Subgroups — C₃×C₅×#2669 #14275703

Order 1920.

1864 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#120	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2669	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#127	—	2	4	no	—
21	C₃×C₅×#121	—	2	8	no	—
22	C₃×C₅×#120	—	2	4	no	—
23	C₃×C₅×#120	—	2	8	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#95	C₂²	1	2	yes	complemented
35	C₃×C₅×#95	C₂²	1	2	yes	complemented
36	C₃×#2669	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
39	C₂×C₅×#120	C₂×C₃	1	2	yes	complemented
40	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#394	C₂×C₃	1	2	yes	complemented
42	C₅×#392	C₂×C₃	1	2	yes	complemented
43	C₅×#392	C₂×C₃	1	2	yes	complemented
44	C₅×#388	C₂×C₃	1	2	yes	complemented
45	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	—	2	2	no	—
47	C₂⁴×C₃×C₅	—	2	4	no	—
48	C₂⁴×C₃×C₅	—	4	1	no	—
49	C₂⁴×C₃×C₅	—	4	2	no	—
50	C₂⁴×C₃×C₅	—	4	1	no	—
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
54	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	4	no	—
56	C₂×C₃×C₅×D₄	—	2	4	no	—
57	C₂×C₃×C₅×D₄	—	2	4	no	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	4	no	—
61	C₂×C₃×C₅×D₄	—	2	4	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	4	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	4	2	no	—
66	C₂×C₃×C₅×D₄	—	4	1	no	—
67	C₂×C₃×C₅×D₄	—	4	1	no	—
68	C₂×C₃×C₅×D₄	—	4	2	no	—
69	C₂×C₃×C₅×D₄	—	4	2	no	—
70	C₂×C₃×C₅×D₄	—	4	2	no	—
71	C₂×C₃×C₅×D₄	—	4	2	no	—
72	C₂×C₃×C₅×D₄	—	4	2	no	—
73	C₂×C₃×C₅×D₄	—	4	1	no	—
74	C₂×C₃×C₅×D₄	—	4	1	no	—
75	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
76	C₂²×C₃×C₄×C₅	—	2	4	no	—
77	C₂²×C₃×C₄×C₅	—	4	1	no	—
78	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	C₃×C₅×C₄⋊C₄	—	2	4	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
89	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
90	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
91	C₃×C₅×C₂²⋊C₄	D₄	1	8	yes	complemented
92	C₃×C₄²×C₅	—	2	2	no	—
93	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
95	C₂×C₃×#120	C₂×C₅	1	2	yes	complemented
96	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#394	C₂×C₅	1	2	yes	complemented
98	C₃×#392	C₂×C₅	1	2	yes	complemented
99	C₃×#392	C₂×C₅	1	2	yes	complemented
100	C₃×#388	C₂×C₅	1	2	yes	complemented
101	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
104	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
105	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
106	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
107	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
109	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₅×#127	—	2	4	no	—
112	C₅×#121	—	2	8	no	—
113	C₅×#120	—	2	4	no	—
114	C₅×#120	—	2	8	no	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
116	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
122	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
124	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₅×#95	C₂²×C₃	1	2	yes	complemented
126	C₅×#95	C₂²×C₃	1	2	yes	complemented
127	#2669	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂³×C₃×C₅	—	2	2	no	—
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	2	1	no	—
133	C₂³×C₃×C₅	—	2	1	no	—
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	1	no	—
137	C₂³×C₃×C₅	—	2	2	no	—
138	C₂³×C₃×C₅	—	2	2	no	—
139	C₂³×C₃×C₅	—	2	2	no	—
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	2	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	2	2	no	—
149	C₂³×C₃×C₅	—	4	4	no	—
150	C₂³×C₃×C₅	—	4	8	no	—
151	C₂³×C₃×C₅	—	4	4	no	—
152	C₂³×C₃×C₅	—	4	8	no	—
153	C₂³×C₃×C₅	—	4	4	no	—
154	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
155	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
156	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
157	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
158	C₃×C₅×D₄	—	4	4	no	—
159	C₃×C₅×D₄	—	4	8	no	—
160	C₃×C₅×D₄	—	4	8	no	—
161	C₃×C₅×D₄	—	4	8	no	—
162	C₃×C₅×D₄	—	4	4	no	—
163	C₃×C₅×D₄	—	4	8	no	—
164	C₃×C₅×D₄	—	4	8	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	2	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	2	no	—
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	4	4	no	—
178	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
179	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
180	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
181	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
183	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
184	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
185	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
186	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
188	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₃×#127	—	2	4	no	—
191	C₃×#121	—	2	8	no	—
192	C₃×#120	—	2	4	no	—
193	C₃×#120	—	2	8	no	—
194	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
195	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
201	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
202	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
203	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₃×#95	C₂²×C₅	1	2	yes	complemented
205	C₃×#95	C₂²×C₅	1	2	yes	complemented
206	C₂⁴×C₅	—	2	2	no	—
207	C₂⁴×C₅	—	2	4	no	—
208	C₂⁴×C₅	—	4	1	no	—
209	C₂⁴×C₅	—	4	2	no	—
210	C₂⁴×C₅	—	4	1	no	—
211	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
212	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
214	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₅×D₄	—	2	4	no	—
216	C₂×C₅×D₄	—	2	4	no	—
217	C₂×C₅×D₄	—	2	4	no	—
218	C₂×C₅×D₄	—	2	4	no	—
219	C₂×C₅×D₄	—	2	4	no	—
220	C₂×C₅×D₄	—	2	4	no	—
221	C₂×C₅×D₄	—	2	4	no	—
222	C₂×C₅×D₄	—	2	4	no	—
223	C₂×C₅×D₄	—	2	4	no	—
224	C₂×C₅×D₄	—	2	2	no	—
225	C₂×C₅×D₄	—	4	2	no	—
226	C₂×C₅×D₄	—	4	1	no	—
227	C₂×C₅×D₄	—	4	1	no	—
228	C₂×C₅×D₄	—	4	2	no	—
229	C₂×C₅×D₄	—	4	2	no	—
230	C₂×C₅×D₄	—	4	2	no	—
231	C₂×C₅×D₄	—	4	2	no	—
232	C₂×C₅×D₄	—	4	2	no	—
233	C₂×C₅×D₄	—	4	1	no	—
234	C₂×C₅×D₄	—	4	1	no	—
235	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
236	C₂²×C₄×C₅	—	2	4	no	—
237	C₂²×C₄×C₅	—	4	1	no	—
238	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
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	C₅×C₄⋊C₄	—	2	4	no	—
244	C₅×C₂²⋊C₄	—	2	2	no	—
245	C₅×C₂²⋊C₄	—	2	4	no	—
246	C₅×C₂²⋊C₄	—	2	4	no	—
247	C₅×C₂²⋊C₄	—	2	4	no	—
248	C₅×C₂²⋊C₄	—	2	4	no	—
249	C₅×C₂²⋊C₄	—	4	1	no	—
250	C₅×C₂²⋊C₄	—	4	2	no	—
251	C₅×C₂²⋊C₄	C₃×D₄	1	8	yes	complemented
252	C₄²×C₅	—	2	2	no	—
253	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
254	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
255	C₂×#120	C₂×C₃×C₅	1	2	yes	complemented
256	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
257	#394	C₂×C₃×C₅	1	2	yes	complemented
258	#392	C₂×C₃×C₅	1	2	yes	complemented
259	#392	C₂×C₃×C₅	1	2	yes	complemented
260	#388	C₂×C₃×C₅	1	2	yes	complemented
261	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	—	2	2	no	—
264	C₂²×C₃×C₅	—	2	4	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	2	4	no	—
267	C₂²×C₃×C₅	—	2	4	no	—
268	C₂²×C₃×C₅	—	2	4	no	—
269	C₂²×C₃×C₅	—	4	16	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	1	no	—
275	C₂²×C₃×C₅	—	4	1	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	—	4	1	no	—
278	C₂²×C₃×C₅	—	4	1	no	—
279	C₂²×C₃×C₅	—	4	2	no	—
280	C₂²×C₃×C₅	—	4	2	no	—
281	C₂²×C₃×C₅	—	4	2	no	—
282	C₂²×C₃×C₅	—	4	2	no	—
283	C₂²×C₃×C₅	—	4	2	no	—
284	C₂²×C₃×C₅	—	4	2	no	—
285	C₂²×C₃×C₅	—	4	2	no	—
286	C₂²×C₃×C₅	—	4	2	no	—
287	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
288	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
289	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
290	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
292	C₃×C₄×C₅	—	2	2	no	—
293	C₃×C₄×C₅	—	2	4	no	—
294	C₃×C₄×C₅	—	2	4	no	—
295	C₃×C₄×C₅	—	4	2	no	—
296	C₃×C₄×C₅	—	4	2	no	—
297	C₂⁴×C₃	—	2	2	no	—
298	C₂⁴×C₃	—	2	4	no	—
299	C₂⁴×C₃	—	4	1	no	—
300	C₂⁴×C₃	—	4	2	no	—
301	C₂⁴×C₃	—	4	1	no	—
302	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
303	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
304	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
305	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₃×D₄	—	2	4	no	—
307	C₂×C₃×D₄	—	2	4	no	—
308	C₂×C₃×D₄	—	2	4	no	—
309	C₂×C₃×D₄	—	2	4	no	—
310	C₂×C₃×D₄	—	2	4	no	—
311	C₂×C₃×D₄	—	2	4	no	—
312	C₂×C₃×D₄	—	2	4	no	—
313	C₂×C₃×D₄	—	2	4	no	—
314	C₂×C₃×D₄	—	2	4	no	—
315	C₂×C₃×D₄	—	2	2	no	—
316	C₂×C₃×D₄	—	4	2	no	—
317	C₂×C₃×D₄	—	4	1	no	—
318	C₂×C₃×D₄	—	4	1	no	—
319	C₂×C₃×D₄	—	4	2	no	—
320	C₂×C₃×D₄	—	4	2	no	—
321	C₂×C₃×D₄	—	4	2	no	—
322	C₂×C₃×D₄	—	4	2	no	—
323	C₂×C₃×D₄	—	4	2	no	—
324	C₂×C₃×D₄	—	4	1	no	—
325	C₂×C₃×D₄	—	4	1	no	—
326	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
327	C₂²×C₃×C₄	—	2	4	no	—
328	C₂²×C₃×C₄	—	4	1	no	—
329	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
330	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
331	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
332	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
333	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
334	C₃×C₄⋊C₄	—	2	4	no	—
335	C₃×C₂²⋊C₄	—	2	2	no	—
336	C₃×C₂²⋊C₄	—	2	4	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	4	no	—
340	C₃×C₂²⋊C₄	—	4	1	no	—
341	C₃×C₂²⋊C₄	—	4	2	no	—
342	C₃×C₂²⋊C₄	C₅×D₄	1	8	yes	complemented
343	C₃×C₄²	—	2	2	no	—
344	C₂³×C₅	—	2	2	no	—
345	C₂³×C₅	—	2	2	no	—
346	C₂³×C₅	—	2	2	no	—
347	C₂³×C₅	—	2	2	no	—
348	C₂³×C₅	—	2	1	no	—
349	C₂³×C₅	—	2	1	no	—
350	C₂³×C₅	—	2	2	no	—
351	C₂³×C₅	—	2	1	no	—
352	C₂³×C₅	—	2	1	no	—
353	C₂³×C₅	—	2	2	no	—
354	C₂³×C₅	—	2	2	no	—
355	C₂³×C₅	—	2	2	no	—
356	C₂³×C₅	—	2	2	no	—
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	—	2	2	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂³×C₅	—	2	2	no	—
361	C₂³×C₅	—	2	2	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	2	no	—
365	C₂³×C₅	—	4	4	no	—
366	C₂³×C₅	—	4	8	no	—
367	C₂³×C₅	—	4	4	no	—
368	C₂³×C₅	—	4	8	no	—
369	C₂³×C₅	—	4	4	no	—
370	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
371	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
372	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
373	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
374	C₅×D₄	—	4	4	no	—
375	C₅×D₄	—	4	8	no	—
376	C₅×D₄	—	4	8	no	—
377	C₅×D₄	—	4	8	no	—
378	C₅×D₄	—	4	4	no	—
379	C₅×D₄	—	4	8	no	—
380	C₅×D₄	—	4	8	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	2	no	—
389	C₂×C₄×C₅	—	2	2	no	—
390	C₂×C₄×C₅	—	2	2	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	—	4	4	no	—
394	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
395	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
396	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
397	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
398	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
399	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
400	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
401	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
402	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
403	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
404	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
405	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
406	#127	—	2	4	no	—
407	#121	—	2	8	no	—
408	#120	—	2	4	no	—
409	#120	—	2	8	no	—
410	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
411	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
417	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
418	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
419	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
420	#95	C₂²×C₃×C₅	1	2	yes	complemented
421	#95	C₂²×C₃×C₅	1	2	yes	complemented
422	C₂×C₃×C₅	—	4	2	no	—
423	C₂×C₃×C₅	—	4	2	no	—
424	C₂×C₃×C₅	—	4	4	no	—
425	C₂×C₃×C₅	—	8	2	no	—
426	C₂×C₃×C₅	#534	1	1	yes	characteristic
427	C₂×C₃×C₅	#535	1	2	yes	—
428	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
429	C₂×C₃×C₅	D₄²	1	2	yes	—
430	C₂×C₃×C₅	#560	1	1	yes	characteristic
431	C₂³×C₃	—	2	2	no	—
432	C₂³×C₃	—	2	2	no	—
433	C₂³×C₃	—	2	2	no	—
434	C₂³×C₃	—	2	2	no	—
435	C₂³×C₃	—	2	1	no	—
436	C₂³×C₃	—	2	1	no	—
437	C₂³×C₃	—	2	2	no	—
438	C₂³×C₃	—	2	1	no	—
439	C₂³×C₃	—	2	1	no	—
440	C₂³×C₃	—	2	2	no	—
441	C₂³×C₃	—	2	2	no	—
442	C₂³×C₃	—	2	2	no	—
443	C₂³×C₃	—	2	2	no	—
444	C₂³×C₃	—	2	2	no	—
445	C₂³×C₃	—	2	2	no	—
446	C₂³×C₃	—	2	2	no	—
447	C₂³×C₃	—	2	2	no	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	2	no	—
450	C₂³×C₃	—	2	2	no	—
451	C₂³×C₃	—	2	2	no	—
452	C₂³×C₃	—	4	4	no	—
453	C₂³×C₃	—	4	8	no	—
454	C₂³×C₃	—	4	4	no	—
455	C₂³×C₃	—	4	8	no	—
456	C₂³×C₃	—	4	4	no	—
457	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
458	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
459	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
460	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
461	C₃×D₄	—	4	4	no	—
462	C₃×D₄	—	4	8	no	—
463	C₃×D₄	—	4	8	no	—
464	C₃×D₄	—	4	8	no	—
465	C₃×D₄	—	4	4	no	—
466	C₃×D₄	—	4	8	no	—
467	C₃×D₄	—	4	8	no	—
468	C₂×C₃×C₄	—	2	2	no	—
469	C₂×C₃×C₄	—	2	2	no	—
470	C₂×C₃×C₄	—	2	2	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	2	no	—
475	C₂×C₃×C₄	—	2	2	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	2	no	—
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	4	4	no	—
481	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
482	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
483	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
484	C₂²×C₅	—	2	2	no	—
485	C₂²×C₅	—	2	2	no	—
486	C₂²×C₅	—	2	4	no	—
487	C₂²×C₅	—	2	4	no	—
488	C₂²×C₅	—	2	4	no	—
489	C₂²×C₅	—	2	4	no	—
490	C₂²×C₅	—	2	4	no	—
491	C₂²×C₅	—	4	16	no	—
492	C₂²×C₅	—	4	1	no	—
493	C₂²×C₅	—	4	1	no	—
494	C₂²×C₅	—	4	2	no	—
495	C₂²×C₅	—	4	2	no	—
496	C₂²×C₅	—	4	2	no	—
497	C₂²×C₅	—	4	2	no	—
498	C₂²×C₅	—	4	2	no	—
499	C₂²×C₅	—	4	1	no	—
500	C₂²×C₅	—	4	1	no	—
501	C₂²×C₅	—	4	2	no	—
502	C₂²×C₅	—	4	2	no	—
503	C₂²×C₅	—	4	2	no	—
504	C₂²×C₅	—	4	2	no	—
505	C₂²×C₅	—	4	2	no	—
506	C₂²×C₅	—	4	2	no	—
507	C₂²×C₅	—	4	2	no	—
508	C₂²×C₅	—	4	2	no	—
509	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
510	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
511	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
513	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
514	C₄×C₅	—	2	2	no	—
515	C₄×C₅	—	2	4	no	—
516	C₄×C₅	—	2	4	no	—
517	C₄×C₅	—	4	2	no	—
518	C₄×C₅	—	4	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	2	4	no	—
521	C₂⁴	—	4	1	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	1	no	—
524	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
525	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
526	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
527	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	2	no	—
539	C₂×D₄	—	4	1	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	1	no	—
547	C₂×D₄	—	4	1	no	—
548	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	4	1	no	—
551	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
552	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
553	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
555	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
556	C₄⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	C₃×C₅×D₄	1	8	yes	complemented
565	C₄²	—	2	2	no	—
566	C₃×C₅	#2669	1	1	yes	characteristic, direct product factor, Hall
567	C₂²×C₃	—	2	2	no	—
568	C₂²×C₃	—	2	2	no	—
569	C₂²×C₃	—	2	4	no	—
570	C₂²×C₃	—	2	4	no	—
571	C₂²×C₃	—	2	4	no	—
572	C₂²×C₃	—	2	4	no	—
573	C₂²×C₃	—	2	4	no	—
574	C₂²×C₃	—	4	16	no	—
575	C₂²×C₃	—	4	2	no	—
576	C₂²×C₃	—	4	2	no	—
577	C₂²×C₃	—	4	2	no	—
578	C₂²×C₃	—	4	2	no	—
579	C₂²×C₃	—	4	1	no	—
580	C₂²×C₃	—	4	1	no	—
581	C₂²×C₃	—	4	2	no	—
582	C₂²×C₃	—	4	1	no	—
583	C₂²×C₃	—	4	1	no	—
584	C₂²×C₃	—	4	2	no	—
585	C₂²×C₃	—	4	2	no	—
586	C₂²×C₃	—	4	2	no	—
587	C₂²×C₃	—	4	2	no	—
588	C₂²×C₃	—	4	2	no	—
589	C₂²×C₃	—	4	2	no	—
590	C₂²×C₃	—	4	2	no	—
591	C₂²×C₃	—	4	2	no	—
592	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
593	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
594	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
597	C₃×C₄	—	2	2	no	—
598	C₃×C₄	—	2	4	no	—
599	C₃×C₄	—	2	4	no	—
600	C₃×C₄	—	4	2	no	—
601	C₃×C₄	—	4	2	no	—
602	C₂×C₅	—	4	2	no	—
603	C₂×C₅	—	4	4	no	—
604	C₂×C₅	—	4	2	no	—
605	C₂×C₅	—	8	2	no	—
606	C₂×C₅	C₃×#534	1	1	yes	characteristic
607	C₂×C₅	C₃×#535	1	2	yes	—
608	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
609	C₂×C₅	C₃×D₄²	1	2	yes	—
610	C₂×C₅	C₃×#560	1	1	yes	characteristic
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	4	4	no	—
633	C₂³	—	4	8	no	—
634	C₂³	—	4	4	no	—
635	C₂³	—	4	8	no	—
636	C₂³	—	4	4	no	—
637	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
638	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
639	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
640	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
641	D₄	—	4	4	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	8	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	8	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
662	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
663	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
664	C₂×C₃	—	4	2	no	—
665	C₂×C₃	—	4	4	no	—
666	C₂×C₃	—	4	2	no	—
667	C₂×C₃	—	8	2	no	—
668	C₂×C₃	C₅×#534	1	1	yes	characteristic
669	C₂×C₃	C₅×#535	1	2	yes	—
670	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
671	C₂×C₃	C₅×D₄²	1	2	yes	—
672	C₂×C₃	C₅×#560	1	1	yes	characteristic
673	C₅	C₃×#2669	1	1	yes	characteristic, direct product factor, Sylow
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	4	16	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
700	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
701	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	4	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₃	C₅×#2669	1	1	yes	characteristic, direct product factor, Sylow
710	C₂	—	4	2	no	—
711	C₂	—	4	4	no	—
712	C₂	—	4	2	no	—
713	C₂	—	8	2	no	—
714	C₂	C₃×C₅×#534	1	1	yes	characteristic
715	C₂	C₃×C₅×#535	1	2	yes	—
716	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
717	C₂	C₃×C₅×D₄²	1	2	yes	—
718	C₂	C₃×C₅×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#127	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₃×C₅×#120	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#392	C₂	semidirect
8. C₃×C₅×#388	C₂	semidirect
9. C₃×C₅×#386	C₂	semidirect
10. C₅×#2669	C₃	direct (N × H)
17. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
19. C₂³×C₃×C₄×C₅	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
32. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₂×C₃×C₄²×C₅	C₂²	semidirect
34. C₃×C₅×#95	C₂²	semidirect
35. C₃×C₅×#95	C₂²	semidirect
36. C₃×#2669	C₅	direct (N × H)
37. C₂×C₅×#127	C₂×C₃	semidirect
38. C₂×C₅×#121	C₂×C₃	semidirect
39. C₂×C₅×#120	C₂×C₃	semidirect
40. C₂×C₅×#120	C₂×C₃	semidirect
41. C₅×#394	C₂×C₃	semidirect
42. C₅×#392	C₂×C₃	semidirect
43. C₅×#392	C₂×C₃	semidirect
44. C₅×#388	C₂×C₃	semidirect
45. C₅×#386	C₂×C₃	semidirect
75. C₂×C₃×C₅×D₄	D₄	semidirect
91. C₃×C₅×C₂²⋊C₄	D₄	semidirect
93. C₂×C₃×#127	C₂×C₅	semidirect
94. C₂×C₃×#121	C₂×C₅	semidirect
95. C₂×C₃×#120	C₂×C₅	semidirect
96. C₂×C₃×#120	C₂×C₅	semidirect
97. C₃×#394	C₂×C₅	semidirect
98. C₃×#392	C₂×C₅	semidirect
99. C₃×#392	C₂×C₅	semidirect
100. C₃×#388	C₂×C₅	semidirect
101. C₃×#386	C₂×C₅	semidirect
108. C₂²×C₅×D₄	C₂²×C₃	semidirect
109. C₂²×C₅×D₄	C₂²×C₃	semidirect
110. C₂³×C₄×C₅	C₂²×C₃	semidirect
115. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
121. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
122. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
123. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
124. C₂×C₄²×C₅	C₂²×C₃	semidirect
125. C₅×#95	C₂²×C₃	semidirect
126. C₅×#95	C₂²×C₃	semidirect
127. #2669	C₃×C₅	direct (N × H)
187. C₂²×C₃×D₄	C₂²×C₅	semidirect
188. C₂²×C₃×D₄	C₂²×C₅	semidirect
189. C₂³×C₃×C₄	C₂²×C₅	semidirect
194. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
200. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
201. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
202. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
203. C₂×C₃×C₄²	C₂²×C₅	semidirect
204. C₃×#95	C₂²×C₅	semidirect
205. C₃×#95	C₂²×C₅	semidirect
235. C₂×C₅×D₄	C₃×D₄	semidirect
251. C₅×C₂²⋊C₄	C₃×D₄	semidirect
253. C₂×#127	C₂×C₃×C₅	semidirect
254. C₂×#121	C₂×C₃×C₅	semidirect
255. C₂×#120	C₂×C₃×C₅	semidirect
256. C₂×#120	C₂×C₃×C₅	semidirect
257. #394	C₂×C₃×C₅	semidirect
258. #392	C₂×C₃×C₅	semidirect
259. #392	C₂×C₃×C₅	semidirect
260. #388	C₂×C₃×C₅	semidirect
261. #386	C₂×C₃×C₅	semidirect
326. C₂×C₃×D₄	C₅×D₄	semidirect
342. C₃×C₂²⋊C₄	C₅×D₄	semidirect
403. C₂²×D₄	C₂²×C₃×C₅	semidirect
404. C₂²×D₄	C₂²×C₃×C₅	semidirect
405. C₂³×C₄	C₂²×C₃×C₅	semidirect
410. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
416. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
417. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
418. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
419. C₂×C₄²	C₂²×C₃×C₅	semidirect
420. #95	C₂²×C₃×C₅	semidirect
421. #95	C₂²×C₃×C₅	semidirect
548. C₂×D₄	C₃×C₅×D₄	semidirect
564. C₂²⋊C₄	C₃×C₅×D₄	semidirect
566. C₃×C₅	#2669	direct (N × H)
673. C₅	C₃×#2669	direct (N × H)
709. C₃	C₅×#2669	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₅×#2669	3
C₃×#2669	5

Subgroups — C3×C5×#2669 #14275703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2669 #14275703