Subgroups — C₃×C₅×#3537 #14276571

Order 1920.

2540 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#560	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#553	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×D₄²	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×D₄²	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#540	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#538	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#534	C₂	1	4	yes	maximal, complemented
9	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
11	C₅×#3537	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#127	C₂²	1	4	yes	complemented
19	C₃×C₅×#127	C₂²	1	2	yes	complemented
20	C₃×C₅×#126	C₂²	1	8	yes	complemented
21	C₃×C₅×#125	C₂²	1	2	yes	complemented
22	C₃×C₅×#124	C₂²	1	4	yes	complemented
23	C₃×C₅×#123	C₂²	1	2	yes	complemented
24	C₃×C₅×#123	C₂²	1	8	yes	complemented
25	C₃×C₅×#123	C₂²	1	8	yes	complemented
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃×C₅×#121	C₂²	1	4	yes	complemented
28	C₃×C₅×#121	C₂²	1	4	yes	complemented
29	C₃×C₅×#121	C₂²	1	4	yes	complemented
30	C₃×C₅×#121	C₂²	1	4	yes	complemented
31	C₃×C₅×#121	C₂²	1	2	yes	complemented
32	C₃×C₅×#121	C₂²	1	8	yes	complemented
33	C₃×C₅×#121	C₂²	1	4	yes	complemented
34	C₃×C₅×#121	C₂²	1	8	yes	complemented
35	C₃×C₅×#121	C₂²	1	8	yes	complemented
36	C₃×C₅×#120	C₂²	1	2	yes	complemented
37	C₃×C₅×#120	C₂²	1	4	yes	complemented
38	C₃×C₅×#120	C₂²	1	8	yes	complemented
39	C₃×C₅×#120	C₂²	1	4	yes	complemented
40	C₃×C₅×#120	C₂²	1	8	yes	complemented
41	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
42	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
43	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
44	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#117	C₂²	1	2	yes	complemented
46	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
47	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
48	C₃×#3537	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#560	C₂×C₃	1	4	yes	complemented
50	C₅×#553	C₂×C₃	1	4	yes	complemented
51	C₅×D₄²	C₂×C₃	1	4	yes	complemented
52	C₅×D₄²	C₂×C₃	1	4	yes	complemented
53	C₅×#540	C₂×C₃	1	2	yes	complemented
54	C₅×#538	C₂×C₃	1	4	yes	complemented
55	C₅×#535	C₂×C₃	1	2	yes	complemented
56	C₅×#534	C₂×C₃	1	4	yes	complemented
57	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
59	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
60	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
61	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
62	C₃×C₅×#41	—	4	2	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	—	4	4	no	—
65	C₂×C₃×C₅×D₄	—	4	4	no	—
66	C₂×C₃×C₅×D₄	—	4	8	no	—
67	C₂×C₃×C₅×D₄	—	4	16	no	—
68	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
69	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
70	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
71	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
73	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
74	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
75	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
76	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
77	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
78	C₂²×C₃×C₄×C₅	—	4	2	no	—
79	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
80	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
83	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
84	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
91	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
95	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₃×C₄²×C₅	C₂³	1	2	yes	—
100	C₃×C₄²×C₅	C₂³	1	4	yes	—
101	C₃×#560	C₂×C₅	1	4	yes	complemented
102	C₃×#553	C₂×C₅	1	4	yes	complemented
103	C₃×D₄²	C₂×C₅	1	4	yes	complemented
104	C₃×D₄²	C₂×C₅	1	4	yes	complemented
105	C₃×#540	C₂×C₅	1	2	yes	complemented
106	C₃×#538	C₂×C₅	1	4	yes	complemented
107	C₃×#535	C₂×C₅	1	2	yes	complemented
108	C₃×#534	C₂×C₅	1	4	yes	complemented
109	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
111	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
113	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
114	C₂²×C₅×D₄	C₂²×C₃	1	8	yes	complemented
115	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
116	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₅×#127	C₂²×C₃	1	4	yes	complemented
118	C₅×#127	C₂²×C₃	1	2	yes	complemented
119	C₅×#126	C₂²×C₃	1	8	yes	complemented
120	C₅×#125	C₂²×C₃	1	2	yes	complemented
121	C₅×#124	C₂²×C₃	1	4	yes	complemented
122	C₅×#123	C₂²×C₃	1	2	yes	complemented
123	C₅×#123	C₂²×C₃	1	8	yes	complemented
124	C₅×#123	C₂²×C₃	1	8	yes	complemented
125	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
126	C₅×#121	C₂²×C₃	1	4	yes	complemented
127	C₅×#121	C₂²×C₃	1	4	yes	complemented
128	C₅×#121	C₂²×C₃	1	4	yes	complemented
129	C₅×#121	C₂²×C₃	1	4	yes	complemented
130	C₅×#121	C₂²×C₃	1	2	yes	complemented
131	C₅×#121	C₂²×C₃	1	8	yes	complemented
132	C₅×#121	C₂²×C₃	1	4	yes	complemented
133	C₅×#121	C₂²×C₃	1	8	yes	complemented
134	C₅×#121	C₂²×C₃	1	8	yes	complemented
135	C₅×#120	C₂²×C₃	1	2	yes	complemented
136	C₅×#120	C₂²×C₃	1	4	yes	complemented
137	C₅×#120	C₂²×C₃	1	8	yes	complemented
138	C₅×#120	C₂²×C₃	1	4	yes	complemented
139	C₅×#120	C₂²×C₃	1	8	yes	complemented
140	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
141	C₄×C₅×D₄	C₂²×C₃	1	8	yes	complemented
142	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
143	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₅×#117	C₂²×C₃	1	2	yes	complemented
145	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
146	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
147	#3537	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
148	C₂³×C₃×C₅	—	2	4	no	—
149	C₂³×C₃×C₅	—	2	8	no	—
150	C₂³×C₃×C₅	—	4	1	no	—
151	C₂³×C₃×C₅	—	4	4	no	—
152	C₂³×C₃×C₅	—	4	4	no	—
153	C₂³×C₃×C₅	—	4	4	no	—
154	C₂³×C₃×C₅	—	4	8	no	—
155	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
156	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
157	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
158	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
159	C₃×C₅×Q₈	—	4	1	no	—
160	C₃×C₅×D₄	—	2	16	no	—
161	C₃×C₅×D₄	—	2	8	no	—
162	C₃×C₅×D₄	—	2	8	no	—
163	C₃×C₅×D₄	—	4	4	no	—
164	C₃×C₅×D₄	—	4	4	no	—
165	C₃×C₅×D₄	—	4	8	no	—
166	C₃×C₅×D₄	—	4	8	no	—
167	C₃×C₅×D₄	—	4	8	no	—
168	C₃×C₅×D₄	—	4	1	no	—
169	C₃×C₅×D₄	—	4	2	no	—
170	C₂×C₃×C₄×C₅	—	2	4	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	2	4	no	—
173	C₂×C₃×C₄×C₅	—	4	1	no	—
174	C₂×C₃×C₄×C₅	—	4	2	no	—
175	C₂×C₃×C₄×C₅	—	4	4	no	—
176	C₂×C₃×C₄×C₅	—	4	8	no	—
177	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
178	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
179	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
180	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
182	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
185	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
186	C₂²×C₃×D₄	C₂²×C₅	1	8	yes	complemented
187	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
188	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₃×#127	C₂²×C₅	1	4	yes	complemented
190	C₃×#127	C₂²×C₅	1	2	yes	complemented
191	C₃×#126	C₂²×C₅	1	8	yes	complemented
192	C₃×#125	C₂²×C₅	1	2	yes	complemented
193	C₃×#124	C₂²×C₅	1	4	yes	complemented
194	C₃×#123	C₂²×C₅	1	2	yes	complemented
195	C₃×#123	C₂²×C₅	1	8	yes	complemented
196	C₃×#123	C₂²×C₅	1	8	yes	complemented
197	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
198	C₃×#121	C₂²×C₅	1	4	yes	complemented
199	C₃×#121	C₂²×C₅	1	8	yes	complemented
200	C₃×#121	C₂²×C₅	1	8	yes	complemented
201	C₃×#121	C₂²×C₅	1	4	yes	complemented
202	C₃×#121	C₂²×C₅	1	4	yes	complemented
203	C₃×#121	C₂²×C₅	1	4	yes	complemented
204	C₃×#121	C₂²×C₅	1	2	yes	complemented
205	C₃×#121	C₂²×C₅	1	8	yes	complemented
206	C₃×#121	C₂²×C₅	1	4	yes	complemented
207	C₃×#120	C₂²×C₅	1	8	yes	complemented
208	C₃×#120	C₂²×C₅	1	4	yes	complemented
209	C₃×#120	C₂²×C₅	1	2	yes	complemented
210	C₃×#120	C₂²×C₅	1	4	yes	complemented
211	C₃×#120	C₂²×C₅	1	8	yes	complemented
212	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
213	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
214	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
215	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₃×#117	C₂²×C₅	1	2	yes	complemented
217	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
218	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
219	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
221	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
222	C₅×#41	—	4	2	no	—
223	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₅×D₄	—	4	4	no	—
225	C₂×C₅×D₄	—	4	4	no	—
226	C₂×C₅×D₄	—	4	8	no	—
227	C₂×C₅×D₄	—	4	16	no	—
228	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
229	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
230	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
231	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
232	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
233	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
234	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
235	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
236	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
237	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
238	C₂²×C₄×C₅	—	4	2	no	—
239	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
240	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
241	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
243	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
244	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
245	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
247	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
248	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
249	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
250	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
251	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
252	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
253	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
254	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
255	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
256	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
257	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
258	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
259	C₄²×C₅	C₂³×C₃	1	2	yes	—
260	C₄²×C₅	C₂³×C₃	1	4	yes	—
261	#560	C₂×C₃×C₅	1	4	yes	complemented
262	#553	C₂×C₃×C₅	1	4	yes	complemented
263	D₄²	C₂×C₃×C₅	1	4	yes	complemented
264	D₄²	C₂×C₃×C₅	1	4	yes	complemented
265	#540	C₂×C₃×C₅	1	2	yes	complemented
266	#538	C₂×C₃×C₅	1	4	yes	complemented
267	#535	C₂×C₃×C₅	1	2	yes	complemented
268	#534	C₂×C₃×C₅	1	4	yes	complemented
269	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
270	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
271	C₂²×C₃×C₅	—	2	2	no	—
272	C₂²×C₃×C₅	—	2	2	no	—
273	C₂²×C₃×C₅	—	2	1	no	—
274	C₂²×C₃×C₅	—	2	2	no	—
275	C₂²×C₃×C₅	—	2	8	no	—
276	C₂²×C₃×C₅	—	2	4	no	—
277	C₂²×C₃×C₅	—	2	8	no	—
278	C₂²×C₃×C₅	—	2	8	no	—
279	C₂²×C₃×C₅	—	2	2	no	—
280	C₂²×C₃×C₅	—	4	4	no	—
281	C₂²×C₃×C₅	—	8	8	no	—
282	C₂²×C₃×C₅	—	8	8	no	—
283	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
284	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
285	C₃×C₄×C₅	—	2	2	no	—
286	C₃×C₄×C₅	—	2	1	no	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	—	2	8	no	—
289	C₃×C₄×C₅	—	2	4	no	—
290	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
291	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
292	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
293	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
294	C₃×#41	—	4	2	no	—
295	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₃×D₄	—	4	4	no	—
297	C₂×C₃×D₄	—	4	4	no	—
298	C₂×C₃×D₄	—	4	8	no	—
299	C₂×C₃×D₄	—	4	16	no	—
300	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
301	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
302	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
303	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
305	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
306	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
307	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
308	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
309	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
310	C₂²×C₃×C₄	—	4	2	no	—
311	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
312	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
313	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
315	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
316	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
317	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
318	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
319	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
320	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
321	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
322	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
323	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
324	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
325	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
326	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
327	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
328	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
329	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
330	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
331	C₃×C₄²	C₂³×C₅	1	2	yes	—
332	C₃×C₄²	C₂³×C₅	1	4	yes	—
333	C₂³×C₅	—	2	4	no	—
334	C₂³×C₅	—	2	8	no	—
335	C₂³×C₅	—	4	1	no	—
336	C₂³×C₅	—	4	4	no	—
337	C₂³×C₅	—	4	4	no	—
338	C₂³×C₅	—	4	4	no	—
339	C₂³×C₅	—	4	8	no	—
340	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
341	C₂³×C₅	C₂⁴×C₃	1	8	yes	—
342	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
343	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
344	C₅×Q₈	—	4	1	no	—
345	C₅×D₄	—	2	16	no	—
346	C₅×D₄	—	2	8	no	—
347	C₅×D₄	—	2	8	no	—
348	C₅×D₄	—	4	4	no	—
349	C₅×D₄	—	4	4	no	—
350	C₅×D₄	—	4	8	no	—
351	C₅×D₄	—	4	8	no	—
352	C₅×D₄	—	4	8	no	—
353	C₅×D₄	—	4	1	no	—
354	C₅×D₄	—	4	2	no	—
355	C₂×C₄×C₅	—	2	4	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	2	4	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	2	no	—
360	C₂×C₄×C₅	—	4	4	no	—
361	C₂×C₄×C₅	—	4	8	no	—
362	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
363	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
364	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
365	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
367	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
368	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
369	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
370	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
371	C₂²×D₄	C₂²×C₃×C₅	1	8	yes	complemented
372	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
373	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
374	#127	C₂²×C₃×C₅	1	4	yes	complemented
375	#127	C₂²×C₃×C₅	1	2	yes	complemented
376	#126	C₂²×C₃×C₅	1	8	yes	complemented
377	#125	C₂²×C₃×C₅	1	2	yes	complemented
378	#124	C₂²×C₃×C₅	1	4	yes	complemented
379	#123	C₂²×C₃×C₅	1	2	yes	complemented
380	#123	C₂²×C₃×C₅	1	8	yes	complemented
381	#123	C₂²×C₃×C₅	1	8	yes	complemented
382	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
383	#121	C₂²×C₃×C₅	1	4	yes	complemented
384	#121	C₂²×C₃×C₅	1	4	yes	complemented
385	#121	C₂²×C₃×C₅	1	4	yes	complemented
386	#121	C₂²×C₃×C₅	1	4	yes	complemented
387	#121	C₂²×C₃×C₅	1	2	yes	complemented
388	#121	C₂²×C₃×C₅	1	8	yes	complemented
389	#121	C₂²×C₃×C₅	1	4	yes	complemented
390	#121	C₂²×C₃×C₅	1	8	yes	complemented
391	#121	C₂²×C₃×C₅	1	8	yes	complemented
392	#120	C₂²×C₃×C₅	1	2	yes	complemented
393	#120	C₂²×C₃×C₅	1	4	yes	complemented
394	#120	C₂²×C₃×C₅	1	8	yes	complemented
395	#120	C₂²×C₃×C₅	1	4	yes	complemented
396	#120	C₂²×C₃×C₅	1	8	yes	complemented
397	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
398	C₄×D₄	C₂²×C₃×C₅	1	8	yes	complemented
399	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
400	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
401	#117	C₂²×C₃×C₅	1	2	yes	complemented
402	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
403	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
404	C₂×C₃×C₅	—	2	4	no	—
405	C₂×C₃×C₅	—	4	1	no	—
406	C₂×C₃×C₅	—	4	2	no	—
407	C₂×C₃×C₅	—	4	8	no	—
408	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂³×C₃	—	2	4	no	—
411	C₂³×C₃	—	2	8	no	—
412	C₂³×C₃	—	4	1	no	—
413	C₂³×C₃	—	4	4	no	—
414	C₂³×C₃	—	4	4	no	—
415	C₂³×C₃	—	4	4	no	—
416	C₂³×C₃	—	4	8	no	—
417	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
418	C₂³×C₃	C₂⁴×C₅	1	8	yes	—
419	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
420	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
421	C₃×Q₈	—	4	1	no	—
422	C₃×D₄	—	2	16	no	—
423	C₃×D₄	—	2	8	no	—
424	C₃×D₄	—	2	8	no	—
425	C₃×D₄	—	4	4	no	—
426	C₃×D₄	—	4	4	no	—
427	C₃×D₄	—	4	8	no	—
428	C₃×D₄	—	4	8	no	—
429	C₃×D₄	—	4	8	no	—
430	C₃×D₄	—	4	1	no	—
431	C₃×D₄	—	4	2	no	—
432	C₂×C₃×C₄	—	2	4	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	4	no	—
435	C₂×C₃×C₄	—	4	1	no	—
436	C₂×C₃×C₄	—	4	2	no	—
437	C₂×C₃×C₄	—	4	4	no	—
438	C₂×C₃×C₄	—	4	8	no	—
439	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
440	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
441	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
442	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
444	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	2	2	no	—
447	C₂²×C₅	—	2	1	no	—
448	C₂²×C₅	—	2	2	no	—
449	C₂²×C₅	—	2	8	no	—
450	C₂²×C₅	—	2	4	no	—
451	C₂²×C₅	—	2	8	no	—
452	C₂²×C₅	—	2	8	no	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	4	4	no	—
455	C₂²×C₅	—	8	8	no	—
456	C₂²×C₅	—	8	8	no	—
457	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
458	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
459	C₄×C₅	—	2	2	no	—
460	C₄×C₅	—	2	1	no	—
461	C₄×C₅	—	2	2	no	—
462	C₄×C₅	—	2	8	no	—
463	C₄×C₅	—	2	4	no	—
464	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
465	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
466	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
467	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
468	#41	—	4	2	no	—
469	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	—	4	8	no	—
473	C₂×D₄	—	4	16	no	—
474	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
475	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
476	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
477	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
478	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
479	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
480	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
481	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
482	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
483	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
486	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
487	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
488	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
489	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
490	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
491	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
492	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
493	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
494	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
495	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
496	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
497	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
498	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
499	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
500	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
501	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
502	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
503	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
504	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
505	C₄²	C₂³×C₃×C₅	1	2	yes	—
506	C₄²	C₂³×C₃×C₅	1	4	yes	—
507	C₃×C₅	#3537	1	1	yes	characteristic, direct product factor, Hall
508	C₂²×C₃	—	2	2	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	1	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	8	no	—
513	C₂²×C₃	—	2	4	no	—
514	C₂²×C₃	—	2	8	no	—
515	C₂²×C₃	—	2	8	no	—
516	C₂²×C₃	—	2	2	no	—
517	C₂²×C₃	—	4	4	no	—
518	C₂²×C₃	—	8	8	no	—
519	C₂²×C₃	—	8	8	no	—
520	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
521	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	2	8	no	—
526	C₃×C₄	—	2	4	no	—
527	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
528	C₂×C₅	—	2	4	no	—
529	C₂×C₅	—	4	1	no	—
530	C₂×C₅	—	4	2	no	—
531	C₂×C₅	—	4	8	no	—
532	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
533	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	8	no	—
541	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
542	C₂³	C₂⁴×C₃×C₅	1	8	yes	—
543	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
544	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
545	Q₈	—	4	1	no	—
546	D₄	—	2	16	no	—
547	D₄	—	2	8	no	—
548	D₄	—	2	8	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	8	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	8	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	8	no	—
563	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
564	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
565	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
566	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
567	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
568	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
569	C₂×C₃	—	2	4	no	—
570	C₂×C₃	—	4	1	no	—
571	C₂×C₃	—	4	2	no	—
572	C₂×C₃	—	4	8	no	—
573	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
574	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
575	C₅	C₃×#3537	1	1	yes	characteristic, direct product factor, Sylow
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	8	no	—
587	C₂²	—	8	8	no	—
588	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
589	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	4	no	—
595	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
596	C₃	C₅×#3537	1	1	yes	characteristic, direct product factor, Sylow
597	C₂	—	2	4	no	—
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	8	no	—
601	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	2	yes	—
602	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
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×#560	C₂	semidirect
2. C₃×C₅×#553	C₂	semidirect
3. C₃×C₅×D₄²	C₂	semidirect
4. C₃×C₅×D₄²	C₂	semidirect
5. C₃×C₅×#540	C₂	semidirect
6. C₃×C₅×#538	C₂	semidirect
7. C₃×C₅×#535	C₂	semidirect
8. C₃×C₅×#534	C₂	semidirect
9. C₃×C₅×#525	C₂	semidirect
10. C₂×C₃×C₅×#121	C₂	semidirect
11. C₅×#3537	C₃	direct (N × H)
12. C₂×C₃×C₅×#41	C₂²	semidirect
13. C₂²×C₃×C₅×D₄	C₂²	semidirect
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂³×C₃×C₄×C₅	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
19. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₅×#126	C₂²	semidirect
21. C₃×C₅×#125	C₂²	semidirect
22. C₃×C₅×#124	C₂²	semidirect
23. C₃×C₅×#123	C₂²	semidirect
24. C₃×C₅×#123	C₂²	semidirect
25. C₃×C₅×#123	C₂²	semidirect
26. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₃×C₅×#121	C₂²	semidirect
28. C₃×C₅×#121	C₂²	semidirect
29. C₃×C₅×#121	C₂²	semidirect
30. C₃×C₅×#121	C₂²	semidirect
31. C₃×C₅×#121	C₂²	semidirect
32. C₃×C₅×#121	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
34. C₃×C₅×#121	C₂²	semidirect
35. C₃×C₅×#121	C₂²	semidirect
36. C₃×C₅×#120	C₂²	semidirect
37. C₃×C₅×#120	C₂²	semidirect
38. C₃×C₅×#120	C₂²	semidirect
39. C₃×C₅×#120	C₂²	semidirect
40. C₃×C₅×#120	C₂²	semidirect
41. C₃×C₄×C₅×D₄	C₂²	semidirect
42. C₃×C₄×C₅×D₄	C₂²	semidirect
43. C₃×C₄×C₅×D₄	C₂²	semidirect
44. C₃×C₅×#117	C₂²	semidirect
45. C₃×C₅×#117	C₂²	semidirect
46. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
47. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
48. C₃×#3537	C₅	direct (N × H)
49. C₅×#560	C₂×C₃	semidirect
50. C₅×#553	C₂×C₃	semidirect
51. C₅×D₄²	C₂×C₃	semidirect
52. C₅×D₄²	C₂×C₃	semidirect
53. C₅×#540	C₂×C₃	semidirect
54. C₅×#538	C₂×C₃	semidirect
55. C₅×#535	C₂×C₃	semidirect
56. C₅×#534	C₂×C₃	semidirect
57. C₅×#525	C₂×C₃	semidirect
58. C₂×C₅×#121	C₂×C₃	semidirect
101. C₃×#560	C₂×C₅	semidirect
102. C₃×#553	C₂×C₅	semidirect
103. C₃×D₄²	C₂×C₅	semidirect
104. C₃×D₄²	C₂×C₅	semidirect
105. C₃×#540	C₂×C₅	semidirect
106. C₃×#538	C₂×C₅	semidirect
107. C₃×#535	C₂×C₅	semidirect
108. C₃×#534	C₂×C₅	semidirect
109. C₃×#525	C₂×C₅	semidirect
110. C₂×C₃×#121	C₂×C₅	semidirect
111. C₂×C₅×#41	C₂²×C₃	semidirect
112. C₂²×C₅×D₄	C₂²×C₃	semidirect
113. C₂²×C₅×D₄	C₂²×C₃	semidirect
114. C₂²×C₅×D₄	C₂²×C₃	semidirect
115. C₂²×C₅×D₄	C₂²×C₃	semidirect
116. C₂³×C₄×C₅	C₂²×C₃	semidirect
117. C₅×#127	C₂²×C₃	semidirect
118. C₅×#127	C₂²×C₃	semidirect
119. C₅×#126	C₂²×C₃	semidirect
120. C₅×#125	C₂²×C₃	semidirect
121. C₅×#124	C₂²×C₃	semidirect
122. C₅×#123	C₂²×C₃	semidirect
123. C₅×#123	C₂²×C₃	semidirect
124. C₅×#123	C₂²×C₃	semidirect
125. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
126. C₅×#121	C₂²×C₃	semidirect
127. C₅×#121	C₂²×C₃	semidirect
128. C₅×#121	C₂²×C₃	semidirect
129. C₅×#121	C₂²×C₃	semidirect
130. C₅×#121	C₂²×C₃	semidirect
131. C₅×#121	C₂²×C₃	semidirect
132. C₅×#121	C₂²×C₃	semidirect
133. C₅×#121	C₂²×C₃	semidirect
134. C₅×#121	C₂²×C₃	semidirect
135. C₅×#120	C₂²×C₃	semidirect
136. C₅×#120	C₂²×C₃	semidirect
137. C₅×#120	C₂²×C₃	semidirect
138. C₅×#120	C₂²×C₃	semidirect
139. C₅×#120	C₂²×C₃	semidirect
140. C₄×C₅×D₄	C₂²×C₃	semidirect
141. C₄×C₅×D₄	C₂²×C₃	semidirect
142. C₄×C₅×D₄	C₂²×C₃	semidirect
143. C₅×#117	C₂²×C₃	semidirect
144. C₅×#117	C₂²×C₃	semidirect
145. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
146. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
147. #3537	C₃×C₅	direct (N × H)
183. C₂×C₃×#41	C₂²×C₅	semidirect
184. C₂²×C₃×D₄	C₂²×C₅	semidirect
185. C₂²×C₃×D₄	C₂²×C₅	semidirect
186. C₂²×C₃×D₄	C₂²×C₅	semidirect
187. C₂²×C₃×D₄	C₂²×C₅	semidirect
188. C₂³×C₃×C₄	C₂²×C₅	semidirect
189. C₃×#127	C₂²×C₅	semidirect
190. C₃×#127	C₂²×C₅	semidirect
191. C₃×#126	C₂²×C₅	semidirect
192. C₃×#125	C₂²×C₅	semidirect
193. C₃×#124	C₂²×C₅	semidirect
194. C₃×#123	C₂²×C₅	semidirect
195. C₃×#123	C₂²×C₅	semidirect
196. C₃×#123	C₂²×C₅	semidirect
197. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
198. C₃×#121	C₂²×C₅	semidirect
199. C₃×#121	C₂²×C₅	semidirect
200. C₃×#121	C₂²×C₅	semidirect
201. C₃×#121	C₂²×C₅	semidirect
202. C₃×#121	C₂²×C₅	semidirect
203. C₃×#121	C₂²×C₅	semidirect
204. C₃×#121	C₂²×C₅	semidirect
205. C₃×#121	C₂²×C₅	semidirect
206. C₃×#121	C₂²×C₅	semidirect
207. C₃×#120	C₂²×C₅	semidirect
208. C₃×#120	C₂²×C₅	semidirect
209. C₃×#120	C₂²×C₅	semidirect
210. C₃×#120	C₂²×C₅	semidirect
211. C₃×#120	C₂²×C₅	semidirect
212. C₃×C₄×D₄	C₂²×C₅	semidirect
213. C₃×C₄×D₄	C₂²×C₅	semidirect
214. C₃×C₄×D₄	C₂²×C₅	semidirect
215. C₃×#117	C₂²×C₅	semidirect
216. C₃×#117	C₂²×C₅	semidirect
217. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
218. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
261. #560	C₂×C₃×C₅	semidirect
262. #553	C₂×C₃×C₅	semidirect
263. D₄²	C₂×C₃×C₅	semidirect
264. D₄²	C₂×C₃×C₅	semidirect
265. #540	C₂×C₃×C₅	semidirect
266. #538	C₂×C₃×C₅	semidirect
267. #535	C₂×C₃×C₅	semidirect
268. #534	C₂×C₃×C₅	semidirect
269. #525	C₂×C₃×C₅	semidirect
270. C₂×#121	C₂×C₃×C₅	semidirect
368. C₂×#41	C₂²×C₃×C₅	semidirect
369. C₂²×D₄	C₂²×C₃×C₅	semidirect
370. C₂²×D₄	C₂²×C₃×C₅	semidirect
371. C₂²×D₄	C₂²×C₃×C₅	semidirect
372. C₂²×D₄	C₂²×C₃×C₅	semidirect
373. C₂³×C₄	C₂²×C₃×C₅	semidirect
374. #127	C₂²×C₃×C₅	semidirect
375. #127	C₂²×C₃×C₅	semidirect
376. #126	C₂²×C₃×C₅	semidirect
377. #125	C₂²×C₃×C₅	semidirect
378. #124	C₂²×C₃×C₅	semidirect
379. #123	C₂²×C₃×C₅	semidirect
380. #123	C₂²×C₃×C₅	semidirect
381. #123	C₂²×C₃×C₅	semidirect
382. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
383. #121	C₂²×C₃×C₅	semidirect
384. #121	C₂²×C₃×C₅	semidirect
385. #121	C₂²×C₃×C₅	semidirect
386. #121	C₂²×C₃×C₅	semidirect
387. #121	C₂²×C₃×C₅	semidirect
388. #121	C₂²×C₃×C₅	semidirect
389. #121	C₂²×C₃×C₅	semidirect
390. #121	C₂²×C₃×C₅	semidirect
391. #121	C₂²×C₃×C₅	semidirect
392. #120	C₂²×C₃×C₅	semidirect
393. #120	C₂²×C₃×C₅	semidirect
394. #120	C₂²×C₃×C₅	semidirect
395. #120	C₂²×C₃×C₅	semidirect
396. #120	C₂²×C₃×C₅	semidirect
397. C₄×D₄	C₂²×C₃×C₅	semidirect
398. C₄×D₄	C₂²×C₃×C₅	semidirect
399. C₄×D₄	C₂²×C₃×C₅	semidirect
400. #117	C₂²×C₃×C₅	semidirect
401. #117	C₂²×C₃×C₅	semidirect
402. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
403. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
507. C₃×C₅	#3537	direct (N × H)
575. C₅	C₃×#3537	direct (N × H)
596. C₃	C₅×#3537	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×#560	2
C₃×C₅×#553	2
C₃×C₅×D₄²	2
C₃×C₅×#540	2
C₃×C₅×#538	2
C₃×C₅×#535	2
C₃×C₅×#534	2
C₃×C₅×#525	2
C₂×C₃×C₅×#121	2
C₅×#3537	3
C₃×#3537	5

Subgroups — C3×C5×#3537 #14276571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3537 #14276571