Subgroups — C₂×C₅×#4883 #14427687

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#895	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#809	C₂	1	2	yes	maximal, complemented
6	C₅×#4883	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#466	—	3	1	no	maximal, Hall
8	C₂²×C₅×D₁₂	—	2	2	no	—
9	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₂₄	—	2	4	no	—
16	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
17	C₂×C₅×D₃×C₈	—	2	4	no	—
18	C₂×C₅×D₃×C₈	C₂²	1	4	yes	complemented
19	C₅×#895	—	2	4	no	—
20	C₅×#895	C₂²	1	8	yes	complemented
21	C₃×C₅×#107	C₂²	1	4	yes	complemented
22	C₅×#809	C₂²	1	8	yes	complemented
23	C₂×#4883	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	—	3	1	no	—
25	C₂³×C₅×C₈	—	3	1	no	—
26	C₂×C₅×#121	—	3	2	no	—
27	C₅×#466	—	3	8	no	—
28	C₂×C₅×#107	D₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#102	—	3	2	no	—
30	C₂³×C₅×D₃	—	2	2	no	—
31	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
35	C₂×C₅×D₁₂	—	2	4	no	—
36	C₂×C₅×D₁₂	—	2	4	no	—
37	C₂×C₅×D₁₂	—	2	8	no	—
38	C₂×C₅×D₁₂	—	2	2	no	—
39	C₂×C₅×D₁₂	—	4	8	no	—
40	C₂×C₅×D₁₂	C₂³	1	4	yes	—
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	2	2	no	—
43	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	—	2	2	no	—
48	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
49	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
52	C₅×D₂₄	—	2	8	no	—
53	C₅×D₃×C₈	—	2	8	no	—
54	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×#895	C₂×C₅	1	2	yes	complemented
57	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×#809	C₂×C₅	1	2	yes	complemented
59	#4883	C₂×C₅	1	8	yes	direct product factor
60	C₂²×C₅×D₄	—	3	2	no	—
61	C₂²×C₅×D₄	—	6	2	no	—
62	C₂³×C₄×C₅	—	3	1	no	—
63	C₂×C₅×D₈	—	3	4	no	—
64	C₂×C₅×D₈	—	6	4	no	—
65	C₂²×C₅×C₈	—	3	1	no	—
66	C₂²×C₅×C₈	—	3	4	no	—
67	C₂²×C₅×C₈	—	6	4	no	—
68	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
69	C₅×#121	—	3	8	no	—
70	C₅×#121	—	6	4	no	—
71	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
73	C₅×#107	C₂×D₃	1	4	yes	complemented
74	C₅×#102	—	3	8	no	—
75	C₂×#466	—	3	1	no	Sylow
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₅×D₃	—	2	2	no	—
78	C₂²×C₅×D₃	—	2	2	no	—
79	C₂²×C₅×D₃	—	2	4	no	—
80	C₂²×C₅×D₃	—	4	4	no	—
81	C₂²×C₅×D₃	—	4	4	no	—
82	C₂²×C₅×D₃	—	4	4	no	—
83	C₂²×C₅×D₃	D₈	1	4	yes	complemented
84	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₂×C₅×Dic₃	—	2	2	no	—
92	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
93	C₅×D₁₂	—	2	4	no	—
94	C₅×D₁₂	—	2	4	no	—
95	C₅×D₁₂	—	4	16	no	—
96	C₅×D₁₂	—	4	4	no	—
97	C₄×C₅×D₃	—	2	4	no	—
98	C₄×C₅×D₃	—	2	2	no	—
99	C₄×C₅×D₃	—	2	2	no	—
100	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
101	C₅×C₃⋊C₈	—	2	2	no	—
102	C₂²×D₁₂	—	2	2	no	—
103	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
104	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
105	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
107	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
108	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
109	C₂×D₂₄	—	2	4	no	—
110	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
111	C₂×D₃×C₈	—	2	4	no	—
112	C₂×D₃×C₈	C₂²×C₅	1	4	yes	complemented
113	#895	—	2	4	no	—
114	#895	C₂²×C₅	1	8	yes	complemented
115	C₃×#107	C₂²×C₅	1	4	yes	complemented
116	#809	C₂²×C₅	1	8	yes	complemented
117	C₂⁴×C₅	—	3	1	no	—
118	C₂⁴×C₅	—	6	2	no	—
119	C₂×C₅×D₄	—	3	4	no	—
120	C₂×C₅×D₄	—	6	8	no	—
121	C₂×C₅×D₄	—	6	4	no	—
122	C₂×C₅×D₄	—	6	2	no	—
123	C₂×C₅×D₄	—	6	4	no	—
124	C₂×C₅×D₄	—	12	8	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	3	1	no	—
127	C₂²×C₄×C₅	—	3	2	no	—
128	C₂²×C₄×C₅	—	3	2	no	—
129	C₂²×C₄×C₅	—	6	2	no	—
130	C₂²×C₄×C₅	—	6	2	no	—
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₅×D₈	—	6	8	no	—
133	C₂×C₅×C₈	—	3	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₂×C₅×C₈	—	6	8	no	—
136	C₂×C₅×C₈	D₁₂	1	4	yes	complemented
137	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
140	C₅×C₂²⋊C₄	—	6	8	no	—
141	C₂²×D₈	—	3	1	no	—
142	C₂³×C₈	—	3	1	no	—
143	C₂×#121	—	3	2	no	—
144	#466	—	3	8	no	—
145	C₂×#107	C₅×D₃	1	1	yes	characteristic, complemented
146	C₂×#102	—	3	2	no	—
147	C₂²×C₃×C₅	#121	1	2	yes	—
148	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
149	C₂²×C₃×C₅	#135	1	2	yes	—
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₅×D₃	—	2	2	no	—
152	C₂×C₅×D₃	—	2	2	no	—
153	C₂×C₅×D₃	—	2	8	no	—
154	C₂×C₅×D₃	—	4	4	no	—
155	C₂×C₅×D₃	—	4	4	no	—
156	C₂×C₅×D₃	—	4	4	no	—
157	C₂×C₅×D₃	—	8	8	no	—
158	C₂×C₅×D₃	C₂×D₈	1	4	yes	complemented
159	C₃×C₄×C₅	—	4	4	no	—
160	C₃×C₄×C₅	#121	1	2	yes	—
161	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
163	C₅×Dic₃	—	2	2	no	—
164	C₂³×D₃	—	2	2	no	—
165	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
169	C₂×D₁₂	—	2	4	no	—
170	C₂×D₁₂	—	2	4	no	—
171	C₂×D₁₂	—	2	8	no	—
172	C₂×D₁₂	—	2	2	no	—
173	C₂×D₁₂	—	4	8	no	—
174	C₂×D₁₂	C₂³×C₅	1	4	yes	—
175	C₂×C₄×D₃	—	2	2	no	—
176	C₂×C₄×D₃	—	2	2	no	—
177	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
178	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
179	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
180	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
183	(C₂×D₃)⋊C₄	—	2	8	no	—
184	C₂×C₃⋊C₈	—	2	2	no	—
185	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
186	D₂₄	—	2	8	no	—
187	D₃×C₈	—	2	8	no	—
188	C₂³×C₅	—	3	4	no	—
189	C₂³×C₅	—	3	2	no	—
190	C₂³×C₅	—	6	2	no	—
191	C₂³×C₅	—	6	2	no	—
192	C₂³×C₅	—	6	4	no	—
193	C₂³×C₅	—	12	4	no	—
194	C₂³×C₅	—	12	4	no	—
195	C₂³×C₅	—	12	4	no	—
196	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
197	C₅×D₄	—	6	4	no	—
198	C₅×D₄	—	6	4	no	—
199	C₅×D₄	—	12	16	no	—
200	C₅×D₄	—	12	4	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	3	2	no	—
203	C₂×C₄×C₅	—	4	4	no	—
204	C₂×C₄×C₅	—	6	2	no	—
205	C₂×C₄×C₅	—	6	4	no	—
206	C₂×C₄×C₅	—	6	2	no	—
207	C₂×C₄×C₅	—	6	2	no	—
208	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
209	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	#239	1	2	yes	—
211	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
212	C₅×C₈	—	6	2	no	—
213	C₅×C₈	C₂×D₁₂	1	4	yes	complemented
214	C₂²×D₄	—	3	2	no	—
215	C₂²×D₄	—	6	2	no	—
216	C₂³×C₄	—	3	1	no	—
217	C₂×D₈	—	3	4	no	—
218	C₂×D₈	—	6	4	no	—
219	C₂²×C₈	—	3	1	no	—
220	C₂²×C₈	—	3	4	no	—
221	C₂²×C₈	—	6	4	no	—
222	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
223	#121	—	3	8	no	—
224	#121	—	6	4	no	—
225	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
226	C₂×C₂²⋊C₄	—	6	2	no	—
227	#107	C₂×C₅×D₃	1	4	yes	complemented
228	#102	—	3	8	no	—
229	C₂×C₃×C₅	#466	1	4	yes	complemented
230	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
231	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
233	C₅×D₃	—	2	4	no	—
234	C₅×D₃	—	8	4	no	—
235	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
236	C₂²×D₃	—	2	2	no	—
237	C₂²×D₃	—	2	2	no	—
238	C₂²×D₃	—	2	4	no	—
239	C₂²×D₃	—	4	4	no	—
240	C₂²×D₃	—	4	4	no	—
241	C₂²×D₃	—	4	4	no	—
242	C₂²×D₃	C₅×D₈	1	4	yes	complemented
243	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	4	4	no	—
246	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₅×#41	1	2	yes	—
249	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
250	C₂×Dic₃	—	2	2	no	—
251	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
252	D₁₂	—	2	4	no	—
253	D₁₂	—	2	4	no	—
254	D₁₂	—	4	16	no	—
255	D₁₂	—	4	4	no	—
256	C₄×D₃	—	2	4	no	—
257	C₄×D₃	—	2	2	no	—
258	C₄×D₃	—	2	2	no	—
259	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
260	C₃⋊C₈	—	2	2	no	—
261	C₂²×C₅	—	3	4	no	—
262	C₂²×C₅	—	6	8	no	—
263	C₂²×C₅	—	6	2	no	—
264	C₂²×C₅	—	6	2	no	—
265	C₂²×C₅	—	12	4	no	—
266	C₂²×C₅	—	12	4	no	—
267	C₂²×C₅	—	12	4	no	—
268	C₂²×C₅	—	24	8	no	—
269	C₂²×C₅	#895	1	2	yes	—
270	C₂²×C₅	D₃×D₈	1	2	yes	—
271	C₂²×C₅	#919	1	2	yes	—
272	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
273	C₄×C₅	—	4	4	no	—
274	C₄×C₅	—	6	2	no	—
275	C₄×C₅	#895	1	2	yes	—
276	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
277	C₄×C₅	C₂×#239	1	1	yes	characteristic
278	C₂⁴	—	3	1	no	—
279	C₂⁴	—	6	2	no	—
280	C₂×D₄	—	3	4	no	—
281	C₂×D₄	—	6	8	no	—
282	C₂×D₄	—	6	4	no	—
283	C₂×D₄	—	6	2	no	—
284	C₂×D₄	—	6	4	no	—
285	C₂×D₄	—	12	8	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	3	1	no	—
288	C₂²×C₄	—	3	2	no	—
289	C₂²×C₄	—	3	2	no	—
290	C₂²×C₄	—	6	2	no	—
291	C₂²×C₄	—	6	2	no	—
292	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
293	D₈	—	6	8	no	—
294	C₂×C₈	—	3	2	no	—
295	C₂×C₈	—	6	2	no	—
296	C₂×C₈	—	6	8	no	—
297	C₂×C₈	C₅×D₁₂	1	4	yes	complemented
298	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
301	C₂²⋊C₄	—	6	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	C₅×#121	1	2	yes	—
304	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
305	C₂²×C₃	C₅×#135	1	2	yes	—
306	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
307	C₂×D₃	—	2	8	no	—
308	C₂×D₃	—	2	2	no	—
309	C₂×D₃	—	2	2	no	—
310	C₂×D₃	—	4	4	no	—
311	C₂×D₃	—	4	4	no	—
312	C₂×D₃	—	4	4	no	—
313	C₂×D₃	—	8	8	no	—
314	C₂×D₃	C₂×C₅×D₈	1	4	yes	complemented
315	C₃×C₄	—	4	4	no	—
316	C₃×C₄	C₅×#121	1	2	yes	—
317	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
318	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
319	Dic₃	—	2	2	no	—
320	C₂×C₅	—	6	4	no	—
321	C₂×C₅	—	24	4	no	—
322	C₂×C₅	#4883	1	4	yes	direct product factor
323	C₂×C₅	C₂×#895	1	1	yes	characteristic
324	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
325	C₂×C₅	C₂×#919	1	1	yes	characteristic
326	C₂³	—	3	4	no	—
327	C₂³	—	3	2	no	—
328	C₂³	—	6	2	no	—
329	C₂³	—	6	2	no	—
330	C₂³	—	6	4	no	—
331	C₂³	—	12	4	no	—
332	C₂³	—	12	4	no	—
333	C₂³	—	12	4	no	—
334	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
335	D₄	—	6	4	no	—
336	D₄	—	6	4	no	—
337	D₄	—	12	16	no	—
338	D₄	—	12	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	3	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	—	6	4	no	—
344	C₂×C₄	—	6	2	no	—
345	C₂×C₄	—	6	2	no	—
346	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
347	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
348	C₂×C₄	C₅×#239	1	2	yes	—
349	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
350	C₈	—	6	2	no	—
351	C₈	C₂×C₅×D₁₂	1	4	yes	complemented
352	C₂×C₃	C₅×#466	1	4	yes	complemented
353	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
354	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
355	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
356	D₃	—	2	4	no	—
357	D₃	—	8	4	no	—
358	C₅	C₂×#4883	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	3	4	no	—
360	C₂²	—	6	2	no	—
361	C₂²	—	6	2	no	—
362	C₂²	—	6	8	no	—
363	C₂²	—	12	4	no	—
364	C₂²	—	12	4	no	—
365	C₂²	—	12	4	no	—
366	C₂²	—	24	8	no	—
367	C₂²	C₅×#895	1	2	yes	—
368	C₂²	C₅×D₃×D₈	1	2	yes	—
369	C₂²	C₅×#919	1	2	yes	—
370	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
371	C₄	—	4	4	no	—
372	C₄	—	6	2	no	—
373	C₄	C₅×#895	1	2	yes	—
374	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
375	C₄	C₂×C₅×#239	1	1	yes	characteristic
376	C₃	C₂×C₅×#466	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	6	4	no	—
378	C₂	—	24	4	no	—
379	C₂	C₅×#4883	1	4	yes	direct product factor
380	C₂	C₂×C₅×#895	1	1	yes	characteristic
381	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
382	C₂	C₂×C₅×#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#107	D₃
hypocenter	C₃	C₂×C₅×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#107

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₂₄	C₂	semidirect
2. C₂²×C₅×D₃×C₈	C₂	semidirect
3. C₂×C₅×#895	C₂	semidirect
4. C₂×C₃×C₅×#107	C₂	semidirect
5. C₂×C₅×#809	C₂	semidirect
6. C₅×#4883	C₂	direct (N × H)
16. C₂×C₅×D₂₄	C₂²	semidirect
18. C₂×C₅×D₃×C₈	C₂²	semidirect
20. C₅×#895	C₂²	semidirect
21. C₃×C₅×#107	C₂²	semidirect
22. C₅×#809	C₂²	semidirect
23. C₂×#4883	C₅	direct (N × H)
28. C₂×C₅×#107	D₃	semidirect
45. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×D₂₄	C₂×C₅	semidirect
55. C₂²×D₃×C₈	C₂×C₅	semidirect
56. C₂×#895	C₂×C₅	semidirect
57. C₂×C₃×#107	C₂×C₅	semidirect
58. C₂×#809	C₂×C₅	semidirect
59. #4883	C₂×C₅	direct (N × H)
73. C₅×#107	C₂×D₃	semidirect
83. C₂²×C₅×D₃	D₈	semidirect
100. C₃×C₅×C₈	C₂×D₄	semidirect
110. C₂×D₂₄	C₂²×C₅	semidirect
112. C₂×D₃×C₈	C₂²×C₅	semidirect
114. #895	C₂²×C₅	semidirect
115. C₃×#107	C₂²×C₅	semidirect
116. #809	C₂²×C₅	semidirect
136. C₂×C₅×C₈	D₁₂	semidirect
145. C₂×#107	C₅×D₃	semidirect
158. C₂×C₅×D₃	C₂×D₈	semidirect
179. C₂×C₃×C₈	C₅×D₄	semidirect
213. C₅×C₈	C₂×D₁₂	semidirect
227. #107	C₂×C₅×D₃	semidirect
229. C₂×C₃×C₅	#466	semidirect
242. C₂²×D₃	C₅×D₈	semidirect
259. C₃×C₈	C₂×C₅×D₄	semidirect
297. C₂×C₈	C₅×D₁₂	semidirect
302. C₃×C₅	C₂×#466	semidirect
314. C₂×D₃	C₂×C₅×D₈	semidirect
322. C₂×C₅	#4883	direct (N × H)
351. C₈	C₂×C₅×D₁₂	semidirect
352. C₂×C₃	C₅×#466	semidirect
358. C₅	C₂×#4883	direct (N × H)
376. C₃	C₂×C₅×#466	semidirect
379. C₂	C₅×#4883	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₂₄	2
C₂²×C₅×D₃×C₈	2
C₂×C₅×#895	2
C₂×C₃×C₅×#107	2
C₂×C₅×#809	2
C₅×#4883	2
C₂×C₅×#466	3
C₂×#4883	5

Subgroups — C2×C5×#4883 #14427687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4883 #14427687