Subgroups — C₂×C₅×#5115 #14427684

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	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5115	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#821	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#466	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₅×#67	—	2	2	no	—
10	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	—	2	4	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	complemented
15	C₅×#930	—	2	4	no	—
16	C₅×#930	C₂²	1	8	yes	complemented
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×D₂₄	—	2	4	no	—
20	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
21	C₅×#821	C₂²	1	8	yes	complemented
22	C₅×#818	C₂²	1	4	yes	complemented
23	C₂×#5115	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	—	3	1	no	—
25	C₂³×C₅×C₈	D₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#121	—	3	2	no	—
27	C₅×#466	—	3	8	no	—
28	C₂×C₅×#107	—	3	1	no	—
29	C₂×C₅×#102	—	3	2	no	—
30	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
31	C₂³×C₅×D₃	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₅×#67	—	2	8	no	—
39	C₂×C₅×#67	—	4	8	no	—
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₂×C₅×D₁₂	—	2	4	no	—
42	C₂×C₅×D₁₂	—	2	4	no	—
43	C₂×C₅×D₁₂	—	2	2	no	—
44	C₂×C₅×D₁₂	C₂³	1	4	yes	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	—	2	8	no	—
47	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
51	C₅×C₄⋊Dic₃	—	2	2	no	—
52	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
53	C₅×D₂₄	—	2	8	no	—
54	C₂³×C₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#930	C₂×C₅	1	2	yes	complemented
56	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
57	#5115	C₂×C₅	1	8	yes	direct product factor
58	C₂×#821	C₂×C₅	1	2	yes	complemented
59	C₂×#818	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×C₅×D₄	—	3	2	no	—
61	C₂²×C₅×D₄	—	6	2	no	—
62	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
63	C₂×C₅×D₈	—	3	4	no	—
64	C₂×C₅×D₈	—	6	4	no	—
65	C₂²×C₅×C₈	—	2	4	no	—
66	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂×D₃	1	4	yes	complemented
69	C₅×#121	—	3	8	no	—
70	C₅×#121	—	6	4	no	—
71	C₂×C₅×C₄⋊C₄	—	3	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
73	C₅×#107	—	3	4	no	—
74	C₅×#102	—	3	8	no	—
75	C₂×#466	—	3	1	no	Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	D₈	1	4	yes	complemented
79	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	4	no	—
82	C₂²×C₅×D₃	—	4	4	no	—
83	C₂²×C₅×D₃	—	4	4	no	—
84	C₂²×C₅×D₃	—	4	4	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	C₅×#67	—	4	16	no	—
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	4	4	no	—
97	C₅×D₁₂	—	2	4	no	—
98	C₅×D₁₂	—	2	4	no	—
99	C₅×D₁₂	—	4	4	no	—
100	C₃×C₅×C₈	—	2	2	no	—
101	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂²×#67	—	2	2	no	—
104	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
105	C₂²×C₃×C₈	—	2	4	no	—
106	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₅	1	4	yes	complemented
109	#930	—	2	4	no	—
110	#930	C₂²×C₅	1	8	yes	complemented
111	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
112	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
113	C₂×D₂₄	—	2	4	no	—
114	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
115	#821	C₂²×C₅	1	8	yes	complemented
116	#818	C₂²×C₅	1	4	yes	complemented
117	C₂⁴×C₅	—	6	2	no	—
118	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
119	C₂×C₅×D₄	—	3	4	no	—
120	C₂×C₅×D₄	—	6	8	no	—
121	C₂×C₅×D₄	—	6	2	no	—
122	C₂×C₅×D₄	—	6	4	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	—	2	2	no	—
127	C₂²×C₄×C₅	—	6	2	no	—
128	C₂²×C₄×C₅	D₁₂	1	2	yes	—
129	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₅×D₈	—	6	8	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	8	no	—
135	C₂×C₅×C₈	#67	1	4	yes	complemented
136	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
137	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
138	C₅×C₄⋊C₄	—	3	4	no	—
139	C₅×C₄⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	—	6	8	no	—
141	C₂²×D₈	—	3	1	no	—
142	C₂³×C₈	C₅×D₃	1	1	yes	characteristic, complemented
143	C₂×#121	—	3	2	no	—
144	#466	—	3	8	no	—
145	C₂×#107	—	3	1	no	—
146	C₂×#102	—	3	2	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	8	no	—
150	C₂²×C₃×C₅	#121	1	2	yes	—
151	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
152	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
153	C₂²×C₃×C₅	#135	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₅×D₃	—	4	4	no	—
156	C₂×C₅×D₃	—	4	4	no	—
157	C₂×C₅×D₃	—	4	4	no	—
158	C₂×C₅×D₃	—	8	8	no	—
159	C₃×C₄×C₅	—	2	2	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	—	4	4	no	—
164	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
165	C₂³×D₃	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂×#67	—	2	8	no	—
173	C₂×#67	—	4	8	no	—
174	C₂²×Dic₃	—	2	2	no	—
175	C₂×D₁₂	—	2	4	no	—
176	C₂×D₁₂	—	2	4	no	—
177	C₂×D₁₂	—	2	2	no	—
178	C₂×D₁₂	C₂³×C₅	1	4	yes	—
179	C₂×C₃×C₈	—	2	2	no	—
180	C₂×C₃×C₈	—	2	8	no	—
181	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
182	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
183	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
184	(C₂×D₃)⋊C₄	—	2	8	no	—
185	C₄⋊Dic₃	—	2	2	no	—
186	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
187	D₂₄	—	2	8	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	—	6	4	no	—
191	C₂³×C₅	—	12	4	no	—
192	C₂³×C₅	—	12	4	no	—
193	C₂³×C₅	—	12	4	no	—
194	C₂³×C₅	D₂₄	1	4	yes	complemented
195	C₂³×C₅	C₂×D₁₂	1	2	yes	—
196	C₂³×C₅	C₂×D₁₂	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	2	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	6	4	no	—
206	C₂×C₄×C₅	—	12	4	no	—
207	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
208	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
209	C₂×C₄×C₅	#235	1	2	yes	—
210	C₂×C₄×C₅	C₂×#67	1	2	yes	—
211	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
212	C₅×C₈	—	2	2	no	—
213	C₅×C₈	C₂×#67	1	4	yes	complemented
214	C₂²×D₄	—	3	2	no	—
215	C₂²×D₄	—	6	2	no	—
216	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
217	C₂×D₈	—	3	4	no	—
218	C₂×D₈	—	6	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
221	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₅×D₃	1	4	yes	complemented
223	#121	—	3	8	no	—
224	#121	—	6	4	no	—
225	C₂×C₄⋊C₄	—	3	2	no	—
226	C₂×C₂²⋊C₄	—	6	2	no	—
227	#107	—	3	4	no	—
228	#102	—	3	8	no	—
229	C₂×C₃×C₅	—	2	4	no	—
230	C₂×C₃×C₅	#466	1	4	yes	complemented
231	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
234	C₅×D₃	—	8	4	no	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	C₅×D₈	1	4	yes	complemented
238	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
239	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
240	C₂²×D₃	—	2	4	no	—
241	C₂²×D₃	—	4	4	no	—
242	C₂²×D₃	—	4	4	no	—
243	C₂²×D₃	—	4	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
251	C₂×C₃×C₄	C₅×#41	1	2	yes	—
252	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
253	#67	—	4	16	no	—
254	C₂×Dic₃	—	2	4	no	—
255	C₂×Dic₃	—	4	4	no	—
256	D₁₂	—	2	4	no	—
257	D₁₂	—	2	4	no	—
258	D₁₂	—	4	4	no	—
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	8	no	—
264	C₂²×C₅	—	12	4	no	—
265	C₂²×C₅	—	12	4	no	—
266	C₂²×C₅	—	12	4	no	—
267	C₂²×C₅	—	24	8	no	—
268	C₂²×C₅	C₂×D₂₄	1	2	yes	—
269	C₂²×C₅	C₂×D₂₄	1	4	yes	complemented
270	C₂²×C₅	#904	1	2	yes	—
271	C₂²×C₅	#930	1	2	yes	—
272	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	12	4	no	—
275	C₄×C₅	#930	1	2	yes	—
276	C₄×C₅	C₂×#235	1	1	yes	characteristic
277	C₄×C₅	C₂²×#67	1	1	yes	characteristic
278	C₂⁴	—	6	2	no	—
279	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
280	C₂×D₄	—	3	4	no	—
281	C₂×D₄	—	6	8	no	—
282	C₂×D₄	—	6	2	no	—
283	C₂×D₄	—	6	4	no	—
284	C₂×D₄	—	6	4	no	—
285	C₂×D₄	—	12	8	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	6	2	no	—
289	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
290	C₂²×C₄	C₅×D₁₂	1	2	yes	—
291	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
292	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
293	D₈	—	6	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	C₅×#67	1	4	yes	complemented
297	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
298	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
299	C₄⋊C₄	—	3	4	no	—
300	C₄⋊C₄	—	6	2	no	—
301	C₂²⋊C₄	—	6	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	8	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	C₅×#121	1	2	yes	—
307	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
308	C₂²×C₃	C₂×C₅×D₈	1	4	yes	complemented
309	C₂²×C₃	C₅×#135	1	2	yes	—
310	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
311	C₂×D₃	—	4	4	no	—
312	C₂×D₃	—	4	4	no	—
313	C₂×D₃	—	4	4	no	—
314	C₂×D₃	—	8	8	no	—
315	C₃×C₄	—	2	2	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	—	4	4	no	—
320	C₂×C₅	—	2	4	no	—
321	C₂×C₅	—	24	4	no	—
322	C₂×C₅	#5115	1	4	yes	direct product factor
323	C₂×C₅	C₂²×D₂₄	1	1	yes	characteristic
324	C₂×C₅	C₂×#904	1	1	yes	characteristic
325	C₂×C₅	C₂×#930	1	1	yes	characteristic
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	6	4	no	—
329	C₂³	—	12	4	no	—
330	C₂³	—	12	4	no	—
331	C₂³	—	12	4	no	—
332	C₂³	C₅×D₂₄	1	4	yes	complemented
333	C₂³	C₂×C₅×D₁₂	1	2	yes	—
334	C₂³	C₂×C₅×D₁₂	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	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	6	4	no	—
344	C₂×C₄	—	12	4	no	—
345	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
346	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
347	C₂×C₄	C₅×#235	1	2	yes	—
348	C₂×C₄	C₂×C₅×#67	1	2	yes	—
349	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	C₂×C₅×#67	1	4	yes	complemented
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	C₅×#466	1	4	yes	complemented
354	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
355	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
356	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
357	D₃	—	8	4	no	—
358	C₅	C₂×#5115	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	8	no	—
362	C₂²	—	12	4	no	—
363	C₂²	—	12	4	no	—
364	C₂²	—	12	4	no	—
365	C₂²	—	24	8	no	—
366	C₂²	C₂×C₅×D₂₄	1	2	yes	—
367	C₂²	C₂×C₅×D₂₄	1	4	yes	complemented
368	C₂²	C₅×#904	1	2	yes	—
369	C₂²	C₅×#930	1	2	yes	—
370	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	12	4	no	—
373	C₄	C₅×#930	1	2	yes	—
374	C₄	C₂×C₅×#235	1	1	yes	characteristic
375	C₄	C₂²×C₅×#67	1	1	yes	characteristic
376	C₃	C₂×C₅×#466	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	24	4	no	—
379	C₂	C₅×#5115	1	4	yes	direct product factor
380	C₂	C₂²×C₅×D₂₄	1	1	yes	characteristic
381	C₂	C₂×C₅×#904	1	1	yes	characteristic
382	C₂	C₂×C₅×#930	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂³×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂³×C₅×C₈	D₃
hypocenter	C₃	C₂×C₅×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×C₈	C₂	semidirect
2. C₂×C₅×#930	C₂	semidirect
3. C₂²×C₅×D₂₄	C₂	semidirect
4. C₅×#5115	C₂	direct (N × H)
5. C₂×C₅×#821	C₂	semidirect
6. C₂×C₅×#818	C₂	semidirect
14. C₂²×C₃×C₅×C₈	C₂²	semidirect
16. C₅×#930	C₂²	semidirect
20. C₂×C₅×D₂₄	C₂²	semidirect
21. C₅×#821	C₂²	semidirect
22. C₅×#818	C₂²	semidirect
23. C₂×#5115	C₅	direct (N × H)
25. C₂³×C₅×C₈	D₃	semidirect
47. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂³×C₃×C₈	C₂×C₅	semidirect
55. C₂×#930	C₂×C₅	semidirect
56. C₂²×D₂₄	C₂×C₅	semidirect
57. #5115	C₂×C₅	direct (N × H)
58. C₂×#821	C₂×C₅	semidirect
59. C₂×#818	C₂×C₅	semidirect
68. C₂²×C₅×C₈	C₂×D₃	semidirect
78. C₂³×C₃×C₅	D₈	semidirect
101. C₃×C₅×C₈	C₂×D₄	semidirect
108. C₂²×C₃×C₈	C₂²×C₅	semidirect
110. #930	C₂²×C₅	semidirect
114. C₂×D₂₄	C₂²×C₅	semidirect
115. #821	C₂²×C₅	semidirect
116. #818	C₂²×C₅	semidirect
135. C₂×C₅×C₈	#67	semidirect
142. C₂³×C₈	C₅×D₃	semidirect
152. C₂²×C₃×C₅	C₂×D₈	semidirect
181. C₂×C₃×C₈	C₅×D₄	semidirect
194. C₂³×C₅	D₂₄	semidirect
213. C₅×C₈	C₂×#67	semidirect
222. C₂²×C₈	C₂×C₅×D₃	semidirect
230. C₂×C₃×C₅	#466	semidirect
237. C₂³×C₃	C₅×D₈	semidirect
260. C₃×C₈	C₂×C₅×D₄	semidirect
269. C₂²×C₅	C₂×D₂₄	semidirect
296. C₂×C₈	C₅×#67	semidirect
302. C₃×C₅	C₂×#466	semidirect
308. C₂²×C₃	C₂×C₅×D₈	semidirect
322. C₂×C₅	#5115	direct (N × H)
332. C₂³	C₅×D₂₄	semidirect
351. C₈	C₂×C₅×#67	semidirect
353. C₂×C₃	C₅×#466	semidirect
358. C₅	C₂×#5115	direct (N × H)
367. C₂²	C₂×C₅×D₂₄	semidirect
376. C₃	C₂×C₅×#466	semidirect
379. C₂	C₅×#5115	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×C₈	2
C₂×C₅×#930	2
C₂²×C₅×D₂₄	2
C₅×#5115	2
C₂×C₅×#821	2
C₂×C₅×#818	2
C₂×C₅×#466	3
C₂×#5115	5

Subgroups — C2×C5×#5115 #14427684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5115 #14427684