Subgroups — C₂×C₃×#67×C₅⋊D₅ #72231421

Order 7200.

4312 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#10597114	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#10597159	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#10597115	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅²×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×D₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×Dic₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#67×C₅⋊D₅	C₂	1	8	yes	maximal, direct product factor
8	C₂×#67×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×D₄×C₅⋊D₅	—	3	1	no	maximal
10	C₂³×C₃²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₃²×C₅²	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₃²×C₅⋊D₅	—	2	4	no	—
13	C₂²×C₃²×C₅⋊D₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×C₅⋊D₅	C₂²	1	4	yes	complemented
15	C₂²×C₃²×C₅⋊D₅	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅²×D₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₃⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×D₃×C₅⋊D₅	—	2	4	no	—
19	C₂×C₃×D₃×C₅⋊D₅	C₂²	1	4	yes	complemented
20	C₃×#10597159	C₂²	1	4	yes	complemented
21	C₂×C₃×C₃⋊#1039	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅²×#67	C₂²	1	4	yes	complemented
23	C₂×C₃×C₅²×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₃×#10597115	C₂²	1	4	yes	complemented
25	C₃×#10597114	C₂²	1	4	yes	complemented
26	C₃×Dic₃×C₅⋊D₅	C₂²	1	4	yes	complemented
27	C₂×C₃×D₅×#67	—	5	6	no	maximal
28	C₂³×C₃×C₅⋊D₅	—	2	1	no	—
29	C₂³×C₃×C₅⋊D₅	—	3	1	no	—
30	C₂³×C₃×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
31	C₂³×C₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×D₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₃×C₅²×D₄	—	3	1	no	—
34	C₂×#10597159	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₅²×#67	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₂²⋊(C₅⋊D₅)	—	3	1	no	—
37	C₂×C₃×C₂²⋊(C₅⋊D₅)	—	3	1	no	—
38	C₃×D₄×C₅⋊D₅	—	3	8	no	—
39	C₂×C₃×C₄⋊(C₅⋊D₅)	—	3	1	no	—
40	C₂×C₃×C₄×C₅⋊D₅	—	3	1	no	—
41	#67×C₅⋊D₅	C₂×C₃	1	8	yes	direct product factor
42	C₂×#10597115	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#10597114	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×Dic₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×C₃²×C₅²	—	2	2	no	—
46	C₂²×C₃²×C₅²	C₂³	1	1	yes	characteristic
47	C₂²×C₃²×C₅²	C₂³	1	2	yes	complemented
48	C₂×C₃×C₃⋊(C₅⋊D₅)	—	2	2	no	—
49	C₂×C₃×C₃⋊(C₅⋊D₅)	C₂³	1	2	yes	complemented
50	C₂×C₃×C₅²×D₃	—	2	2	no	—
51	C₂×C₃×C₅²×D₃	C₂³	1	2	yes	complemented
52	C₂×C₃²×C₅⋊D₅	—	2	2	no	—
53	C₂×C₃²×C₅⋊D₅	—	2	8	no	—
54	C₂×C₃²×C₅⋊D₅	D₄	1	4	yes	complemented
55	C₂×C₃²×C₅⋊D₅	C₂³	1	2	yes	—
56	C₂×C₃²×C₅⋊D₅	C₂³	1	2	yes	complemented
57	C₃×D₃×C₅⋊D₅	—	2	8	no	—
58	C₃×C₃⋊#1039	C₂³	1	2	yes	complemented
59	C₃×C₅²×Dic₃	C₂³	1	2	yes	complemented
60	C₂×D₄×C₅⋊D₅	—	3	1	no	Hall
61	C₂³×C₃²×D₅	—	5	6	no	—
62	C₂²×C₃×D₃×D₅	—	5	6	no	—
63	C₂×C₃×#1220	—	5	6	no	—
64	C₂×C₃×C₅×#67	D₅	1	6	yes	complemented
65	C₃×D₅×#67	—	5	48	no	—
66	C₂×C₃×#1202	—	5	6	no	—
67	C₂×C₃×#1201	—	5	6	no	—
68	C₂×C₃×D₅×Dic₃	—	5	6	no	—
69	C₂³×C₃×C₅²	—	2	1	no	—
70	C₂³×C₃×C₅²	—	3	1	no	—
71	C₂³×C₃×C₅²	C₂×D₃	1	1	yes	characteristic, complemented
72	C₂³×C₃×C₅²	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂²×C₃⋊(C₅⋊D₅)	C₂²×C₃	1	1	yes	characteristic, complemented
74	C₂²×C₅²×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
75	C₂²×C₃×C₅⋊D₅	—	2	4	no	—
76	C₂²×C₃×C₅⋊D₅	—	2	4	no	—
77	C₂²×C₃×C₅⋊D₅	—	2	4	no	—
78	C₂²×C₃×C₅⋊D₅	—	2	4	no	—
79	C₂²×C₃×C₅⋊D₅	—	2	1	no	—
80	C₂²×C₃×C₅⋊D₅	—	2	4	no	—
81	C₂²×C₃×C₅⋊D₅	—	2	1	no	—
82	C₂²×C₃×C₅⋊D₅	—	3	1	no	—
83	C₂²×C₃×C₅⋊D₅	—	3	4	no	—
84	C₂²×C₃×C₅⋊D₅	—	6	4	no	—
85	C₂²×C₃×C₅⋊D₅	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₃×C₅⋊D₅	C₂×D₃	1	4	yes	complemented
87	C₂²×C₃×C₅⋊D₅	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂²×C₃×C₅⋊D₅	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃×C₅⋊D₅	C₂²×C₃	1	4	yes	complemented
90	C₂²×C₃×C₅⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₂×D₃×C₅⋊D₅	—	2	4	no	—
92	C₂×D₃×C₅⋊D₅	C₂²×C₃	1	4	yes	complemented
93	C₃×C₅²×D₄	—	3	4	no	—
94	C₂×C₃×C₄×C₅²	—	3	1	no	—
95	#10597159	C₂²×C₃	1	4	yes	complemented
96	C₂×C₃⋊#1039	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₅²×#67	C₂²×C₃	1	4	yes	complemented
98	C₂×C₅²×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₃×C₂²⋊(C₅⋊D₅)	—	3	4	no	—
100	C₃×C₂²⋊(C₅⋊D₅)	—	3	4	no	—
101	C₂×C₃×#1039	—	3	1	no	—
102	C₃×C₄⋊(C₅⋊D₅)	—	3	4	no	—
103	C₃×C₄×C₅⋊D₅	—	3	4	no	—
104	#10597115	C₂²×C₃	1	4	yes	complemented
105	#10597114	C₂²×C₃	1	4	yes	complemented
106	Dic₃×C₅⋊D₅	C₂²×C₃	1	4	yes	complemented
107	C₂×C₃×D₄×D₅	—	15	6	no	—
108	C₂×D₅×#67	—	5	6	no	—
109	C₂×C₃²×C₅²	—	2	2	no	—
110	C₂×C₃²×C₅²	C₂×D₄	1	2	yes	complemented
111	C₂×C₃²×C₅²	C₂⁴	1	1	yes	characteristic
112	C₃×C₃⋊(C₅⋊D₅)	—	2	2	no	—
113	C₃×C₅²×D₃	—	2	2	no	—
114	C₃²×C₅⋊D₅	—	2	2	no	—
115	C₃²×C₅⋊D₅	C₂×D₄	1	4	yes	complemented
116	C₂³×C₅⋊D₅	—	3	1	no	—
117	C₂³×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic, complemented
118	C₂×C₅²×D₄	—	3	1	no	—
119	C₂×C₂²⋊(C₅⋊D₅)	—	3	1	no	—
120	C₂×C₂²⋊(C₅⋊D₅)	—	3	1	no	—
121	D₄×C₅⋊D₅	—	3	8	no	—
122	C₂×C₄⋊(C₅⋊D₅)	—	3	1	no	—
123	C₂×C₄×C₅⋊D₅	—	3	1	no	—
124	C₂³×C₃²×C₅	C₂×D₅	1	6	yes	complemented
125	C₂²×C₃×D₁₅	—	5	6	no	—
126	C₂²×C₃×C₅×D₃	C₂×D₅	1	6	yes	complemented
127	C₂²×C₃²×D₅	—	5	6	no	—
128	C₂²×C₃²×D₅	—	5	6	no	—
129	C₂²×C₃²×D₅	—	5	24	no	—
130	C₂²×C₃²×D₅	—	10	24	no	—
131	C₂×C₃×D₃×D₅	—	5	24	no	—
132	C₂×C₃×D₃×D₅	—	10	24	no	—
133	C₃×#1220	—	5	24	no	—
134	C₂×C₃×Dic₁₅	—	5	6	no	—
135	C₃×C₅×#67	C₂×D₅	1	24	yes	complemented
136	C₂×C₃×C₅×Dic₃	C₂×D₅	1	6	yes	complemented
137	C₃×#1202	—	5	24	no	—
138	C₃×#1201	—	5	24	no	—
139	C₃×D₅×Dic₃	—	5	24	no	—
140	C₂²×C₃×C₅²	—	2	2	no	—
141	C₂²×C₃×C₅²	—	2	2	no	—
142	C₂²×C₃×C₅²	—	2	2	no	—
143	C₂²×C₃×C₅²	—	2	2	no	—
144	C₂²×C₃×C₅²	—	2	1	no	—
145	C₂²×C₃×C₅²	—	2	2	no	—
146	C₂²×C₃×C₅²	—	3	2	no	—
147	C₂²×C₃×C₅²	—	6	2	no	—
148	C₂²×C₃×C₅²	C₂²×D₃	1	1	yes	characteristic
149	C₂²×C₃×C₅²	C₂²×D₃	1	2	yes	complemented
150	C₂²×C₃×C₅²	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₃×C₅²	C₂³×C₃	1	2	yes	complemented
152	C₂×C₃⋊(C₅⋊D₅)	—	2	2	no	—
153	C₂×C₃⋊(C₅⋊D₅)	C₂³×C₃	1	2	yes	complemented
154	C₂×C₅²×D₃	—	2	2	no	—
155	C₂×C₅²×D₃	C₂³×C₃	1	2	yes	complemented
156	C₂×C₃×C₅⋊D₅	—	2	2	no	—
157	C₂×C₃×C₅⋊D₅	—	2	8	no	—
158	C₂×C₃×C₅⋊D₅	—	2	2	no	—
159	C₂×C₃×C₅⋊D₅	—	2	8	no	—
160	C₂×C₃×C₅⋊D₅	—	2	2	no	—
161	C₂×C₃×C₅⋊D₅	—	2	2	no	—
162	C₂×C₃×C₅⋊D₅	—	2	8	no	—
163	C₂×C₃×C₅⋊D₅	—	2	8	no	—
164	C₂×C₃×C₅⋊D₅	—	2	4	no	—
165	C₂×C₃×C₅⋊D₅	—	2	2	no	—
166	C₂×C₃×C₅⋊D₅	—	2	2	no	—
167	C₂×C₃×C₅⋊D₅	—	3	2	no	—
168	C₂×C₃×C₅⋊D₅	—	6	2	no	—
169	C₂×C₃×C₅⋊D₅	—	6	8	no	—
170	C₂×C₃×C₅⋊D₅	#67	1	4	yes	direct product factor
171	C₂×C₃×C₅⋊D₅	C₃×D₄	1	4	yes	complemented
172	C₂×C₃×C₅⋊D₅	C₂²×D₃	1	2	yes	—
173	C₂×C₃×C₅⋊D₅	C₂²×D₃	1	2	yes	complemented
174	C₂×C₃×C₅⋊D₅	C₂³×C₃	1	2	yes	—
175	C₂×C₃×C₅⋊D₅	C₂³×C₃	1	2	yes	complemented
176	D₃×C₅⋊D₅	—	2	8	no	—
177	C₃×C₄×C₅²	—	3	2	no	—
178	C₃⋊#1039	C₂³×C₃	1	2	yes	complemented
179	C₅²×Dic₃	C₂³×C₃	1	2	yes	complemented
180	C₃×#1039	—	3	2	no	—
181	C₂²×C₃×#67	—	25	1	no	Hall
182	C₂³×C₃×D₅	—	5	6	no	—
183	C₂³×C₃×D₅	—	5	6	no	—
184	C₂³×C₃×D₅	—	10	6	no	—
185	C₂³×C₃×D₅	—	15	6	no	—
186	C₂²×D₃×D₅	—	5	6	no	—
187	C₂×C₃×C₅×D₄	—	3	6	no	—
188	C₂×#1220	—	5	6	no	—
189	C₂×C₅×#67	C₃×D₅	1	6	yes	complemented
190	C₂×C₃×C₂²⋊D₅	—	15	6	no	—
191	C₂×C₃×C₂²⋊D₅	—	15	6	no	—
192	C₃×D₄×D₅	—	15	48	no	—
193	C₂×C₃×D₂₀	—	15	6	no	—
194	C₂×C₃×C₄×D₅	—	15	6	no	—
195	D₅×#67	—	5	48	no	—
196	C₂×#1202	—	5	6	no	—
197	C₂×#1201	—	5	6	no	—
198	C₂×D₅×Dic₃	—	5	6	no	—
199	C₃²×C₅²	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
200	C₂³×C₅²	—	3	1	no	—
201	C₂³×C₅²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
202	C₂²×C₅⋊D₅	—	2	4	no	—
203	C₂²×C₅⋊D₅	—	3	1	no	—
204	C₂²×C₅⋊D₅	—	3	4	no	—
205	C₂²×C₅⋊D₅	—	6	4	no	—
206	C₂²×C₅⋊D₅	C₂×C₃×D₃	1	1	yes	characteristic
207	C₂²×C₅⋊D₅	C₂×C₃×D₃	1	4	yes	complemented
208	C₂²×C₅⋊D₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented
209	C₅²×D₄	—	3	4	no	—
210	C₂×C₄×C₅²	—	3	1	no	—
211	C₂²⋊(C₅⋊D₅)	—	3	4	no	—
212	C₂²⋊(C₅⋊D₅)	—	3	4	no	—
213	C₂×#1039	—	3	1	no	—
214	C₄⋊(C₅⋊D₅)	—	3	4	no	—
215	C₄×C₅⋊D₅	—	3	4	no	—
216	C₂²×C₃²×C₅	—	2	12	no	—
217	C₂²×C₃²×C₅	C₂²×D₅	1	6	yes	—
218	C₂²×C₃²×C₅	C₂²×D₅	1	12	yes	complemented
219	C₂×C₃×D₁₅	—	5	12	no	—
220	C₂×C₃×D₁₅	—	10	12	no	—
221	C₂×C₃×C₅×D₃	—	2	12	no	—
222	C₂×C₃×C₅×D₃	C₂²×D₅	1	12	yes	complemented
223	C₂×C₃²×D₅	—	5	24	no	—
224	C₂×C₃²×D₅	—	5	12	no	—
225	C₂×C₃²×D₅	—	5	12	no	—
226	C₂×C₃²×D₅	—	10	48	no	—
227	C₂×C₃²×D₅	—	10	12	no	—
228	C₃×D₃×D₅	—	10	48	no	—
229	C₃×Dic₁₅	—	5	12	no	—
230	C₃×C₅×Dic₃	C₂²×D₅	1	12	yes	complemented
231	C₂×D₄×D₅	—	15	6	no	—
232	C₂×C₃×C₅²	—	2	2	no	—
233	C₂×C₃×C₅²	—	2	2	no	—
234	C₂×C₃×C₅²	—	2	2	no	—
235	C₂×C₃×C₅²	—	2	2	no	—
236	C₂×C₃×C₅²	—	2	1	no	—
237	C₂×C₃×C₅²	—	2	2	no	—
238	C₂×C₃×C₅²	—	6	2	no	—
239	C₂×C₃×C₅²	C₂×#67	1	2	yes	complemented
240	C₂×C₃×C₅²	C₂×C₃×D₄	1	2	yes	complemented
241	C₂×C₃×C₅²	C₂³×D₃	1	1	yes	characteristic
242	C₂×C₃×C₅²	C₂⁴×C₃	1	1	yes	characteristic
243	C₃⋊(C₅⋊D₅)	—	2	2	no	—
244	C₅²×D₃	—	2	2	no	—
245	C₃×C₅⋊D₅	—	2	2	no	—
246	C₃×C₅⋊D₅	—	2	2	no	—
247	C₃×C₅⋊D₅	—	2	2	no	—
248	C₃×C₅⋊D₅	—	2	2	no	—
249	C₃×C₅⋊D₅	—	2	4	no	—
250	C₃×C₅⋊D₅	—	6	2	no	—
251	C₃×C₅⋊D₅	C₂×#67	1	4	yes	direct product factor
252	C₃×C₅⋊D₅	C₂×C₃×D₄	1	4	yes	complemented
253	C₂⁴×C₃²	—	25	1	no	—
254	C₂³×C₃×D₃	—	25	1	no	—
255	C₂×C₃×#67	—	25	1	no	—
256	C₂×C₃×#67	—	25	1	no	—
257	C₂×C₃×#67	—	25	8	no	—
258	C₂×C₃×#67	—	25	1	no	—
259	C₂×C₃×#67	C₅⋊D₅	1	1	yes	characteristic, direct product factor
260	C₂²×C₃×Dic₃	—	25	1	no	—
261	C₂³×C₃×C₅	—	2	6	no	—
262	C₂³×C₃×C₅	—	3	6	no	—
263	C₂³×C₃×C₅	D₃×D₅	1	6	yes	complemented
264	C₂³×C₃×C₅	C₂×C₃×D₅	1	6	yes	complemented
265	C₂²×D₁₅	—	5	6	no	—
266	C₂²×C₅×D₃	C₂×C₃×D₅	1	6	yes	complemented
267	C₂²×C₃×D₅	—	5	6	no	—
268	C₂²×C₃×D₅	—	5	6	no	—
269	C₂²×C₃×D₅	—	5	6	no	—
270	C₂²×C₃×D₅	—	5	24	no	—
271	C₂²×C₃×D₅	—	5	6	no	—
272	C₂²×C₃×D₅	—	5	24	no	—
273	C₂²×C₃×D₅	—	10	24	no	—
274	C₂²×C₃×D₅	—	10	24	no	—
275	C₂²×C₃×D₅	—	10	6	no	—
276	C₂²×C₃×D₅	—	10	24	no	—
277	C₂²×C₃×D₅	—	10	24	no	—
278	C₂²×C₃×D₅	—	10	24	no	—
279	C₂²×C₃×D₅	—	10	6	no	—
280	C₂²×C₃×D₅	—	15	24	no	—
281	C₂²×C₃×D₅	—	15	6	no	—
282	C₂²×C₃×D₅	—	30	24	no	—
283	C₂×D₃×D₅	—	5	24	no	—
284	C₂×D₃×D₅	—	10	24	no	—
285	C₃×C₅×D₄	—	3	24	no	—
286	C₂×C₃×C₄×C₅	—	3	6	no	—
287	#1220	—	5	24	no	—
288	C₂×Dic₁₅	—	5	6	no	—
289	C₅×#67	C₂×C₃×D₅	1	24	yes	complemented
290	C₂×C₅×Dic₃	C₂×C₃×D₅	1	6	yes	complemented
291	C₃×C₂²⋊D₅	—	15	24	no	—
292	C₃×C₂²⋊D₅	—	15	24	no	—
293	C₂×C₃×Dic₅	—	15	6	no	—
294	C₃×D₂₀	—	15	24	no	—
295	C₃×C₄×D₅	—	15	24	no	—
296	#1202	—	5	24	no	—
297	#1201	—	5	24	no	—
298	D₅×Dic₃	—	5	24	no	—
299	C₂²×C₅²	—	2	2	no	—
300	C₂²×C₅²	—	3	2	no	—
301	C₂²×C₅²	—	6	2	no	—
302	C₂²×C₅²	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₂²×C₅²	C₂²×C₃×D₃	1	2	yes	complemented
304	C₂×C₅⋊D₅	—	2	2	no	—
305	C₂×C₅⋊D₅	—	2	8	no	—
306	C₂×C₅⋊D₅	—	3	2	no	—
307	C₂×C₅⋊D₅	—	6	2	no	—
308	C₂×C₅⋊D₅	—	6	8	no	—
309	C₂×C₅⋊D₅	C₃×#67	1	4	yes	direct product factor
310	C₂×C₅⋊D₅	C₂²×C₃×D₃	1	2	yes	—
311	C₂×C₅⋊D₅	C₂²×C₃×D₃	1	2	yes	complemented
312	C₄×C₅²	—	3	2	no	—
313	#1039	—	3	2	no	—
314	C₂²×C₃×D₄	—	75	1	no	—
315	C₂²×#67	—	25	1	no	—
316	C₂×C₃²×C₅	—	2	12	no	—
317	C₂×C₃²×C₅	D₄×D₅	1	12	yes	complemented
318	C₂×C₃²×C₅	C₂³×D₅	1	6	yes	—
319	C₃×D₁₅	—	10	12	no	—
320	C₃×C₅×D₃	—	2	12	no	—
321	C₃²×D₅	—	5	24	no	—
322	C₃²×D₅	—	10	12	no	—
323	C₂³×D₅	—	5	6	no	—
324	C₂³×D₅	—	15	6	no	—
325	C₂×C₅×D₄	—	3	6	no	—
326	C₂×C₂²⋊D₅	—	15	6	no	—
327	C₂×C₂²⋊D₅	—	15	6	no	—
328	D₄×D₅	—	15	48	no	—
329	C₂×D₂₀	—	15	6	no	—
330	C₂×C₄×D₅	—	15	6	no	—
331	C₃×C₅²	—	2	1	no	—
332	C₃×C₅²	C₂²×#67	1	1	yes	characteristic, complemented
333	C₃×C₅²	C₂²×C₃×D₄	1	1	yes	characteristic, complemented
334	C₂³×C₃²	—	25	1	no	—
335	C₂³×C₃²	—	25	1	no	—
336	C₂³×C₃²	—	25	4	no	—
337	C₂³×C₃²	—	50	4	no	—
338	C₂³×C₃²	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented
339	C₂²×C₃×D₃	—	25	1	no	—
340	C₂²×C₃×D₃	—	25	4	no	—
341	C₂²×C₃×D₃	—	50	4	no	—
342	C₂²×C₃×D₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented
343	C₃×#67	—	25	4	no	—
344	C₃×#67	—	25	4	no	—
345	C₃×#67	—	25	4	no	—
346	C₃×#67	C₂×C₅⋊D₅	1	4	yes	direct product factor
347	C₂×C₃×Dic₃	—	25	1	no	—
348	C₂×C₃×Dic₃	—	25	4	no	—
349	C₂×C₃×Dic₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented
350	C₂²×C₃×C₅	—	2	12	no	—
351	C₂²×C₃×C₅	—	2	12	no	—
352	C₂²×C₃×C₅	—	2	12	no	—
353	C₂²×C₃×C₅	—	2	12	no	—
354	C₂²×C₃×C₅	—	2	6	no	—
355	C₂²×C₃×C₅	—	2	12	no	—
356	C₂²×C₃×C₅	—	3	12	no	—
357	C₂²×C₃×C₅	—	6	12	no	—
358	C₂²×C₃×C₅	C₂×D₃×D₅	1	6	yes	—
359	C₂²×C₃×C₅	C₂×D₃×D₅	1	12	yes	complemented
360	C₂²×C₃×C₅	C₂²×C₃×D₅	1	6	yes	—
361	C₂²×C₃×C₅	C₂²×C₃×D₅	1	12	yes	complemented
362	C₂×D₁₅	—	5	12	no	—
363	C₂×D₁₅	—	10	12	no	—
364	C₂×C₅×D₃	—	2	12	no	—
365	C₂×C₅×D₃	C₂²×C₃×D₅	1	12	yes	complemented
366	C₂×C₃×D₅	—	5	24	no	—
367	C₂×C₃×D₅	—	5	24	no	—
368	C₂×C₃×D₅	—	5	12	no	—
369	C₂×C₃×D₅	—	5	12	no	—
370	C₂×C₃×D₅	—	5	12	no	—
371	C₂×C₃×D₅	—	5	12	no	—
372	C₂×C₃×D₅	—	10	12	no	—
373	C₂×C₃×D₅	—	10	24	no	—
374	C₂×C₃×D₅	—	10	12	no	—
375	C₂×C₃×D₅	—	10	48	no	—
376	C₂×C₃×D₅	—	10	48	no	—
377	C₂×C₃×D₅	—	10	48	no	—
378	C₂×C₃×D₅	—	10	12	no	—
379	C₂×C₃×D₅	—	10	48	no	—
380	C₂×C₃×D₅	—	10	12	no	—
381	C₂×C₃×D₅	—	10	12	no	—
382	C₂×C₃×D₅	—	10	12	no	—
383	C₂×C₃×D₅	—	15	12	no	—
384	C₂×C₃×D₅	—	30	48	no	—
385	C₂×C₃×D₅	—	30	12	no	—
386	D₃×D₅	—	10	48	no	—
387	C₃×C₄×C₅	—	3	12	no	—
388	Dic₁₅	—	5	12	no	—
389	C₃×Dic₅	—	15	12	no	—
390	C₅×Dic₃	C₂²×C₃×D₅	1	12	yes	complemented
391	C₂×C₅²	—	2	2	no	—
392	C₂×C₅²	—	6	2	no	—
393	C₂×C₅²	C₂×C₃×#67	1	2	yes	complemented
394	C₂×C₅²	C₂³×C₃×D₃	1	1	yes	characteristic
395	C₅⋊D₅	—	2	2	no	—
396	C₅⋊D₅	—	6	2	no	—
397	C₅⋊D₅	C₂×C₃×#67	1	4	yes	direct product factor
398	C₂⁴×C₃	—	25	1	no	—
399	C₂⁴×C₃	—	25	1	no	—
400	C₂⁴×C₃	—	50	1	no	—
401	C₂⁴×C₃	—	75	1	no	—
402	C₂³×D₃	—	25	1	no	—
403	C₂×C₃×D₄	—	3	1	no	—
404	C₂×C₃×D₄	—	75	1	no	—
405	C₂×C₃×D₄	—	75	8	no	—
406	C₂×C₃×D₄	—	75	1	no	—
407	C₂×C₃×D₄	—	75	1	no	—
408	C₂²×C₃×C₄	—	75	1	no	—
409	C₂×#67	—	25	1	no	—
410	C₂×#67	—	25	1	no	—
411	C₂×#67	—	25	8	no	—
412	C₂×#67	—	25	1	no	—
413	C₂×#67	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
414	C₂²×Dic₃	—	25	1	no	—
415	C₃²×C₅	C₂×D₄×D₅	1	6	yes	complemented
416	C₂³×C₅	—	3	6	no	—
417	C₂³×C₅	C₃×D₃×D₅	1	6	yes	complemented
418	C₂²×D₅	—	5	6	no	—
419	C₂²×D₅	—	5	6	no	—
420	C₂²×D₅	—	5	24	no	—
421	C₂²×D₅	—	10	24	no	—
422	C₂²×D₅	—	15	24	no	—
423	C₂²×D₅	—	15	6	no	—
424	C₂²×D₅	—	30	24	no	—
425	C₅×D₄	—	3	24	no	—
426	C₂×C₄×C₅	—	3	6	no	—
427	C₂²⋊D₅	—	15	24	no	—
428	C₂²⋊D₅	—	15	24	no	—
429	C₂×Dic₅	—	15	6	no	—
430	D₂₀	—	15	24	no	—
431	C₄×D₅	—	15	24	no	—
432	C₂²×C₃²	—	2	2	no	—
433	C₂²×C₃²	—	25	4	no	—
434	C₂²×C₃²	—	25	2	no	—
435	C₂²×C₃²	—	25	2	no	—
436	C₂²×C₃²	—	50	8	no	—
437	C₂²×C₃²	—	50	2	no	—
438	C₂²×C₃²	C₂²×C₅⋊D₅	1	1	yes	characteristic
439	C₂²×C₃²	C₂²×C₅⋊D₅	1	2	yes	complemented
440	C₂×C₃×D₃	—	2	2	no	—
441	C₂×C₃×D₃	—	25	2	no	—
442	C₂×C₃×D₃	—	50	8	no	—
443	C₂×C₃×D₃	—	50	2	no	—
444	C₂×C₃×D₃	C₂²×C₅⋊D₅	1	2	yes	complemented
445	C₃×Dic₃	—	25	2	no	—
446	C₃×Dic₃	C₂²×C₅⋊D₅	1	2	yes	complemented
447	C₂²×D₄	—	75	1	no	Sylow
448	C₂×C₃×C₅	—	2	12	no	—
449	C₂×C₃×C₅	—	2	12	no	—
450	C₂×C₃×C₅	—	2	12	no	—
451	C₂×C₃×C₅	—	2	12	no	—
452	C₂×C₃×C₅	—	2	6	no	—
453	C₂×C₃×C₅	—	2	12	no	—
454	C₂×C₃×C₅	—	6	12	no	—
455	C₂×C₃×C₅	D₅×#67	1	12	yes	complemented
456	C₂×C₃×C₅	C₃×D₄×D₅	1	12	yes	complemented
457	C₂×C₃×C₅	C₂²×D₃×D₅	1	6	yes	—
458	C₂×C₃×C₅	C₂³×C₃×D₅	1	6	yes	—
459	D₁₅	—	10	12	no	—
460	C₃×D₅	—	5	24	no	—
461	C₃×D₅	—	5	24	no	—
462	C₃×D₅	—	10	24	no	—
463	C₃×D₅	—	10	12	no	—
464	C₃×D₅	—	10	12	no	—
465	C₃×D₅	—	10	12	no	—
466	C₃×D₅	—	10	12	no	—
467	C₃×D₅	—	30	12	no	—
468	C₅×D₃	—	2	12	no	—
469	C₅²	C₂²×C₃×#67	1	1	yes	characteristic, complemented, Sylow
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	3	1	no	—
472	C₂³×C₃	—	25	1	no	—
473	C₂³×C₃	—	25	1	no	—
474	C₂³×C₃	—	25	1	no	—
475	C₂³×C₃	—	25	4	no	—
476	C₂³×C₃	—	25	1	no	—
477	C₂³×C₃	—	25	4	no	—
478	C₂³×C₃	—	50	1	no	—
479	C₂³×C₃	—	50	4	no	—
480	C₂³×C₃	—	50	1	no	—
481	C₂³×C₃	—	50	4	no	—
482	C₂³×C₃	—	50	4	no	—
483	C₂³×C₃	—	50	4	no	—
484	C₂³×C₃	—	50	4	no	—
485	C₂³×C₃	—	75	4	no	—
486	C₂³×C₃	—	75	1	no	—
487	C₂³×C₃	—	150	4	no	—
488	C₂³×C₃	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented
489	C₂³×C₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
490	C₂²×D₃	—	25	1	no	—
491	C₂²×D₃	—	25	4	no	—
492	C₂²×D₃	—	50	4	no	—
493	C₂²×D₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
494	C₃×D₄	—	3	4	no	—
495	C₃×D₄	—	75	4	no	—
496	C₃×D₄	—	75	4	no	—
497	C₃×D₄	—	75	4	no	—
498	C₂×C₃×C₄	—	3	1	no	—
499	C₂×C₃×C₄	—	75	4	no	—
500	C₂×C₃×C₄	—	75	1	no	—
501	#67	—	25	4	no	—
502	#67	—	25	4	no	—
503	#67	—	25	4	no	—
504	#67	C₂×C₃×C₅⋊D₅	1	4	yes	direct product factor
505	C₂×Dic₃	—	25	1	no	—
506	C₂×Dic₃	—	25	4	no	—
507	C₂×Dic₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
508	C₂²×C₅	—	2	12	no	—
509	C₂²×C₅	—	3	12	no	—
510	C₂²×C₅	—	6	12	no	—
511	C₂²×C₅	C₂×C₃×D₃×D₅	1	6	yes	—
512	C₂²×C₅	C₂×C₃×D₃×D₅	1	12	yes	complemented
513	C₂×D₅	—	5	12	no	—
514	C₂×D₅	—	5	24	no	—
515	C₂×D₅	—	5	12	no	—
516	C₂×D₅	—	10	48	no	—
517	C₂×D₅	—	10	12	no	—
518	C₂×D₅	—	15	12	no	—
519	C₂×D₅	—	30	48	no	—
520	C₂×D₅	—	30	12	no	—
521	C₄×C₅	—	3	12	no	—
522	Dic₅	—	15	12	no	—
523	C₂×C₃²	—	2	2	no	—
524	C₂×C₃²	—	25	4	no	—
525	C₂×C₃²	—	50	2	no	—
526	C₂×C₃²	D₄×C₅⋊D₅	1	2	yes	complemented
527	C₂×C₃²	C₂³×C₅⋊D₅	1	1	yes	characteristic
528	C₃×D₃	—	2	2	no	—
529	C₃×D₃	—	50	2	no	—
530	C₂⁴	—	25	1	no	—
531	C₂⁴	—	75	1	no	—
532	C₂×D₄	—	3	1	no	—
533	C₂×D₄	—	75	1	no	—
534	C₂×D₄	—	75	8	no	—
535	C₂×D₄	—	75	1	no	—
536	C₂×D₄	—	75	1	no	—
537	C₂²×C₄	—	75	1	no	—
538	C₃×C₅	—	2	6	no	—
539	C₃×C₅	C₂×D₅×#67	1	6	yes	complemented
540	C₃×C₅	C₂×C₃×D₄×D₅	1	6	yes	complemented
541	C₂²×C₃	—	2	2	no	—
542	C₂²×C₃	—	2	2	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	2	2	no	—
545	C₂²×C₃	—	2	1	no	—
546	C₂²×C₃	—	2	2	no	—
547	C₂²×C₃	—	3	2	no	—
548	C₂²×C₃	—	6	2	no	—
549	C₂²×C₃	—	25	2	no	—
550	C₂²×C₃	—	25	2	no	—
551	C₂²×C₃	—	25	4	no	—
552	C₂²×C₃	—	25	4	no	—
553	C₂²×C₃	—	25	2	no	—
554	C₂²×C₃	—	25	2	no	—
555	C₂²×C₃	—	50	2	no	—
556	C₂²×C₃	—	50	2	no	—
557	C₂²×C₃	—	50	4	no	—
558	C₂²×C₃	—	50	8	no	—
559	C₂²×C₃	—	50	8	no	—
560	C₂²×C₃	—	50	8	no	—
561	C₂²×C₃	—	50	2	no	—
562	C₂²×C₃	—	50	8	no	—
563	C₂²×C₃	—	50	2	no	—
564	C₂²×C₃	—	50	2	no	—
565	C₂²×C₃	—	50	2	no	—
566	C₂²×C₃	—	75	2	no	—
567	C₂²×C₃	—	150	8	no	—
568	C₂²×C₃	—	150	2	no	—
569	C₂²×C₃	C₂×D₃×C₅⋊D₅	1	1	yes	characteristic
570	C₂²×C₃	C₂×D₃×C₅⋊D₅	1	2	yes	complemented
571	C₂²×C₃	C₂²×C₃×C₅⋊D₅	1	1	yes	characteristic
572	C₂²×C₃	C₂²×C₃×C₅⋊D₅	1	2	yes	complemented
573	C₂×D₃	—	2	2	no	—
574	C₂×D₃	—	25	2	no	—
575	C₂×D₃	—	50	8	no	—
576	C₂×D₃	—	50	2	no	—
577	C₂×D₃	C₂²×C₃×C₅⋊D₅	1	2	yes	complemented
578	C₃×C₄	—	3	2	no	—
579	C₃×C₄	—	75	2	no	—
580	Dic₃	—	25	2	no	—
581	Dic₃	C₂²×C₃×C₅⋊D₅	1	2	yes	complemented
582	C₂×C₅	—	2	12	no	—
583	C₂×C₅	—	6	12	no	—
584	C₂×C₅	C₃×D₅×#67	1	12	yes	complemented
585	C₂×C₅	C₂²×C₃×D₃×D₅	1	6	yes	—
586	D₅	—	5	24	no	—
587	D₅	—	10	12	no	—
588	D₅	—	30	12	no	—
589	C₃²	C₂×D₄×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
590	C₂³	—	3	1	no	—
591	C₂³	—	25	1	no	—
592	C₂³	—	25	1	no	—
593	C₂³	—	25	4	no	—
594	C₂³	—	50	4	no	—
595	C₂³	—	75	4	no	—
596	C₂³	—	75	1	no	—
597	C₂³	—	150	4	no	—
598	C₂³	C₃×D₃×C₅⋊D₅	1	1	yes	characteristic, complemented
599	D₄	—	3	4	no	—
600	D₄	—	75	4	no	—
601	D₄	—	75	4	no	—
602	D₄	—	75	4	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	75	4	no	—
605	C₂×C₄	—	75	1	no	—
606	C₂×C₃	—	2	2	no	—
607	C₂×C₃	—	2	2	no	—
608	C₂×C₃	—	2	2	no	—
609	C₂×C₃	—	2	2	no	—
610	C₂×C₃	—	2	1	no	—
611	C₂×C₃	—	2	2	no	—
612	C₂×C₃	—	6	2	no	—
613	C₂×C₃	—	25	4	no	—
614	C₂×C₃	—	25	4	no	—
615	C₂×C₃	—	50	4	no	—
616	C₂×C₃	—	50	2	no	—
617	C₂×C₃	—	50	2	no	—
618	C₂×C₃	—	50	2	no	—
619	C₂×C₃	—	50	2	no	—
620	C₂×C₃	—	150	2	no	—
621	C₂×C₃	#67×C₅⋊D₅	1	2	yes	direct product factor
622	C₂×C₃	C₃×D₄×C₅⋊D₅	1	2	yes	complemented
623	C₂×C₃	C₂²×D₃×C₅⋊D₅	1	1	yes	characteristic
624	C₂×C₃	C₂³×C₃×C₅⋊D₅	1	1	yes	characteristic
625	D₃	—	2	2	no	—
626	D₃	—	50	2	no	—
627	C₅	C₂×C₃×D₅×#67	1	6	yes	complemented
628	C₂²	—	2	2	no	—
629	C₂²	—	3	2	no	—
630	C₂²	—	6	2	no	—
631	C₂²	—	25	2	no	—
632	C₂²	—	25	4	no	—
633	C₂²	—	25	2	no	—
634	C₂²	—	50	8	no	—
635	C₂²	—	50	2	no	—
636	C₂²	—	75	2	no	—
637	C₂²	—	150	8	no	—
638	C₂²	—	150	2	no	—
639	C₂²	C₂×C₃×D₃×C₅⋊D₅	1	1	yes	characteristic
640	C₂²	C₂×C₃×D₃×C₅⋊D₅	1	2	yes	complemented
641	C₄	—	3	2	no	—
642	C₄	—	75	2	no	—
643	C₃	—	2	1	no	—
644	C₃	C₂×C₃×D₄×C₅⋊D₅	1	1	yes	characteristic, complemented
645	C₃	C₂×#67×C₅⋊D₅	1	1	yes	characteristic, direct product factor
646	C₂	—	2	2	no	—
647	C₂	—	6	2	no	—
648	C₂	—	25	4	no	—
649	C₂	—	50	2	no	—
650	C₂	—	150	2	no	—
651	C₂	C₃×#67×C₅⋊D₅	1	2	yes	direct product factor
652	C₂	C₂²×C₃×D₃×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×C₅⋊D₅
commutator, cosocle	C₂×C₃×C₅²	C₂⁴×C₃
Frattini	C₂	C₂²×C₃×D₃×C₅⋊D₅
Fitting	C₂³×C₃²×C₅²	C₂²
socle	C₂²×C₃²×C₅²	C₂³
hypercenter	C₂³×C₃	D₃×C₅⋊D₅
hypocenter	C₃×C₅²	C₂²×C₃×D₄
LCS	G ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂³×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#10597114	C₂	semidirect
2. C₂×C₃×#10597159	C₂	semidirect
3. C₂×C₃×#10597115	C₂	semidirect
4. C₂×C₃×C₅²×#67	C₂	semidirect
5. C₂²×C₃×D₃×C₅⋊D₅	C₂	semidirect
6. C₂×C₃×Dic₃×C₅⋊D₅	C₂	semidirect
7. C₃×#67×C₅⋊D₅	C₂	direct (N × H)
8. C₂×#67×C₅⋊D₅	C₃	direct (N × H)
10. C₂³×C₃²×C₅⋊D₅	C₂	semidirect
11. C₂³×C₃²×C₅²	C₂²	semidirect
14. C₂²×C₃²×C₅⋊D₅	C₂²	semidirect
15. C₂²×C₃²×C₅⋊D₅	C₂²	semidirect
16. C₂²×C₃×C₅²×D₃	C₂²	semidirect
17. C₂²×C₃×C₃⋊(C₅⋊D₅)	C₂²	semidirect
19. C₂×C₃×D₃×C₅⋊D₅	C₂²	semidirect
20. C₃×#10597159	C₂²	semidirect
21. C₂×C₃×C₃⋊#1039	C₂²	semidirect
22. C₃×C₅²×#67	C₂²	semidirect
23. C₂×C₃×C₅²×Dic₃	C₂²	semidirect
24. C₃×#10597115	C₂²	semidirect
25. C₃×#10597114	C₂²	semidirect
26. C₃×Dic₃×C₅⋊D₅	C₂²	semidirect
30. C₂³×C₃×C₅⋊D₅	D₃	semidirect
31. C₂³×C₃×C₅⋊D₅	C₂×C₃	semidirect
32. C₂²×D₃×C₅⋊D₅	C₂×C₃	semidirect
34. C₂×#10597159	C₂×C₃	semidirect
35. C₂×C₅²×#67	C₂×C₃	semidirect
41. #67×C₅⋊D₅	C₂×C₃	direct (N × H)
42. C₂×#10597115	C₂×C₃	semidirect
43. C₂×#10597114	C₂×C₃	semidirect
44. C₂×Dic₃×C₅⋊D₅	C₂×C₃	semidirect
47. C₂²×C₃²×C₅²	C₂³	semidirect
49. C₂×C₃×C₃⋊(C₅⋊D₅)	C₂³	semidirect
51. C₂×C₃×C₅²×D₃	C₂³	semidirect
54. C₂×C₃²×C₅⋊D₅	D₄	semidirect
56. C₂×C₃²×C₅⋊D₅	C₂³	semidirect
58. C₃×C₃⋊#1039	C₂³	semidirect
59. C₃×C₅²×Dic₃	C₂³	semidirect
64. C₂×C₃×C₅×#67	D₅	semidirect
71. C₂³×C₃×C₅²	C₂×D₃	semidirect
72. C₂³×C₃×C₅²	C₂²×C₃	semidirect
73. C₂²×C₃⋊(C₅⋊D₅)	C₂²×C₃	semidirect
74. C₂²×C₅²×D₃	C₂²×C₃	semidirect
86. C₂²×C₃×C₅⋊D₅	C₂×D₃	semidirect
87. C₂²×C₃×C₅⋊D₅	C₂×D₃	semidirect
89. C₂²×C₃×C₅⋊D₅	C₂²×C₃	semidirect
90. C₂²×C₃×C₅⋊D₅	C₂²×C₃	semidirect
92. C₂×D₃×C₅⋊D₅	C₂²×C₃	semidirect
95. #10597159	C₂²×C₃	semidirect
96. C₂×C₃⋊#1039	C₂²×C₃	semidirect
97. C₅²×#67	C₂²×C₃	semidirect
98. C₂×C₅²×Dic₃	C₂²×C₃	semidirect
104. #10597115	C₂²×C₃	semidirect
105. #10597114	C₂²×C₃	semidirect
106. Dic₃×C₅⋊D₅	C₂²×C₃	semidirect
110. C₂×C₃²×C₅²	C₂×D₄	semidirect
115. C₃²×C₅⋊D₅	C₂×D₄	semidirect
117. C₂³×C₅⋊D₅	C₃×D₃	semidirect
124. C₂³×C₃²×C₅	C₂×D₅	semidirect
126. C₂²×C₃×C₅×D₃	C₂×D₅	semidirect
135. C₃×C₅×#67	C₂×D₅	semidirect
136. C₂×C₃×C₅×Dic₃	C₂×D₅	semidirect
149. C₂²×C₃×C₅²	C₂²×D₃	semidirect
151. C₂²×C₃×C₅²	C₂³×C₃	semidirect
153. C₂×C₃⋊(C₅⋊D₅)	C₂³×C₃	semidirect
155. C₂×C₅²×D₃	C₂³×C₃	semidirect
170. C₂×C₃×C₅⋊D₅	#67	direct (N × H)
171. C₂×C₃×C₅⋊D₅	C₃×D₄	semidirect
173. C₂×C₃×C₅⋊D₅	C₂²×D₃	semidirect
175. C₂×C₃×C₅⋊D₅	C₂³×C₃	semidirect
178. C₃⋊#1039	C₂³×C₃	semidirect
179. C₅²×Dic₃	C₂³×C₃	semidirect
189. C₂×C₅×#67	C₃×D₅	semidirect
199. C₃²×C₅²	C₂²×D₄	semidirect
201. C₂³×C₅²	C₂×C₃×D₃	semidirect
207. C₂²×C₅⋊D₅	C₂×C₃×D₃	semidirect
208. C₂²×C₅⋊D₅	C₂×C₃×D₃	semidirect
218. C₂²×C₃²×C₅	C₂²×D₅	semidirect
222. C₂×C₃×C₅×D₃	C₂²×D₅	semidirect
230. C₃×C₅×Dic₃	C₂²×D₅	semidirect
239. C₂×C₃×C₅²	C₂×#67	semidirect
240. C₂×C₃×C₅²	C₂×C₃×D₄	semidirect
251. C₃×C₅⋊D₅	C₂×#67	direct (N × H)
252. C₃×C₅⋊D₅	C₂×C₃×D₄	semidirect
259. C₂×C₃×#67	C₅⋊D₅	direct (N × H)
263. C₂³×C₃×C₅	D₃×D₅	semidirect
264. C₂³×C₃×C₅	C₂×C₃×D₅	semidirect
266. C₂²×C₅×D₃	C₂×C₃×D₅	semidirect
289. C₅×#67	C₂×C₃×D₅	semidirect
290. C₂×C₅×Dic₃	C₂×C₃×D₅	semidirect
303. C₂²×C₅²	C₂²×C₃×D₃	semidirect
309. C₂×C₅⋊D₅	C₃×#67	direct (N × H)
311. C₂×C₅⋊D₅	C₂²×C₃×D₃	semidirect
317. C₂×C₃²×C₅	D₄×D₅	semidirect
332. C₃×C₅²	C₂²×#67	semidirect
333. C₃×C₅²	C₂²×C₃×D₄	semidirect
338. C₂³×C₃²	C₂×C₅⋊D₅	semidirect
342. C₂²×C₃×D₃	C₂×C₅⋊D₅	semidirect
346. C₃×#67	C₂×C₅⋊D₅	direct (N × H)
349. C₂×C₃×Dic₃	C₂×C₅⋊D₅	semidirect
359. C₂²×C₃×C₅	C₂×D₃×D₅	semidirect
361. C₂²×C₃×C₅	C₂²×C₃×D₅	semidirect
365. C₂×C₅×D₃	C₂²×C₃×D₅	semidirect
390. C₅×Dic₃	C₂²×C₃×D₅	semidirect
393. C₂×C₅²	C₂×C₃×#67	semidirect
397. C₅⋊D₅	C₂×C₃×#67	direct (N × H)
413. C₂×#67	C₃×C₅⋊D₅	direct (N × H)
415. C₃²×C₅	C₂×D₄×D₅	semidirect
417. C₂³×C₅	C₃×D₃×D₅	semidirect
439. C₂²×C₃²	C₂²×C₅⋊D₅	semidirect
444. C₂×C₃×D₃	C₂²×C₅⋊D₅	semidirect
446. C₃×Dic₃	C₂²×C₅⋊D₅	semidirect
455. C₂×C₃×C₅	D₅×#67	semidirect
456. C₂×C₃×C₅	C₃×D₄×D₅	semidirect
469. C₅²	C₂²×C₃×#67	semidirect
488. C₂³×C₃	D₃×C₅⋊D₅	semidirect
489. C₂³×C₃	C₂×C₃×C₅⋊D₅	semidirect
493. C₂²×D₃	C₂×C₃×C₅⋊D₅	semidirect
504. #67	C₂×C₃×C₅⋊D₅	direct (N × H)
507. C₂×Dic₃	C₂×C₃×C₅⋊D₅	semidirect
512. C₂²×C₅	C₂×C₃×D₃×D₅	semidirect
526. C₂×C₃²	D₄×C₅⋊D₅	semidirect
539. C₃×C₅	C₂×D₅×#67	semidirect
540. C₃×C₅	C₂×C₃×D₄×D₅	semidirect
570. C₂²×C₃	C₂×D₃×C₅⋊D₅	semidirect
572. C₂²×C₃	C₂²×C₃×C₅⋊D₅	semidirect
577. C₂×D₃	C₂²×C₃×C₅⋊D₅	semidirect
581. Dic₃	C₂²×C₃×C₅⋊D₅	semidirect
584. C₂×C₅	C₃×D₅×#67	semidirect
589. C₃²	C₂×D₄×C₅⋊D₅	semidirect
598. C₂³	C₃×D₃×C₅⋊D₅	semidirect
621. C₂×C₃	#67×C₅⋊D₅	direct (N × H)
622. C₂×C₃	C₃×D₄×C₅⋊D₅	semidirect
627. C₅	C₂×C₃×D₅×#67	semidirect
640. C₂²	C₂×C₃×D₃×C₅⋊D₅	semidirect
644. C₃	C₂×C₃×D₄×C₅⋊D₅	semidirect
645. C₃	C₂×#67×C₅⋊D₅	direct (N × H)
651. C₂	C₃×#67×C₅⋊D₅	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×#10597114	2
C₂×C₃×#10597159	2
C₂×C₃×#10597115	2
C₂×C₃×C₅²×#67	2
C₂²×C₃×D₃×C₅⋊D₅	2
C₂×C₃×Dic₃×C₅⋊D₅	2
C₃×#67×C₅⋊D₅	2
C₂×#67×C₅⋊D₅	3
C₂×C₃×D₄×C₅⋊D₅	3
C₂³×C₃²×C₅⋊D₅	2
C₂×C₃×D₅×#67	5

Subgroups — C2×C3×#67×C5⋊D5 #72231421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#67×C₅⋊D₅ #72231421