂²×C₄²×C₅	—	2	2	no	—
18	C₂²×C₄²×C₅	C₂²	1	2	yes	—
19	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₅×#423	—	2	2	no	—
21	C₅×#423	C₂²	1	4	yes	complemented
22	C₂×C₅×C₄⋊C₈	—	2	2	no	—
23	C₂×C₅×#104	—	2	16	no	—
24	C₂×C₅×#104	C₂²	1	16	yes	complemented
25	C₄³×C₅	—	2	2	no	—
26	C₄³×C₅	C₂²	1	4	yes	complemented
27	C₂×#1962	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₅×#41	—	2	2	no	—
29	C₂×C₅×#41	—	2	2	no	—
30	C₂×C₅×#41	—	2	8	no	—
31	C₂×C₅×#41	—	2	8	no	—
32	C₂×C₅×#41	C₂×C₄	1	4	yes	—
33	C₂×C₅×#41	C₂³	1	4	yes	—
34	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
35	C₂²×C₅×D₄	—	2	2	no	—
36	C₂²×C₅×D₄	—	2	2	no	—
37	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₅	—	2	2	no	—
39	C₂³×C₄×C₅	—	2	2	no	—
40	C₂³×C₄×C₅	D₄	1	2	yes	—
41	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×M₁₆	—	2	2	no	—
43	C₂×C₅×M₁₆	—	2	8	no	—
44	C₂×C₅×M₁₆	C₂³	1	4	yes	—
45	C₂²×C₅×C₈	—	2	2	no	—
46	C₅×C₄⋊Q₈	—	2	2	no	—
47	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
48	C₅×#127	—	2	2	no	—
49	C₅×#127	C₂×C₄	1	4	yes	complemented
50	C₅×#124	—	2	4	no	—
51	C₅×#124	C₂×C₄	1	8	yes	complemented
52	C₅×#121	—	2	8	no	—
53	C₅×#121	—	2	8	no	—
54	C₄×C₅×D₄	—	2	8	no	—
55	C₄×C₅×D₄	—	2	8	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₂×C₄²×C₅	—	2	16	no	—
59	C₂×C₄²×C₅	—	2	2	no	—
60	C₂×C₄²×C₅	—	2	8	no	—
61	C₂×C₄²×C₅	—	2	4	no	—
62	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₅	D₄	1	2	yes	—
66	C₂×C₄²×C₅	D₄	1	2	yes	—
67	C₂×C₄²×C₅	D₄	1	2	yes	—
68	C₂×C₄²×C₅	D₄	1	8	yes	complemented
69	C₂×C₄²×C₅	C₂³	1	4	yes	—
70	C₂×C₄²×C₅	C₂³	1	2	yes	—
71	C₅×C₄⋊C₈	—	2	8	no	—
72	C₅×#104	—	2	32	no	—
73	C₂×#532	C₂×C₅	1	1	yes	characteristic
74	C₂×#423	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×#104	C₂×C₅	1	4	yes	complemented
76	C₂×C₄³	C₂×C₅	1	1	yes	characteristic, complemented
77	#1962	C₂×C₅	1	8	yes	direct product factor
78	C₂⁴×C₅	—	2	2	no	—
79	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
80	C₅×#41	—	2	16	no	—
81	C₅×#41	—	2	8	no	—
82	C₅×#41	—	2	8	no	—
83	C₅×#41	—	4	8	no	—
84	C₅×#41	—	4	4	no	—
85	C₅×#41	—	4	4	no	—
86	C₂×C₅×Q₈	—	2	2	no	—
87	C₂×C₅×Q₈	—	2	8	no	—
88	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
89	C₂×C₅×D₄	—	2	4	no	—
90	C₂×C₅×D₄	—	2	4	no	—
91	C₂×C₅×D₄	—	2	8	no	—
92	C₂×C₅×D₄	—	2	2	no	—
93	C₂×C₅×D₄	—	2	8	no	—
94	C₂×C₅×D₄	—	4	8	no	—
95	C₂×C₅×D₄	—	4	8	no	—
96	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₅	—	2	16	no	—
98	C₂²×C₄×C₅	—	2	8	no	—
99	C₂²×C₄×C₅	—	2	4	no	—
100	C₂²×C₄×C₅	—	2	8	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	4	no	—
103	C₂²×C₄×C₅	—	2	4	no	—
104	C₂²×C₄×C₅	—	4	4	no	—
105	C₂²×C₄×C₅	—	4	4	no	—
106	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂²⋊C₄	1	4	yes	—
108	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	#41	1	4	yes	—
117	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×M₁₆	—	2	8	no	—
119	C₅×M₁₆	—	4	4	no	—
120	C₂×C₅×C₈	—	2	4	no	—
121	C₂×C₅×C₈	—	4	4	no	—
122	C₅×C₄⋊C₄	—	2	8	no	—
123	C₅×C₂²⋊C₄	—	2	16	no	—
124	C₄²×C₅	—	2	32	no	—
125	C₄²×C₅	—	2	8	no	—
126	C₄²×C₅	—	2	4	no	—
127	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₅	C₂²×C₄	1	2	yes	—
131	C₄²×C₅	C₂²×C₄	1	2	yes	—
132	C₄²×C₅	C₂×D₄	1	4	yes	—
133	C₄²×C₅	C₂×D₄	1	8	yes	complemented
134	C₂²×#41	C₂²×C₅	1	2	yes	—
135	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
136	#532	—	2	2	no	—
137	#532	—	2	2	no	—
138	#532	C₄×C₅	1	4	yes	complemented
139	#532	C₂²×C₅	1	4	yes	—
140	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic, complemented
141	C₂×#127	C₄×C₅	1	1	yes	characteristic, complemented
142	C₂×#124	C₄×C₅	1	2	yes	complemented
143	C₂×#121	—	2	2	no	—
144	C₂×C₄×D₄	—	2	2	no	—
145	C₂²×C₄²	—	2	2	no	—
146	C₂²×C₄²	C₂²×C₅	1	2	yes	—
147	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
148	#423	—	2	2	no	—
149	#423	C₂²×C₅	1	4	yes	complemented
150	C₂×C₄⋊C₈	—	2	2	no	—
151	C₂×#104	—	2	16	no	—
152	C₂×#104	C₂²×C₅	1	16	yes	complemented
153	C₄³	—	2	2	no	—
154	C₄³	C₂²×C₅	1	4	yes	complemented
155	C₂³×C₅	—	2	4	no	—
156	C₂³×C₅	—	2	4	no	—
157	C₂³×C₅	—	4	4	no	—
158	C₂³×C₅	—	4	8	no	—
159	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂³×C₅	#121	1	4	yes	—
162	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₅×Q₈	—	2	8	no	—
164	C₅×Q₈	—	4	4	no	—
165	C₅×D₄	—	2	8	no	—
166	C₅×D₄	—	4	8	no	—
167	C₅×D₄	—	4	8	no	—
168	C₅×D₄	—	4	4	no	—
169	C₅×D₄	—	4	16	no	—
170	C₂×C₄×C₅	—	2	16	no	—
171	C₂×C₄×C₅	—	2	32	no	—
172	C₂×C₄×C₅	—	2	8	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	8	no	—
175	C₂×C₄×C₅	—	2	8	no	—
176	C₂×C₄×C₅	—	2	4	no	—
177	C₂×C₄×C₅	—	4	4	no	—
178	C₂×C₄×C₅	—	4	4	no	—
179	C₂×C₄×C₅	—	4	4	no	—
180	C₂×C₄×C₅	—	4	8	no	—
181	C₂×C₄×C₅	#104	1	8	yes	complemented
182	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₅	#121	1	4	yes	—
189	C₂×C₄×C₅	#124	1	2	yes	—
190	C₂×C₄×C₅	#124	1	2	yes	—
191	C₂×C₄×C₅	#127	1	2	yes	—
192	C₂×C₄×C₅	#127	1	2	yes	—
193	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×#41	1	2	yes	—
197	C₅×C₈	—	4	4	no	—
198	C₂×#41	—	2	2	no	—
199	C₂×#41	—	2	2	no	—
200	C₂×#41	—	2	8	no	—
201	C₂×#41	—	2	8	no	—
202	C₂×#41	C₂×C₄×C₅	1	4	yes	—
203	C₂×#41	C₂³×C₅	1	4	yes	—
204	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
205	C₂²×D₄	—	2	2	no	—
206	C₂²×D₄	—	2	2	no	—
207	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
208	C₂³×C₄	—	2	2	no	—
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	C₅×D₄	1	2	yes	—
211	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	8	no	—
214	C₂×M₁₆	C₂³×C₅	1	4	yes	—
215	C₂²×C₈	—	2	2	no	—
216	C₄⋊Q₈	—	2	2	no	—
217	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
218	#127	—	2	2	no	—
219	#127	C₂×C₄×C₅	1	4	yes	complemented
220	#124	—	2	4	no	—
221	#124	C₂×C₄×C₅	1	8	yes	complemented
222	#121	—	2	8	no	—
223	#121	—	2	8	no	—
224	C₄×D₄	—	2	8	no	—
225	C₄×D₄	—	2	8	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₄²	—	2	16	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	8	no	—
231	C₂×C₄²	—	2	4	no	—
232	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
235	C₂×C₄²	C₅×D₄	1	2	yes	—
236	C₂×C₄²	C₅×D₄	1	2	yes	—
237	C₂×C₄²	C₅×D₄	1	2	yes	—
238	C₂×C₄²	C₅×D₄	1	8	yes	complemented
239	C₂×C₄²	C₂³×C₅	1	4	yes	—
240	C₂×C₄²	C₂³×C₅	1	2	yes	—
241	C₄⋊C₈	—	2	8	no	—
242	#104	—	2	32	no	—
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	8	no	—
246	C₂²×C₅	—	4	8	no	—
247	C₂²×C₅	—	4	4	no	—
248	C₂²×C₅	—	8	8	no	—
249	C₂²×C₅	#390	1	2	yes	—
250	C₂²×C₅	#390	1	2	yes	—
251	C₂²×C₅	C₂×#104	1	4	yes	—
252	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₅	C₂×#121	1	2	yes	—
254	C₄×C₅	—	2	16	no	—
255	C₄×C₅	—	2	4	no	—
256	C₄×C₅	—	4	4	no	—
257	C₄×C₅	#390	1	2	yes	—
258	C₄×C₅	#390	1	2	yes	—
259	C₄×C₅	C₂×#104	1	8	yes	complemented
260	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
261	C₄×C₅	C₂×#124	1	1	yes	characteristic
262	C₄×C₅	C₂×#127	1	1	yes	characteristic
263	C₂⁴	—	2	2	no	—
264	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
265	#41	—	2	16	no	—
266	#41	—	2	8	no	—
267	#41	—	2	8	no	—
268	#41	—	4	8	no	—
269	#41	—	4	4	no	—
270	#41	—	4	4	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	8	no	—
273	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	4	8	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
292	C₂²×C₄	C₅×C₂²⋊C₄	1	4	yes	—
293	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
297	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
301	C₂²×C₄	C₅×#41	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
303	M₁₆	—	2	8	no	—
304	M₁₆	—	4	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	4	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₄²	—	2	32	no	—
310	C₄²	—	2	8	no	—
311	C₄²	—	2	4	no	—
312	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
313	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
314	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
315	C₄²	C₂²×C₄×C₅	1	2	yes	—
316	C₄²	C₂²×C₄×C₅	1	2	yes	—
317	C₄²	C₂×C₅×D₄	1	4	yes	—
318	C₄²	C₂×C₅×D₄	1	8	yes	complemented
319	C₂×C₅	—	2	2	no	—
320	C₂×C₅	—	2	2	no	—
321	C₂×C₅	—	8	4	no	—
322	C₂×C₅	#1962	1	4	yes	direct product factor
323	C₂×C₅	C₂×#390	1	1	yes	characteristic
324	C₂×C₅	C₂²×#104	1	2	yes	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	4	4	no	—
328	C₂³	—	4	8	no	—
329	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
330	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
331	C₂³	C₅×#121	1	4	yes	—
332	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
333	Q₈	—	2	8	no	—
334	Q₈	—	4	4	no	—
335	D₄	—	2	8	no	—
336	D₄	—	4	8	no	—
337	D₄	—	4	8	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	16	no	—
340	C₂×C₄	—	2	16	no	—
341	C₂×C₄	—	2	32	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	C₅×#104	1	8	yes	complemented
352	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
353	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
356	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
357	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
358	C₂×C₄	C₅×#121	1	4	yes	—
359	C₂×C₄	C₅×#124	1	2	yes	—
360	C₂×C₄	C₅×#124	1	2	yes	—
361	C₂×C₄	C₅×#127	1	2	yes	—
362	C₂×C₄	C₅×#127	1	2	yes	—
363	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
365	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂×C₅×#41	1	2	yes	—
367	C₈	—	4	4	no	—
368	C₅	C₂×#1962	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	8	8	no	—
375	C₂²	C₅×#390	1	2	yes	—
376	C₂²	C₅×#390	1	2	yes	—
377	C₂²	C₂×C₅×#104	1	4	yes	—
378	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
379	C₂²	C₂×C₅×#121	1	2	yes	—
380	C₄	—	2	16	no	—
381	C₄	—	2	4	no	—
382	C₄	—	4	4	no	—
383	C₄	C₅×#390	1	2	yes	—
384	C₄	C₅×#390	1	2	yes	—
385	C₄	C₂×C₅×#104	1	8	yes	complemented
386	C₄	C₂×C₄×C₅×D₄	1	2	yes	—
387	C₄	C₂×C₅×#124	1	1	yes	characteristic
388	C₄	C₂×C₅×#127	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	8	4	no	—
392	C₂	C₅×#1962	1	4	yes	direct product factor
393	C₂	C₂×C₅×#390	1	1	yes	characteristic
394	C₂	C₂²×C₅×#104	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#423	C₂	semidirect
3. C₂²×C₅×#104	C₂	semidirect
4. C₂×C₄³×C₅	C₂	semidirect
5. C₅×#1962	C₂	direct (N × H)
10. C₅×#532	C₄	semidirect
12. C₂×C₅×C₄⋊Q₈	C₄	semidirect
13. C₂×C₅×#127	C₄	semidirect
14. C₂×C₅×#124	C₄	semidirect
21. C₅×#423	C₂²	semidirect
24. C₂×C₅×#104	C₂²	semidirect
26. C₄³×C₅	C₂²	semidirect
27. C₂×#1962	C₅	direct (N × H)
47. C₅×C₄⋊Q₈	C₂×C₄	semidirect
49. C₅×#127	C₂×C₄	semidirect
51. C₅×#124	C₂×C₄	semidirect
68. C₂×C₄²×C₅	D₄	semidirect
74. C₂×#423	C₂×C₅	semidirect
75. C₂²×#104	C₂×C₅	semidirect
76. C₂×C₄³	C₂×C₅	semidirect
77. #1962	C₂×C₅	direct (N × H)
133. C₄²×C₅	C₂×D₄	semidirect
138. #532	C₄×C₅	semidirect
140. C₂×C₄⋊Q₈	C₄×C₅	semidirect
141. C₂×#127	C₄×C₅	semidirect
142. C₂×#124	C₄×C₅	semidirect
149. #423	C₂²×C₅	semidirect
152. C₂×#104	C₂²×C₅	semidirect
154. C₄³	C₂²×C₅	semidirect
181. C₂×C₄×C₅	#104	semidirect
217. C₄⋊Q₈	C₂×C₄×C₅	semidirect
219. #127	C₂×C₄×C₅	semidirect
221. #124	C₂×C₄×C₅	semidirect
238. C₂×C₄²	C₅×D₄	semidirect
259. C₄×C₅	C₂×#104	semidirect
318. C₄²	C₂×C₅×D₄	semidirect
322. C₂×C₅	#1962	direct (N × H)
351. C₂×C₄	C₅×#104	semidirect
368. C₅	C₂×#1962	direct (N × H)
385. C₄	C₂×C₅×#104	semidirect
392. C₂	C₅×#1962	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#532	2
C₂×C₅×#423	2
C₂²×C₅×#104	2
C₂×C₄³×C₅	2
C₅×#1962	2
C₂×#1962	5

Subgroups — C2×C5×#1962 #11943927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1962 #11943927