Subgroups — C₃×C₅×#2097 #14275131

Order 1920.

476 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×#107	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₅×#2097	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#107	—	2	2	no	—
17	C₃×C₅×#106	—	2	2	no	—
18	C₃×C₅×#103	—	2	2	no	—
19	C₃×C₅×#103	—	2	2	no	—
20	C₃×C₅×#95	—	2	2	no	—
21	C₃×C₅×#95	—	2	2	no	—
22	C₃×#2097	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic
25	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
26	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
27	C₅×#391	C₂×C₃	1	1	yes	characteristic
28	C₅×#382	C₂×C₃	1	1	yes	characteristic
29	C₅×#336	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×C₅×Q₈	—	2	1	no	—
31	C₂×C₃×C₅×Q₈	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	Q₈	1	2	yes	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
57	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic
58	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
60	C₃×#391	C₂×C₅	1	1	yes	characteristic
61	C₃×#382	C₂×C₅	1	1	yes	characteristic
62	C₃×#336	C₂×C₅	1	1	yes	characteristic
63	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₅×#107	—	2	2	no	—
71	C₅×#106	—	2	2	no	—
72	C₅×#103	—	2	2	no	—
73	C₅×#103	—	2	2	no	—
74	C₅×#95	—	2	2	no	—
75	C₅×#95	—	2	2	no	—
76	#2097	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
77	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
78	C₃×C₅×Q₈	—	2	2	no	—
79	C₃×C₅×Q₈	—	2	2	no	—
80	C₃×C₅×Q₈	—	4	1	no	—
81	C₃×C₅×Q₈	—	4	1	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₃×C₅×C₈	—	2	2	no	—
101	C₃×C₅×C₈	—	2	2	no	—
102	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₃×#107	—	2	2	no	—
110	C₃×#106	—	2	2	no	—
111	C₃×#103	—	2	2	no	—
112	C₃×#103	—	2	2	no	—
113	C₃×#95	—	2	2	no	—
114	C₃×#95	—	2	2	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	1	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	C₃×Q₈	1	2	yes	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₅×C₈	—	2	1	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
132	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₄²×C₅	—	2	1	no	—
140	C₄²×C₅	—	2	1	no	—
141	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
142	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic
143	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
144	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
145	#391	C₂×C₃×C₅	1	1	yes	characteristic
146	#382	C₂×C₃×C₅	1	1	yes	characteristic
147	#336	C₂×C₃×C₅	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂²×C₃×C₅	#123	1	1	yes	characteristic
150	C₂²×C₃×C₅	#127	1	1	yes	characteristic
151	C₂²×C₃×C₅	#135	1	2	yes	—
152	C₂²×C₃×C₅	#137	1	2	yes	—
153	C₃×C₄×C₅	—	4	2	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	8	1	no	—
156	C₃×C₄×C₅	—	8	1	no	—
157	C₃×C₄×C₅	—	8	1	no	—
158	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
159	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
160	C₃×C₄×C₅	#123	1	1	yes	characteristic
161	C₃×C₄×C₅	#123	1	1	yes	characteristic
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	—	2	1	no	—
166	C₂×C₃×Q₈	—	2	1	no	—
167	C₂×C₃×Q₈	C₅×Q₈	1	2	yes	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	2	1	no	—
177	C₂×C₃×C₈	—	2	1	no	—
178	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
179	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	2	2	no	—
191	C₅×Q₈	—	4	1	no	—
192	C₅×Q₈	—	4	1	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	4	1	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
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×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
209	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
210	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
211	C₅×C₈	—	2	2	no	—
212	C₅×C₈	—	2	2	no	—
213	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
215	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
220	#107	—	2	2	no	—
221	#106	—	2	2	no	—
222	#103	—	2	2	no	—
223	#103	—	2	2	no	—
224	#95	—	2	2	no	—
225	#95	—	2	2	no	—
226	C₂×C₃×C₅	#399	1	1	yes	characteristic
227	C₂×C₃×C₅	#479	1	2	yes	—
228	C₂×C₃×C₅	#485	1	2	yes	—
229	C₂×C₃×C₅	#495	1	1	yes	characteristic
230	C₂×C₃×C₅	#497	1	1	yes	characteristic
231	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
232	C₃×Q₈	—	2	2	no	—
233	C₃×Q₈	—	2	2	no	—
234	C₃×Q₈	—	4	1	no	—
235	C₃×Q₈	—	4	1	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	1	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	—	4	1	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	—	4	2	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
251	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
254	C₃×C₈	—	2	2	no	—
255	C₃×C₈	—	2	2	no	—
256	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
257	C₂²×C₅	C₃×#123	1	1	yes	characteristic
258	C₂²×C₅	C₃×#127	1	1	yes	characteristic
259	C₂²×C₅	C₃×#135	1	2	yes	—
260	C₂²×C₅	C₃×#137	1	2	yes	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	—	4	2	no	—
263	C₄×C₅	—	8	1	no	—
264	C₄×C₅	—	8	1	no	—
265	C₄×C₅	—	8	1	no	—
266	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
267	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
268	C₄×C₅	C₃×#123	1	1	yes	characteristic
269	C₄×C₅	C₃×#123	1	1	yes	characteristic
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	C₃×C₅×Q₈	1	2	yes	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
281	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
287	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	2	1	no	—
296	C₃×C₅	#2097	1	1	yes	characteristic, direct product factor, Hall
297	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
298	C₂²×C₃	C₅×#123	1	1	yes	characteristic
299	C₂²×C₃	C₅×#127	1	1	yes	characteristic
300	C₂²×C₃	C₅×#135	1	2	yes	—
301	C₂²×C₃	C₅×#137	1	2	yes	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	—	4	2	no	—
304	C₃×C₄	—	8	1	no	—
305	C₃×C₄	—	8	1	no	—
306	C₃×C₄	—	8	1	no	—
307	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
308	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
309	C₃×C₄	C₅×#123	1	1	yes	characteristic
310	C₃×C₄	C₅×#123	1	1	yes	characteristic
311	C₂×C₅	C₃×#399	1	1	yes	characteristic
312	C₂×C₅	C₃×#479	1	2	yes	—
313	C₂×C₅	C₃×#485	1	2	yes	—
314	C₂×C₅	C₃×#495	1	1	yes	characteristic
315	C₂×C₅	C₃×#497	1	1	yes	characteristic
316	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	1	no	—
320	Q₈	—	4	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
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	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
338	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₂×C₃	C₅×#399	1	1	yes	characteristic
342	C₂×C₃	C₅×#479	1	2	yes	—
343	C₂×C₃	C₅×#485	1	2	yes	—
344	C₂×C₃	C₅×#495	1	1	yes	characteristic
345	C₂×C₃	C₅×#497	1	1	yes	characteristic
346	C₅	C₃×#2097	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
348	C₂²	C₃×C₅×#123	1	1	yes	characteristic
349	C₂²	C₃×C₅×#127	1	1	yes	characteristic
350	C₂²	C₃×C₅×#135	1	2	yes	—
351	C₂²	C₃×C₅×#137	1	2	yes	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	8	1	no	—
355	C₄	—	8	1	no	—
356	C₄	—	8	1	no	—
357	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
358	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
359	C₄	C₃×C₅×#123	1	1	yes	characteristic
360	C₄	C₃×C₅×#123	1	1	yes	characteristic
361	C₃	C₅×#2097	1	1	yes	characteristic, direct product factor, Sylow
362	C₂	C₃×C₅×#399	1	1	yes	characteristic
363	C₂	C₃×C₅×#479	1	2	yes	—
364	C₂	C₃×C₅×#485	1	2	yes	—
365	C₂	C₃×C₅×#495	1	1	yes	characteristic
366	C₂	C₃×C₅×#497	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#2097	C₃	direct (N × H)
22. C₃×#2097	C₅	direct (N × H)
76. #2097	C₃×C₅	direct (N × H)
296. C₃×C₅	#2097	direct (N × H)
346. C₅	C₃×#2097	direct (N × H)
361. C₃	C₅×#2097	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×#107	2
C₂×C₃×C₅×#106	2
C₂×C₃×C₅×#103	2
C₃×C₅×#391	2
C₃×C₅×#382	2
C₃×C₅×#336	2
C₅×#2097	3
C₃×#2097	5

Subgroups — C3×C5×#2097 #14275131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2097 #14275131