Subgroups — C₃×C₅×#3263 #14276297

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#476	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#475	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3263	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×#126	—	2	2	no	—
18	C₃×C₅×#124	—	2	2	no	—
19	C₃×C₅×#124	C₂²	1	2	yes	—
20	C₃×C₅×#123	—	2	2	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#121	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
26	C₃×C₅×#117	C₂²	1	1	yes	characteristic
27	C₃×C₅×#106	C₂²	1	2	yes	—
28	C₃×C₅×#106	C₂²	1	1	yes	characteristic
29	C₃×C₅×#106	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×C₄⋊C₈	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×#3263	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#542	C₂×C₃	1	2	yes	complemented
38	C₅×#476	C₂×C₃	1	2	yes	complemented
39	C₅×#475	C₂×C₃	1	2	yes	complemented
40	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#469	C₂×C₃	1	1	yes	characteristic
42	C₅×#465	C₂×C₃	1	2	yes	complemented
43	C₅×#464	C₂×C₃	1	2	yes	complemented
44	C₅×#463	C₂×C₃	1	2	yes	complemented
45	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×Q₁₆	—	4	1	no	—
53	C₃×C₅×SD₁₆	—	4	2	no	—
54	C₃×C₅×D₈	—	4	1	no	—
55	C₃×C₅×M₁₆	—	4	1	no	—
56	C₂×C₃×C₅×C₈	—	4	1	no	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
72	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	—	2	2	no	—
74	C₃×C₄²×C₅	C₂³	1	2	yes	—
75	C₃×#542	C₂×C₅	1	2	yes	complemented
76	C₃×#476	C₂×C₅	1	2	yes	complemented
77	C₃×#475	C₂×C₅	1	2	yes	complemented
78	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#469	C₂×C₅	1	1	yes	characteristic
80	C₃×#465	C₂×C₅	1	2	yes	complemented
81	C₃×#464	C₂×C₅	1	2	yes	complemented
82	C₃×#463	C₂×C₅	1	2	yes	complemented
83	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
86	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
90	C₅×#126	—	2	2	no	—
91	C₅×#124	—	2	2	no	—
92	C₅×#124	C₂²×C₃	1	2	yes	—
93	C₅×#123	—	2	2	no	—
94	C₅×C₂²⋊Q₈	—	2	2	no	—
95	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
96	C₅×#121	C₂²×C₃	1	2	yes	—
97	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
98	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
99	C₅×#117	C₂²×C₃	1	1	yes	characteristic
100	C₅×#106	C₂²×C₃	1	2	yes	—
101	C₅×#106	C₂²×C₃	1	1	yes	characteristic
102	C₅×#106	C₂²×C₃	1	1	yes	characteristic
103	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
105	C₅×#103	C₂²×C₃	1	2	yes	—
106	C₅×#103	C₂²×C₃	1	2	yes	—
107	C₅×#102	C₂²×C₃	1	2	yes	—
108	C₅×#102	C₂²×C₃	1	2	yes	—
109	#3263	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×Q₈	—	8	2	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	8	2	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	1	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	1	no	—
130	C₃×C₅×C₈	—	2	1	no	—
131	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
133	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
135	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
136	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
137	C₃×#126	—	2	2	no	—
138	C₃×#124	—	2	2	no	—
139	C₃×#124	C₂²×C₅	1	2	yes	—
140	C₃×#123	—	2	2	no	—
141	C₃×C₂²⋊Q₈	—	2	2	no	—
142	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
143	C₃×#121	C₂²×C₅	1	2	yes	—
144	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
145	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
146	C₃×#117	C₂²×C₅	1	1	yes	characteristic
147	C₃×#106	C₂²×C₅	1	2	yes	—
148	C₃×#106	C₂²×C₅	1	1	yes	characteristic
149	C₃×#106	C₂²×C₅	1	1	yes	characteristic
150	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
152	C₃×#103	C₂²×C₅	1	2	yes	—
153	C₃×#103	C₂²×C₅	1	2	yes	—
154	C₃×#102	C₂²×C₅	1	2	yes	—
155	C₃×#102	C₂²×C₅	1	2	yes	—
156	C₂×C₅×Q₈	—	2	2	no	—
157	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₅×Q₁₆	—	4	1	no	—
163	C₅×SD₁₆	—	4	2	no	—
164	C₅×D₈	—	4	1	no	—
165	C₅×M₁₆	—	4	1	no	—
166	C₂×C₅×C₈	—	4	1	no	—
167	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
168	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
169	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
174	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
175	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	2	2	no	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₅×C₂²⋊C₄	—	2	2	no	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
182	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	C₂³×C₃	1	2	yes	—
185	#542	C₂×C₃×C₅	1	2	yes	complemented
186	#476	C₂×C₃×C₅	1	2	yes	complemented
187	#475	C₂×C₃×C₅	1	2	yes	complemented
188	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
189	#469	C₂×C₃×C₅	1	1	yes	characteristic
190	#465	C₂×C₃×C₅	1	2	yes	complemented
191	#464	C₂×C₃×C₅	1	2	yes	complemented
192	#463	C₂×C₃×C₅	1	2	yes	complemented
193	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
194	C₂²×C₃×C₅	—	2	1	no	—
195	C₂²×C₃×C₅	—	2	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₃×C₄×C₅	—	2	1	no	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	2	2	no	—
203	C₃×C₄×C₅	—	4	2	no	—
204	C₃×C₄×C₅	—	4	2	no	—
205	C₃×C₄×C₅	—	4	2	no	—
206	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
207	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×C₃×Q₈	—	2	2	no	—
209	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
212	C₂²×C₃×C₄	—	2	2	no	—
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₃×Q₁₆	—	4	1	no	—
215	C₃×SD₁₆	—	4	2	no	—
216	C₃×D₈	—	4	1	no	—
217	C₃×M₁₆	—	4	1	no	—
218	C₂×C₃×C₈	—	4	1	no	—
219	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
221	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	2	2	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
226	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
227	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
228	C₃×C₂²⋊C₄	—	2	2	no	—
229	C₃×C₂²⋊C₄	—	2	2	no	—
230	C₃×C₂²⋊C₄	—	2	2	no	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	2	2	no	—
233	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
234	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
235	C₃×C₄²	—	2	2	no	—
236	C₃×C₄²	C₂³×C₅	1	2	yes	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
239	C₅×Q₈	—	2	2	no	—
240	C₅×Q₈	—	2	2	no	—
241	C₅×Q₈	—	8	2	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	—	8	2	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	8	2	no	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
252	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
253	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	2	1	no	—
257	C₅×C₈	—	2	1	no	—
258	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
259	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
260	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
261	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
264	#126	—	2	2	no	—
265	#124	—	2	2	no	—
266	#124	C₂²×C₃×C₅	1	2	yes	—
267	#123	—	2	2	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
270	#121	C₂²×C₃×C₅	1	2	yes	—
271	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
272	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
273	#117	C₂²×C₃×C₅	1	1	yes	characteristic
274	#106	C₂²×C₃×C₅	1	2	yes	—
275	#106	C₂²×C₃×C₅	1	1	yes	characteristic
276	#106	C₂²×C₃×C₅	1	1	yes	characteristic
277	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
278	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
279	#103	C₂²×C₃×C₅	1	2	yes	—
280	#103	C₂²×C₃×C₅	1	2	yes	—
281	#102	C₂²×C₃×C₅	1	2	yes	—
282	#102	C₂²×C₃×C₅	1	2	yes	—
283	C₂×C₃×C₅	—	4	1	no	—
284	C₂×C₃×C₅	—	8	2	no	—
285	C₂×C₃×C₅	#537	1	1	yes	characteristic
286	C₂×C₃×C₅	#577	1	2	yes	—
287	C₂³×C₃	—	2	2	no	—
288	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
289	C₃×Q₈	—	2	2	no	—
290	C₃×Q₈	—	2	2	no	—
291	C₃×Q₈	—	8	2	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	—	2	2	no	—
294	C₃×D₄	—	8	2	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	8	2	no	—
301	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
305	C₃×C₈	—	2	2	no	—
306	C₃×C₈	—	2	1	no	—
307	C₃×C₈	—	2	1	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	2	1	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
321	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
328	Q₁₆	—	4	1	no	—
329	SD₁₆	—	4	2	no	—
330	D₈	—	4	1	no	—
331	M₁₆	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
334	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
335	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
340	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
341	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
348	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
349	C₄²	—	2	2	no	—
350	C₄²	C₂³×C₃×C₅	1	2	yes	—
351	C₃×C₅	#3263	1	1	yes	characteristic, direct product factor, Hall
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
365	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
366	C₂×C₅	—	4	1	no	—
367	C₂×C₅	—	8	2	no	—
368	C₂×C₅	C₃×#537	1	1	yes	characteristic
369	C₂×C₅	C₃×#577	1	2	yes	—
370	C₂³	—	2	2	no	—
371	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
372	Q₈	—	2	2	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	8	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
385	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
386	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₂×C₃	—	4	1	no	—
392	C₂×C₃	—	8	2	no	—
393	C₂×C₃	C₅×#537	1	1	yes	characteristic
394	C₂×C₃	C₅×#577	1	2	yes	—
395	C₅	C₃×#3263	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
409	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
410	C₃	C₅×#3263	1	1	yes	characteristic, direct product factor, Sylow
411	C₂	—	4	1	no	—
412	C₂	—	8	2	no	—
413	C₂	C₃×C₅×#537	1	1	yes	characteristic
414	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×#469	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×#542	C₂	semidirect
2. C₃×C₅×#476	C₂	semidirect
3. C₃×C₅×#475	C₂	semidirect
4. C₃×C₅×#470	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#424	C₂	semidirect
10. C₅×#3263	C₃	direct (N × H)
36. C₃×#3263	C₅	direct (N × H)
37. C₅×#542	C₂×C₃	semidirect
38. C₅×#476	C₂×C₃	semidirect
39. C₅×#475	C₂×C₃	semidirect
40. C₅×#470	C₂×C₃	semidirect
42. C₅×#465	C₂×C₃	semidirect
43. C₅×#464	C₂×C₃	semidirect
44. C₅×#463	C₂×C₃	semidirect
45. C₅×#424	C₂×C₃	semidirect
75. C₃×#542	C₂×C₅	semidirect
76. C₃×#476	C₂×C₅	semidirect
77. C₃×#475	C₂×C₅	semidirect
78. C₃×#470	C₂×C₅	semidirect
80. C₃×#465	C₂×C₅	semidirect
81. C₃×#464	C₂×C₅	semidirect
82. C₃×#463	C₂×C₅	semidirect
83. C₃×#424	C₂×C₅	semidirect
109. #3263	C₃×C₅	direct (N × H)
185. #542	C₂×C₃×C₅	semidirect
186. #476	C₂×C₃×C₅	semidirect
187. #475	C₂×C₃×C₅	semidirect
188. #470	C₂×C₃×C₅	semidirect
190. #465	C₂×C₃×C₅	semidirect
191. #464	C₂×C₃×C₅	semidirect
192. #463	C₂×C₃×C₅	semidirect
193. #424	C₂×C₃×C₅	semidirect
351. C₃×C₅	#3263	direct (N × H)
395. C₅	C₃×#3263	direct (N × H)
410. C₃	C₅×#3263	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×#542	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#470	2
C₃×C₅×#469	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#424	2
C₅×#3263	3
C₃×#3263	5

Subgroups — C3×C5×#3263 #14276297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3263 #14276297