Subgroups — C₅×D₃×#349 #14312894

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×M₃₂	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4514	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#349	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₅×#208	C₄	1	1	yes	characteristic
10	C₅×D₃×M₁₆	—	2	2	no	—
11	C₅×D₃×M₁₆	—	2	2	no	—
12	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic
13	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×C₈	C₄	1	1	yes	characteristic
15	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×M₃₂	C₂²	1	2	yes	complemented
17	C₅×#812	C₂²	1	2	yes	complemented
18	C₅×#798	—	2	2	no	—
19	C₅×D₃×C₁₆	—	2	2	no	—
20	D₃×#349	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×M₁₆	—	3	1	no	—
22	C₂×C₅×M₃₂	—	3	2	no	—
23	C₅×#349	—	3	2	no	—
24	C₅×#349	—	3	1	no	—
25	C₅×#349	D₃	1	1	yes	characteristic, direct product factor
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	1	yes	characteristic
34	C₂×C₄×C₅×D₃	C₈	1	1	yes	characteristic
35	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
37	C₃×C₅×M₁₆	—	2	2	no	—
38	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
40	C₅×#208	—	2	2	no	—
41	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
44	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
45	C₅×D₃×C₈	—	2	1	no	—
46	C₅×D₃×C₈	—	2	1	no	—
47	C₅×D₃×C₈	D₄	1	2	yes	—
48	C₅×D₃×C₈	D₄	1	2	yes	—
49	C₃×C₅×C₁₆	—	2	2	no	—
50	C₅×C₃⋊C₁₆	—	2	2	no	—
51	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic
52	D₃×M₃₂	C₂×C₅	1	2	yes	complemented
53	C₃×#349	C₂×C₅	1	1	yes	characteristic, complemented
54	#4553	C₂×C₅	1	1	yes	characteristic, complemented
55	#4514	C₂×C₅	1	2	yes	complemented
56	C₂³×C₄×C₅	—	3	1	no	—
57	C₂×C₅×M₁₆	—	3	1	no	—
58	C₂×C₅×M₁₆	—	3	1	no	—
59	C₂×C₅×M₁₆	—	3	1	no	—
60	C₂×C₅×M₁₆	—	6	2	no	—
61	C₂×C₅×M₁₆	—	6	2	no	—
62	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₅×C₈	—	3	1	no	—
64	C₂²×C₅×C₈	—	3	1	no	—
65	C₅×M₃₂	—	3	2	no	—
66	C₅×M₃₂	—	6	2	no	—
67	C₅×M₃₂	C₂×D₃	1	2	yes	complemented
68	C₂×C₅×C₁₆	—	6	2	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	1	yes	characteristic
75	C₂²×C₅×D₃	C₂×C₈	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	2	1	no	—
78	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₅×Dic₃	—	2	1	no	—
81	C₂×C₅×Dic₃	—	2	1	no	—
82	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
83	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
84	C₄×C₅×D₃	—	2	1	no	—
85	C₄×C₅×D₃	—	2	1	no	—
86	C₄×C₅×D₃	—	2	1	no	—
87	C₄×C₅×D₃	—	2	1	no	—
88	C₄×C₅×D₃	—	2	1	no	—
89	C₄×C₅×D₃	—	2	1	no	—
90	C₄×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₄×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₄×C₅×D₃	M₁₆	1	1	yes	characteristic
93	C₄×C₅×D₃	M₁₆	1	1	yes	characteristic
94	C₃×C₅×C₈	—	2	1	no	—
95	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
96	C₅×C₃⋊C₈	—	2	1	no	—
97	C₅×C₃⋊C₈	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
99	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
100	C₂×#208	C₄×C₅	1	1	yes	characteristic
101	D₃×M₁₆	—	2	2	no	—
102	D₃×M₁₆	—	2	2	no	—
103	C₂×ΓL(1,𝔽₂₅)	C₄×C₅	1	1	yes	characteristic
104	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
105	C₂×D₃×C₈	C₄×C₅	1	1	yes	characteristic
106	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
107	C₃×M₃₂	C₂²×C₅	1	2	yes	complemented
108	#812	C₂²×C₅	1	2	yes	complemented
109	#798	—	2	2	no	—
110	D₃×C₁₆	—	2	2	no	—
111	C₂⁴×C₅	—	3	1	no	—
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	—	3	1	no	—
115	C₂²×C₄×C₅	—	3	1	no	—
116	C₂²×C₄×C₅	—	3	1	no	—
117	C₂²×C₄×C₅	—	6	1	no	—
118	C₂²×C₄×C₅	—	6	1	no	—
119	C₂²×C₄×C₅	—	6	1	no	—
120	C₂²×C₄×C₅	—	6	1	no	—
121	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
122	C₅×M₁₆	—	2	2	no	—
123	C₅×M₁₆	—	6	2	no	—
124	C₅×M₁₆	—	6	2	no	—
125	C₅×M₁₆	—	6	2	no	—
126	C₂×C₅×C₈	—	3	1	no	—
127	C₂×C₅×C₈	—	3	2	no	—
128	C₂×C₅×C₈	—	3	2	no	—
129	C₂×C₅×C₈	—	3	1	no	—
130	C₂×C₅×C₈	—	6	1	no	—
131	C₂×C₅×C₈	—	6	1	no	—
132	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
133	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
134	C₅×C₁₆	—	2	2	no	—
135	C₅×C₁₆	—	6	2	no	—
136	C₂²×M₁₆	—	3	1	no	—
137	C₂×M₃₂	—	3	2	no	—
138	#349	—	3	1	no	—
139	#349	—	3	2	no	—
140	#349	C₅×D₃	1	1	yes	characteristic, direct product factor
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	4	1	no	—
143	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₅×D₃	—	2	2	no	—
145	C₂×C₅×D₃	—	2	1	no	—
146	C₂×C₅×D₃	—	4	2	no	—
147	C₂×C₅×D₃	—	4	2	no	—
148	C₂×C₅×D₃	—	4	1	no	—
149	C₂×C₅×D₃	C₂²⋊C₈	1	1	yes	characteristic
150	C₂×C₅×D₃	C₂²⋊C₈	1	1	yes	characteristic
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
154	C₅×Dic₃	—	2	1	no	—
155	C₅×Dic₃	C₂²⋊C₈	1	1	yes	characteristic
156	C₅×Dic₃	C₂²⋊C₈	1	1	yes	characteristic
157	C₂³×D₃	C₅×C₈	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
159	C₂²×Dic₃	C₅×C₈	1	1	yes	characteristic
160	C₂×C₄×D₃	—	2	1	no	—
161	C₂×C₄×D₃	—	2	1	no	—
162	C₂×C₄×D₃	—	2	1	no	—
163	C₂×C₄×D₃	—	2	1	no	—
164	C₂×C₄×D₃	C₅×C₈	1	1	yes	characteristic
165	C₂×C₄×D₃	C₅×C₈	1	1	yes	characteristic
166	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
167	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
168	C₃×M₁₆	—	2	2	no	—
169	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
171	#208	—	2	2	no	—
172	C₂×C₃⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂×C₃⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
174	ΓL(1,𝔽₂₅)	—	2	2	no	—
175	ΓL(1,𝔽₂₅)	—	2	2	no	—
176	D₃×C₈	—	2	1	no	—
177	D₃×C₈	—	2	1	no	—
178	D₃×C₈	C₅×D₄	1	2	yes	—
179	D₃×C₈	C₅×D₄	1	2	yes	—
180	C₃×C₁₆	—	2	2	no	—
181	C₃⋊C₁₆	—	2	2	no	—
182	C₂³×C₅	—	3	1	no	—
183	C₂³×C₅	—	3	1	no	—
184	C₂³×C₅	—	6	1	no	—
185	C₂³×C₅	—	6	1	no	—
186	C₂³×C₅	—	12	2	no	—
187	C₂³×C₅	D₃×C₈	1	1	yes	characteristic
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	3	1	no	—
191	C₂×C₄×C₅	—	3	1	no	—
192	C₂×C₄×C₅	—	3	1	no	—
193	C₂×C₄×C₅	—	3	1	no	—
194	C₂×C₄×C₅	—	3	1	no	—
195	C₂×C₄×C₅	—	3	1	no	—
196	C₂×C₄×C₅	—	6	1	no	—
197	C₂×C₄×C₅	—	6	1	no	—
198	C₂×C₄×C₅	—	6	1	no	—
199	C₂×C₄×C₅	—	6	1	no	—
200	C₂×C₄×C₅	—	6	1	no	—
201	C₂×C₄×C₅	—	6	1	no	—
202	C₂×C₄×C₅	—	6	1	no	—
203	C₂×C₄×C₅	—	6	1	no	—
204	C₂×C₄×C₅	D₃×C₈	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
206	C₅×C₈	—	2	1	no	—
207	C₅×C₈	—	3	2	no	—
208	C₅×C₈	—	6	1	no	—
209	C₅×C₈	D₃×D₄	1	2	yes	—
210	C₂³×C₄	—	3	1	no	—
211	C₂×M₁₆	—	3	1	no	—
212	C₂×M₁₆	—	3	1	no	—
213	C₂×M₁₆	—	3	1	no	—
214	C₂×M₁₆	—	6	2	no	—
215	C₂×M₁₆	—	6	2	no	—
216	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
217	C₂²×C₈	—	3	1	no	—
218	C₂²×C₈	—	3	1	no	—
219	M₃₂	—	3	2	no	—
220	M₃₂	—	6	2	no	—
221	M₃₂	C₂×C₅×D₃	1	2	yes	complemented
222	C₂×C₁₆	—	6	2	no	—
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	—	4	1	no	—
225	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
226	C₅×D₃	—	2	1	no	—
227	C₅×D₃	—	4	1	no	—
228	C₅×D₃	#349	1	2	yes	direct product factor
229	C₂³×C₃	C₂×C₅×C₈	1	1	yes	characteristic
230	C₂²×D₃	—	2	1	no	—
231	C₂²×D₃	—	2	1	no	—
232	C₂²×D₃	—	4	2	no	—
233	C₂²×D₃	C₂×C₅×C₈	1	1	yes	characteristic
234	C₂²×D₃	C₂×C₅×C₈	1	1	yes	characteristic
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
239	C₂×Dic₃	—	2	1	no	—
240	C₂×Dic₃	—	2	1	no	—
241	C₂×Dic₃	C₂×C₅×C₈	1	1	yes	characteristic
242	C₂×Dic₃	C₂×C₅×C₈	1	1	yes	characteristic
243	C₄×D₃	—	2	1	no	—
244	C₄×D₃	—	2	1	no	—
245	C₄×D₃	—	2	1	no	—
246	C₄×D₃	—	2	1	no	—
247	C₄×D₃	—	2	1	no	—
248	C₄×D₃	—	2	1	no	—
249	C₄×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
250	C₄×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
251	C₄×D₃	C₅×M₁₆	1	1	yes	characteristic
252	C₄×D₃	C₅×M₁₆	1	1	yes	characteristic
253	C₃×C₈	—	2	1	no	—
254	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
255	C₃⋊C₈	—	2	1	no	—
256	C₃⋊C₈	C₅×C₂²⋊C₄	1	2	yes	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	3	1	no	—
259	C₂²×C₅	—	3	1	no	—
260	C₂²×C₅	—	4	1	no	—
261	C₂²×C₅	—	6	2	no	—
262	C₂²×C₅	—	6	1	no	—
263	C₂²×C₅	—	12	1	no	—
264	C₂²×C₅	—	12	2	no	—
265	C₂²×C₅	—	12	2	no	—
266	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	3	1	no	—
269	C₄×C₅	—	3	1	no	—
270	C₄×C₅	—	6	1	no	—
271	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
273	C₂⁴	—	3	1	no	—
274	C₂²×C₄	—	3	1	no	—
275	C₂²×C₄	—	3	1	no	—
276	C₂²×C₄	—	3	1	no	—
277	C₂²×C₄	—	3	1	no	—
278	C₂²×C₄	—	3	1	no	—
279	C₂²×C₄	—	6	1	no	—
280	C₂²×C₄	—	6	1	no	—
281	C₂²×C₄	—	6	1	no	—
282	C₂²×C₄	—	6	1	no	—
283	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
284	M₁₆	—	2	2	no	—
285	M₁₆	—	6	2	no	—
286	M₁₆	—	6	2	no	—
287	M₁₆	—	6	2	no	—
288	C₂×C₈	—	3	1	no	—
289	C₂×C₈	—	3	2	no	—
290	C₂×C₈	—	3	2	no	—
291	C₂×C₈	—	3	1	no	—
292	C₂×C₈	—	6	1	no	—
293	C₂×C₈	—	6	1	no	—
294	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
296	C₁₆	—	2	2	no	—
297	C₁₆	—	6	2	no	—
298	C₃×C₅	C₂×#349	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
302	C₂×D₃	—	2	2	no	—
303	C₂×D₃	—	2	1	no	—
304	C₂×D₃	—	4	2	no	—
305	C₂×D₃	—	4	2	no	—
306	C₂×D₃	—	4	1	no	—
307	C₂×D₃	C₅×C₂²⋊C₈	1	1	yes	characteristic
308	C₂×D₃	C₅×C₂²⋊C₈	1	1	yes	characteristic
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
311	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
312	Dic₃	—	2	1	no	—
313	Dic₃	C₅×C₂²⋊C₈	1	1	yes	characteristic
314	Dic₃	C₅×C₂²⋊C₈	1	1	yes	characteristic
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	3	2	no	—
317	C₂×C₅	—	4	1	no	—
318	C₂×C₅	—	6	1	no	—
319	C₂×C₅	—	12	1	no	—
320	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
321	C₂³	—	3	1	no	—
322	C₂³	—	3	1	no	—
323	C₂³	—	6	1	no	—
324	C₂³	—	6	1	no	—
325	C₂³	—	12	2	no	—
326	C₂³	C₅×D₃×C₈	1	1	yes	characteristic
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	3	1	no	—
330	C₂×C₄	—	3	1	no	—
331	C₂×C₄	—	3	1	no	—
332	C₂×C₄	—	3	1	no	—
333	C₂×C₄	—	3	1	no	—
334	C₂×C₄	—	3	1	no	—
335	C₂×C₄	—	6	1	no	—
336	C₂×C₄	—	6	1	no	—
337	C₂×C₄	—	6	1	no	—
338	C₂×C₄	—	6	1	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	—	6	1	no	—
341	C₂×C₄	—	6	1	no	—
342	C₂×C₄	—	6	1	no	—
343	C₂×C₄	C₅×D₃×C₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	3	2	no	—
347	C₈	—	6	1	no	—
348	C₈	C₅×D₃×D₄	1	2	yes	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	4	1	no	—
351	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
352	D₃	—	2	1	no	—
353	D₃	—	4	1	no	—
354	D₃	C₅×#349	1	2	yes	direct product factor
355	C₅	D₃×#349	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²	—	2	1	no	—
357	C₂²	—	3	1	no	—
358	C₂²	—	3	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	6	2	no	—
361	C₂²	—	6	1	no	—
362	C₂²	—	12	1	no	—
363	C₂²	—	12	2	no	—
364	C₂²	—	12	2	no	—
365	C₂²	C₂×C₅×D₃×C₈	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	3	1	no	—
368	C₄	—	3	1	no	—
369	C₄	—	6	1	no	—
370	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
371	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
372	C₃	C₂×C₅×#349	1	1	yes	characteristic, complemented, Sylow
373	C₂	—	2	1	no	—
374	C₂	—	3	2	no	—
375	C₂	—	4	1	no	—
376	C₂	—	6	1	no	—
377	C₂	—	12	1	no	—
378	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅×D₃×M₃₂	C₂	semidirect
3. C₃×C₅×#349	C₂	semidirect
4. C₅×#4553	C₂	semidirect
5. C₅×#4514	C₂	semidirect
16. C₃×C₅×M₃₂	C₂²	semidirect
17. C₅×#812	C₂²	semidirect
20. D₃×#349	C₅	direct (N × H)
25. C₅×#349	D₃	direct (N × H)
52. D₃×M₃₂	C₂×C₅	semidirect
53. C₃×#349	C₂×C₅	semidirect
54. #4553	C₂×C₅	semidirect
55. #4514	C₂×C₅	semidirect
67. C₅×M₃₂	C₂×D₃	semidirect
107. C₃×M₃₂	C₂²×C₅	semidirect
108. #812	C₂²×C₅	semidirect
140. #349	C₅×D₃	direct (N × H)
221. M₃₂	C₂×C₅×D₃	semidirect
228. C₅×D₃	#349	direct (N × H)
298. C₃×C₅	C₂×#349	semidirect
354. D₃	C₅×#349	direct (N × H)
355. C₅	D₃×#349	direct (N × H)
372. C₃	C₂×C₅×#349	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₅×D₃×M₃₂	2
C₃×C₅×#349	2
C₅×#4553	2
C₅×#4514	2
C₂×C₅×#349	3
D₃×#349	5

Subgroups — C5×D3×#349 #14312894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#349 #14312894