Subgroups — C₃×C₅×#3215 #14276249

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#497	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#489	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#464	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#450	C₂	1	2	yes	maximal
8	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3215	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#125	—	2	1	no	—
17	C₃×C₅×#124	—	2	1	no	—
18	C₃×C₅×#124	—	2	1	no	—
19	C₃×C₅×#124	C₂²	1	2	yes	—
20	C₃×C₅×#124	C₂²	1	2	yes	—
21	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₄×C₅×Q₈	—	2	1	no	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#117	—	2	1	no	—
26	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
27	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₃×C₅×#103	C₂²	1	4	yes	complemented
31	C₃×C₅×#102	C₂²	1	4	yes	—
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#97	C₂²	1	2	yes	complemented
34	C₃×#3215	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
37	C₅×#497	C₂×C₃	1	2	yes	complemented
38	C₅×#489	C₂×C₃	1	2	yes	complemented
39	C₅×#464	C₂×C₃	1	4	yes	complemented
40	C₅×#451	C₂×C₃	1	2	yes	complemented
41	C₅×#450	C₂×C₃	1	2	yes	—
42	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×Q₈	—	4	2	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	4	2	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₃×C₅×Q₁₆	—	4	4	no	—
57	C₃×C₅×SD₁₆	—	4	4	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	—	2	1	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
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×C₄²×C₅	—	2	2	no	—
71	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
77	C₃×#497	C₂×C₅	1	2	yes	complemented
78	C₃×#489	C₂×C₅	1	2	yes	complemented
79	C₃×#464	C₂×C₅	1	4	yes	complemented
80	C₃×#451	C₂×C₅	1	2	yes	complemented
81	C₃×#450	C₂×C₅	1	2	yes	—
82	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
86	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
87	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₅×#125	—	2	1	no	—
90	C₅×#124	—	2	1	no	—
91	C₅×#124	—	2	1	no	—
92	C₅×#124	C₂²×C₃	1	2	yes	—
93	C₅×#124	C₂²×C₃	1	2	yes	—
94	C₅×C₂²⋊Q₈	—	2	1	no	—
95	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
96	C₄×C₅×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
98	C₅×#117	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
102	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
103	C₅×#103	C₂²×C₃	1	4	yes	complemented
104	C₅×#102	C₂²×C₃	1	4	yes	—
105	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₅×#97	C₂²×C₃	1	2	yes	complemented
107	#3215	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	4	2	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	—	4	2	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₅×Q₈	—	2	4	no	—
114	C₃×C₅×Q₈	—	2	4	no	—
115	C₃×C₅×Q₈	—	4	2	no	—
116	C₃×C₅×Q₈	—	4	2	no	—
117	C₃×C₅×D₄	—	2	4	no	—
118	C₃×C₅×D₄	—	4	2	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	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	1	no	—
125	C₂×C₃×C₄×C₅	—	4	2	no	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₃×C₅×C₈	—	2	4	no	—
133	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
136	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
137	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
138	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₃×#125	—	2	1	no	—
140	C₃×#124	—	2	1	no	—
141	C₃×#124	—	2	1	no	—
142	C₃×#124	C₂²×C₅	1	2	yes	—
143	C₃×#124	C₂²×C₅	1	2	yes	—
144	C₃×C₂²⋊Q₈	—	2	1	no	—
145	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
146	C₃×C₄×Q₈	—	2	1	no	—
147	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
148	C₃×#117	—	2	1	no	—
149	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
152	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
153	C₃×#103	C₂²×C₅	1	4	yes	complemented
154	C₃×#102	C₂²×C₅	1	4	yes	—
155	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
156	C₃×#97	C₂²×C₅	1	2	yes	complemented
157	C₂⁴×C₅	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	4	2	no	—
161	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
162	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	4	2	no	—
165	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₅×Q₁₆	—	4	4	no	—
171	C₅×SD₁₆	—	4	4	no	—
172	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	2	1	no	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
179	C₅×C₂²⋊C₄	—	2	2	no	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₅×C₂²⋊C₄	—	2	2	no	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₄²×C₅	—	2	2	no	—
185	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
186	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
187	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
189	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
190	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
191	#497	C₂×C₃×C₅	1	2	yes	complemented
192	#489	C₂×C₃×C₅	1	2	yes	complemented
193	#464	C₂×C₃×C₅	1	4	yes	complemented
194	#451	C₂×C₃×C₅	1	2	yes	complemented
195	#450	C₂×C₃×C₅	1	2	yes	—
196	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
197	C₂²×C₃×C₅	—	2	1	no	—
198	C₂²×C₃×C₅	—	2	1	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	8	4	no	—
203	C₂²×C₃×C₅	#137	1	2	yes	—
204	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₃×C₄×C₅	—	2	1	no	—
206	C₃×C₄×C₅	—	2	1	no	—
207	C₃×C₄×C₅	—	2	1	no	—
208	C₃×C₄×C₅	—	2	1	no	—
209	C₃×C₄×C₅	—	2	1	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
214	C₂⁴×C₃	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	—	2	1	no	—
217	C₂×C₃×Q₈	—	4	2	no	—
218	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
219	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
220	C₂×C₃×D₄	—	2	1	no	—
221	C₂×C₃×D₄	—	4	2	no	—
222	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	—	2	1	no	—
224	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₃×Q₁₆	—	4	4	no	—
228	C₃×SD₁₆	—	4	4	no	—
229	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
230	C₃×C₄⋊C₄	—	2	1	no	—
231	C₃×C₄⋊C₄	—	2	1	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	2	2	no	—
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
236	C₃×C₂²⋊C₄	—	2	2	no	—
237	C₃×C₂²⋊C₄	—	2	2	no	—
238	C₃×C₂²⋊C₄	—	2	2	no	—
239	C₃×C₂²⋊C₄	—	2	2	no	—
240	C₃×C₂²⋊C₄	—	2	2	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
243	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
244	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	4	2	no	—
248	C₂³×C₅	—	4	2	no	—
249	C₂³×C₅	—	4	2	no	—
250	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₅×Q₈	—	2	4	no	—
252	C₅×Q₈	—	2	4	no	—
253	C₅×Q₈	—	4	2	no	—
254	C₅×Q₈	—	4	2	no	—
255	C₅×D₄	—	2	4	no	—
256	C₅×D₄	—	4	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	4	1	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
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	4	no	—
271	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
272	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
273	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	complemented
274	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
275	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
276	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
277	#125	—	2	1	no	—
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#124	C₂²×C₃×C₅	1	2	yes	—
281	#124	C₂²×C₃×C₅	1	2	yes	—
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
286	#117	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
291	#103	C₂²×C₃×C₅	1	4	yes	complemented
292	#102	C₂²×C₃×C₅	1	4	yes	—
293	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
294	#97	C₂²×C₃×C₅	1	2	yes	complemented
295	C₂×C₃×C₅	—	2	2	no	—
296	C₂×C₃×C₅	—	8	2	no	—
297	C₂×C₃×C₅	#535	1	1	yes	characteristic
298	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
299	C₂×C₃×C₅	#575	1	1	yes	characteristic
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	—	4	2	no	—
302	C₂³×C₃	—	4	2	no	—
303	C₂³×C₃	—	4	2	no	—
304	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
305	C₃×Q₈	—	2	4	no	—
306	C₃×Q₈	—	2	4	no	—
307	C₃×Q₈	—	4	2	no	—
308	C₃×Q₈	—	4	2	no	—
309	C₃×D₄	—	2	4	no	—
310	C₃×D₄	—	4	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	4	1	no	—
317	C₂×C₃×C₄	—	4	2	no	—
318	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
324	C₃×C₈	—	2	4	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	—	4	2	no	—
330	C₂²×C₅	—	8	4	no	—
331	C₂²×C₅	C₃×#137	1	2	yes	—
332	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	2	1	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	4	2	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	4	2	no	—
341	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
347	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
355	Q₁₆	—	4	4	no	—
356	SD₁₆	—	4	4	no	—
357	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
371	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
372	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
373	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
374	C₃×C₅	#3215	1	1	yes	characteristic, direct product factor, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	4	2	no	—
378	C₂²×C₃	—	4	2	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	8	4	no	—
381	C₂²×C₃	C₅×#137	1	2	yes	—
382	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	—	8	2	no	—
394	C₂×C₅	C₃×#535	1	1	yes	characteristic
395	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
396	C₂×C₅	C₃×#575	1	1	yes	characteristic
397	C₂³	—	2	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
418	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
420	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₂×C₃	—	2	2	no	—
423	C₂×C₃	—	8	2	no	—
424	C₂×C₃	C₅×#535	1	1	yes	characteristic
425	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
426	C₂×C₃	C₅×#575	1	1	yes	characteristic
427	C₅	C₃×#3215	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	8	4	no	—
434	C₂²	C₃×C₅×#137	1	2	yes	—
435	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
445	C₃	C₅×#3215	1	1	yes	characteristic, direct product factor, Sylow
446	C₂	—	2	2	no	—
447	C₂	—	8	2	no	—
448	C₂	C₃×C₅×#535	1	1	yes	characteristic
449	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
450	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₃×C₅×#489	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₃×C₅×#451	C₂	semidirect
8. C₃×C₅×#432	C₂	semidirect
9. C₅×#3215	C₃	direct (N × H)
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
29. C₃×C₅×C₄⋊C₈	C₂²	semidirect
30. C₃×C₅×#103	C₂²	semidirect
33. C₃×C₅×#97	C₂²	semidirect
34. C₃×#3215	C₅	direct (N × H)
35. C₅×#533	C₂×C₃	semidirect
37. C₅×#497	C₂×C₃	semidirect
38. C₅×#489	C₂×C₃	semidirect
39. C₅×#464	C₂×C₃	semidirect
40. C₅×#451	C₂×C₃	semidirect
42. C₅×#432	C₂×C₃	semidirect
75. C₃×#533	C₂×C₅	semidirect
77. C₃×#497	C₂×C₅	semidirect
78. C₃×#489	C₂×C₅	semidirect
79. C₃×#464	C₂×C₅	semidirect
80. C₃×#451	C₂×C₅	semidirect
82. C₃×#432	C₂×C₅	semidirect
85. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
87. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
88. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
97. C₄×C₅×Q₈	C₂²×C₃	semidirect
102. C₅×C₄⋊C₈	C₂²×C₃	semidirect
103. C₅×#103	C₂²×C₃	semidirect
106. C₅×#97	C₂²×C₃	semidirect
107. #3215	C₃×C₅	direct (N × H)
135. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
137. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
138. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
147. C₃×C₄×Q₈	C₂²×C₅	semidirect
152. C₃×C₄⋊C₈	C₂²×C₅	semidirect
153. C₃×#103	C₂²×C₅	semidirect
156. C₃×#97	C₂²×C₅	semidirect
189. #533	C₂×C₃×C₅	semidirect
191. #497	C₂×C₃×C₅	semidirect
192. #489	C₂×C₃×C₅	semidirect
193. #464	C₂×C₃×C₅	semidirect
194. #451	C₂×C₃×C₅	semidirect
196. #432	C₂×C₃×C₅	semidirect
273. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
275. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
276. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
285. C₄×Q₈	C₂²×C₃×C₅	semidirect
290. C₄⋊C₈	C₂²×C₃×C₅	semidirect
291. #103	C₂²×C₃×C₅	semidirect
294. #97	C₂²×C₃×C₅	semidirect
374. C₃×C₅	#3215	direct (N × H)
427. C₅	C₃×#3215	direct (N × H)
445. C₃	C₅×#3215	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×#533	2
C₂×C₃×C₅×#124	2
C₃×C₅×#497	2
C₃×C₅×#489	2
C₃×C₅×#464	2
C₃×C₅×#451	2
C₃×C₅×#450	2
C₃×C₅×#432	2
C₅×#3215	3
C₃×#3215	5

Subgroups — C3×C5×#3215 #14276249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3215 #14276249