Subgroups — C₄×C₅×#904 #14416221

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#235	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5113	C₂	1	2	yes	maximal, complemented
5	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×Dic₁₂	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×D₂₄	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#204	C₂	1	4	yes	maximal, complemented
9	C₄×C₅×#135	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₄×C₅×#67	—	2	4	no	—
15	C₅×#926	C₂²	1	2	yes	—
16	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
17	C₅×#904	C₄	1	8	yes	direct product factor
18	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×#204	C₂²	1	2	yes	—
20	C₄×C₅×D₁₂	C₂²	1	4	yes	—
21	C₅×#872	—	2	2	no	—
22	C₄²×C₅×D₃	—	2	2	no	—
23	C₄×C₅×Dic₆	C₂²	1	4	yes	—
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#821	C₂²	1	4	yes	—
27	C₅×#818	C₂²	1	2	yes	—
28	C₅×#817	C₂²	1	2	yes	—
29	C₅×#816	C₂²	1	4	yes	—
30	C₄×#904	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₄×C₅×#41	—	3	2	no	—
33	C₄×C₅×Q₁₆	—	3	2	no	—
34	C₄×C₅×SD₁₆	—	3	4	no	—
35	C₄×C₅×D₈	—	3	2	no	—
36	C₅×#427	—	3	1	no	—
37	C₅×#416	—	3	2	no	—
38	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₅×#67	—	2	2	no	—
42	C₅×#235	—	2	4	no	—
43	C₅×#235	C₂×C₄	1	8	yes	complemented
44	C₂×C₅×D₁₂	C₂³	1	2	yes	—
45	C₂×C₄×C₅×D₃	—	2	2	no	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₅×Dic₆	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	2	yes	—
56	C₅×#217	—	2	2	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
58	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
59	C₅×Dic₃⋊C₄	—	2	4	no	—
60	C₄×C₅×Dic₃	—	2	4	no	—
61	C₄×C₅×Dic₃	—	2	2	no	—
62	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
63	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
64	C₅×#204	C₂×C₄	1	8	yes	complemented
65	C₂×#904	C₂×C₅	1	1	yes	characteristic
66	C₄×#235	C₂×C₅	1	2	yes	complemented
67	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
68	#5113	C₂×C₅	1	2	yes	complemented
69	#5106	C₂×C₅	1	1	yes	characteristic, complemented
70	C₄×Dic₁₂	C₂×C₅	1	2	yes	complemented
71	C₄×D₂₄	C₂×C₅	1	2	yes	complemented
72	C₄×#204	C₂×C₅	1	4	yes	complemented
73	C₂×C₅×#41	—	3	2	no	—
74	C₅×#135	—	3	8	no	—
75	C₂×C₅×Q₁₆	—	3	1	no	—
76	C₂×C₅×SD₁₆	—	3	2	no	—
77	C₂×C₅×D₈	—	3	1	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₄×C₅×Q₈	—	3	4	no	—
81	C₄×C₅×D₄	—	3	4	no	—
82	C₄×C₅×D₄	—	6	4	no	—
83	C₅×#117	—	3	2	no	—
84	C₅×#117	—	6	2	no	—
85	C₂×C₄²×C₅	—	6	2	no	—
86	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
87	C₅×#107	—	3	2	no	—
88	C₅×#106	—	3	2	no	—
89	C₅×#103	—	3	4	no	—
90	C₅×#102	—	3	4	no	—
91	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
92	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
93	C₄×#135	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	#41	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
103	C₅×#67	—	2	8	no	—
104	C₂×C₅×Dic₃	—	2	2	no	—
105	C₂×C₅×Dic₃	—	2	4	no	—
106	C₅×D₁₂	—	2	2	no	—
107	C₅×D₁₂	C₂²×C₄	1	4	yes	—
108	C₄×C₅×D₃	—	2	8	no	—
109	C₄×C₅×D₃	—	4	8	no	—
110	C₅×Dic₆	—	2	2	no	—
111	C₅×Dic₆	C₂²×C₄	1	4	yes	—
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
115	C₂×#235	C₂²×C₅	1	2	yes	—
116	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
119	C₄×#67	—	2	4	no	—
120	#926	C₂²×C₅	1	2	yes	—
121	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
122	#904	C₄×C₅	1	8	yes	direct product factor
123	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
124	C₂×#204	C₂²×C₅	1	2	yes	—
125	C₄×D₁₂	C₂²×C₅	1	4	yes	—
126	#872	—	2	2	no	—
127	C₄²×D₃	—	2	2	no	—
128	C₄×Dic₆	C₂²×C₅	1	4	yes	—
129	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
130	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
131	#821	C₂²×C₅	1	4	yes	—
132	#818	C₂²×C₅	1	2	yes	—
133	#817	C₂²×C₅	1	2	yes	—
134	#816	C₂²×C₅	1	4	yes	—
135	C₅×#41	—	3	8	no	—
136	C₅×#41	—	6	4	no	—
137	C₂×C₅×Q₈	—	3	2	no	—
138	C₂×C₅×D₄	—	3	2	no	—
139	C₂×C₅×D₄	—	6	2	no	—
140	C₂²×C₄×C₅	—	6	2	no	—
141	C₂²×C₄×C₅	—	6	4	no	—
142	C₂²×C₄×C₅	D₁₂	1	2	yes	—
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×Q₁₆	—	3	4	no	—
145	C₅×SD₁₆	—	3	8	no	—
146	C₅×D₈	—	3	4	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
149	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
150	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	3	4	no	—
153	C₅×C₄⋊C₄	—	6	4	no	—
154	C₅×C₂²⋊C₄	—	6	2	no	—
155	C₅×C₂²⋊C₄	—	6	4	no	—
156	C₄²×C₅	—	6	2	no	—
157	C₄²×C₅	—	6	4	no	—
158	C₄²×C₅	D₁₂	1	1	yes	characteristic
159	C₄²×C₅	D₁₂	1	1	yes	characteristic
160	C₄²×C₅	C₂²×D₃	1	2	yes	—
161	C₂×#135	—	3	1	no	—
162	C₄×#41	—	3	2	no	—
163	C₄×Q₁₆	—	3	2	no	—
164	C₄×SD₁₆	—	3	4	no	—
165	C₄×D₈	—	3	2	no	—
166	#427	—	3	1	no	—
167	#416	—	3	2	no	—
168	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	4	no	—
173	C₂×C₅×D₃	—	4	4	no	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
176	C₃×C₄×C₅	#135	1	4	yes	complemented
177	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
179	C₅×Dic₃	—	2	4	no	—
180	C₅×Dic₃	—	4	4	no	—
181	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₂×#67	—	2	2	no	—
184	#235	—	2	4	no	—
185	#235	C₂×C₄×C₅	1	8	yes	complemented
186	C₂×D₁₂	C₂³×C₅	1	2	yes	—
187	C₂×C₄×D₃	—	2	2	no	—
188	C₂×C₄×D₃	—	2	4	no	—
189	C₂×Dic₆	C₂³×C₅	1	2	yes	—
190	C₂×C₃×C₈	—	2	2	no	—
191	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
192	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
193	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
195	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
196	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
197	C₃×C₄²	C₂³×C₅	1	2	yes	—
198	#217	—	2	2	no	—
199	(C₂×D₃)⋊C₄	—	2	4	no	—
200	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
201	Dic₃⋊C₄	—	2	4	no	—
202	C₄×Dic₃	—	2	4	no	—
203	C₄×Dic₃	—	2	2	no	—
204	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
205	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
206	#204	C₂×C₄×C₅	1	8	yes	complemented
207	C₂³×C₅	—	6	2	no	—
208	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
209	C₅×Q₈	—	3	4	no	—
210	C₅×Q₈	—	6	2	no	—
211	C₅×D₄	—	3	4	no	—
212	C₅×D₄	—	6	8	no	—
213	C₅×D₄	—	6	2	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	6	2	no	—
216	C₂×C₄×C₅	—	6	8	no	—
217	C₂×C₄×C₅	—	6	4	no	—
218	C₂×C₄×C₅	—	12	8	no	—
219	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
220	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
221	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
223	C₂×C₄×C₅	#235	1	2	yes	—
224	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
227	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
228	C₂×#41	—	3	2	no	—
229	#135	—	3	8	no	—
230	C₂×Q₁₆	—	3	1	no	—
231	C₂×SD₁₆	—	3	2	no	—
232	C₂×D₈	—	3	1	no	—
233	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
234	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄×Q₈	—	3	4	no	—
236	C₄×D₄	—	3	4	no	—
237	C₄×D₄	—	6	4	no	—
238	#117	—	3	2	no	—
239	#117	—	6	2	no	—
240	C₂×C₄²	—	6	2	no	—
241	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
242	#107	—	3	2	no	—
243	#106	—	3	2	no	—
244	#103	—	3	4	no	—
245	#102	—	3	4	no	—
246	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
247	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#135	1	2	yes	—
251	C₅×D₃	—	4	4	no	—
252	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂²×D₃	—	2	2	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
259	C₂×C₃×C₄	C₅×#41	1	2	yes	—
260	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
261	#67	—	2	8	no	—
262	C₂×Dic₃	—	2	2	no	—
263	C₂×Dic₃	—	2	4	no	—
264	D₁₂	—	2	2	no	—
265	D₁₂	C₂²×C₄×C₅	1	4	yes	—
266	C₄×D₃	—	2	8	no	—
267	C₄×D₃	—	4	8	no	—
268	Dic₆	—	2	2	no	—
269	Dic₆	C₂²×C₄×C₅	1	4	yes	—
270	C₃×C₈	—	2	2	no	—
271	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
272	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	6	4	no	—
275	C₂²×C₅	—	12	4	no	—
276	C₂²×C₅	C₄×D₁₂	1	2	yes	—
277	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	6	4	no	—
280	C₄×C₅	—	12	4	no	—
281	C₄×C₅	C₄×D₁₂	1	2	yes	—
282	C₄×C₅	#904	1	4	yes	direct product factor
283	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
284	C₄×C₅	C₂×#235	1	1	yes	characteristic
285	#41	—	3	8	no	—
286	#41	—	6	4	no	—
287	C₂×Q₈	—	3	2	no	—
288	C₂×D₄	—	3	2	no	—
289	C₂×D₄	—	6	2	no	—
290	C₂²×C₄	—	6	2	no	—
291	C₂²×C₄	—	6	4	no	—
292	C₂²×C₄	C₅×D₁₂	1	2	yes	—
293	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
294	Q₁₆	—	3	4	no	—
295	SD₁₆	—	3	8	no	—
296	D₈	—	3	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
299	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
300	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₄⋊C₄	—	3	4	no	—
303	C₄⋊C₄	—	6	4	no	—
304	C₂²⋊C₄	—	6	2	no	—
305	C₂²⋊C₄	—	6	4	no	—
306	C₄²	—	6	2	no	—
307	C₄²	—	6	4	no	—
308	C₄²	C₅×D₁₂	1	1	yes	characteristic
309	C₄²	C₅×D₁₂	1	1	yes	characteristic
310	C₄²	C₂²×C₅×D₃	1	2	yes	—
311	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
314	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
315	C₂×D₃	—	2	4	no	—
316	C₂×D₃	—	4	4	no	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
319	C₃×C₄	C₅×#135	1	4	yes	complemented
320	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
321	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
322	Dic₃	—	2	4	no	—
323	Dic₃	—	4	4	no	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	12	4	no	—
326	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
327	C₂×C₅	C₂×#904	1	2	yes	—
328	C₂³	—	6	2	no	—
329	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
330	Q₈	—	3	4	no	—
331	Q₈	—	6	2	no	—
332	D₄	—	3	4	no	—
333	D₄	—	6	8	no	—
334	D₄	—	6	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	6	2	no	—
337	C₂×C₄	—	6	8	no	—
338	C₂×C₄	—	6	4	no	—
339	C₂×C₄	—	12	8	no	—
340	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
341	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
342	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
344	C₂×C₄	C₅×#235	1	2	yes	—
345	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₈	—	2	2	no	—
347	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
348	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
351	C₂×C₃	C₂×C₅×#135	1	2	yes	—
352	D₃	—	4	4	no	—
353	C₅	C₄×#904	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	2	no	—
355	C₂²	—	6	4	no	—
356	C₂²	—	12	4	no	—
357	C₂²	C₄×C₅×D₁₂	1	2	yes	—
358	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	6	4	no	—
361	C₄	—	12	4	no	—
362	C₄	C₄×C₅×D₁₂	1	2	yes	—
363	C₄	C₅×#904	1	4	yes	direct product factor
364	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
365	C₄	C₂×C₅×#235	1	1	yes	characteristic
366	C₃	C₄×C₅×#135	1	1	yes	characteristic, complemented, Sylow
367	C₂	—	2	2	no	—
368	C₂	—	12	4	no	—
369	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic
370	C₂	C₂×C₅×#904	1	2	yes	—

	subgroup	G/H
center	C₄²×C₅	D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₄×C₅×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×#235	C₂	semidirect
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₅×#5113	C₂	semidirect
5. C₅×#5106	C₂	semidirect
6. C₄×C₅×Dic₁₂	C₂	semidirect
7. C₄×C₅×D₂₄	C₂	semidirect
8. C₄×C₅×#204	C₂	semidirect
17. C₅×#904	C₄	direct (N × H)
30. C₄×#904	C₅	direct (N × H)
38. C₂×C₄×C₅×C₈	D₃	semidirect
43. C₅×#235	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₅×Dic₁₂	C₂×C₄	semidirect
63. C₅×D₂₄	C₂×C₄	semidirect
64. C₅×#204	C₂×C₄	semidirect
66. C₄×#235	C₂×C₅	semidirect
67. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
68. #5113	C₂×C₅	semidirect
69. #5106	C₂×C₅	semidirect
70. C₄×Dic₁₂	C₂×C₅	semidirect
71. C₄×D₂₄	C₂×C₅	semidirect
72. C₄×#204	C₂×C₅	semidirect
122. #904	C₄×C₅	direct (N × H)
148. C₂×C₅×C₈	C₄×D₃	semidirect
168. C₂×C₄×C₈	C₅×D₃	semidirect
176. C₃×C₄×C₅	#135	semidirect
185. #235	C₂×C₄×C₅	semidirect
191. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
204. Dic₁₂	C₂×C₄×C₅	semidirect
205. D₂₄	C₂×C₄×C₅	semidirect
206. #204	C₂×C₄×C₅	semidirect
282. C₄×C₅	#904	direct (N × H)
298. C₂×C₈	C₄×C₅×D₃	semidirect
311. C₃×C₅	C₄×#135	semidirect
319. C₃×C₄	C₅×#135	semidirect
353. C₅	C₄×#904	direct (N × H)
363. C₄	C₅×#904	direct (N × H)
366. C₃	C₄×C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#904	2
C₄×C₅×#235	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#5113	2
C₅×#5106	2
C₄×C₅×Dic₁₂	2
C₄×C₅×D₂₄	2
C₄×C₅×#204	2
C₄×C₅×#135	3
C₄×#904	5

Subgroups — C4×C5×#904 #14416221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#904 #14416221