Subgroups — C₂×C₅×#4915 #14478377

Order 1920.

720 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×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#912	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#829	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#827	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4915	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×Dic₂₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#510	—	3	1	no	maximal, Hall
10	C₂×C₅×D₃×Q₈	—	2	1	no	—
11	C₂×C₅×#237	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#216	—	2	1	no	—
15	C₂×C₅×#214	—	2	1	no	—
16	C₅×D₃×Q₁₆	—	2	2	no	—
17	C₅×D₃×Q₁₆	C₂²	1	4	yes	complemented
18	C₅×#912	—	2	2	no	—
19	C₅×#912	C₂²	1	4	yes	—
20	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×SD₃₂	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
25	C₅×#829	C₂²	1	4	yes	complemented
26	C₅×#827	C₂²	1	4	yes	complemented
27	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₅×Dic₂₄	C₂²	1	4	yes	complemented
29	C₅×#798	C₂²	1	4	yes	complemented
30	C₂×#4915	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₂²×C₅×Q₁₆	—	3	1	no	—
33	C₅×#510	—	3	8	no	—
34	C₂×C₅×Q₃₂	—	3	1	no	—
35	C₂×C₅×Q₃₂	—	3	1	no	—
36	C₂×C₅×SD₃₂	—	3	1	no	—
37	C₂×C₅×SD₃₂	D₃	1	1	yes	characteristic, complemented
38	C₂×C₅×M₃₂	—	3	1	no	—
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₅×#67	—	4	1	no	—
42	C₂²×C₅×Dic₃	—	4	1	no	—
43	C₅×D₃×Q₈	—	2	4	no	—
44	C₅×D₃×Q₈	—	4	2	no	—
45	C₅×#237	—	2	4	no	—
46	C₅×#237	—	4	2	no	—
47	C₂×C₄×C₅×D₃	—	4	1	no	—
48	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
49	C₂×C₅×Dic₆	—	2	1	no	—
50	C₂×C₅×Dic₆	—	2	1	no	—
51	C₂×C₅×Dic₆	—	4	1	no	—
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
54	C₃×C₅×D₈	—	2	1	no	—
55	C₃×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×#216	—	2	4	no	—
58	C₅×#214	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
60	C₅×Dic₁₂	—	2	1	no	—
61	C₅×Dic₁₂	—	2	1	no	—
62	C₅×Dic₁₂	C₂³	1	2	yes	—
63	C₅×Dic₁₂	C₂³	1	2	yes	—
64	C₅×D₃×C₈	D₄	1	2	yes	—
65	C₅×D₃×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	—
67	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
68	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#912	C₂×C₅	1	1	yes	characteristic
70	C₂×C₃×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#829	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#827	C₂×C₅	1	1	yes	characteristic, complemented
73	#4915	C₂×C₅	1	8	yes	direct product factor
74	C₂×Dic₂₄	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#798	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	—	6	1	no	—
77	C₂²×C₅×Q₈	—	6	1	no	—
78	C₅×#135	—	3	4	no	—
79	C₅×#135	—	6	2	no	—
80	C₂×C₅×Q₁₆	—	3	4	no	—
81	C₂×C₅×Q₁₆	—	3	1	no	—
82	C₂×C₅×Q₁₆	—	3	1	no	—
83	C₂×C₅×Q₁₆	—	6	2	no	—
84	C₂×C₅×Q₁₆	—	6	1	no	—
85	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
86	C₂×C₅×SD₁₆	—	6	1	no	—
87	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	—	3	1	no	—
89	C₅×Q₃₂	—	3	4	no	—
90	C₅×Q₃₂	—	3	4	no	—
91	C₅×SD₃₂	—	3	4	no	—
92	C₅×SD₃₂	C₂×D₃	1	4	yes	complemented
93	C₅×M₃₂	—	3	4	no	—
94	C₂×C₅×C₁₆	—	3	1	no	—
95	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic
96	C₂×#510	—	3	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×C₅×D₃	D₈	1	1	yes	characteristic
99	C₃×C₅×Q₈	—	2	2	no	—
100	C₃×C₅×Q₈	—	4	1	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₅×#67	—	4	4	no	—
106	C₂×C₅×Dic₃	—	4	1	no	—
107	C₂×C₅×Dic₃	—	4	1	no	—
108	C₂×C₅×Dic₃	—	4	4	no	—
109	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
110	C₄×C₅×D₃	—	4	4	no	—
111	C₄×C₅×D₃	D₈	1	2	yes	—
112	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
113	C₅×Dic₆	—	2	2	no	—
114	C₅×Dic₆	—	2	2	no	—
115	C₅×Dic₆	—	4	1	no	—
116	C₅×Dic₆	—	4	1	no	—
117	C₅×Dic₆	—	4	4	no	—
118	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
119	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
120	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
121	C₂×D₃×Q₈	—	2	1	no	—
122	C₂×#237	—	2	1	no	—
123	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
125	C₂×#216	—	2	1	no	—
126	C₂×#214	—	2	1	no	—
127	D₃×Q₁₆	—	2	2	no	—
128	D₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
129	#912	—	2	2	no	—
130	#912	C₂²×C₅	1	4	yes	—
131	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
132	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
133	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
134	C₃×SD₃₂	C₂²×C₅	1	4	yes	complemented
135	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
136	#829	C₂²×C₅	1	4	yes	complemented
137	#827	C₂²×C₅	1	4	yes	complemented
138	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
139	Dic₂₄	C₂²×C₅	1	4	yes	complemented
140	#798	C₂²×C₅	1	4	yes	complemented
141	C₅×#41	—	6	4	no	—
142	C₅×#41	—	12	2	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	6	4	no	—
145	C₂×C₅×Q₈	—	6	1	no	—
146	C₂×C₅×Q₈	—	6	1	no	—
147	C₂×C₅×Q₈	—	12	1	no	—
148	C₂×C₅×Q₈	—	12	2	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	12	1	no	—
151	C₂²×C₄×C₅	—	3	1	no	—
152	C₂²×C₄×C₅	—	12	1	no	—
153	C₂²×C₄×C₅	—	12	1	no	—
154	C₅×Q₁₆	—	2	1	no	—
155	C₅×Q₁₆	—	3	2	no	—
156	C₅×Q₁₆	—	3	2	no	—
157	C₅×Q₁₆	—	6	4	no	—
158	C₅×Q₁₆	—	6	1	no	—
159	C₅×Q₁₆	—	6	1	no	—
160	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
161	C₅×SD₁₆	—	6	4	no	—
162	C₅×D₈	—	2	1	no	—
163	C₅×D₈	C₂²×D₃	1	2	yes	—
164	C₂×C₅×C₈	—	3	1	no	—
165	C₂×C₅×C₈	—	3	2	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
168	C₅×C₁₆	—	3	2	no	—
169	C₅×C₁₆	C₂²×D₃	1	2	yes	—
170	C₂×#135	—	3	1	no	—
171	C₂²×Q₁₆	—	3	1	no	—
172	#510	—	3	8	no	—
173	C₂×Q₃₂	—	3	1	no	—
174	C₂×Q₃₂	—	3	1	no	—
175	C₂×SD₃₂	—	3	1	no	—
176	C₂×SD₃₂	C₅×D₃	1	1	yes	characteristic, complemented
177	C₂×M₃₂	—	3	1	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	8	2	no	—
180	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
185	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₅×Dic₃	—	4	2	no	—
187	C₅×Dic₃	—	4	2	no	—
188	C₅×Dic₃	C₂×D₈	1	2	yes	—
189	C₂×C₃×Q₈	—	2	1	no	—
190	C₂×C₃×D₄	—	2	1	no	—
191	C₂×#67	—	4	1	no	—
192	C₂²×Dic₃	—	4	1	no	—
193	D₃×Q₈	—	2	4	no	—
194	D₃×Q₈	—	4	2	no	—
195	#237	—	2	4	no	—
196	#237	—	4	2	no	—
197	C₂×C₄×D₃	—	4	1	no	—
198	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
199	C₂×Dic₆	—	2	1	no	—
200	C₂×Dic₆	—	2	1	no	—
201	C₂×Dic₆	—	4	1	no	—
202	C₃×Q₁₆	—	2	1	no	—
203	C₃×Q₁₆	C₂³×C₅	1	2	yes	—
204	C₃×D₈	—	2	1	no	—
205	C₃×D₈	C₂³×C₅	1	2	yes	—
206	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
207	#216	—	2	4	no	—
208	#214	—	2	4	no	—
209	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
210	Dic₁₂	—	2	1	no	—
211	Dic₁₂	—	2	1	no	—
212	Dic₁₂	C₂³×C₅	1	2	yes	—
213	Dic₁₂	C₂³×C₅	1	2	yes	—
214	D₃×C₈	C₅×D₄	1	2	yes	—
215	D₃×C₈	C₂³×C₅	1	2	yes	—
216	C₃×C₁₆	C₂³×C₅	1	2	yes	—
217	C₃⋊C₁₆	C₂³×C₅	1	2	yes	—
218	C₂³×C₅	—	3	1	no	—
219	C₂³×C₅	—	4	1	no	—
220	C₅×Q₈	—	2	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	6	2	no	—
223	C₅×Q₈	—	6	2	no	—
224	C₅×Q₈	—	12	4	no	—
225	C₅×Q₈	—	12	1	no	—
226	C₅×Q₈	—	12	1	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	12	4	no	—
230	C₂×C₄×C₅	—	3	1	no	—
231	C₂×C₄×C₅	—	3	2	no	—
232	C₂×C₄×C₅	—	3	2	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	12	4	no	—
235	C₂×C₄×C₅	—	12	4	no	—
236	C₂×C₄×C₅	—	12	1	no	—
237	C₂×C₄×C₅	—	12	1	no	—
238	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
239	C₅×C₈	—	3	2	no	—
240	C₅×C₈	D₃×D₄	1	1	yes	characteristic
241	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
242	C₂×#41	—	6	1	no	—
243	C₂²×Q₈	—	6	1	no	—
244	#135	—	3	4	no	—
245	#135	—	6	2	no	—
246	C₂×Q₁₆	—	3	4	no	—
247	C₂×Q₁₆	—	3	1	no	—
248	C₂×Q₁₆	—	3	1	no	—
249	C₂×Q₁₆	—	6	2	no	—
250	C₂×Q₁₆	—	6	1	no	—
251	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
252	C₂×SD₁₆	—	6	1	no	—
253	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
254	C₂²×C₈	—	3	1	no	—
255	Q₃₂	—	3	4	no	—
256	Q₃₂	—	3	4	no	—
257	SD₃₂	—	3	4	no	—
258	SD₃₂	C₂×C₅×D₃	1	4	yes	complemented
259	M₃₂	—	3	4	no	—
260	C₂×C₁₆	—	3	1	no	—
261	C₂×C₁₆	C₂×C₅×D₃	1	1	yes	characteristic
262	C₂×C₃×C₅	—	8	2	no	—
263	C₂×C₃×C₅	#510	1	2	yes	complemented
264	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
265	C₅×D₃	—	2	2	no	—
266	C₂³×C₃	—	4	1	no	—
267	C₂²×D₃	C₅×D₈	1	1	yes	characteristic
268	C₃×Q₈	—	2	2	no	—
269	C₃×Q₈	—	4	1	no	—
270	C₃×D₄	—	2	2	no	—
271	C₃×D₄	—	4	1	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
274	#67	—	4	4	no	—
275	C₂×Dic₃	—	4	1	no	—
276	C₂×Dic₃	—	4	1	no	—
277	C₂×Dic₃	—	4	4	no	—
278	C₂×Dic₃	C₅×D₈	1	1	yes	characteristic
279	C₄×D₃	—	4	4	no	—
280	C₄×D₃	C₅×D₈	1	2	yes	—
281	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
282	Dic₆	—	2	2	no	—
283	Dic₆	—	2	2	no	—
284	Dic₆	—	4	1	no	—
285	Dic₆	—	4	1	no	—
286	Dic₆	—	4	4	no	—
287	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
288	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
289	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
290	C₂²×C₅	—	3	2	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	—	6	2	no	—
293	C₂²×C₅	—	8	2	no	—
294	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
295	C₄×C₅	—	3	2	no	—
296	C₄×C₅	—	4	2	no	—
297	C₄×C₅	—	12	2	no	—
298	C₄×C₅	—	12	2	no	—
299	C₄×C₅	D₃×D₈	1	1	yes	characteristic
300	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
301	#41	—	6	4	no	—
302	#41	—	12	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	6	4	no	—
305	C₂×Q₈	—	6	1	no	—
306	C₂×Q₈	—	6	1	no	—
307	C₂×Q₈	—	12	1	no	—
308	C₂×Q₈	—	12	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	12	1	no	—
311	C₂²×C₄	—	3	1	no	—
312	C₂²×C₄	—	12	1	no	—
313	C₂²×C₄	—	12	1	no	—
314	Q₁₆	—	2	1	no	—
315	Q₁₆	—	3	2	no	—
316	Q₁₆	—	3	2	no	—
317	Q₁₆	—	6	4	no	—
318	Q₁₆	—	6	1	no	—
319	Q₁₆	—	6	1	no	—
320	Q₁₆	C₂²×C₅×D₃	1	2	yes	—
321	SD₁₆	—	6	4	no	—
322	D₈	—	2	1	no	—
323	D₈	C₂²×C₅×D₃	1	2	yes	—
324	C₂×C₈	—	3	1	no	—
325	C₂×C₈	—	3	2	no	—
326	C₂×C₈	—	3	2	no	—
327	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
328	C₁₆	—	3	2	no	—
329	C₁₆	C₂²×C₅×D₃	1	2	yes	—
330	C₃×C₅	C₂×#510	1	1	yes	characteristic, complemented, Hall
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	—	8	2	no	—
333	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
334	C₂×D₃	—	2	2	no	—
335	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
336	C₃×C₄	—	4	2	no	—
337	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
338	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
339	Dic₃	—	4	2	no	—
340	Dic₃	—	4	2	no	—
341	Dic₃	C₂×C₅×D₈	1	2	yes	—
342	C₂×C₅	—	6	2	no	—
343	C₂×C₅	—	8	2	no	—
344	C₂×C₅	#4915	1	2	yes	direct product factor
345	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
346	C₂³	—	3	1	no	—
347	C₂³	—	4	1	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	1	no	—
350	Q₈	—	6	2	no	—
351	Q₈	—	6	2	no	—
352	Q₈	—	12	4	no	—
353	Q₈	—	12	1	no	—
354	Q₈	—	12	1	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	12	4	no	—
358	C₂×C₄	—	3	1	no	—
359	C₂×C₄	—	3	2	no	—
360	C₂×C₄	—	3	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	12	4	no	—
363	C₂×C₄	—	12	4	no	—
364	C₂×C₄	—	12	1	no	—
365	C₂×C₄	—	12	1	no	—
366	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
367	C₈	—	3	2	no	—
368	C₈	C₅×D₃×D₄	1	1	yes	characteristic
369	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
370	C₂×C₃	—	8	2	no	—
371	C₂×C₃	C₅×#510	1	2	yes	complemented
372	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
373	D₃	—	2	2	no	—
374	C₅	C₂×#4915	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	—	3	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	6	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
380	C₄	—	3	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	12	2	no	—
383	C₄	—	12	2	no	—
384	C₄	C₅×D₃×D₈	1	1	yes	characteristic
385	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
386	C₃	C₂×C₅×#510	1	1	yes	characteristic, complemented, Sylow
387	C₂	—	6	2	no	—
388	C₂	—	8	2	no	—
389	C₂	C₅×#4915	1	2	yes	direct product factor
390	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
prime radical	C₂×C₅×#912	C₂
hypercenter	C₂×C₅×SD₃₂	D₃
hypocenter	C₃	C₂×C₅×#510
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₂×C₅×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×Q₁₆	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×C₅×#829	C₂	semidirect
5. C₂×C₅×#827	C₂	semidirect
6. C₅×#4915	C₂	direct (N × H)
7. C₂×C₅×Dic₂₄	C₂	semidirect
8. C₂×C₅×#798	C₂	semidirect
17. C₅×D₃×Q₁₆	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
25. C₅×#829	C₂²	semidirect
26. C₅×#827	C₂²	semidirect
28. C₅×Dic₂₄	C₂²	semidirect
29. C₅×#798	C₂²	semidirect
30. C₂×#4915	C₅	direct (N × H)
37. C₂×C₅×SD₃₂	D₃	semidirect
68. C₂×D₃×Q₁₆	C₂×C₅	semidirect
70. C₂×C₃×SD₃₂	C₂×C₅	semidirect
71. C₂×#829	C₂×C₅	semidirect
72. C₂×#827	C₂×C₅	semidirect
73. #4915	C₂×C₅	direct (N × H)
74. C₂×Dic₂₄	C₂×C₅	semidirect
75. C₂×#798	C₂×C₅	semidirect
92. C₅×SD₃₂	C₂×D₃	semidirect
128. D₃×Q₁₆	C₂²×C₅	semidirect
134. C₃×SD₃₂	C₂²×C₅	semidirect
136. #829	C₂²×C₅	semidirect
137. #827	C₂²×C₅	semidirect
139. Dic₂₄	C₂²×C₅	semidirect
140. #798	C₂²×C₅	semidirect
176. C₂×SD₃₂	C₅×D₃	semidirect
258. SD₃₂	C₂×C₅×D₃	semidirect
263. C₂×C₃×C₅	#510	semidirect
330. C₃×C₅	C₂×#510	semidirect
344. C₂×C₅	#4915	direct (N × H)
371. C₂×C₃	C₅×#510	semidirect
374. C₅	C₂×#4915	direct (N × H)
386. C₃	C₂×C₅×#510	semidirect
389. C₂	C₅×#4915	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×D₃×Q₁₆	2
C₂×C₅×#912	2
C₂×C₃×C₅×SD₃₂	2
C₂×C₅×#829	2
C₂×C₅×#827	2
C₅×#4915	2
C₂×C₅×Dic₂₄	2
C₂×C₅×#798	2
C₂×C₅×#510	3
C₂×#4915	5

Subgroups — C2×C5×#4915 #14478377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4915 #14478377