Subgroups — C₃×C₅×#3174 #14276208

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#440	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3174	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₅×#126	—	2	2	no	—
20	C₃×C₅×#125	—	2	2	no	—
21	C₃×C₅×#125	C₂²	1	1	yes	characteristic
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic
23	C₃×C₅×#123	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×#121	—	2	2	no	—
26	C₃×C₅×#121	C₂²	1	2	yes	—
27	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
28	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₃×C₅×#117	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	2	yes	—
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₃×C₅×#97	C₂²	1	1	yes	characteristic
37	C₃×C₅×#97	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₃×#3174	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#540	C₂×C₃	1	1	yes	characteristic
43	C₅×#499	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#490	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#468	C₂×C₃	1	2	yes	complemented
48	C₅×#465	C₂×C₃	1	2	yes	complemented
49	C₅×#440	C₂×C₃	1	2	yes	complemented
50	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
51	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₄	—	2	2	no	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×SD₁₆	—	2	4	no	—
59	C₃×C₅×SD₁₆	—	2	4	no	—
60	C₃×C₅×M₁₆	—	2	2	no	—
61	C₂×C₃×C₅×C₈	—	2	2	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#540	C₂×C₅	1	1	yes	characteristic
83	C₃×#499	C₂×C₅	1	1	yes	characteristic, complemented
84	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#491	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#490	C₂×C₅	1	1	yes	characteristic, complemented
87	C₃×#468	C₂×C₅	1	2	yes	complemented
88	C₃×#465	C₂×C₅	1	2	yes	complemented
89	C₃×#440	C₂×C₅	1	2	yes	complemented
90	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
91	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
93	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
94	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
96	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
97	C₅×#127	C₂²×C₃	1	1	yes	characteristic
98	C₅×#126	—	2	2	no	—
99	C₅×#125	—	2	2	no	—
100	C₅×#125	C₂²×C₃	1	1	yes	characteristic
101	C₅×#125	C₂²×C₃	1	1	yes	characteristic
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
104	C₅×#121	—	2	2	no	—
105	C₅×#121	C₂²×C₃	1	2	yes	—
106	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
107	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
108	C₅×#117	C₂²×C₃	1	1	yes	characteristic
109	C₅×#107	C₂²×C₃	1	2	yes	—
110	C₅×#106	C₂²×C₃	1	2	yes	—
111	C₅×#103	C₂²×C₃	1	2	yes	—
112	C₅×#103	C₂²×C₃	1	2	yes	—
113	C₅×#102	C₂²×C₃	1	2	yes	—
114	C₅×#102	C₂²×C₃	1	2	yes	—
115	C₅×#97	C₂²×C₃	1	1	yes	characteristic
116	C₅×#97	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
118	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
119	#3174	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×Q₈	—	2	2	no	—
124	C₃×C₅×D₄	—	2	2	no	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	8	2	no	—
127	C₃×C₅×D₄	—	8	2	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	8	2	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₅×C₈	—	2	1	no	—
139	C₃×C₅×C₈	—	2	1	no	—
140	C₃×C₅×C₈	#41	1	2	yes	—
141	C₃×C₅×C₈	#41	1	2	yes	—
142	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
143	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
144	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
147	C₃×#127	C₂²×C₅	1	1	yes	characteristic
148	C₃×#126	—	2	2	no	—
149	C₃×#125	—	2	2	no	—
150	C₃×#125	C₂²×C₅	1	1	yes	characteristic
151	C₃×#125	C₂²×C₅	1	1	yes	characteristic
152	C₃×#123	—	2	2	no	—
153	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
154	C₃×#121	—	2	2	no	—
155	C₃×#121	C₂²×C₅	1	2	yes	—
156	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
157	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
158	C₃×#117	C₂²×C₅	1	1	yes	characteristic
159	C₃×#107	C₂²×C₅	1	2	yes	—
160	C₃×#106	C₂²×C₅	1	2	yes	—
161	C₃×#103	C₂²×C₅	1	2	yes	—
162	C₃×#103	C₂²×C₅	1	2	yes	—
163	C₃×#102	C₂²×C₅	1	2	yes	—
164	C₃×#102	C₂²×C₅	1	2	yes	—
165	C₃×#97	C₂²×C₅	1	1	yes	characteristic
166	C₃×#97	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
170	C₂×C₅×D₄	—	2	2	no	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
173	C₂²×C₄×C₅	—	2	2	no	—
174	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
175	C₅×SD₁₆	—	2	4	no	—
176	C₅×SD₁₆	—	2	4	no	—
177	C₅×M₁₆	—	2	2	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
182	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
189	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
190	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
195	C₄²×C₅	—	2	2	no	—
196	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
198	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	#540	C₂×C₃×C₅	1	1	yes	characteristic
200	#499	C₂×C₃×C₅	1	1	yes	characteristic, complemented
201	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#491	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
204	#468	C₂×C₃×C₅	1	2	yes	complemented
205	#465	C₂×C₃×C₅	1	2	yes	complemented
206	#440	C₂×C₃×C₅	1	2	yes	complemented
207	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
208	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	C₂²×C₃×C₅	—	2	1	no	—
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	4	2	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	2	no	—
217	C₃×C₄×C₅	—	2	2	no	—
218	C₃×C₄×C₅	—	4	2	no	—
219	C₃×C₄×C₅	—	4	2	no	—
220	C₃×C₄×C₅	—	4	2	no	—
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃×D₄	—	2	2	no	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
227	C₂²×C₃×C₄	—	2	2	no	—
228	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₃×SD₁₆	—	2	4	no	—
230	C₃×SD₁₆	—	2	4	no	—
231	C₃×M₁₆	—	2	2	no	—
232	C₂×C₃×C₈	—	2	2	no	—
233	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
237	C₃×C₄⋊C₄	—	2	2	no	—
238	C₃×C₄⋊C₄	—	2	2	no	—
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	—	2	2	no	—
242	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
243	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
244	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₂²⋊C₄	—	2	2	no	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₂²⋊C₄	—	2	2	no	—
248	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
249	C₃×C₄²	—	2	2	no	—
250	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
251	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
252	C₂³×C₅	—	2	2	no	—
253	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₅×Q₈	—	2	2	no	—
255	C₅×Q₈	—	2	2	no	—
256	C₅×D₄	—	2	2	no	—
257	C₅×D₄	—	2	2	no	—
258	C₅×D₄	—	8	2	no	—
259	C₅×D₄	—	8	2	no	—
260	C₂×C₄×C₅	—	2	1	no	—
261	C₂×C₄×C₅	—	2	1	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	8	2	no	—
266	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
267	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
270	C₅×C₈	—	2	1	no	—
271	C₅×C₈	—	2	1	no	—
272	C₅×C₈	C₃×#41	1	2	yes	—
273	C₅×C₈	C₃×#41	1	2	yes	—
274	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
275	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
276	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
277	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
279	#127	C₂²×C₃×C₅	1	1	yes	characteristic
280	#126	—	2	2	no	—
281	#125	—	2	2	no	—
282	#125	C₂²×C₃×C₅	1	1	yes	characteristic
283	#125	C₂²×C₃×C₅	1	1	yes	characteristic
284	#123	—	2	2	no	—
285	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
286	#121	—	2	2	no	—
287	#121	C₂²×C₃×C₅	1	2	yes	—
288	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
289	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
290	#117	C₂²×C₃×C₅	1	1	yes	characteristic
291	#107	C₂²×C₃×C₅	1	2	yes	—
292	#106	C₂²×C₃×C₅	1	2	yes	—
293	#103	C₂²×C₃×C₅	1	2	yes	—
294	#103	C₂²×C₃×C₅	1	2	yes	—
295	#102	C₂²×C₃×C₅	1	2	yes	—
296	#102	C₂²×C₃×C₅	1	2	yes	—
297	#97	C₂²×C₃×C₅	1	1	yes	characteristic
298	#97	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
300	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
301	C₂×C₃×C₅	—	4	1	no	—
302	C₂×C₃×C₅	—	8	2	no	—
303	C₂×C₃×C₅	#532	1	1	yes	characteristic
304	C₂×C₃×C₅	#577	1	2	yes	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	2	2	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	2	2	no	—
311	C₃×D₄	—	8	2	no	—
312	C₃×D₄	—	8	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	8	2	no	—
319	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
320	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
323	C₃×C₈	—	2	1	no	—
324	C₃×C₈	—	2	1	no	—
325	C₃×C₈	C₅×#41	1	2	yes	—
326	C₃×C₈	C₅×#41	1	2	yes	—
327	C₂²×C₅	—	2	2	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	4	2	no	—
331	C₂²×C₅	—	4	2	no	—
332	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	2	2	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	—	4	2	no	—
339	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
340	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
341	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
347	SD₁₆	—	2	4	no	—
348	SD₁₆	—	2	4	no	—
349	M₁₆	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
352	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
353	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
354	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
361	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
362	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
367	C₄²	—	2	2	no	—
368	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
369	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
370	C₃×C₅	#3174	1	1	yes	characteristic, direct product factor, Hall
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	4	2	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	4	2	no	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	—	4	2	no	—
383	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
384	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
385	C₂×C₅	—	4	1	no	—
386	C₂×C₅	—	8	2	no	—
387	C₂×C₅	C₃×#532	1	1	yes	characteristic
388	C₂×C₅	C₃×#577	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
404	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
405	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	C₃×C₅×#41	1	2	yes	—
410	C₈	C₃×C₅×#41	1	2	yes	—
411	C₂×C₃	—	4	1	no	—
412	C₂×C₃	—	8	2	no	—
413	C₂×C₃	C₅×#532	1	1	yes	characteristic
414	C₂×C₃	C₅×#577	1	2	yes	—
415	C₅	C₃×#3174	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
429	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
430	C₃	C₅×#3174	1	1	yes	characteristic, direct product factor, Sylow
431	C₂	—	4	1	no	—
432	C₂	—	8	2	no	—
433	C₂	C₃×C₅×#532	1	1	yes	characteristic
434	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#541	C₂	semidirect
3. C₃×C₅×#499	C₂	semidirect
4. C₃×C₅×#492	C₂	semidirect
5. C₃×C₅×#491	C₂	semidirect
6. C₃×C₅×#490	C₂	semidirect
7. C₃×C₅×#468	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#440	C₂	semidirect
10. C₃×C₄×C₅×SD₁₆	C₂	semidirect
11. C₃×C₅×#405	C₂	semidirect
12. C₅×#3174	C₃	direct (N × H)
40. C₃×#3174	C₅	direct (N × H)
41. C₅×#541	C₂×C₃	semidirect
43. C₅×#499	C₂×C₃	semidirect
44. C₅×#492	C₂×C₃	semidirect
45. C₅×#491	C₂×C₃	semidirect
46. C₅×#490	C₂×C₃	semidirect
47. C₅×#468	C₂×C₃	semidirect
48. C₅×#465	C₂×C₃	semidirect
49. C₅×#440	C₂×C₃	semidirect
50. C₄×C₅×SD₁₆	C₂×C₃	semidirect
51. C₅×#405	C₂×C₃	semidirect
81. C₃×#541	C₂×C₅	semidirect
83. C₃×#499	C₂×C₅	semidirect
84. C₃×#492	C₂×C₅	semidirect
85. C₃×#491	C₂×C₅	semidirect
86. C₃×#490	C₂×C₅	semidirect
87. C₃×#468	C₂×C₅	semidirect
88. C₃×#465	C₂×C₅	semidirect
89. C₃×#440	C₂×C₅	semidirect
90. C₃×C₄×SD₁₆	C₂×C₅	semidirect
91. C₃×#405	C₂×C₅	semidirect
119. #3174	C₃×C₅	direct (N × H)
198. #541	C₂×C₃×C₅	semidirect
200. #499	C₂×C₃×C₅	semidirect
201. #492	C₂×C₃×C₅	semidirect
202. #491	C₂×C₃×C₅	semidirect
203. #490	C₂×C₃×C₅	semidirect
204. #468	C₂×C₃×C₅	semidirect
205. #465	C₂×C₃×C₅	semidirect
206. #440	C₂×C₃×C₅	semidirect
207. C₄×SD₁₆	C₂×C₃×C₅	semidirect
208. #405	C₂×C₃×C₅	semidirect
370. C₃×C₅	#3174	direct (N × H)
415. C₅	C₃×#3174	direct (N × H)
430. C₃	C₅×#3174	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#541	2
C₃×C₅×#540	2
C₃×C₅×#499	2
C₃×C₅×#492	2
C₃×C₅×#491	2
C₃×C₅×#490	2
C₃×C₅×#468	2
C₃×C₅×#465	2
C₃×C₅×#440	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#405	2
C₅×#3174	3
C₃×#3174	5

Subgroups — C3×C5×#3174 #14276208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3174 #14276208