Subgroups — C₃×C₅×#3543 #14276577

Order 1920.

2520 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×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#550	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#546	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×D₄²	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#540	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#535	C₂	1	4	yes	maximal, complemented
9	C₃×C₅×#534	C₂	1	4	yes	maximal, complemented
10	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#529	C₂	1	2	yes	maximal, complemented
12	C₅×#3543	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	4	yes	complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
16	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
17	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
18	C₃×C₅×#127	C₂²	1	1	yes	characteristic
19	C₃×C₅×#127	C₂²	1	4	yes	complemented
20	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#127	C₂²	1	2	yes	complemented
22	C₃×C₅×#127	C₂²	1	4	yes	complemented
23	C₃×C₅×#126	C₂²	1	4	yes	complemented
24	C₃×C₅×#125	C₂²	1	2	yes	complemented
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#124	C₂²	1	4	yes	complemented
27	C₃×C₅×#123	C₂²	1	4	yes	complemented
28	C₃×C₅×#123	C₂²	1	4	yes	complemented
29	C₃×C₅×#123	C₂²	1	4	yes	complemented
30	C₃×C₅×#123	C₂²	1	8	yes	complemented
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₃×C₅×#121	C₂²	1	2	yes	—
33	C₃×C₅×#121	C₂²	1	8	yes	complemented
34	C₃×C₅×#121	C₂²	1	8	yes	complemented
35	C₃×C₅×#121	C₂²	1	8	yes	complemented
36	C₃×C₅×#121	C₂²	1	4	yes	complemented
37	C₃×C₅×#121	C₂²	1	4	yes	complemented
38	C₃×C₅×#121	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×C₅×#120	C₂²	1	4	yes	complemented
42	C₃×C₅×#120	C₂²	1	8	yes	complemented
43	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
44	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
45	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
46	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
47	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
48	C₃×C₅×#117	C₂²	1	4	yes	complemented
49	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
50	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
51	C₃×#3543	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
52	C₅×#560	C₂×C₃	1	4	yes	complemented
53	C₅×#559	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#550	C₂×C₃	1	2	yes	complemented
55	C₅×#546	C₂×C₃	1	4	yes	complemented
56	C₅×D₄²	C₂×C₃	1	4	yes	complemented
57	C₅×D₄²	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#540	C₂×C₃	1	4	yes	complemented
59	C₅×#535	C₂×C₃	1	4	yes	complemented
60	C₅×#534	C₂×C₃	1	4	yes	complemented
61	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#529	C₂×C₃	1	2	yes	complemented
63	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
64	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
65	C₃×C₅×#41	—	4	8	no	—
66	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₄	—	4	8	no	—
68	C₂×C₃×C₅×D₄	—	4	8	no	—
69	C₂×C₃×C₅×D₄	—	4	4	no	—
70	C₂×C₃×C₅×D₄	—	4	8	no	—
71	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
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	4	yes	—
75	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
76	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
77	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
78	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
80	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
81	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
82	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
85	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
86	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
91	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
92	C₃×C₅×C₄⋊C₄	C₂³	1	4	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	4	yes	—
96	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₃×C₄²×C₅	C₂³	1	2	yes	—
103	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₃×C₄²×C₅	C₂³	1	4	yes	—
106	C₃×#560	C₂×C₅	1	4	yes	complemented
107	C₃×#559	C₂×C₅	1	1	yes	characteristic, complemented
108	C₃×#550	C₂×C₅	1	2	yes	complemented
109	C₃×#546	C₂×C₅	1	4	yes	complemented
110	C₃×D₄²	C₂×C₅	1	4	yes	complemented
111	C₃×D₄²	C₂×C₅	1	1	yes	characteristic, complemented
112	C₃×#540	C₂×C₅	1	4	yes	complemented
113	C₃×#535	C₂×C₅	1	4	yes	complemented
114	C₃×#534	C₂×C₅	1	4	yes	complemented
115	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
116	C₃×#529	C₂×C₅	1	2	yes	complemented
117	C₂×C₅×#41	C₂²×C₃	1	4	yes	complemented
118	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
119	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
120	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
121	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
122	C₅×#127	C₂²×C₃	1	1	yes	characteristic
123	C₅×#127	C₂²×C₃	1	4	yes	complemented
124	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₅×#127	C₂²×C₃	1	2	yes	complemented
126	C₅×#127	C₂²×C₃	1	4	yes	complemented
127	C₅×#126	C₂²×C₃	1	4	yes	complemented
128	C₅×#125	C₂²×C₃	1	2	yes	complemented
129	C₅×#124	C₂²×C₃	1	2	yes	complemented
130	C₅×#124	C₂²×C₃	1	4	yes	complemented
131	C₅×#123	C₂²×C₃	1	4	yes	complemented
132	C₅×#123	C₂²×C₃	1	4	yes	complemented
133	C₅×#123	C₂²×C₃	1	4	yes	complemented
134	C₅×#123	C₂²×C₃	1	8	yes	complemented
135	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
136	C₅×#121	C₂²×C₃	1	2	yes	—
137	C₅×#121	C₂²×C₃	1	8	yes	complemented
138	C₅×#121	C₂²×C₃	1	8	yes	complemented
139	C₅×#121	C₂²×C₃	1	8	yes	complemented
140	C₅×#121	C₂²×C₃	1	4	yes	complemented
141	C₅×#121	C₂²×C₃	1	4	yes	complemented
142	C₅×#121	C₂²×C₃	1	8	yes	complemented
143	C₅×#120	C₂²×C₃	1	4	yes	complemented
144	C₅×#120	C₂²×C₃	1	8	yes	complemented
145	C₅×#120	C₂²×C₃	1	4	yes	complemented
146	C₅×#120	C₂²×C₃	1	8	yes	complemented
147	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
148	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
149	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
150	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
151	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
152	C₅×#117	C₂²×C₃	1	4	yes	complemented
153	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
154	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
155	#3543	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³×C₃×C₅	—	2	8	no	—
157	C₂³×C₃×C₅	—	4	8	no	—
158	C₂³×C₃×C₅	—	4	8	no	—
159	C₂³×C₃×C₅	—	4	4	no	—
160	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
161	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
162	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
163	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₅×Q₈	—	2	4	no	—
165	C₃×C₅×D₄	—	2	8	no	—
166	C₃×C₅×D₄	—	2	4	no	—
167	C₃×C₅×D₄	—	2	8	no	—
168	C₃×C₅×D₄	—	2	8	no	—
169	C₃×C₅×D₄	—	4	8	no	—
170	C₃×C₅×D₄	—	4	8	no	—
171	C₃×C₅×D₄	—	4	2	no	—
172	C₃×C₅×D₄	—	4	4	no	—
173	C₃×C₅×D₄	—	4	2	no	—
174	C₃×C₅×D₄	—	4	8	no	—
175	C₃×C₅×D₄	—	4	8	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	4	no	—
178	C₂×C₃×C₄×C₅	—	2	8	no	—
179	C₂×C₃×C₄×C₅	—	4	4	no	—
180	C₂×C₃×C₄×C₅	—	4	8	no	—
181	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
182	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
183	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
184	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
185	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
186	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
187	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂×C₃×#41	C₂²×C₅	1	4	yes	complemented
189	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
190	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
191	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
192	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
193	C₃×#127	C₂²×C₅	1	1	yes	characteristic
194	C₃×#127	C₂²×C₅	1	2	yes	complemented
195	C₃×#127	C₂²×C₅	1	4	yes	complemented
196	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₃×#127	C₂²×C₅	1	4	yes	complemented
198	C₃×#126	C₂²×C₅	1	4	yes	complemented
199	C₃×#125	C₂²×C₅	1	2	yes	complemented
200	C₃×#124	C₂²×C₅	1	4	yes	complemented
201	C₃×#124	C₂²×C₅	1	2	yes	complemented
202	C₃×#123	C₂²×C₅	1	4	yes	complemented
203	C₃×#123	C₂²×C₅	1	8	yes	complemented
204	C₃×#123	C₂²×C₅	1	4	yes	complemented
205	C₃×#123	C₂²×C₅	1	4	yes	complemented
206	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
207	C₃×#121	C₂²×C₅	1	2	yes	—
208	C₃×#121	C₂²×C₅	1	8	yes	complemented
209	C₃×#121	C₂²×C₅	1	8	yes	complemented
210	C₃×#121	C₂²×C₅	1	8	yes	complemented
211	C₃×#121	C₂²×C₅	1	8	yes	complemented
212	C₃×#121	C₂²×C₅	1	4	yes	complemented
213	C₃×#121	C₂²×C₅	1	4	yes	complemented
214	C₃×#120	C₂²×C₅	1	4	yes	complemented
215	C₃×#120	C₂²×C₅	1	8	yes	complemented
216	C₃×#120	C₂²×C₅	1	4	yes	complemented
217	C₃×#120	C₂²×C₅	1	8	yes	complemented
218	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
219	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
220	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
221	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
222	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
223	C₃×#117	C₂²×C₅	1	4	yes	complemented
224	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
225	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
226	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
227	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
228	C₅×#41	—	4	8	no	—
229	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
230	C₂×C₅×D₄	—	4	8	no	—
231	C₂×C₅×D₄	—	4	8	no	—
232	C₂×C₅×D₄	—	4	4	no	—
233	C₂×C₅×D₄	—	4	8	no	—
234	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
235	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
236	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
237	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
238	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
239	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
240	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
241	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
242	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
243	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
244	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
245	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
246	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
248	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
249	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
250	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
251	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
252	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
253	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
254	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
255	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
256	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
257	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
258	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
259	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
260	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
261	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
262	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
263	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
264	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
265	C₄²×C₅	C₂³×C₃	1	2	yes	—
266	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
268	C₄²×C₅	C₂³×C₃	1	4	yes	—
269	#560	C₂×C₃×C₅	1	4	yes	complemented
270	#559	C₂×C₃×C₅	1	1	yes	characteristic, complemented
271	#550	C₂×C₃×C₅	1	2	yes	complemented
272	#546	C₂×C₃×C₅	1	4	yes	complemented
273	D₄²	C₂×C₃×C₅	1	4	yes	complemented
274	D₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
275	#540	C₂×C₃×C₅	1	4	yes	complemented
276	#535	C₂×C₃×C₅	1	4	yes	complemented
277	#534	C₂×C₃×C₅	1	4	yes	complemented
278	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
279	#529	C₂×C₃×C₅	1	2	yes	complemented
280	C₂²×C₃×C₅	—	2	2	no	—
281	C₂²×C₃×C₅	—	2	4	no	—
282	C₂²×C₃×C₅	—	2	8	no	—
283	C₂²×C₃×C₅	—	2	4	no	—
284	C₂²×C₃×C₅	—	2	4	no	—
285	C₂²×C₃×C₅	—	2	4	no	—
286	C₂²×C₃×C₅	—	2	8	no	—
287	C₂²×C₃×C₅	—	2	4	no	—
288	C₂²×C₃×C₅	—	8	8	no	—
289	C₂²×C₃×C₅	—	8	8	no	—
290	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
291	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
292	C₃×C₄×C₅	—	2	4	no	—
293	C₃×C₄×C₅	—	2	1	no	—
294	C₃×C₄×C₅	—	2	1	no	—
295	C₃×C₄×C₅	—	2	2	no	—
296	C₃×C₄×C₅	—	2	4	no	—
297	C₃×C₄×C₅	—	2	4	no	—
298	C₃×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
299	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
300	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
301	C₃×#41	—	4	8	no	—
302	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
303	C₂×C₃×D₄	—	4	8	no	—
304	C₂×C₃×D₄	—	4	8	no	—
305	C₂×C₃×D₄	—	4	4	no	—
306	C₂×C₃×D₄	—	4	8	no	—
307	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
308	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
309	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
310	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
311	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
312	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
313	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
314	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
315	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
316	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
317	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
318	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
319	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
321	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
322	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
323	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
324	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
325	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
326	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
327	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
328	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
329	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
330	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
331	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
332	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
333	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
334	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
335	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
336	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
337	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
338	C₃×C₄²	C₂³×C₅	1	2	yes	—
339	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
340	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
341	C₃×C₄²	C₂³×C₅	1	4	yes	—
342	C₂³×C₅	—	2	8	no	—
343	C₂³×C₅	—	4	8	no	—
344	C₂³×C₅	—	4	8	no	—
345	C₂³×C₅	—	4	4	no	—
346	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
347	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
348	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
349	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
350	C₅×Q₈	—	2	4	no	—
351	C₅×D₄	—	2	8	no	—
352	C₅×D₄	—	2	4	no	—
353	C₅×D₄	—	2	8	no	—
354	C₅×D₄	—	2	8	no	—
355	C₅×D₄	—	4	8	no	—
356	C₅×D₄	—	4	8	no	—
357	C₅×D₄	—	4	2	no	—
358	C₅×D₄	—	4	4	no	—
359	C₅×D₄	—	4	2	no	—
360	C₅×D₄	—	4	8	no	—
361	C₅×D₄	—	4	8	no	—
362	C₂×C₄×C₅	—	2	2	no	—
363	C₂×C₄×C₅	—	2	4	no	—
364	C₂×C₄×C₅	—	2	8	no	—
365	C₂×C₄×C₅	—	4	4	no	—
366	C₂×C₄×C₅	—	4	8	no	—
367	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
369	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
371	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
372	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
373	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
374	C₂×#41	C₂²×C₃×C₅	1	4	yes	complemented
375	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
376	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
377	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
378	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	complemented
379	#127	C₂²×C₃×C₅	1	1	yes	characteristic
380	#127	C₂²×C₃×C₅	1	4	yes	complemented
381	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
382	#127	C₂²×C₃×C₅	1	2	yes	complemented
383	#127	C₂²×C₃×C₅	1	4	yes	complemented
384	#126	C₂²×C₃×C₅	1	4	yes	complemented
385	#125	C₂²×C₃×C₅	1	2	yes	complemented
386	#124	C₂²×C₃×C₅	1	2	yes	complemented
387	#124	C₂²×C₃×C₅	1	4	yes	complemented
388	#123	C₂²×C₃×C₅	1	4	yes	complemented
389	#123	C₂²×C₃×C₅	1	4	yes	complemented
390	#123	C₂²×C₃×C₅	1	4	yes	complemented
391	#123	C₂²×C₃×C₅	1	8	yes	complemented
392	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
393	#121	C₂²×C₃×C₅	1	2	yes	—
394	#121	C₂²×C₃×C₅	1	8	yes	complemented
395	#121	C₂²×C₃×C₅	1	8	yes	complemented
396	#121	C₂²×C₃×C₅	1	8	yes	complemented
397	#121	C₂²×C₃×C₅	1	4	yes	complemented
398	#121	C₂²×C₃×C₅	1	4	yes	complemented
399	#121	C₂²×C₃×C₅	1	8	yes	complemented
400	#120	C₂²×C₃×C₅	1	4	yes	complemented
401	#120	C₂²×C₃×C₅	1	8	yes	complemented
402	#120	C₂²×C₃×C₅	1	4	yes	complemented
403	#120	C₂²×C₃×C₅	1	8	yes	complemented
404	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
405	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
406	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
407	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
408	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
409	#117	C₂²×C₃×C₅	1	4	yes	complemented
410	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
411	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
412	C₂×C₃×C₅	—	2	2	no	—
413	C₂×C₃×C₅	—	4	4	no	—
414	C₂×C₃×C₅	—	4	4	no	—
415	C₂×C₃×C₅	—	4	4	no	—
416	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂³×C₃	—	2	8	no	—
419	C₂³×C₃	—	4	8	no	—
420	C₂³×C₃	—	4	8	no	—
421	C₂³×C₃	—	4	4	no	—
422	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
423	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
424	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
425	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
426	C₃×Q₈	—	2	4	no	—
427	C₃×D₄	—	2	8	no	—
428	C₃×D₄	—	2	4	no	—
429	C₃×D₄	—	2	8	no	—
430	C₃×D₄	—	2	8	no	—
431	C₃×D₄	—	4	8	no	—
432	C₃×D₄	—	4	8	no	—
433	C₃×D₄	—	4	2	no	—
434	C₃×D₄	—	4	4	no	—
435	C₃×D₄	—	4	2	no	—
436	C₃×D₄	—	4	8	no	—
437	C₃×D₄	—	4	8	no	—
438	C₂×C₃×C₄	—	2	2	no	—
439	C₂×C₃×C₄	—	2	4	no	—
440	C₂×C₃×C₄	—	2	8	no	—
441	C₂×C₃×C₄	—	4	4	no	—
442	C₂×C₃×C₄	—	4	8	no	—
443	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
444	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
445	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
446	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
447	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
448	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
449	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
450	C₂²×C₅	—	2	2	no	—
451	C₂²×C₅	—	2	4	no	—
452	C₂²×C₅	—	2	8	no	—
453	C₂²×C₅	—	2	4	no	—
454	C₂²×C₅	—	2	4	no	—
455	C₂²×C₅	—	2	4	no	—
456	C₂²×C₅	—	2	8	no	—
457	C₂²×C₅	—	2	4	no	—
458	C₂²×C₅	—	8	8	no	—
459	C₂²×C₅	—	8	8	no	—
460	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
461	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
462	C₄×C₅	—	2	4	no	—
463	C₄×C₅	—	2	1	no	—
464	C₄×C₅	—	2	1	no	—
465	C₄×C₅	—	2	2	no	—
466	C₄×C₅	—	2	4	no	—
467	C₄×C₅	—	2	4	no	—
468	C₄×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
469	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
470	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
471	#41	—	4	8	no	—
472	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	8	no	—
475	C₂×D₄	—	4	4	no	—
476	C₂×D₄	—	4	8	no	—
477	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
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	4	yes	—
481	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
482	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
483	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
484	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
485	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
486	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
487	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
488	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
489	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
491	C₂²×C₄	C₂³×C₃×C₅	1	8	yes	—
492	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
493	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
494	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
495	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
496	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
497	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
498	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
499	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
500	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
501	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
502	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
503	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
504	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
505	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
506	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
507	C₂²⋊C₄	C₂³×C₃×C₅	1	8	yes	—
508	C₄²	C₂³×C₃×C₅	1	2	yes	—
509	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
510	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
511	C₄²	C₂³×C₃×C₅	1	4	yes	—
512	C₃×C₅	#3543	1	1	yes	characteristic, direct product factor, Hall
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	2	4	no	—
515	C₂²×C₃	—	2	8	no	—
516	C₂²×C₃	—	2	4	no	—
517	C₂²×C₃	—	2	4	no	—
518	C₂²×C₃	—	2	4	no	—
519	C₂²×C₃	—	2	8	no	—
520	C₂²×C₃	—	2	4	no	—
521	C₂²×C₃	—	8	8	no	—
522	C₂²×C₃	—	8	8	no	—
523	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
524	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
525	C₃×C₄	—	2	4	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	2	no	—
529	C₃×C₄	—	2	4	no	—
530	C₃×C₄	—	2	4	no	—
531	C₃×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
532	C₂×C₅	—	2	2	no	—
533	C₂×C₅	—	4	4	no	—
534	C₂×C₅	—	4	4	no	—
535	C₂×C₅	—	4	4	no	—
536	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
538	C₂³	—	2	8	no	—
539	C₂³	—	4	8	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	4	4	no	—
542	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
543	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
544	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
545	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
546	Q₈	—	2	4	no	—
547	D₄	—	2	8	no	—
548	D₄	—	2	4	no	—
549	D₄	—	2	8	no	—
550	D₄	—	2	8	no	—
551	D₄	—	4	8	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	8	no	—
557	D₄	—	4	8	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	8	no	—
563	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
564	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
565	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
566	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
567	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
568	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
569	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
570	C₂×C₃	—	2	2	no	—
571	C₂×C₃	—	4	4	no	—
572	C₂×C₃	—	4	4	no	—
573	C₂×C₃	—	4	4	no	—
574	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
576	C₅	C₃×#3543	1	1	yes	characteristic, direct product factor, Sylow
577	C₂²	—	2	2	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	8	8	no	—
586	C₂²	—	8	8	no	—
587	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
588	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
589	C₄	—	2	4	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	4	no	—
595	C₄	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
596	C₃	C₅×#3543	1	1	yes	characteristic, direct product factor, Sylow
597	C₂	—	2	2	no	—
598	C₂	—	4	4	no	—
599	C₂	—	4	4	no	—
600	C₂	—	4	4	no	—
601	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	2	yes	—

	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×#559	C₂	semidirect
3. C₃×C₅×#550	C₂	semidirect
4. C₃×C₅×#546	C₂	semidirect
5. C₃×C₅×D₄²	C₂	semidirect
6. C₃×C₅×D₄²	C₂	semidirect
7. C₃×C₅×#540	C₂	semidirect
8. C₃×C₅×#535	C₂	semidirect
9. C₃×C₅×#534	C₂	semidirect
10. C₂×C₃×C₅×#127	C₂	semidirect
11. C₃×C₅×#529	C₂	semidirect
12. C₅×#3543	C₃	direct (N × H)
13. C₂×C₃×C₅×#41	C₂²	semidirect
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂²×C₃×C₅×D₄	C₂²	semidirect
19. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₅×#127	C₂²	semidirect
21. C₃×C₅×#127	C₂²	semidirect
22. C₃×C₅×#127	C₂²	semidirect
23. C₃×C₅×#126	C₂²	semidirect
24. C₃×C₅×#125	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
26. C₃×C₅×#124	C₂²	semidirect
27. C₃×C₅×#123	C₂²	semidirect
28. C₃×C₅×#123	C₂²	semidirect
29. C₃×C₅×#123	C₂²	semidirect
30. C₃×C₅×#123	C₂²	semidirect
31. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
34. C₃×C₅×#121	C₂²	semidirect
35. C₃×C₅×#121	C₂²	semidirect
36. C₃×C₅×#121	C₂²	semidirect
37. C₃×C₅×#121	C₂²	semidirect
38. C₃×C₅×#121	C₂²	semidirect
39. C₃×C₅×#120	C₂²	semidirect
40. C₃×C₅×#120	C₂²	semidirect
41. C₃×C₅×#120	C₂²	semidirect
42. C₃×C₅×#120	C₂²	semidirect
43. C₃×C₄×C₅×Q₈	C₂²	semidirect
44. C₃×C₄×C₅×D₄	C₂²	semidirect
45. C₃×C₄×C₅×D₄	C₂²	semidirect
46. C₃×C₄×C₅×D₄	C₂²	semidirect
47. C₃×C₄×C₅×D₄	C₂²	semidirect
48. C₃×C₅×#117	C₂²	semidirect
49. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
50. C₂×C₃×C₄²×C₅	C₂²	semidirect
51. C₃×#3543	C₅	direct (N × H)
52. C₅×#560	C₂×C₃	semidirect
53. C₅×#559	C₂×C₃	semidirect
54. C₅×#550	C₂×C₃	semidirect
55. C₅×#546	C₂×C₃	semidirect
56. C₅×D₄²	C₂×C₃	semidirect
57. C₅×D₄²	C₂×C₃	semidirect
58. C₅×#540	C₂×C₃	semidirect
59. C₅×#535	C₂×C₃	semidirect
60. C₅×#534	C₂×C₃	semidirect
61. C₂×C₅×#127	C₂×C₃	semidirect
62. C₅×#529	C₂×C₃	semidirect
106. C₃×#560	C₂×C₅	semidirect
107. C₃×#559	C₂×C₅	semidirect
108. C₃×#550	C₂×C₅	semidirect
109. C₃×#546	C₂×C₅	semidirect
110. C₃×D₄²	C₂×C₅	semidirect
111. C₃×D₄²	C₂×C₅	semidirect
112. C₃×#540	C₂×C₅	semidirect
113. C₃×#535	C₂×C₅	semidirect
114. C₃×#534	C₂×C₅	semidirect
115. C₂×C₃×#127	C₂×C₅	semidirect
116. C₃×#529	C₂×C₅	semidirect
117. C₂×C₅×#41	C₂²×C₃	semidirect
118. C₂²×C₅×D₄	C₂²×C₃	semidirect
119. C₂²×C₅×D₄	C₂²×C₃	semidirect
120. C₂²×C₅×D₄	C₂²×C₃	semidirect
121. C₂²×C₅×D₄	C₂²×C₃	semidirect
123. C₅×#127	C₂²×C₃	semidirect
124. C₅×#127	C₂²×C₃	semidirect
125. C₅×#127	C₂²×C₃	semidirect
126. C₅×#127	C₂²×C₃	semidirect
127. C₅×#126	C₂²×C₃	semidirect
128. C₅×#125	C₂²×C₃	semidirect
129. C₅×#124	C₂²×C₃	semidirect
130. C₅×#124	C₂²×C₃	semidirect
131. C₅×#123	C₂²×C₃	semidirect
132. C₅×#123	C₂²×C₃	semidirect
133. C₅×#123	C₂²×C₃	semidirect
134. C₅×#123	C₂²×C₃	semidirect
135. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
137. C₅×#121	C₂²×C₃	semidirect
138. C₅×#121	C₂²×C₃	semidirect
139. C₅×#121	C₂²×C₃	semidirect
140. C₅×#121	C₂²×C₃	semidirect
141. C₅×#121	C₂²×C₃	semidirect
142. C₅×#121	C₂²×C₃	semidirect
143. C₅×#120	C₂²×C₃	semidirect
144. C₅×#120	C₂²×C₃	semidirect
145. C₅×#120	C₂²×C₃	semidirect
146. C₅×#120	C₂²×C₃	semidirect
147. C₄×C₅×Q₈	C₂²×C₃	semidirect
148. C₄×C₅×D₄	C₂²×C₃	semidirect
149. C₄×C₅×D₄	C₂²×C₃	semidirect
150. C₄×C₅×D₄	C₂²×C₃	semidirect
151. C₄×C₅×D₄	C₂²×C₃	semidirect
152. C₅×#117	C₂²×C₃	semidirect
153. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
154. C₂×C₄²×C₅	C₂²×C₃	semidirect
155. #3543	C₃×C₅	direct (N × H)
188. C₂×C₃×#41	C₂²×C₅	semidirect
189. C₂²×C₃×D₄	C₂²×C₅	semidirect
190. C₂²×C₃×D₄	C₂²×C₅	semidirect
191. C₂²×C₃×D₄	C₂²×C₅	semidirect
192. C₂²×C₃×D₄	C₂²×C₅	semidirect
194. C₃×#127	C₂²×C₅	semidirect
195. C₃×#127	C₂²×C₅	semidirect
196. C₃×#127	C₂²×C₅	semidirect
197. C₃×#127	C₂²×C₅	semidirect
198. C₃×#126	C₂²×C₅	semidirect
199. C₃×#125	C₂²×C₅	semidirect
200. C₃×#124	C₂²×C₅	semidirect
201. C₃×#124	C₂²×C₅	semidirect
202. C₃×#123	C₂²×C₅	semidirect
203. C₃×#123	C₂²×C₅	semidirect
204. C₃×#123	C₂²×C₅	semidirect
205. C₃×#123	C₂²×C₅	semidirect
206. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
208. C₃×#121	C₂²×C₅	semidirect
209. C₃×#121	C₂²×C₅	semidirect
210. C₃×#121	C₂²×C₅	semidirect
211. C₃×#121	C₂²×C₅	semidirect
212. C₃×#121	C₂²×C₅	semidirect
213. C₃×#121	C₂²×C₅	semidirect
214. C₃×#120	C₂²×C₅	semidirect
215. C₃×#120	C₂²×C₅	semidirect
216. C₃×#120	C₂²×C₅	semidirect
217. C₃×#120	C₂²×C₅	semidirect
218. C₃×C₄×Q₈	C₂²×C₅	semidirect
219. C₃×C₄×D₄	C₂²×C₅	semidirect
220. C₃×C₄×D₄	C₂²×C₅	semidirect
221. C₃×C₄×D₄	C₂²×C₅	semidirect
222. C₃×C₄×D₄	C₂²×C₅	semidirect
223. C₃×#117	C₂²×C₅	semidirect
224. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
225. C₂×C₃×C₄²	C₂²×C₅	semidirect
269. #560	C₂×C₃×C₅	semidirect
270. #559	C₂×C₃×C₅	semidirect
271. #550	C₂×C₃×C₅	semidirect
272. #546	C₂×C₃×C₅	semidirect
273. D₄²	C₂×C₃×C₅	semidirect
274. D₄²	C₂×C₃×C₅	semidirect
275. #540	C₂×C₃×C₅	semidirect
276. #535	C₂×C₃×C₅	semidirect
277. #534	C₂×C₃×C₅	semidirect
278. C₂×#127	C₂×C₃×C₅	semidirect
279. #529	C₂×C₃×C₅	semidirect
374. C₂×#41	C₂²×C₃×C₅	semidirect
375. C₂²×D₄	C₂²×C₃×C₅	semidirect
376. C₂²×D₄	C₂²×C₃×C₅	semidirect
377. C₂²×D₄	C₂²×C₃×C₅	semidirect
378. C₂²×D₄	C₂²×C₃×C₅	semidirect
380. #127	C₂²×C₃×C₅	semidirect
381. #127	C₂²×C₃×C₅	semidirect
382. #127	C₂²×C₃×C₅	semidirect
383. #127	C₂²×C₃×C₅	semidirect
384. #126	C₂²×C₃×C₅	semidirect
385. #125	C₂²×C₃×C₅	semidirect
386. #124	C₂²×C₃×C₅	semidirect
387. #124	C₂²×C₃×C₅	semidirect
388. #123	C₂²×C₃×C₅	semidirect
389. #123	C₂²×C₃×C₅	semidirect
390. #123	C₂²×C₃×C₅	semidirect
391. #123	C₂²×C₃×C₅	semidirect
392. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
394. #121	C₂²×C₃×C₅	semidirect
395. #121	C₂²×C₃×C₅	semidirect
396. #121	C₂²×C₃×C₅	semidirect
397. #121	C₂²×C₃×C₅	semidirect
398. #121	C₂²×C₃×C₅	semidirect
399. #121	C₂²×C₃×C₅	semidirect
400. #120	C₂²×C₃×C₅	semidirect
401. #120	C₂²×C₃×C₅	semidirect
402. #120	C₂²×C₃×C₅	semidirect
403. #120	C₂²×C₃×C₅	semidirect
404. C₄×Q₈	C₂²×C₃×C₅	semidirect
405. C₄×D₄	C₂²×C₃×C₅	semidirect
406. C₄×D₄	C₂²×C₃×C₅	semidirect
407. C₄×D₄	C₂²×C₃×C₅	semidirect
408. C₄×D₄	C₂²×C₃×C₅	semidirect
409. #117	C₂²×C₃×C₅	semidirect
410. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
411. C₂×C₄²	C₂²×C₃×C₅	semidirect
512. C₃×C₅	#3543	direct (N × H)
576. C₅	C₃×#3543	direct (N × H)
596. C₃	C₅×#3543	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×#559	2
C₃×C₅×#550	2
C₃×C₅×#546	2
C₃×C₅×D₄²	2
C₃×C₅×#540	2
C₃×C₅×#535	2
C₃×C₅×#534	2
C₂×C₃×C₅×#127	2
C₃×C₅×#529	2
C₅×#3543	3
C₃×#3543	5

Subgroups — C3×C5×#3543 #14276577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3543 #14276577