Subgroups — C₃×C₅×#1814 #14274848

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#421	C₂	1	2	yes	maximal
5	C₃×C₅×#344	C₂	1	2	yes	maximal, complemented
6	C₅×#1814	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₃×C₅×#131	—	2	1	no	—
9	C₃×C₅×#131	—	2	1	no	—
10	C₃×C₅×#131	C₄	1	2	yes	complemented
11	C₃×C₅×#131	C₄	1	2	yes	complemented
12	C₂×C₃×C₅×M₁₆	—	2	1	no	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	—	2	1	no	—
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	2	yes	—
18	C₃×C₅×#108	—	2	1	no	—
19	C₃×C₅×#108	—	2	1	no	—
20	C₃×C₅×#107	—	2	1	no	—
21	C₃×C₅×#106	—	2	1	no	—
22	C₃×C₅×#104	—	2	4	no	—
23	C₃×#1814	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
25	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
26	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×#421	C₂×C₃	1	2	yes	—
28	C₅×#344	C₂×C₃	1	2	yes	complemented
29	C₃×C₅×#41	—	2	1	no	—
30	C₃×C₅×#41	—	2	1	no	—
31	C₃×C₅×#41	C₂×C₄	1	2	yes	—
32	C₃×C₅×#41	D₄	1	2	yes	—
33	C₂×C₃×C₅×Q₈	Q₈	1	1	yes	characteristic
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	Q₈	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₃×C₅×M₁₆	—	2	1	no	—
39	C₃×C₅×M₁₆	—	2	2	no	—
40	C₃×C₅×M₁₆	—	2	2	no	—
41	C₃×C₅×M₁₆	—	2	2	no	—
42	C₃×C₅×M₁₆	—	2	2	no	—
43	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	—	2	2	no	—
47	C₂×C₃×C₅×C₈	—	2	2	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₄²×C₅	—	2	2	no	—
57	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
58	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
59	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
60	C₃×#421	C₂×C₅	1	2	yes	—
61	C₃×#344	C₂×C₅	1	2	yes	complemented
62	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
63	C₅×#131	—	2	1	no	—
64	C₅×#131	—	2	1	no	—
65	C₅×#131	C₃×C₄	1	2	yes	complemented
66	C₅×#131	C₃×C₄	1	2	yes	complemented
67	C₂×C₅×M₁₆	—	2	1	no	—
68	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
69	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₅×#117	C₂²×C₃	1	2	yes	—
73	C₅×#108	—	2	1	no	—
74	C₅×#108	—	2	1	no	—
75	C₅×#107	—	2	1	no	—
76	C₅×#106	—	2	1	no	—
77	C₅×#104	—	2	4	no	—
78	#1814	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	#41	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	2	1	no	—
82	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
83	C₃×C₅×D₄	—	2	2	no	—
84	C₃×C₅×D₄	—	2	2	no	—
85	C₃×C₅×D₄	—	2	1	no	—
86	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₃×C₅×C₈	—	2	2	no	—
98	C₃×C₅×C₈	—	4	2	no	—
99	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
100	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
101	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
102	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
104	C₃×#131	—	2	1	no	—
105	C₃×#131	—	2	1	no	—
106	C₃×#131	C₄×C₅	1	2	yes	complemented
107	C₃×#131	C₄×C₅	1	2	yes	complemented
108	C₂×C₃×M₁₆	—	2	1	no	—
109	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
110	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₃×C₈	—	2	1	no	—
112	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
113	C₃×#117	C₂²×C₅	1	2	yes	—
114	C₃×#108	—	2	1	no	—
115	C₃×#108	—	2	1	no	—
116	C₃×#107	—	2	1	no	—
117	C₃×#106	—	2	1	no	—
118	C₃×#104	—	2	4	no	—
119	C₅×#41	—	2	1	no	—
120	C₅×#41	—	2	1	no	—
121	C₅×#41	C₂×C₃×C₄	1	2	yes	—
122	C₅×#41	C₃×D₄	1	2	yes	—
123	C₂×C₅×Q₈	C₃×Q₈	1	1	yes	characteristic
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	C₃×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₅×M₁₆	—	2	1	no	—
129	C₅×M₁₆	—	2	2	no	—
130	C₅×M₁₆	—	2	2	no	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	—	2	2	no	—
133	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₂²⋊C₄	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
148	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
149	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
150	#421	C₂×C₃×C₅	1	2	yes	—
151	#344	C₂×C₃×C₅	1	2	yes	complemented
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	#117	1	1	yes	characteristic
156	C₂²×C₃×C₅	#121	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
158	C₃×C₄×C₅	—	2	2	no	—
159	C₃×C₄×C₅	—	8	2	no	—
160	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₃×C₄×C₅	#121	1	1	yes	characteristic
163	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
164	C₃×#41	—	2	1	no	—
165	C₃×#41	—	2	1	no	—
166	C₃×#41	C₂×C₄×C₅	1	2	yes	—
167	C₃×#41	C₅×D₄	1	2	yes	—
168	C₂×C₃×Q₈	C₅×Q₈	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	1	no	—
170	C₂×C₃×D₄	C₅×Q₈	1	1	yes	characteristic
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
173	C₃×M₁₆	—	2	1	no	—
174	C₃×M₁₆	—	2	2	no	—
175	C₃×M₁₆	—	2	2	no	—
176	C₃×M₁₆	—	2	2	no	—
177	C₃×M₁₆	—	2	2	no	—
178	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	2	2	no	—
183	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
184	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
186	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
187	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
188	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₄²	—	2	2	no	—
192	C₂³×C₅	—	2	1	no	—
193	C₂³×C₅	C₃×#41	1	1	yes	characteristic
194	C₅×Q₈	—	2	1	no	—
195	C₅×Q₈	C₃×C₄⋊C₄	1	2	yes	—
196	C₅×D₄	—	2	2	no	—
197	C₅×D₄	—	2	2	no	—
198	C₅×D₄	—	2	1	no	—
199	C₅×D₄	C₃×C₄⋊C₄	1	2	yes	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
209	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
210	C₅×C₈	—	2	2	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
213	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
214	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
215	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
217	#131	—	2	1	no	—
218	#131	—	2	1	no	—
219	#131	C₃×C₄×C₅	1	2	yes	complemented
220	#131	C₃×C₄×C₅	1	2	yes	complemented
221	C₂×M₁₆	—	2	1	no	—
222	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
223	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
226	#117	C₂²×C₃×C₅	1	2	yes	—
227	#108	—	2	1	no	—
228	#108	—	2	1	no	—
229	#107	—	2	1	no	—
230	#106	—	2	1	no	—
231	#104	—	2	4	no	—
232	C₂×C₃×C₅	—	2	1	no	—
233	C₂×C₃×C₅	—	2	1	no	—
234	C₂×C₃×C₅	—	2	1	no	—
235	C₂×C₃×C₅	—	4	2	no	—
236	C₂×C₃×C₅	#380	1	1	yes	characteristic
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	C₅×#41	1	1	yes	characteristic
239	C₃×Q₈	—	2	1	no	—
240	C₃×Q₈	C₅×C₄⋊C₄	1	2	yes	—
241	C₃×D₄	—	2	2	no	—
242	C₃×D₄	—	2	2	no	—
243	C₃×D₄	—	2	1	no	—
244	C₃×D₄	C₅×C₄⋊C₄	1	2	yes	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	4	2	no	—
249	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
255	C₃×C₈	—	2	2	no	—
256	C₃×C₈	—	4	2	no	—
257	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
258	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
259	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
260	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	4	1	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	C₃×#117	1	1	yes	characteristic
265	C₂²×C₅	C₃×#121	1	1	yes	characteristic
266	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
267	C₄×C₅	—	2	2	no	—
268	C₄×C₅	—	8	2	no	—
269	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
270	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
271	C₄×C₅	C₃×#121	1	1	yes	characteristic
272	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
273	#41	—	2	1	no	—
274	#41	—	2	1	no	—
275	#41	C₂×C₃×C₄×C₅	1	2	yes	—
276	#41	C₃×C₅×D₄	1	2	yes	—
277	C₂×Q₈	C₃×C₅×Q₈	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	C₃×C₅×Q₈	1	1	yes	characteristic
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
282	M₁₆	—	2	1	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	C₂×C₃×C₄×C₅	1	2	yes	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
293	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
294	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
295	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
296	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
297	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
298	C₄⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₃×C₅	#1814	1	1	yes	characteristic, direct product factor, Hall
302	C₂²×C₃	—	2	2	no	—
303	C₂²×C₃	—	4	1	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	C₅×#117	1	1	yes	characteristic
306	C₂²×C₃	C₅×#121	1	1	yes	characteristic
307	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	8	2	no	—
310	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
311	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
312	C₃×C₄	C₅×#121	1	1	yes	characteristic
313	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	4	2	no	—
318	C₂×C₅	C₃×#380	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	C₃×C₅×#41	1	1	yes	characteristic
321	Q₈	—	2	1	no	—
322	Q₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	2	1	no	—
326	D₄	C₃×C₅×C₄⋊C₄	1	2	yes	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
332	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
336	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	4	2	no	—
339	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
340	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	4	2	no	—
347	C₂×C₃	C₅×#380	1	1	yes	characteristic
348	C₅	C₃×#1814	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²	—	2	2	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	2	no	—
352	C₂²	C₃×C₅×#117	1	1	yes	characteristic
353	C₂²	C₃×C₅×#121	1	1	yes	characteristic
354	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	8	2	no	—
357	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
359	C₄	C₃×C₅×#121	1	1	yes	characteristic
360	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
361	C₃	C₅×#1814	1	1	yes	characteristic, direct product factor, Sylow
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	2	1	no	—
365	C₂	—	4	2	no	—
366	C₂	C₃×C₅×#380	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂×C₃×C₅	#380
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#108	C₂	semidirect
3. C₃×C₅×#427	C₂	semidirect
5. C₃×C₅×#344	C₂	semidirect
6. C₅×#1814	C₃	direct (N × H)
10. C₃×C₅×#131	C₄	semidirect
11. C₃×C₅×#131	C₄	semidirect
23. C₃×#1814	C₅	direct (N × H)
25. C₂×C₅×#108	C₂×C₃	semidirect
26. C₅×#427	C₂×C₃	semidirect
28. C₅×#344	C₂×C₃	semidirect
58. C₂×C₃×#108	C₂×C₅	semidirect
59. C₃×#427	C₂×C₅	semidirect
61. C₃×#344	C₂×C₅	semidirect
65. C₅×#131	C₃×C₄	semidirect
66. C₅×#131	C₃×C₄	semidirect
78. #1814	C₃×C₅	direct (N × H)
106. C₃×#131	C₄×C₅	semidirect
107. C₃×#131	C₄×C₅	semidirect
148. C₂×#108	C₂×C₃×C₅	semidirect
149. #427	C₂×C₃×C₅	semidirect
151. #344	C₂×C₃×C₅	semidirect
219. #131	C₃×C₄×C₅	semidirect
220. #131	C₃×C₄×C₅	semidirect
301. C₃×C₅	#1814	direct (N × H)
348. C₅	C₃×#1814	direct (N × H)
361. C₃	C₅×#1814	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×C₃×C₅×#131	2
C₂×C₃×C₅×#108	2
C₃×C₅×#427	2
C₃×C₅×#421	2
C₃×C₅×#344	2
C₅×#1814	3
C₃×#1814	5

Subgroups — C3×C5×#1814 #14274848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1814 #14274848