Subgroups — C₂×C₅×#4514 #14312897

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4514	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₅×#349	—	3	1	no	maximal, Hall
6	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₅×C₃⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
10	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
11	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
12	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
13	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	2	yes	—
14	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
15	C₃×C₅×M₃₂	—	2	1	no	—
16	C₃×C₅×M₃₂	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×C₁₆	—	2	1	no	—
18	C₅×#812	—	2	1	no	—
19	C₅×#812	C₂²	1	2	yes	complemented
20	C₂×C₅×C₃⋊C₁₆	—	2	1	no	—
21	C₂×#4514	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₅×M₁₆	—	3	1	no	—
23	C₂×C₅×M₃₂	—	3	1	no	—
24	C₂×C₅×M₃₂	D₃	1	1	yes	characteristic, complemented
25	C₅×#349	—	3	4	no	—
26	C₂³×C₅×D₃	C₈	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₅×Dic₃	C₈	1	1	yes	characteristic
29	C₂×C₄×C₅×D₃	—	2	1	no	—
30	C₂×C₄×C₅×D₃	—	2	1	no	—
31	C₂×C₄×C₅×D₃	—	2	1	no	—
32	C₂×C₄×C₅×D₃	—	2	1	no	—
33	C₂×C₄×C₅×D₃	C₈	1	2	yes	—
34	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
35	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
37	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
41	C₂×C₅×C₃⋊C₈	—	2	1	no	—
42	C₂×C₅×C₃⋊C₈	—	2	1	no	—
43	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
44	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
45	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
46	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
47	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
48	C₃×C₅×C₁₆	—	2	2	no	—
49	C₅×C₃⋊C₁₆	—	2	2	no	—
50	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
52	C₂×#812	C₂×C₅	1	1	yes	characteristic, complemented
53	#4514	C₂×C₅	1	4	yes	direct product factor
54	C₂³×C₄×C₅	—	3	1	no	—
55	C₂×C₅×M₁₆	—	3	2	no	—
56	C₂×C₅×M₁₆	—	3	2	no	—
57	C₂×C₅×M₁₆	—	6	1	no	—
58	C₂×C₅×M₁₆	—	6	1	no	—
59	C₂×C₅×M₁₆	—	6	1	no	—
60	C₂×C₅×M₁₆	—	6	1	no	—
61	C₂²×C₅×C₈	—	3	1	no	—
62	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
63	C₅×M₃₂	—	2	1	no	—
64	C₅×M₃₂	—	3	2	no	—
65	C₅×M₃₂	—	6	1	no	—
66	C₅×M₃₂	C₂×D₃	1	2	yes	complemented
67	C₂×C₅×C₁₆	—	2	1	no	—
68	C₂×C₅×C₁₆	—	6	1	no	—
69	C₂×#349	—	3	1	no	Sylow
70	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
71	C₂²×C₅×D₃	—	2	1	no	—
72	C₂²×C₅×D₃	—	2	1	no	—
73	C₂²×C₅×D₃	—	4	2	no	—
74	C₂²×C₅×D₃	C₂×C₈	1	2	yes	—
75	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	M₁₆	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	M₁₆	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₅×Dic₃	—	2	1	no	—
82	C₂×C₅×Dic₃	—	2	1	no	—
83	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
84	C₄×C₅×D₃	—	2	2	no	—
85	C₄×C₅×D₃	—	2	2	no	—
86	C₄×C₅×D₃	—	2	2	no	—
87	C₄×C₅×D₃	—	2	2	no	—
88	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
89	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
90	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
91	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
92	C₅×C₃⋊C₈	—	2	2	no	—
93	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
94	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
95	C₂²×C₃⋊C₈	C₄×C₅	1	1	yes	characteristic
96	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
97	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
98	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
99	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
100	C₂×ΓL(1,𝔽₂₅)	C₄×C₅	1	2	yes	—
101	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
102	C₃×M₃₂	—	2	1	no	—
103	C₃×M₃₂	C₂²×C₅	1	2	yes	complemented
104	C₂×C₃×C₁₆	—	2	1	no	—
105	#812	—	2	1	no	—
106	#812	C₂²×C₅	1	2	yes	complemented
107	C₂×C₃⋊C₁₆	—	2	1	no	—
108	C₂⁴×C₅	—	3	1	no	—
109	C₂²×C₄×C₅	—	3	1	no	—
110	C₂²×C₄×C₅	—	3	2	no	—
111	C₂²×C₄×C₅	—	3	2	no	—
112	C₂²×C₄×C₅	—	6	1	no	—
113	C₂²×C₄×C₅	—	6	1	no	—
114	C₂²×C₄×C₅	—	6	1	no	—
115	C₂²×C₄×C₅	—	6	1	no	—
116	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
117	C₅×M₁₆	—	6	2	no	—
118	C₅×M₁₆	—	6	2	no	—
119	C₅×M₁₆	—	6	2	no	—
120	C₅×M₁₆	—	6	2	no	—
121	C₂×C₅×C₈	—	3	2	no	—
122	C₂×C₅×C₈	—	6	1	no	—
123	C₂×C₅×C₈	—	6	1	no	—
124	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
125	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
126	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
127	C₂×C₅×C₈	#67	1	1	yes	characteristic
128	C₂×C₅×C₈	#67	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
130	C₅×C₁₆	—	2	2	no	—
131	C₅×C₁₆	—	6	2	no	—
132	C₂²×M₁₆	—	3	1	no	—
133	C₂×M₃₂	—	3	1	no	—
134	C₂×M₃₂	C₅×D₃	1	1	yes	characteristic, complemented
135	#349	—	3	4	no	—
136	C₂²×C₃×C₅	—	2	2	no	—
137	C₂²×C₃×C₅	C₂²⋊C₈	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂²⋊C₈	1	1	yes	characteristic
139	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₅×D₃	—	2	2	no	—
141	C₂×C₅×D₃	—	4	2	no	—
142	C₂×C₅×D₃	—	4	2	no	—
143	C₂×C₅×D₃	—	4	2	no	—
144	C₃×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
145	C₃×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
146	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
148	C₅×Dic₃	—	2	2	no	—
149	C₂³×D₃	C₅×C₈	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
151	C₂²×Dic₃	C₅×C₈	1	1	yes	characteristic
152	C₂×C₄×D₃	—	2	1	no	—
153	C₂×C₄×D₃	—	2	1	no	—
154	C₂×C₄×D₃	—	2	1	no	—
155	C₂×C₄×D₃	—	2	1	no	—
156	C₂×C₄×D₃	C₅×C₈	1	2	yes	—
157	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
158	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
159	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
160	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
161	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
162	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
163	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
164	C₂×C₃⋊C₈	—	2	1	no	—
165	C₂×C₃⋊C₈	—	2	1	no	—
166	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
167	ΓL(1,𝔽₂₅)	—	2	2	no	—
168	ΓL(1,𝔽₂₅)	—	2	2	no	—
169	ΓL(1,𝔽₂₅)	—	2	2	no	—
170	ΓL(1,𝔽₂₅)	—	2	2	no	—
171	C₃×C₁₆	—	2	2	no	—
172	C₃⋊C₁₆	—	2	2	no	—
173	C₂³×C₅	—	3	2	no	—
174	C₂³×C₅	—	6	1	no	—
175	C₂³×C₅	—	6	1	no	—
176	C₂³×C₅	—	12	2	no	—
177	C₂³×C₅	D₃×C₈	1	1	yes	characteristic
178	C₂×C₄×C₅	—	3	2	no	—
179	C₂×C₄×C₅	—	6	1	no	—
180	C₂×C₄×C₅	—	6	1	no	—
181	C₂×C₄×C₅	—	6	2	no	—
182	C₂×C₄×C₅	—	6	2	no	—
183	C₂×C₄×C₅	—	6	2	no	—
184	C₂×C₄×C₅	—	6	2	no	—
185	C₂×C₄×C₅	D₃×C₈	1	1	yes	characteristic
186	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
187	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
188	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
191	C₅×C₈	—	6	2	no	—
192	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
193	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
194	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
195	C₅×C₈	C₂×#67	1	1	yes	characteristic
196	C₂³×C₄	—	3	1	no	—
197	C₂×M₁₆	—	3	2	no	—
198	C₂×M₁₆	—	3	2	no	—
199	C₂×M₁₆	—	6	1	no	—
200	C₂×M₁₆	—	6	1	no	—
201	C₂×M₁₆	—	6	1	no	—
202	C₂×M₁₆	—	6	1	no	—
203	C₂²×C₈	—	3	1	no	—
204	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
205	M₃₂	—	2	1	no	—
206	M₃₂	—	3	2	no	—
207	M₃₂	—	6	1	no	—
208	M₃₂	C₂×C₅×D₃	1	2	yes	complemented
209	C₂×C₁₆	—	2	1	no	—
210	C₂×C₁₆	—	6	1	no	—
211	C₂×C₃×C₅	—	2	1	no	—
212	C₂×C₃×C₅	—	2	1	no	—
213	C₂×C₃×C₅	#349	1	2	yes	complemented
214	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
215	C₅×D₃	—	4	2	no	—
216	C₂³×C₃	C₂×C₅×C₈	1	1	yes	characteristic
217	C₂²×D₃	—	2	1	no	—
218	C₂²×D₃	—	2	1	no	—
219	C₂²×D₃	—	4	2	no	—
220	C₂²×D₃	C₂×C₅×C₈	1	2	yes	—
221	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
224	C₂×C₃×C₄	C₅×M₁₆	1	1	yes	characteristic
225	C₂×C₃×C₄	C₅×M₁₆	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
227	C₂×Dic₃	—	2	1	no	—
228	C₂×Dic₃	—	2	1	no	—
229	C₂×Dic₃	C₂×C₅×C₈	1	2	yes	—
230	C₄×D₃	—	2	2	no	—
231	C₄×D₃	—	2	2	no	—
232	C₄×D₃	—	2	2	no	—
233	C₄×D₃	—	2	2	no	—
234	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
235	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
236	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
237	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
238	C₃⋊C₈	—	2	2	no	—
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	—	6	2	no	—
241	C₂²×C₅	—	12	2	no	—
242	C₂²×C₅	—	12	2	no	—
243	C₂²×C₅	—	12	2	no	—
244	C₂²×C₅	(C₂×D₃)⋊C₈	1	1	yes	characteristic
245	C₂²×C₅	(C₂×D₃)⋊C₈	1	1	yes	characteristic
246	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
247	C₄×C₅	—	6	2	no	—
248	C₄×C₅	(C₂×D₃)⋊C₈	1	1	yes	characteristic
249	C₄×C₅	(C₂×D₃)⋊C₈	1	1	yes	characteristic
250	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
251	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
252	C₂⁴	—	3	1	no	—
253	C₂²×C₄	—	3	1	no	—
254	C₂²×C₄	—	3	2	no	—
255	C₂²×C₄	—	3	2	no	—
256	C₂²×C₄	—	6	1	no	—
257	C₂²×C₄	—	6	1	no	—
258	C₂²×C₄	—	6	1	no	—
259	C₂²×C₄	—	6	1	no	—
260	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
261	M₁₆	—	6	2	no	—
262	M₁₆	—	6	2	no	—
263	M₁₆	—	6	2	no	—
264	M₁₆	—	6	2	no	—
265	C₂×C₈	—	3	2	no	—
266	C₂×C₈	—	6	1	no	—
267	C₂×C₈	—	6	1	no	—
268	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
269	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
270	C₂×C₈	C₅×D₁₂	1	1	yes	characteristic
271	C₂×C₈	C₅×#67	1	1	yes	characteristic
272	C₂×C₈	C₅×#67	1	1	yes	characteristic
273	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
274	C₁₆	—	2	2	no	—
275	C₁₆	—	6	2	no	—
276	C₃×C₅	C₂×#349	1	1	yes	characteristic, complemented, Hall
277	C₂²×C₃	—	2	2	no	—
278	C₂²×C₃	C₅×C₂²⋊C₈	1	1	yes	characteristic
279	C₂²×C₃	C₅×C₂²⋊C₈	1	1	yes	characteristic
280	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
281	C₂×D₃	—	2	2	no	—
282	C₂×D₃	—	4	2	no	—
283	C₂×D₃	—	4	2	no	—
284	C₂×D₃	—	4	2	no	—
285	C₃×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
286	C₃×C₄	C₅×C₂²⋊C₈	1	1	yes	characteristic
287	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
288	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
289	Dic₃	—	2	2	no	—
290	C₂×C₅	—	2	1	no	—
291	C₂×C₅	—	2	1	no	—
292	C₂×C₅	—	12	2	no	—
293	C₂×C₅	#4514	1	2	yes	direct product factor
294	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
295	C₂³	—	3	2	no	—
296	C₂³	—	6	1	no	—
297	C₂³	—	6	1	no	—
298	C₂³	—	12	2	no	—
299	C₂³	C₅×D₃×C₈	1	1	yes	characteristic
300	C₂×C₄	—	3	2	no	—
301	C₂×C₄	—	6	1	no	—
302	C₂×C₄	—	6	1	no	—
303	C₂×C₄	—	6	2	no	—
304	C₂×C₄	—	6	2	no	—
305	C₂×C₄	—	6	2	no	—
306	C₂×C₄	—	6	2	no	—
307	C₂×C₄	C₅×D₃×C₈	1	1	yes	characteristic
308	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
309	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
310	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
312	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
313	C₈	—	6	2	no	—
314	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
315	C₈	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
316	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
317	C₈	C₂×C₅×#67	1	1	yes	characteristic
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	C₅×#349	1	2	yes	complemented
321	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
322	D₃	—	4	2	no	—
323	C₅	C₂×#4514	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²	—	2	2	no	—
325	C₂²	—	6	2	no	—
326	C₂²	—	12	2	no	—
327	C₂²	—	12	2	no	—
328	C₂²	—	12	2	no	—
329	C₂²	C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
330	C₂²	C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
331	C₂²	C₂×C₅×D₃×C₈	1	1	yes	characteristic
332	C₄	—	6	2	no	—
333	C₄	C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
334	C₄	C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
335	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
336	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
337	C₃	C₂×C₅×#349	1	1	yes	characteristic, complemented, Sylow
338	C₂	—	2	1	no	—
339	C₂	—	2	1	no	—
340	C₂	—	12	2	no	—
341	C₂	C₅×#4514	1	2	yes	direct product factor
342	C₂	C₂×C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂²×C₃×C₅	C₂²⋊C₈
prime radical	C₂³×C₅×D₃	C₈
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₂×C₅×M₃₂	D₃
hypocenter	C₃	C₂×C₅×#349
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×M₃₂	C₂	semidirect
3. C₂×C₅×#812	C₂	semidirect
4. C₅×#4514	C₂	direct (N × H)
16. C₃×C₅×M₃₂	C₂²	semidirect
19. C₅×#812	C₂²	semidirect
21. C₂×#4514	C₅	direct (N × H)
24. C₂×C₅×M₃₂	D₃	semidirect
51. C₂×C₃×M₃₂	C₂×C₅	semidirect
52. C₂×#812	C₂×C₅	semidirect
53. #4514	C₂×C₅	direct (N × H)
66. C₅×M₃₂	C₂×D₃	semidirect
103. C₃×M₃₂	C₂²×C₅	semidirect
106. #812	C₂²×C₅	semidirect
134. C₂×M₃₂	C₅×D₃	semidirect
208. M₃₂	C₂×C₅×D₃	semidirect
213. C₂×C₃×C₅	#349	semidirect
276. C₃×C₅	C₂×#349	semidirect
293. C₂×C₅	#4514	direct (N × H)
320. C₂×C₃	C₅×#349	semidirect
323. C₅	C₂×#4514	direct (N × H)
337. C₃	C₂×C₅×#349	semidirect
341. C₂	C₅×#4514	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×ΓL(1,𝔽₂₅)	2
C₂×C₃×C₅×M₃₂	2
C₂×C₅×#812	2
C₅×#4514	2
C₂×C₅×#349	3
C₂×#4514	5

Subgroups — C2×C5×#4514 #14312897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4514 #14312897