Subgroups — C₃×C₅×#3538 #14276572

Order 1920.

2028 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#552	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#551	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×D₄×Q₈	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#544	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#539	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#536	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₅×#3538	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	complemented
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
19	C₃×C₅×#126	C₂²	1	8	yes	—
20	C₃×C₅×#126	C₂²	1	8	yes	complemented
21	C₃×C₅×#125	C₂²	1	8	yes	complemented
22	C₃×C₅×#125	C₂²	1	2	yes	complemented
23	C₃×C₅×#125	C₂²	1	8	yes	complemented
24	C₃×C₅×#124	C₂²	1	4	yes	—
25	C₃×C₅×#123	C₂²	1	2	yes	—
26	C₃×C₅×#123	C₂²	1	4	yes	—
27	C₃×C₅×#123	C₂²	1	8	yes	—
28	C₃×C₅×#123	C₂²	1	4	yes	complemented
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	—
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
36	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
37	C₃×C₅×#121	C₂²	1	2	yes	—
38	C₃×C₅×#120	C₂²	1	2	yes	—
39	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
40	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
41	C₃×C₄×C₅×D₄	C₂²	1	8	yes	—
42	C₃×C₅×#117	C₂²	1	1	yes	characteristic
43	C₃×C₅×#117	C₂²	1	8	yes	—
44	C₃×C₅×#117	C₂²	1	2	yes	complemented
45	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
46	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
47	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
48	C₃×#3538	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#563	C₂×C₃	1	4	yes	complemented
50	C₅×#552	C₂×C₃	1	4	yes	complemented
51	C₅×#551	C₂×C₃	1	4	yes	complemented
52	C₅×D₄×Q₈	C₂×C₃	1	4	yes	complemented
53	C₅×#544	C₂×C₃	1	4	yes	complemented
54	C₅×#541	C₂×C₃	1	2	yes	complemented
55	C₅×#539	C₂×C₃	1	4	yes	complemented
56	C₅×#536	C₂×C₃	1	2	yes	complemented
57	C₅×#525	C₂×C₃	1	1	yes	characteristic
58	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
59	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₅×#41	—	4	2	no	—
61	C₂×C₃×C₅×Q₈	—	4	4	no	—
62	C₂×C₃×C₅×Q₈	—	4	4	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
64	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
65	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
66	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
68	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
69	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	—	4	2	no	—
71	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
85	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
89	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₃×C₄²×C₅	C₂³	1	4	yes	—
97	C₃×C₄²×C₅	C₂³	1	2	yes	—
98	C₃×C₄²×C₅	C₂³	1	8	yes	—
99	C₃×#563	C₂×C₅	1	4	yes	complemented
100	C₃×#552	C₂×C₅	1	4	yes	complemented
101	C₃×#551	C₂×C₅	1	4	yes	complemented
102	C₃×D₄×Q₈	C₂×C₅	1	4	yes	complemented
103	C₃×#544	C₂×C₅	1	4	yes	complemented
104	C₃×#541	C₂×C₅	1	2	yes	complemented
105	C₃×#539	C₂×C₅	1	4	yes	complemented
106	C₃×#536	C₂×C₅	1	2	yes	complemented
107	C₃×#525	C₂×C₅	1	1	yes	characteristic
108	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
109	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
111	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
112	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
114	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
115	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
116	C₅×#126	C₂²×C₃	1	8	yes	—
117	C₅×#126	C₂²×C₃	1	8	yes	complemented
118	C₅×#125	C₂²×C₃	1	8	yes	complemented
119	C₅×#125	C₂²×C₃	1	2	yes	complemented
120	C₅×#125	C₂²×C₃	1	8	yes	complemented
121	C₅×#124	C₂²×C₃	1	4	yes	—
122	C₅×#123	C₂²×C₃	1	2	yes	—
123	C₅×#123	C₂²×C₃	1	4	yes	—
124	C₅×#123	C₂²×C₃	1	8	yes	—
125	C₅×#123	C₂²×C₃	1	4	yes	complemented
126	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
127	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
128	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
129	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
130	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
131	C₅×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
132	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
133	C₅×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
134	C₅×#121	C₂²×C₃	1	2	yes	—
135	C₅×#120	C₂²×C₃	1	2	yes	—
136	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
137	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
138	C₄×C₅×D₄	C₂²×C₃	1	8	yes	—
139	C₅×#117	C₂²×C₃	1	1	yes	characteristic
140	C₅×#117	C₂²×C₃	1	8	yes	—
141	C₅×#117	C₂²×C₃	1	2	yes	complemented
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
143	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
144	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
145	#3538	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
146	C₂³×C₃×C₅	—	2	4	no	—
147	C₂³×C₃×C₅	—	4	1	no	—
148	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
149	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
150	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
151	C₃×C₅×Q₈	—	2	8	no	—
152	C₃×C₅×Q₈	—	4	4	no	—
153	C₃×C₅×Q₈	—	4	4	no	—
154	C₃×C₅×Q₈	—	4	1	no	—
155	C₃×C₅×D₄	—	2	8	no	—
156	C₃×C₅×D₄	—	4	1	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	2	8	no	—
159	C₂×C₃×C₄×C₅	—	2	4	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	4	no	—
162	C₂×C₃×C₄×C₅	—	4	2	no	—
163	C₂×C₃×C₄×C₅	—	4	1	no	—
164	C₂×C₃×C₄×C₅	—	4	4	no	—
165	C₂×C₃×C₄×C₅	—	4	4	no	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
168	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
169	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
170	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
171	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
174	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
175	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	complemented
176	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₄⋊Q₈	C₂²×C₅	1	8	yes	complemented
178	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	complemented
179	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
180	C₃×#126	C₂²×C₅	1	8	yes	—
181	C₃×#126	C₂²×C₅	1	8	yes	complemented
182	C₃×#125	C₂²×C₅	1	8	yes	complemented
183	C₃×#125	C₂²×C₅	1	8	yes	complemented
184	C₃×#125	C₂²×C₅	1	2	yes	complemented
185	C₃×#124	C₂²×C₅	1	4	yes	—
186	C₃×#123	C₂²×C₅	1	2	yes	—
187	C₃×#123	C₂²×C₅	1	4	yes	—
188	C₃×#123	C₂²×C₅	1	8	yes	—
189	C₃×#123	C₂²×C₅	1	4	yes	complemented
190	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
191	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
192	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
193	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
194	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
195	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	—
196	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	complemented
197	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
198	C₃×#121	C₂²×C₅	1	2	yes	—
199	C₃×#120	C₂²×C₅	1	2	yes	—
200	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	complemented
201	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
202	C₃×C₄×D₄	C₂²×C₅	1	8	yes	—
203	C₃×#117	C₂²×C₅	1	1	yes	characteristic
204	C₃×#117	C₂²×C₅	1	8	yes	—
205	C₃×#117	C₂²×C₅	1	2	yes	complemented
206	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
207	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
209	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₅×#41	—	4	2	no	—
211	C₂×C₅×Q₈	—	4	4	no	—
212	C₂×C₅×Q₈	—	4	4	no	—
213	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
214	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
215	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
216	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
218	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
219	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	—	4	2	no	—
221	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
222	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
223	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
225	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
226	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
227	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
228	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
229	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
230	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
231	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
232	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
233	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
234	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
235	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
236	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
237	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
238	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
239	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
240	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
241	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
242	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
243	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
244	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
245	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
246	C₄²×C₅	C₂³×C₃	1	4	yes	—
247	C₄²×C₅	C₂³×C₃	1	2	yes	—
248	C₄²×C₅	C₂³×C₃	1	8	yes	—
249	#563	C₂×C₃×C₅	1	4	yes	complemented
250	#552	C₂×C₃×C₅	1	4	yes	complemented
251	#551	C₂×C₃×C₅	1	4	yes	complemented
252	D₄×Q₈	C₂×C₃×C₅	1	4	yes	complemented
253	#544	C₂×C₃×C₅	1	4	yes	complemented
254	#541	C₂×C₃×C₅	1	2	yes	complemented
255	#539	C₂×C₃×C₅	1	4	yes	complemented
256	#536	C₂×C₃×C₅	1	2	yes	complemented
257	#525	C₂×C₃×C₅	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	complemented
259	C₂²×C₃×C₅	—	2	2	no	—
260	C₂²×C₃×C₅	—	2	2	no	—
261	C₂²×C₃×C₅	—	2	2	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	4	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	4	4	no	—
266	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
267	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
268	C₃×C₄×C₅	—	2	1	no	—
269	C₃×C₄×C₅	—	2	2	no	—
270	C₃×C₄×C₅	—	2	2	no	—
271	C₃×C₄×C₅	—	2	8	no	—
272	C₃×C₄×C₅	—	2	8	no	—
273	C₃×C₄×C₅	—	2	4	no	—
274	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
275	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
276	C₃×#41	—	4	2	no	—
277	C₂×C₃×Q₈	—	4	4	no	—
278	C₂×C₃×Q₈	—	4	4	no	—
279	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
280	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
281	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
282	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
284	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
285	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
286	C₂²×C₃×C₄	—	4	2	no	—
287	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
288	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
289	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
291	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
292	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
293	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
294	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
295	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
296	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
297	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
298	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
299	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
300	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
301	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
302	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
303	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
304	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
305	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
306	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
307	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
308	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
309	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
310	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
311	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
312	C₃×C₄²	C₂³×C₅	1	4	yes	—
313	C₃×C₄²	C₂³×C₅	1	2	yes	—
314	C₃×C₄²	C₂³×C₅	1	8	yes	—
315	C₂³×C₅	—	2	4	no	—
316	C₂³×C₅	—	4	1	no	—
317	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
318	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
319	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
320	C₅×Q₈	—	2	8	no	—
321	C₅×Q₈	—	4	4	no	—
322	C₅×Q₈	—	4	4	no	—
323	C₅×Q₈	—	4	1	no	—
324	C₅×D₄	—	2	8	no	—
325	C₅×D₄	—	4	1	no	—
326	C₅×D₄	—	4	2	no	—
327	C₂×C₄×C₅	—	2	8	no	—
328	C₂×C₄×C₅	—	2	4	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	4	2	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	4	no	—
334	C₂×C₄×C₅	—	4	4	no	—
335	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
336	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
337	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
338	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
339	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
340	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
342	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
344	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
345	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
347	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
348	C₄⋊Q₈	C₂²×C₃×C₅	1	8	yes	complemented
349	#126	C₂²×C₃×C₅	1	8	yes	—
350	#126	C₂²×C₃×C₅	1	8	yes	complemented
351	#125	C₂²×C₃×C₅	1	8	yes	complemented
352	#125	C₂²×C₃×C₅	1	2	yes	complemented
353	#125	C₂²×C₃×C₅	1	8	yes	complemented
354	#124	C₂²×C₃×C₅	1	4	yes	—
355	#123	C₂²×C₃×C₅	1	2	yes	—
356	#123	C₂²×C₃×C₅	1	4	yes	—
357	#123	C₂²×C₃×C₅	1	8	yes	—
358	#123	C₂²×C₃×C₅	1	4	yes	complemented
359	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
360	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
361	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
362	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
363	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
364	C₂²⋊Q₈	C₂²×C₃×C₅	1	8	yes	—
365	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
366	C₂²⋊Q₈	C₂²×C₃×C₅	1	8	yes	complemented
367	#121	C₂²×C₃×C₅	1	2	yes	—
368	#120	C₂²×C₃×C₅	1	2	yes	—
369	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	complemented
370	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
371	C₄×D₄	C₂²×C₃×C₅	1	8	yes	—
372	#117	C₂²×C₃×C₅	1	1	yes	characteristic
373	#117	C₂²×C₃×C₅	1	8	yes	—
374	#117	C₂²×C₃×C₅	1	2	yes	complemented
375	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
376	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
378	C₂×C₃×C₅	—	2	4	no	—
379	C₂×C₃×C₅	—	4	2	no	—
380	C₂×C₃×C₅	—	4	1	no	—
381	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
383	C₂³×C₃	—	2	4	no	—
384	C₂³×C₃	—	4	1	no	—
385	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
386	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
387	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
388	C₃×Q₈	—	2	8	no	—
389	C₃×Q₈	—	4	4	no	—
390	C₃×Q₈	—	4	4	no	—
391	C₃×Q₈	—	4	1	no	—
392	C₃×D₄	—	2	8	no	—
393	C₃×D₄	—	4	1	no	—
394	C₃×D₄	—	4	2	no	—
395	C₂×C₃×C₄	—	2	8	no	—
396	C₂×C₃×C₄	—	2	4	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	4	no	—
399	C₂×C₃×C₄	—	4	2	no	—
400	C₂×C₃×C₄	—	4	1	no	—
401	C₂×C₃×C₄	—	4	4	no	—
402	C₂×C₃×C₄	—	4	4	no	—
403	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
404	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
405	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
406	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
407	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
408	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
410	C₂²×C₅	—	2	2	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	4	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	4	4	no	—
417	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
418	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	8	no	—
423	C₄×C₅	—	2	8	no	—
424	C₄×C₅	—	2	4	no	—
425	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
426	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
427	#41	—	4	2	no	—
428	C₂×Q₈	—	4	4	no	—
429	C₂×Q₈	—	4	4	no	—
430	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
431	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
432	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
433	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
434	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
435	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
436	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
439	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
440	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
442	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
443	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
444	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
445	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
446	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
447	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
448	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
449	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
450	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
451	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
452	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
453	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
454	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
455	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
456	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
457	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
458	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
459	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
460	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
461	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
462	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
463	C₄²	C₂³×C₃×C₅	1	4	yes	—
464	C₄²	C₂³×C₃×C₅	1	2	yes	—
465	C₄²	C₂³×C₃×C₅	1	8	yes	—
466	C₃×C₅	#3538	1	1	yes	characteristic, direct product factor, Hall
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	4	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	4	4	no	—
474	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
475	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
476	C₃×C₄	—	2	1	no	—
477	C₃×C₄	—	2	2	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	8	no	—
480	C₃×C₄	—	2	8	no	—
481	C₃×C₄	—	2	4	no	—
482	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
483	C₂×C₅	—	2	4	no	—
484	C₂×C₅	—	4	1	no	—
485	C₂×C₅	—	4	2	no	—
486	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
488	C₂³	—	2	4	no	—
489	C₂³	—	4	1	no	—
490	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
491	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
492	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
493	Q₈	—	2	8	no	—
494	Q₈	—	4	4	no	—
495	Q₈	—	4	4	no	—
496	Q₈	—	4	1	no	—
497	D₄	—	2	8	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	2	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
509	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
510	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
511	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
512	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
513	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
514	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
515	C₂×C₃	—	2	4	no	—
516	C₂×C₃	—	4	1	no	—
517	C₂×C₃	—	4	2	no	—
518	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
520	C₅	C₃×#3538	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	4	4	no	—
528	C₂²	C₃×C₅×2₋¹⁺⁴	1	4	yes	—
529	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
530	C₄	—	2	1	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	8	no	—
534	C₄	—	2	8	no	—
535	C₄	—	2	4	no	—
536	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
537	C₃	C₅×#3538	1	1	yes	characteristic, direct product factor, Sylow
538	C₂	—	2	4	no	—
539	C₂	—	4	1	no	—
540	C₂	—	4	2	no	—
541	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
prime radical	C₃×C₅×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#563	C₂	semidirect
2. C₃×C₅×#552	C₂	semidirect
3. C₃×C₅×#551	C₂	semidirect
4. C₃×C₅×D₄×Q₈	C₂	semidirect
5. C₃×C₅×#544	C₂	semidirect
6. C₃×C₅×#541	C₂	semidirect
7. C₃×C₅×#539	C₂	semidirect
8. C₃×C₅×#536	C₂	semidirect
10. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
11. C₅×#3538	C₃	direct (N × H)
14. C₂²×C₃×C₅×Q₈	C₂²	semidirect
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×#126	C₂²	semidirect
21. C₃×C₅×#125	C₂²	semidirect
22. C₃×C₅×#125	C₂²	semidirect
23. C₃×C₅×#125	C₂²	semidirect
28. C₃×C₅×#123	C₂²	semidirect
35. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×C₅×Q₈	C₂²	semidirect
44. C₃×C₅×#117	C₂²	semidirect
48. C₃×#3538	C₅	direct (N × H)
49. C₅×#563	C₂×C₃	semidirect
50. C₅×#552	C₂×C₃	semidirect
51. C₅×#551	C₂×C₃	semidirect
52. C₅×D₄×Q₈	C₂×C₃	semidirect
53. C₅×#544	C₂×C₃	semidirect
54. C₅×#541	C₂×C₃	semidirect
55. C₅×#539	C₂×C₃	semidirect
56. C₅×#536	C₂×C₃	semidirect
58. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
99. C₃×#563	C₂×C₅	semidirect
100. C₃×#552	C₂×C₅	semidirect
101. C₃×#551	C₂×C₅	semidirect
102. C₃×D₄×Q₈	C₂×C₅	semidirect
103. C₃×#544	C₂×C₅	semidirect
104. C₃×#541	C₂×C₅	semidirect
105. C₃×#539	C₂×C₅	semidirect
106. C₃×#536	C₂×C₅	semidirect
108. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
111. C₂²×C₅×Q₈	C₂²×C₃	semidirect
113. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
114. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
115. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
117. C₅×#126	C₂²×C₃	semidirect
118. C₅×#125	C₂²×C₃	semidirect
119. C₅×#125	C₂²×C₃	semidirect
120. C₅×#125	C₂²×C₃	semidirect
125. C₅×#123	C₂²×C₃	semidirect
132. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
133. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
136. C₄×C₅×Q₈	C₂²×C₃	semidirect
141. C₅×#117	C₂²×C₃	semidirect
145. #3538	C₃×C₅	direct (N × H)
175. C₂²×C₃×Q₈	C₂²×C₅	semidirect
177. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
178. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
179. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
181. C₃×#126	C₂²×C₅	semidirect
182. C₃×#125	C₂²×C₅	semidirect
183. C₃×#125	C₂²×C₅	semidirect
184. C₃×#125	C₂²×C₅	semidirect
189. C₃×#123	C₂²×C₅	semidirect
196. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
197. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
200. C₃×C₄×Q₈	C₂²×C₅	semidirect
205. C₃×#117	C₂²×C₅	semidirect
249. #563	C₂×C₃×C₅	semidirect
250. #552	C₂×C₃×C₅	semidirect
251. #551	C₂×C₃×C₅	semidirect
252. D₄×Q₈	C₂×C₃×C₅	semidirect
253. #544	C₂×C₃×C₅	semidirect
254. #541	C₂×C₃×C₅	semidirect
255. #539	C₂×C₃×C₅	semidirect
256. #536	C₂×C₃×C₅	semidirect
258. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
344. C₂²×Q₈	C₂²×C₃×C₅	semidirect
346. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
347. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
348. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
350. #126	C₂²×C₃×C₅	semidirect
351. #125	C₂²×C₃×C₅	semidirect
352. #125	C₂²×C₃×C₅	semidirect
353. #125	C₂²×C₃×C₅	semidirect
358. #123	C₂²×C₃×C₅	semidirect
365. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
366. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
369. C₄×Q₈	C₂²×C₃×C₅	semidirect
374. #117	C₂²×C₃×C₅	semidirect
466. C₃×C₅	#3538	direct (N × H)
520. C₅	C₃×#3538	direct (N × H)
537. C₃	C₅×#3538	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×#563	2
C₃×C₅×#552	2
C₃×C₅×#551	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#544	2
C₃×C₅×#541	2
C₃×C₅×#539	2
C₃×C₅×#536	2
C₃×C₅×#525	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₅×#3538	3
C₃×#3538	5

Subgroups — C3×C5×#3538 #14276572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3538 #14276572