Subgroups — C₃×C₅×#3126 #14276160

Order 1920.

764 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#460	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#448	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#440	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3126	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₅×#125	C₂²	1	1	yes	characteristic
16	C₃×C₅×#123	—	2	2	no	—
17	C₃×C₅×#121	—	2	2	no	—
18	C₃×C₅×#121	C₂²	1	2	yes	—
19	C₃×C₄×C₅×Q₈	—	2	2	no	—
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
23	C₃×C₅×#117	—	2	2	no	—
24	C₃×C₅×#117	C₂²	1	1	yes	characteristic
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₃×C₅×#107	C₂²	1	2	yes	—
27	C₃×C₅×#106	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃×C₅×#103	C₂²	1	2	yes	—
30	C₃×C₅×#103	C₂²	1	2	yes	—
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×C₅×#102	C₂²	1	2	yes	—
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×#97	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
36	C₃×#3126	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#540	C₂×C₃	1	1	yes	characteristic
38	C₅×#519	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#482	C₂×C₃	1	2	yes	complemented
40	C₅×#479	C₂×C₃	1	2	yes	complemented
41	C₅×#460	C₂×C₃	1	2	yes	complemented
42	C₅×#448	C₂×C₃	1	2	yes	complemented
43	C₅×#440	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
45	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	—	2	1	no	—
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	—	2	2	no	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×SD₁₆	—	2	4	no	—
56	C₃×C₅×SD₁₆	—	2	4	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₃×C₄²×C₅	—	2	1	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#540	C₂×C₅	1	1	yes	characteristic
75	C₃×#519	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#482	C₂×C₅	1	2	yes	complemented
77	C₃×#479	C₂×C₅	1	2	yes	complemented
78	C₃×#460	C₂×C₅	1	2	yes	complemented
79	C₃×#448	C₂×C₅	1	2	yes	complemented
80	C₃×#440	C₂×C₅	1	2	yes	complemented
81	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
82	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
85	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
86	C₅×#127	C₂²×C₃	1	1	yes	characteristic
87	C₅×#125	C₂²×C₃	1	1	yes	characteristic
88	C₅×#123	—	2	2	no	—
89	C₅×#121	—	2	2	no	—
90	C₅×#121	C₂²×C₃	1	2	yes	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
93	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
94	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
95	C₅×#117	—	2	2	no	—
96	C₅×#117	C₂²×C₃	1	1	yes	characteristic
97	C₅×#117	C₂²×C₃	1	1	yes	characteristic
98	C₅×#107	C₂²×C₃	1	2	yes	—
99	C₅×#106	C₂²×C₃	1	2	yes	—
100	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
101	C₅×#103	C₂²×C₃	1	2	yes	—
102	C₅×#103	C₂²×C₃	1	2	yes	—
103	C₅×#102	C₂²×C₃	1	2	yes	—
104	C₅×#102	C₂²×C₃	1	2	yes	—
105	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₅×#97	C₂²×C₃	1	1	yes	characteristic
107	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
108	#3126	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
111	C₃×C₅×Q₈	—	2	4	no	—
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	#41	1	4	yes	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	—	8	2	no	—
117	C₃×C₅×D₄	—	8	2	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	8	2	no	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₃×C₅×C₈	—	2	2	no	—
129	C₃×C₅×C₈	—	2	2	no	—
130	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
132	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
133	C₃×#127	C₂²×C₅	1	1	yes	characteristic
134	C₃×#125	C₂²×C₅	1	1	yes	characteristic
135	C₃×#123	—	2	2	no	—
136	C₃×#121	—	2	2	no	—
137	C₃×#121	C₂²×C₅	1	2	yes	—
138	C₃×C₄×Q₈	—	2	2	no	—
139	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
140	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
141	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
142	C₃×#117	—	2	2	no	—
143	C₃×#117	C₂²×C₅	1	1	yes	characteristic
144	C₃×#117	C₂²×C₅	1	1	yes	characteristic
145	C₃×#107	C₂²×C₅	1	2	yes	—
146	C₃×#106	C₂²×C₅	1	2	yes	—
147	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
148	C₃×#103	C₂²×C₅	1	2	yes	—
149	C₃×#103	C₂²×C₅	1	2	yes	—
150	C₃×#102	C₂²×C₅	1	2	yes	—
151	C₃×#102	C₂²×C₅	1	2	yes	—
152	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
153	C₃×#97	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₅×Q₈	—	2	4	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	2	2	no	—
160	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	—	2	2	no	—
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₅×SD₁₆	—	2	4	no	—
165	C₅×SD₁₆	—	2	4	no	—
166	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
167	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
178	C₄²×C₅	—	2	2	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
183	#540	C₂×C₃×C₅	1	1	yes	characteristic
184	#519	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	#482	C₂×C₃×C₅	1	2	yes	complemented
186	#479	C₂×C₃×C₅	1	2	yes	complemented
187	#460	C₂×C₃×C₅	1	2	yes	complemented
188	#448	C₂×C₃×C₅	1	2	yes	complemented
189	#440	C₂×C₃×C₅	1	2	yes	complemented
190	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
191	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₂²×C₃×C₅	—	2	1	no	—
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	—	4	2	no	—
195	C₂²×C₃×C₅	—	4	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
198	C₃×C₄×C₅	—	2	4	no	—
199	C₃×C₄×C₅	—	2	1	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	—	4	2	no	—
204	C₃×C₄×C₅	C₂×#41	1	2	yes	—
205	C₂×C₃×Q₈	—	2	4	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
208	C₂×C₃×D₄	—	2	2	no	—
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	—	2	2	no	—
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₃×SD₁₆	—	2	4	no	—
215	C₃×SD₁₆	—	2	4	no	—
216	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
217	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	—	2	2	no	—
221	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
222	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
223	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
224	C₃×C₂²⋊C₄	—	2	1	no	—
225	C₃×C₂²⋊C₄	—	2	2	no	—
226	C₃×C₂²⋊C₄	—	2	2	no	—
227	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
228	C₃×C₄²	—	2	2	no	—
229	C₃×C₄²	—	2	2	no	—
230	C₃×C₄²	—	2	1	no	—
231	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₅×Q₈	—	2	4	no	—
236	C₅×Q₈	—	2	2	no	—
237	C₅×Q₈	C₃×#41	1	4	yes	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	2	2	no	—
240	C₅×D₄	—	8	2	no	—
241	C₅×D₄	—	8	2	no	—
242	C₂×C₄×C₅	—	2	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	8	2	no	—
248	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
252	C₅×C₈	—	2	2	no	—
253	C₅×C₈	—	2	2	no	—
254	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
256	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
257	#127	C₂²×C₃×C₅	1	1	yes	characteristic
258	#125	C₂²×C₃×C₅	1	1	yes	characteristic
259	#123	—	2	2	no	—
260	#121	—	2	2	no	—
261	#121	C₂²×C₃×C₅	1	2	yes	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
264	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
265	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
266	#117	—	2	2	no	—
267	#117	C₂²×C₃×C₅	1	1	yes	characteristic
268	#117	C₂²×C₃×C₅	1	1	yes	characteristic
269	#107	C₂²×C₃×C₅	1	2	yes	—
270	#106	C₂²×C₃×C₅	1	2	yes	—
271	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
272	#103	C₂²×C₃×C₅	1	2	yes	—
273	#103	C₂²×C₃×C₅	1	2	yes	—
274	#102	C₂²×C₃×C₅	1	2	yes	—
275	#102	C₂²×C₃×C₅	1	2	yes	—
276	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
277	#97	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₃×C₅	—	4	1	no	—
280	C₂×C₃×C₅	—	8	2	no	—
281	C₂×C₃×C₅	#525	1	1	yes	characteristic
282	C₂×C₃×C₅	#577	1	2	yes	—
283	C₂³×C₃	—	2	2	no	—
284	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
285	C₃×Q₈	—	2	4	no	—
286	C₃×Q₈	—	2	2	no	—
287	C₃×Q₈	C₅×#41	1	4	yes	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	2	2	no	—
290	C₃×D₄	—	8	2	no	—
291	C₃×D₄	—	8	2	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	8	2	no	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	1	no	—
306	C₂²×C₅	—	4	2	no	—
307	C₂²×C₅	—	4	2	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	—	2	4	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	C₂×C₃×#41	1	2	yes	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
326	SD₁₆	—	2	4	no	—
327	SD₁₆	—	2	4	no	—
328	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
329	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
334	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
335	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
344	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
345	C₃×C₅	#3126	1	1	yes	characteristic, direct product factor, Hall
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	4	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	C₂×C₅×#41	1	2	yes	—
359	C₂×C₅	—	4	1	no	—
360	C₂×C₅	—	8	2	no	—
361	C₂×C₅	C₃×#525	1	1	yes	characteristic
362	C₂×C₅	C₃×#577	1	2	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	2	no	—
367	Q₈	C₃×C₅×#41	1	4	yes	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
379	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
380	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
381	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₂×C₃	—	4	1	no	—
385	C₂×C₃	—	8	2	no	—
386	C₂×C₃	C₅×#525	1	1	yes	characteristic
387	C₂×C₃	C₅×#577	1	2	yes	—
388	C₅	C₃×#3126	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
395	C₄	—	2	4	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₂×C₃×C₅×#41	1	2	yes	—
402	C₃	C₅×#3126	1	1	yes	characteristic, direct product factor, Sylow
403	C₂	—	4	1	no	—
404	C₂	—	8	2	no	—
405	C₂	C₃×C₅×#525	1	1	yes	characteristic
406	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
2. C₃×C₅×#519	C₂	semidirect
3. C₃×C₅×#482	C₂	semidirect
4. C₃×C₅×#479	C₂	semidirect
5. C₃×C₅×#460	C₂	semidirect
6. C₃×C₅×#448	C₂	semidirect
7. C₃×C₅×#440	C₂	semidirect
8. C₃×C₄×C₅×SD₁₆	C₂	semidirect
9. C₃×C₅×#433	C₂	semidirect
10. C₅×#3126	C₃	direct (N × H)
36. C₃×#3126	C₅	direct (N × H)
38. C₅×#519	C₂×C₃	semidirect
39. C₅×#482	C₂×C₃	semidirect
40. C₅×#479	C₂×C₃	semidirect
41. C₅×#460	C₂×C₃	semidirect
42. C₅×#448	C₂×C₃	semidirect
43. C₅×#440	C₂×C₃	semidirect
44. C₄×C₅×SD₁₆	C₂×C₃	semidirect
45. C₅×#433	C₂×C₃	semidirect
75. C₃×#519	C₂×C₅	semidirect
76. C₃×#482	C₂×C₅	semidirect
77. C₃×#479	C₂×C₅	semidirect
78. C₃×#460	C₂×C₅	semidirect
79. C₃×#448	C₂×C₅	semidirect
80. C₃×#440	C₂×C₅	semidirect
81. C₃×C₄×SD₁₆	C₂×C₅	semidirect
82. C₃×#433	C₂×C₅	semidirect
108. #3126	C₃×C₅	direct (N × H)
184. #519	C₂×C₃×C₅	semidirect
185. #482	C₂×C₃×C₅	semidirect
186. #479	C₂×C₃×C₅	semidirect
187. #460	C₂×C₃×C₅	semidirect
188. #448	C₂×C₃×C₅	semidirect
189. #440	C₂×C₃×C₅	semidirect
190. C₄×SD₁₆	C₂×C₃×C₅	semidirect
191. #433	C₂×C₃×C₅	semidirect
345. C₃×C₅	#3126	direct (N × H)
388. C₅	C₃×#3126	direct (N × H)
402. C₃	C₅×#3126	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×#540	2
C₃×C₅×#519	2
C₃×C₅×#482	2
C₃×C₅×#479	2
C₃×C₅×#460	2
C₃×C₅×#448	2
C₃×C₅×#440	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#433	2
C₅×#3126	3
C₃×#3126	5

Subgroups — C3×C5×#3126 #14276160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3126 #14276160