Subgroups — C₃×#13107821 #72231629

Order 4800.

4064 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11717473	C₂	1	2	yes	maximal, complemented
2	C₃×#11717479	C₂	1	8	yes	maximal, complemented
3	C₃×#11717495	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#4144	C₂	1	2	yes	maximal, complemented
5	C₃×#11717477	C₂	1	4	yes	maximal, complemented
6	C₃×D₄×D₅²	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#87886	C₂	1	4	yes	maximal, complemented
8	C₃×#11717471	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×D₄×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	#13107821	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×C₅⋊D₅	C₂²	1	2	yes	complemented
12	C₂²×C₃×D₅²	C₂²	1	4	yes	complemented
13	C₂×C₃×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₂²⋊(C₅⋊D₅)	C₂²	1	2	yes	complemented
15	C₃×D₄×C₅⋊D₅	C₂²	1	4	yes	complemented
16	C₃×D₄×C₅⋊D₅	C₂²	1	4	yes	complemented
17	C₂×C₃×C₄⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×C₂²⋊D₅	C₂²	1	8	yes	complemented
20	C₃×C₅×#711	C₂²	1	8	yes	complemented
21	C₃×C₅×D₄×D₅	C₂²	1	8	yes	complemented
22	C₃×C₅×#709	C₂²	1	4	yes	complemented
23	C₃×#87886	C₂²	1	4	yes	complemented
24	C₃×#87886	C₂²	1	8	yes	complemented
25	C₃×#87886	C₂²	1	8	yes	complemented
26	C₃×#87886	C₂²	1	8	yes	complemented
27	C₃×D₅×C₂²⋊D₅	C₂²	1	16	yes	complemented
28	C₂×C₃×#6038	C₂²	1	8	yes	complemented
29	C₂×C₃×#6036	C₂²	1	4	yes	complemented
30	C₃×#87880	C₂²	1	4	yes	complemented
31	C₃×#87879	C₂²	1	16	yes	complemented
32	C₃×#87877	C₂²	1	2	yes	complemented
33	C₃×D₅×D₂₀	C₂²	1	8	yes	complemented
34	C₃×C₄×D₅²	C₂²	1	4	yes	complemented
35	C₃×#87874	C₂²	1	8	yes	complemented
36	C₃×#87873	C₂²	1	4	yes	complemented
37	C₃×#87872	C₂²	1	2	yes	complemented
38	C₃×#87871	C₂²	1	4	yes	complemented
39	C₃×D₅×H(5,𝔽₂)	—	5	2	no	maximal
40	C₂×D₄×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#4144	C₂×C₃	1	2	yes	complemented
42	#11717495	C₂×C₃	1	4	yes	complemented
43	C₂×#87886	C₂×C₃	1	4	yes	complemented
44	#11717479	C₂×C₃	1	8	yes	complemented
45	#11717477	C₂×C₃	1	4	yes	complemented
46	D₄×D₅²	C₂×C₃	1	4	yes	complemented
47	#11717473	C₂×C₃	1	2	yes	complemented
48	#11717471	C₂×C₃	1	2	yes	complemented
49	C₂³×C₃×C₅²	C₂³	1	2	yes	complemented
50	C₂²×C₃×C₅⋊D₅	—	4	4	no	—
51	C₂²×C₃×C₅⋊D₅	C₂³	1	4	yes	—
52	C₂²×C₃×C₅⋊D₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₅⋊D₅	C₂³	1	4	yes	complemented
54	C₂²×C₃×C₅⋊D₅	C₂³	1	2	yes	complemented
55	C₂²×C₃×C₅×D₅	C₂³	1	8	yes	complemented
56	C₂×C₃×D₅²	—	4	8	no	—
57	C₂×C₃×D₅²	C₂³	1	4	yes	—
58	C₂×C₃×D₅²	C₂³	1	8	yes	complemented
59	C₃×C₅²×D₄	C₂³	1	4	yes	complemented
60	C₂×C₃×C₄×C₅²	C₂³	1	1	yes	characteristic, complemented
61	C₃×C₂²⋊(C₅⋊D₅)	C₂³	1	8	yes	complemented
62	C₂×C₃×#1039	C₂³	1	1	yes	characteristic, complemented
63	C₃×C₄⋊(C₅⋊D₅)	C₂³	1	4	yes	complemented
64	C₃×C₄×C₅⋊D₅	C₂³	1	2	yes	—
65	C₃×C₄×C₅⋊D₅	C₂³	1	2	yes	complemented
66	C₃×C₅×C₂²⋊D₅	C₂³	1	16	yes	complemented
67	C₃×C₅×C₂²⋊D₅	C₂³	1	8	yes	complemented
68	C₂×C₃×C₅×Dic₅	C₂³	1	8	yes	complemented
69	C₃×C₅×D₂₀	C₂³	1	4	yes	complemented
70	C₃×C₄×C₅×D₅	C₂³	1	8	yes	complemented
71	C₃×C₅×Dic₁₀	C₂³	1	4	yes	complemented
72	C₃×#6039	C₂³	1	4	yes	complemented
73	C₃×#6038	C₂³	1	8	yes	complemented
74	C₃×#6038	C₂³	1	16	yes	complemented
75	C₃×#6037	C₂³	1	4	yes	complemented
76	C₃×#6036	C₂³	1	4	yes	—
77	C₃×#6036	C₂³	1	8	yes	complemented
78	C₃×D₅×Dic₅	C₂³	1	8	yes	complemented
79	C₃×C₅×H(5,𝔽₂)	—	5	2	no	—
80	C₃×#4149	—	5	8	no	—
81	C₃×#4149	—	5	4	no	—
82	C₃×D₅×#41	—	5	8	no	—
83	C₃×D₅×#41	—	5	4	no	—
84	C₃×#4144	—	5	8	no	—
85	C₃×#4144	—	5	8	no	—
86	C₃×#4144	D₅	1	2	yes	complemented
87	C₂×C₃×D₄×D₅	—	5	2	no	—
88	C₂×C₃×D₄×D₅	—	5	8	no	—
89	C₂×C₃×D₄×D₅	—	5	8	no	—
90	C₂×C₃×D₄×D₅	—	10	2	no	—
91	C₂³×C₅⋊D₅	C₂²×C₃	1	2	yes	complemented
92	C₂²×D₅²	C₂²×C₃	1	4	yes	complemented
93	C₂×C₅²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₂×C₂²⋊(C₅⋊D₅)	C₂²×C₃	1	2	yes	complemented
95	D₄×C₅⋊D₅	C₂²×C₃	1	4	yes	complemented
96	D₄×C₅⋊D₅	C₂²×C₃	1	4	yes	complemented
97	C₂×C₄⋊(C₅⋊D₅)	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₂×C₄×C₅⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂×C₅×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
100	C₅×#711	C₂²×C₃	1	8	yes	complemented
101	C₅×D₄×D₅	C₂²×C₃	1	8	yes	complemented
102	C₅×#709	C₂²×C₃	1	4	yes	complemented
103	#87886	C₂²×C₃	1	4	yes	complemented
104	#87886	C₂²×C₃	1	8	yes	complemented
105	#87886	C₂²×C₃	1	8	yes	complemented
106	#87886	C₂²×C₃	1	8	yes	complemented
107	D₅×C₂²⋊D₅	C₂²×C₃	1	16	yes	complemented
108	C₂×#6038	C₂²×C₃	1	8	yes	complemented
109	C₂×#6036	C₂²×C₃	1	4	yes	complemented
110	#87880	C₂²×C₃	1	4	yes	complemented
111	#87879	C₂²×C₃	1	16	yes	complemented
112	#87877	C₂²×C₃	1	2	yes	complemented
113	D₅×D₂₀	C₂²×C₃	1	8	yes	complemented
114	C₄×D₅²	C₂²×C₃	1	4	yes	complemented
115	#87874	C₂²×C₃	1	8	yes	complemented
116	#87873	C₂²×C₃	1	4	yes	complemented
117	#87872	C₂²×C₃	1	2	yes	complemented
118	#87871	C₂²×C₃	1	4	yes	complemented
119	D₅×H(5,𝔽₂)	—	5	2	no	—
120	C₂²×C₃×C₅²	—	4	2	no	—
121	C₂²×C₃×C₅²	C₂⁴	1	4	yes	—
122	C₂²×C₃×C₅²	C₂⁴	1	1	yes	characteristic
123	C₂×C₃×C₅⋊D₅	—	2	2	no	—
124	C₂×C₃×C₅⋊D₅	—	2	8	no	—
125	C₂×C₃×C₅⋊D₅	—	4	4	no	—
126	C₂×C₃×C₅⋊D₅	—	4	2	no	—
127	C₂×C₃×C₅⋊D₅	C₂⁴	1	1	yes	characteristic
128	C₂×C₃×C₅⋊D₅	C₂⁴	1	4	yes	—
129	C₂×C₃×C₅⋊D₅	C₂⁴	1	1	yes	characteristic
130	C₂×C₃×C₅×D₅	—	4	8	no	—
131	C₂×C₃×C₅×D₅	C₂⁴	1	8	yes	—
132	C₃×D₅²	—	2	8	no	—
133	C₃×D₅²	—	4	8	no	—
134	C₃×C₄×C₅²	C₂⁴	1	2	yes	—
135	C₃×#1039	C₂⁴	1	2	yes	—
136	C₃×C₅×Dic₅	C₂⁴	1	8	yes	—
137	C₂³×C₃×D₅	—	5	4	no	—
138	C₂³×C₃×D₅	—	5	8	no	—
139	C₂³×C₃×D₅	—	10	4	no	—
140	C₃×C₅×#41	—	5	8	no	—
141	C₃×C₅×#41	—	5	4	no	—
142	C₂×C₃×C₅×D₄	—	2	2	no	—
143	C₂×C₃×C₅×D₄	—	5	8	no	—
144	C₂×C₃×C₅×D₄	—	5	8	no	—
145	C₂×C₃×C₅×D₄	C₂×D₅	1	2	yes	complemented
146	C₂×C₃×C₂²⋊D₅	—	5	4	no	—
147	C₂×C₃×C₂²⋊D₅	—	5	16	no	—
148	C₂×C₃×C₂²⋊D₅	—	5	8	no	—
149	C₂×C₃×C₂²⋊D₅	—	10	4	no	—
150	C₂×C₃×C₂²⋊D₅	C₂×D₅	1	8	yes	complemented
151	C₃×#713	—	5	4	no	—
152	C₃×#713	—	5	8	no	—
153	C₃×Q₈×D₅	—	5	4	no	—
154	C₃×#711	—	5	8	no	—
155	C₃×#711	—	5	16	no	—
156	C₃×#711	—	5	4	no	—
157	C₃×#711	C₂×D₅	1	8	yes	complemented
158	C₃×D₄×D₅	—	5	16	no	—
159	C₃×D₄×D₅	—	5	8	no	—
160	C₃×D₄×D₅	—	5	8	no	—
161	C₃×D₄×D₅	—	5	16	no	—
162	C₃×D₄×D₅	—	5	8	no	—
163	C₃×D₄×D₅	—	5	16	no	—
164	C₃×D₄×D₅	—	5	16	no	—
165	C₃×D₄×D₅	—	5	4	no	—
166	C₃×D₄×D₅	—	5	8	no	—
167	C₃×D₄×D₅	—	10	8	no	—
168	C₃×D₄×D₅	—	10	8	no	—
169	C₃×D₄×D₅	C₂×D₅	1	8	yes	complemented
170	C₃×#709	—	5	16	no	—
171	C₃×#709	—	5	8	no	—
172	C₃×#709	—	5	8	no	—
173	C₃×#709	C₂×D₅	1	4	yes	complemented
174	C₂×C₃×D₂₀	—	5	8	no	—
175	C₂×C₃×D₂₀	—	5	2	no	—
176	C₂×C₃×D₂₀	—	5	8	no	—
177	C₂×C₃×D₂₀	—	10	2	no	—
178	C₂×C₃×C₄×D₅	—	5	2	no	—
179	C₂×C₃×C₄×D₅	—	5	8	no	—
180	C₂×C₃×C₄×D₅	—	5	8	no	—
181	C₂×C₃×C₄×D₅	—	10	2	no	—
182	C₂³×C₅²	C₂³×C₃	1	2	yes	complemented
183	C₂²×C₅⋊D₅	—	4	4	no	—
184	C₂²×C₅⋊D₅	C₂³×C₃	1	4	yes	—
185	C₂²×C₅⋊D₅	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₅⋊D₅	C₂³×C₃	1	4	yes	complemented
187	C₂²×C₅⋊D₅	C₂³×C₃	1	2	yes	complemented
188	C₂²×C₅×D₅	C₂³×C₃	1	8	yes	complemented
189	C₂×D₅²	—	4	8	no	—
190	C₂×D₅²	C₂³×C₃	1	4	yes	—
191	C₂×D₅²	C₂³×C₃	1	8	yes	complemented
192	C₅²×D₄	C₂³×C₃	1	4	yes	complemented
193	C₂×C₄×C₅²	C₂³×C₃	1	1	yes	characteristic, complemented
194	C₂²⋊(C₅⋊D₅)	C₂³×C₃	1	8	yes	complemented
195	C₂×#1039	C₂³×C₃	1	1	yes	characteristic, complemented
196	C₄⋊(C₅⋊D₅)	C₂³×C₃	1	4	yes	complemented
197	C₄×C₅⋊D₅	C₂³×C₃	1	2	yes	—
198	C₄×C₅⋊D₅	C₂³×C₃	1	2	yes	complemented
199	C₅×C₂²⋊D₅	C₂³×C₃	1	16	yes	complemented
200	C₅×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
201	C₂×C₅×Dic₅	C₂³×C₃	1	8	yes	complemented
202	C₅×D₂₀	C₂³×C₃	1	4	yes	complemented
203	C₄×C₅×D₅	C₂³×C₃	1	8	yes	complemented
204	C₅×Dic₁₀	C₂³×C₃	1	4	yes	complemented
205	#6039	C₂³×C₃	1	4	yes	complemented
206	#6038	C₂³×C₃	1	8	yes	complemented
207	#6038	C₂³×C₃	1	16	yes	complemented
208	#6037	C₂³×C₃	1	4	yes	complemented
209	#6036	C₂³×C₃	1	4	yes	—
210	#6036	C₂³×C₃	1	8	yes	complemented
211	D₅×Dic₅	C₂³×C₃	1	8	yes	complemented
212	C₂×C₃×H(5,𝔽₂)	—	25	1	no	Hall
213	C₅×H(5,𝔽₂)	—	5	2	no	—
214	#4149	—	5	8	no	—
215	#4149	—	5	4	no	—
216	D₅×#41	—	5	8	no	—
217	D₅×#41	—	5	4	no	—
218	#4144	—	5	8	no	—
219	#4144	—	5	8	no	—
220	#4144	C₃×D₅	1	2	yes	complemented
221	C₂×D₄×D₅	—	5	2	no	—
222	C₂×D₄×D₅	—	5	8	no	—
223	C₂×D₄×D₅	—	5	8	no	—
224	C₂×D₄×D₅	—	10	2	no	—
225	C₂×C₃×C₅²	—	2	1	no	—
226	C₂×C₃×C₅²	—	2	4	no	—
227	C₂×C₃×C₅²	C₂⁵	1	1	yes	characteristic
228	C₃×C₅⋊D₅	—	2	1	no	—
229	C₃×C₅⋊D₅	—	2	4	no	—
230	C₃×C₅⋊D₅	H(5,𝔽₂)	1	2	yes	complemented
231	C₃×C₅×D₅	—	2	8	no	—
232	C₂³×C₃×C₅	—	2	4	no	—
233	C₂³×C₃×C₅	—	5	8	no	—
234	C₂³×C₃×C₅	C₂²×D₅	1	4	yes	complemented
235	C₂²×C₃×D₅	—	5	2	no	—
236	C₂²×C₃×D₅	—	5	8	no	—
237	C₂²×C₃×D₅	—	5	4	no	—
238	C₂²×C₃×D₅	—	5	8	no	—
239	C₂²×C₃×D₅	—	5	8	no	—
240	C₂²×C₃×D₅	—	5	16	no	—
241	C₂²×C₃×D₅	—	10	2	no	—
242	C₂²×C₃×D₅	—	10	8	no	—
243	C₂²×C₃×D₅	—	10	4	no	—
244	C₂²×C₃×D₅	—	10	8	no	—
245	C₂²×C₃×D₅	—	20	16	no	—
246	C₂²×C₃×D₅	—	20	8	no	—
247	C₂²×C₃×D₅	—	20	8	no	—
248	C₂²×C₃×D₅	—	20	8	no	—
249	C₂²×C₃×D₅	C₂²×D₅	1	8	yes	complemented
250	C₃×C₅×Q₈	—	5	4	no	—
251	C₃×C₅×D₄	—	2	8	no	—
252	C₃×C₅×D₄	—	5	8	no	—
253	C₃×C₅×D₄	—	5	16	no	—
254	C₃×C₅×D₄	—	5	4	no	—
255	C₃×C₅×D₄	C₂²×D₅	1	8	yes	complemented
256	C₂×C₃×C₄×C₅	—	2	2	no	—
257	C₂×C₃×C₄×C₅	—	5	8	no	—
258	C₂×C₃×C₄×C₅	—	5	8	no	—
259	C₂×C₃×C₄×C₅	C₂²×D₅	1	2	yes	complemented
260	C₃×C₂²⋊D₅	—	5	16	no	—
261	C₃×C₂²⋊D₅	—	5	8	no	—
262	C₃×C₂²⋊D₅	—	5	8	no	—
263	C₃×C₂²⋊D₅	—	5	16	no	—
264	C₃×C₂²⋊D₅	—	10	16	no	—
265	C₃×C₂²⋊D₅	C₂²×D₅	1	16	yes	complemented
266	C₃×C₂²⋊D₅	C₂²×D₅	1	8	yes	complemented
267	C₂×C₃×Dic₅	—	5	2	no	—
268	C₂×C₃×Dic₅	—	5	8	no	—
269	C₂×C₃×Dic₅	—	10	2	no	—
270	C₂×C₃×Dic₅	C₂²×D₅	1	8	yes	complemented
271	C₃×D₂₀	—	5	8	no	—
272	C₃×D₂₀	—	5	16	no	—
273	C₃×D₂₀	—	5	8	no	—
274	C₃×D₂₀	—	10	8	no	—
275	C₃×D₂₀	C₂²×D₅	1	4	yes	complemented
276	C₃×C₄×D₅	—	5	8	no	—
277	C₃×C₄×D₅	—	5	4	no	—
278	C₃×C₄×D₅	—	5	4	no	—
279	C₃×C₄×D₅	—	5	8	no	—
280	C₃×C₄×D₅	—	5	16	no	—
281	C₃×C₄×D₅	—	10	4	no	—
282	C₃×C₄×D₅	—	10	4	no	—
283	C₃×C₄×D₅	C₂²×D₅	1	8	yes	complemented
284	C₃×Dic₁₀	—	5	8	no	—
285	C₃×Dic₁₀	C₂²×D₅	1	4	yes	complemented
286	C₂²×C₅²	—	4	2	no	—
287	C₂²×C₅²	C₂⁴×C₃	1	4	yes	—
288	C₂²×C₅²	C₂⁴×C₃	1	1	yes	characteristic
289	C₂×C₅⋊D₅	—	2	2	no	—
290	C₂×C₅⋊D₅	—	2	8	no	—
291	C₂×C₅⋊D₅	—	4	4	no	—
292	C₂×C₅⋊D₅	—	4	2	no	—
293	C₂×C₅⋊D₅	C₂⁴×C₃	1	4	yes	—
294	C₂×C₅⋊D₅	C₂⁴×C₃	1	1	yes	characteristic
295	C₂×C₅⋊D₅	C₂⁴×C₃	1	1	yes	characteristic
296	C₂×C₅×D₅	—	4	8	no	—
297	C₂×C₅×D₅	C₂⁴×C₃	1	8	yes	—
298	D₅²	—	2	8	no	—
299	D₅²	—	4	8	no	—
300	C₄×C₅²	C₂⁴×C₃	1	2	yes	—
301	#1039	C₂⁴×C₃	1	2	yes	—
302	C₅×Dic₅	C₂⁴×C₃	1	8	yes	—
303	C₃×H(5,𝔽₂)	—	5	2	no	—
304	C₃×H(5,𝔽₂)	—	25	4	no	—
305	C₃×H(5,𝔽₂)	—	25	8	no	—
306	C₃×H(5,𝔽₂)	—	25	2	no	—
307	C₂×C₃×#41	—	25	4	no	—
308	C₂×C₃×#41	—	25	2	no	—
309	C₂²×C₃×D₄	—	25	4	no	—
310	C₂²×C₃×D₄	—	25	4	no	—
311	C₂²×C₃×D₄	—	25	1	no	—
312	C₂³×D₅	—	5	4	no	—
313	C₂³×D₅	—	5	8	no	—
314	C₂³×D₅	—	10	4	no	—
315	C₅×#41	—	5	8	no	—
316	C₅×#41	—	5	4	no	—
317	C₂×C₅×D₄	—	2	2	no	—
318	C₂×C₅×D₄	—	5	8	no	—
319	C₂×C₅×D₄	—	5	8	no	—
320	C₂×C₅×D₄	C₂×C₃×D₅	1	2	yes	complemented
321	C₂×C₂²⋊D₅	—	5	4	no	—
322	C₂×C₂²⋊D₅	—	5	16	no	—
323	C₂×C₂²⋊D₅	—	5	8	no	—
324	C₂×C₂²⋊D₅	—	10	4	no	—
325	C₂×C₂²⋊D₅	C₂×C₃×D₅	1	8	yes	complemented
326	#713	—	5	4	no	—
327	#713	—	5	8	no	—
328	Q₈×D₅	—	5	4	no	—
329	#711	—	5	8	no	—
330	#711	—	5	16	no	—
331	#711	—	5	4	no	—
332	#711	C₂×C₃×D₅	1	8	yes	complemented
333	D₄×D₅	—	5	16	no	—
334	D₄×D₅	—	5	8	no	—
335	D₄×D₅	—	5	8	no	—
336	D₄×D₅	—	5	16	no	—
337	D₄×D₅	—	5	8	no	—
338	D₄×D₅	—	5	16	no	—
339	D₄×D₅	—	5	16	no	—
340	D₄×D₅	—	5	4	no	—
341	D₄×D₅	—	5	8	no	—
342	D₄×D₅	—	10	8	no	—
343	D₄×D₅	—	10	8	no	—
344	D₄×D₅	C₂×C₃×D₅	1	8	yes	complemented
345	#709	—	5	16	no	—
346	#709	—	5	8	no	—
347	#709	—	5	8	no	—
348	#709	C₂×C₃×D₅	1	4	yes	complemented
349	C₂×D₂₀	—	5	8	no	—
350	C₂×D₂₀	—	5	2	no	—
351	C₂×D₂₀	—	5	8	no	—
352	C₂×D₂₀	—	10	2	no	—
353	C₂×C₄×D₅	—	5	2	no	—
354	C₂×C₄×D₅	—	5	8	no	—
355	C₂×C₄×D₅	—	5	8	no	—
356	C₂×C₄×D₅	—	10	2	no	—
357	C₃×C₅²	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
358	C₂×H(5,𝔽₂)	—	25	1	no	Sylow
359	C₂²×C₃×C₅	—	2	2	no	—
360	C₂²×C₃×C₅	—	2	8	no	—
361	C₂²×C₃×C₅	—	4	4	no	—
362	C₂²×C₃×C₅	—	4	4	no	—
363	C₂²×C₃×C₅	—	4	4	no	—
364	C₂²×C₃×C₅	—	5	8	no	—
365	C₂²×C₃×C₅	—	20	8	no	—
366	C₂²×C₃×C₅	C₂³×D₅	1	2	yes	—
367	C₂²×C₃×C₅	C₂³×D₅	1	8	yes	—
368	C₂×C₃×D₅	—	4	8	no	—
369	C₂×C₃×D₅	—	5	2	no	—
370	C₂×C₃×D₅	—	5	2	no	—
371	C₂×C₃×D₅	—	5	8	no	—
372	C₂×C₃×D₅	—	10	2	no	—
373	C₂×C₃×D₅	—	10	2	no	—
374	C₂×C₃×D₅	—	10	8	no	—
375	C₂×C₃×D₅	—	10	16	no	—
376	C₂×C₃×D₅	—	10	4	no	—
377	C₂×C₃×D₅	—	10	16	no	—
378	C₂×C₃×D₅	—	10	4	no	—
379	C₂×C₃×D₅	—	10	4	no	—
380	C₂×C₃×D₅	—	20	16	no	—
381	C₂×C₃×D₅	—	20	16	no	—
382	C₂×C₃×D₅	—	20	8	no	—
383	C₂×C₃×D₅	—	20	4	no	—
384	C₂×C₃×D₅	—	20	8	no	—
385	C₂×C₃×D₅	—	20	8	no	—
386	C₂×C₃×D₅	—	20	4	no	—
387	C₂×C₃×D₅	—	20	4	no	—
388	C₂×C₃×D₅	C₂³×D₅	1	8	yes	—
389	C₃×C₄×C₅	—	2	4	no	—
390	C₃×C₄×C₅	—	5	8	no	—
391	C₃×C₄×C₅	C₂³×D₅	1	4	yes	—
392	C₃×Dic₅	—	5	4	no	—
393	C₃×Dic₅	—	10	4	no	—
394	C₃×Dic₅	C₂³×D₅	1	8	yes	—
395	C₂×C₅²	—	2	1	no	—
396	C₂×C₅²	—	2	4	no	—
397	C₂×C₅²	C₂⁵×C₃	1	1	yes	characteristic
398	C₅⋊D₅	—	2	1	no	—
399	C₅⋊D₅	—	2	4	no	—
400	C₅⋊D₅	C₃×H(5,𝔽₂)	1	2	yes	complemented
401	C₅×D₅	—	2	8	no	—
402	C₂⁴×C₃	—	25	4	no	—
403	C₂⁴×C₃	—	25	2	no	—
404	C₃×#41	—	5	8	no	—
405	C₃×#41	—	5	4	no	—
406	C₃×#41	—	25	4	no	—
407	C₃×#41	—	25	16	no	—
408	C₃×#41	—	25	8	no	—
409	C₃×#41	—	25	4	no	—
410	C₃×#41	—	25	4	no	—
411	C₂×C₃×Q₈	—	25	2	no	—
412	C₂×C₃×D₄	—	5	8	no	—
413	C₂×C₃×D₄	—	5	8	no	—
414	C₂×C₃×D₄	—	25	8	no	—
415	C₂×C₃×D₄	—	25	8	no	—
416	C₂×C₃×D₄	—	25	8	no	—
417	C₂×C₃×D₄	—	25	4	no	—
418	C₂×C₃×D₄	—	25	2	no	—
419	C₂×C₃×D₄	—	25	8	no	—
420	C₂×C₃×D₄	—	25	8	no	—
421	C₂×C₃×D₄	—	25	16	no	—
422	C₂×C₃×D₄	—	25	2	no	—
423	C₂×C₃×D₄	—	25	4	no	—
424	C₂×C₃×D₄	—	25	4	no	—
425	C₂×C₃×D₄	—	25	1	no	—
426	C₂×C₃×D₄	D₅²	1	1	yes	characteristic, complemented
427	C₂²×C₃×C₄	—	25	4	no	—
428	C₂²×C₃×C₄	—	25	4	no	—
429	C₂²×C₃×C₄	—	25	1	no	—
430	C₂³×C₅	—	2	4	no	—
431	C₂³×C₅	—	5	8	no	—
432	C₂³×C₅	C₂²×C₃×D₅	1	4	yes	complemented
433	C₂²×D₅	—	5	2	no	—
434	C₂²×D₅	—	5	8	no	—
435	C₂²×D₅	—	5	4	no	—
436	C₂²×D₅	—	5	8	no	—
437	C₂²×D₅	—	5	8	no	—
438	C₂²×D₅	—	5	16	no	—
439	C₂²×D₅	—	10	2	no	—
440	C₂²×D₅	—	10	8	no	—
441	C₂²×D₅	—	10	4	no	—
442	C₂²×D₅	—	10	8	no	—
443	C₂²×D₅	—	20	16	no	—
444	C₂²×D₅	—	20	8	no	—
445	C₂²×D₅	—	20	8	no	—
446	C₂²×D₅	—	20	8	no	—
447	C₂²×D₅	C₂²×C₃×D₅	1	8	yes	complemented
448	C₅×Q₈	—	5	4	no	—
449	C₅×D₄	—	2	8	no	—
450	C₅×D₄	—	5	8	no	—
451	C₅×D₄	—	5	16	no	—
452	C₅×D₄	—	5	4	no	—
453	C₅×D₄	C₂²×C₃×D₅	1	8	yes	complemented
454	C₂×C₄×C₅	—	2	2	no	—
455	C₂×C₄×C₅	—	5	8	no	—
456	C₂×C₄×C₅	—	5	8	no	—
457	C₂×C₄×C₅	C₂²×C₃×D₅	1	2	yes	complemented
458	C₂²⋊D₅	—	5	16	no	—
459	C₂²⋊D₅	—	5	8	no	—
460	C₂²⋊D₅	—	5	8	no	—
461	C₂²⋊D₅	—	5	16	no	—
462	C₂²⋊D₅	—	10	16	no	—
463	C₂²⋊D₅	C₂²×C₃×D₅	1	16	yes	complemented
464	C₂²⋊D₅	C₂²×C₃×D₅	1	8	yes	complemented
465	C₂×Dic₅	—	5	2	no	—
466	C₂×Dic₅	—	5	8	no	—
467	C₂×Dic₅	—	10	2	no	—
468	C₂×Dic₅	C₂²×C₃×D₅	1	8	yes	complemented
469	D₂₀	—	5	8	no	—
470	D₂₀	—	5	16	no	—
471	D₂₀	—	5	8	no	—
472	D₂₀	—	10	8	no	—
473	D₂₀	C₂²×C₃×D₅	1	4	yes	complemented
474	C₄×D₅	—	5	8	no	—
475	C₄×D₅	—	5	4	no	—
476	C₄×D₅	—	5	4	no	—
477	C₄×D₅	—	5	8	no	—
478	C₄×D₅	—	5	16	no	—
479	C₄×D₅	—	10	4	no	—
480	C₄×D₅	—	10	4	no	—
481	C₄×D₅	C₂²×C₃×D₅	1	8	yes	complemented
482	Dic₁₀	—	5	8	no	—
483	Dic₁₀	C₂²×C₃×D₅	1	4	yes	complemented
484	H(5,𝔽₂)	—	5	2	no	—
485	H(5,𝔽₂)	—	25	4	no	—
486	H(5,𝔽₂)	—	25	8	no	—
487	H(5,𝔽₂)	—	25	2	no	—
488	C₂×#41	—	25	4	no	—
489	C₂×#41	—	25	2	no	—
490	C₂²×D₄	—	25	4	no	—
491	C₂²×D₄	—	25	4	no	—
492	C₂²×D₄	—	25	1	no	—
493	C₂×C₃×C₅	—	2	2	no	—
494	C₂×C₃×C₅	—	2	2	no	—
495	C₂×C₃×C₅	—	2	8	no	—
496	C₂×C₃×C₅	—	2	2	no	—
497	C₂×C₃×C₅	—	2	2	no	—
498	C₂×C₃×C₅	—	4	8	no	—
499	C₂×C₃×C₅	—	10	8	no	—
500	C₂×C₃×C₅	C₂⁴×D₅	1	2	yes	—
501	C₃×D₅	—	2	8	no	—
502	C₃×D₅	—	5	4	no	—
503	C₃×D₅	—	10	4	no	—
504	C₃×D₅	—	10	2	no	—
505	C₃×D₅	—	10	2	no	—
506	C₃×D₅	—	10	2	no	—
507	C₃×D₅	—	10	8	no	—
508	C₃×D₅	—	20	8	no	—
509	C₅²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
510	C₂³×C₃	—	5	8	no	—
511	C₂³×C₃	—	25	4	no	—
512	C₂³×C₃	—	25	8	no	—
513	C₂³×C₃	—	25	1	no	—
514	C₂³×C₃	—	25	4	no	—
515	C₂³×C₃	—	25	4	no	—
516	C₂³×C₃	—	25	2	no	—
517	C₂³×C₃	—	100	4	no	—
518	C₂³×C₃	—	100	8	no	—
519	C₂³×C₃	C₂×D₅²	1	2	yes	complemented
520	C₃×Q₈	—	5	4	no	—
521	C₃×Q₈	—	25	4	no	—
522	C₃×D₄	—	5	16	no	—
523	C₃×D₄	—	5	8	no	—
524	C₃×D₄	—	5	4	no	—
525	C₃×D₄	—	25	16	no	—
526	C₃×D₄	—	25	8	no	—
527	C₃×D₄	—	25	4	no	—
528	C₃×D₄	—	25	8	no	—
529	C₃×D₄	—	25	4	no	—
530	C₃×D₄	C₂×D₅²	1	4	yes	complemented
531	C₂×C₃×C₄	—	5	8	no	—
532	C₂×C₃×C₄	—	5	8	no	—
533	C₂×C₃×C₄	—	25	4	no	—
534	C₂×C₃×C₄	—	25	8	no	—
535	C₂×C₃×C₄	—	25	8	no	—
536	C₂×C₃×C₄	—	25	1	no	—
537	C₂×C₃×C₄	—	25	2	no	—
538	C₂×C₃×C₄	—	25	2	no	—
539	C₂×C₃×C₄	C₂×D₅²	1	1	yes	characteristic, complemented
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	2	8	no	—
542	C₂²×C₅	—	4	4	no	—
543	C₂²×C₅	—	4	4	no	—
544	C₂²×C₅	—	4	4	no	—
545	C₂²×C₅	—	5	8	no	—
546	C₂²×C₅	—	20	8	no	—
547	C₂²×C₅	C₂³×C₃×D₅	1	2	yes	—
548	C₂²×C₅	C₂³×C₃×D₅	1	8	yes	—
549	C₂×D₅	—	4	8	no	—
550	C₂×D₅	—	5	2	no	—
551	C₂×D₅	—	5	8	no	—
552	C₂×D₅	—	5	2	no	—
553	C₂×D₅	—	10	2	no	—
554	C₂×D₅	—	10	2	no	—
555	C₂×D₅	—	10	8	no	—
556	C₂×D₅	—	10	16	no	—
557	C₂×D₅	—	10	4	no	—
558	C₂×D₅	—	10	16	no	—
559	C₂×D₅	—	10	4	no	—
560	C₂×D₅	—	10	4	no	—
561	C₂×D₅	—	20	16	no	—
562	C₂×D₅	—	20	16	no	—
563	C₂×D₅	—	20	8	no	—
564	C₂×D₅	—	20	4	no	—
565	C₂×D₅	—	20	8	no	—
566	C₂×D₅	—	20	8	no	—
567	C₂×D₅	—	20	4	no	—
568	C₂×D₅	—	20	4	no	—
569	C₂×D₅	C₂³×C₃×D₅	1	8	yes	—
570	C₄×C₅	—	2	4	no	—
571	C₄×C₅	—	5	8	no	—
572	C₄×C₅	C₂³×C₃×D₅	1	4	yes	—
573	Dic₅	—	5	4	no	—
574	Dic₅	—	10	4	no	—
575	Dic₅	C₂³×C₃×D₅	1	8	yes	—
576	C₂⁴	—	25	4	no	—
577	C₂⁴	—	25	2	no	—
578	#41	—	5	8	no	—
579	#41	—	5	4	no	—
580	#41	—	25	4	no	—
581	#41	—	25	16	no	—
582	#41	—	25	8	no	—
583	#41	—	25	4	no	—
584	#41	—	25	4	no	—
585	C₂×Q₈	—	25	2	no	—
586	C₂×D₄	—	5	8	no	—
587	C₂×D₄	—	5	8	no	—
588	C₂×D₄	—	25	8	no	—
589	C₂×D₄	—	25	8	no	—
590	C₂×D₄	—	25	8	no	—
591	C₂×D₄	—	25	4	no	—
592	C₂×D₄	—	25	2	no	—
593	C₂×D₄	—	25	8	no	—
594	C₂×D₄	—	25	8	no	—
595	C₂×D₄	—	25	16	no	—
596	C₂×D₄	—	25	2	no	—
597	C₂×D₄	—	25	4	no	—
598	C₂×D₄	—	25	4	no	—
599	C₂×D₄	—	25	1	no	—
600	C₂×D₄	C₃×D₅²	1	1	yes	characteristic, complemented
601	C₂²×C₄	—	25	4	no	—
602	C₂²×C₄	—	25	4	no	—
603	C₂²×C₄	—	25	1	no	—
604	C₃×C₅	—	2	2	no	—
605	C₃×C₅	D₅×H(5,𝔽₂)	1	2	yes	complemented
606	C₂²×C₃	—	4	2	no	—
607	C₂²×C₃	—	5	8	no	—
608	C₂²×C₃	—	20	8	no	—
609	C₂²×C₃	—	25	1	no	—
610	C₂²×C₃	—	25	1	no	—
611	C₂²×C₃	—	25	4	no	—
612	C₂²×C₃	—	50	2	no	—
613	C₂²×C₃	—	50	8	no	—
614	C₂²×C₃	—	50	8	no	—
615	C₂²×C₃	—	100	2	no	—
616	C₂²×C₃	—	100	4	no	—
617	C₂²×C₃	—	100	8	no	—
618	C₂²×C₃	C₂²×D₅²	1	4	yes	—
619	C₂²×C₃	C₂²×D₅²	1	1	yes	characteristic
620	C₃×C₄	—	5	8	no	—
621	C₃×C₄	—	25	2	no	—
622	C₃×C₄	C₂²×D₅²	1	2	yes	—
623	C₂×C₅	—	2	2	no	—
624	C₂×C₅	—	2	2	no	—
625	C₂×C₅	—	2	8	no	—
626	C₂×C₅	—	2	2	no	—
627	C₂×C₅	—	2	2	no	—
628	C₂×C₅	—	4	8	no	—
629	C₂×C₅	—	10	8	no	—
630	C₂×C₅	C₂⁴×C₃×D₅	1	2	yes	—
631	D₅	—	2	8	no	—
632	D₅	—	5	4	no	—
633	D₅	—	10	4	no	—
634	D₅	—	10	2	no	—
635	D₅	—	10	2	no	—
636	D₅	—	10	2	no	—
637	D₅	—	10	8	no	—
638	D₅	—	20	8	no	—
639	C₂³	—	5	8	no	—
640	C₂³	—	25	4	no	—
641	C₂³	—	25	8	no	—
642	C₂³	—	25	1	no	—
643	C₂³	—	25	4	no	—
644	C₂³	—	25	4	no	—
645	C₂³	—	25	2	no	—
646	C₂³	—	100	4	no	—
647	C₂³	—	100	8	no	—
648	C₂³	C₂×C₃×D₅²	1	2	yes	complemented
649	Q₈	—	5	4	no	—
650	Q₈	—	25	4	no	—
651	D₄	—	5	16	no	—
652	D₄	—	5	8	no	—
653	D₄	—	5	4	no	—
654	D₄	—	25	16	no	—
655	D₄	—	25	8	no	—
656	D₄	—	25	4	no	—
657	D₄	—	25	8	no	—
658	D₄	—	25	4	no	—
659	D₄	C₂×C₃×D₅²	1	4	yes	complemented
660	C₂×C₄	—	5	8	no	—
661	C₂×C₄	—	5	8	no	—
662	C₂×C₄	—	25	4	no	—
663	C₂×C₄	—	25	8	no	—
664	C₂×C₄	—	25	8	no	—
665	C₂×C₄	—	25	1	no	—
666	C₂×C₄	—	25	2	no	—
667	C₂×C₄	—	25	2	no	—
668	C₂×C₄	C₂×C₃×D₅²	1	1	yes	characteristic, complemented
669	C₂×C₃	—	2	1	no	—
670	C₂×C₃	—	2	4	no	—
671	C₂×C₃	—	10	8	no	—
672	C₂×C₃	—	25	2	no	—
673	C₂×C₃	—	50	1	no	—
674	C₂×C₃	—	50	4	no	—
675	C₂×C₃	C₂³×D₅²	1	1	yes	characteristic
676	C₅	—	2	2	no	—
677	C₅	C₃×D₅×H(5,𝔽₂)	1	2	yes	complemented
678	C₂²	—	4	2	no	—
679	C₂²	—	5	8	no	—
680	C₂²	—	20	8	no	—
681	C₂²	—	25	1	no	—
682	C₂²	—	25	1	no	—
683	C₂²	—	25	4	no	—
684	C₂²	—	50	2	no	—
685	C₂²	—	50	8	no	—
686	C₂²	—	50	8	no	—
687	C₂²	—	100	2	no	—
688	C₂²	—	100	4	no	—
689	C₂²	—	100	8	no	—
690	C₂²	C₂²×C₃×D₅²	1	4	yes	—
691	C₂²	C₂²×C₃×D₅²	1	1	yes	characteristic
692	C₄	—	5	8	no	—
693	C₄	—	25	2	no	—
694	C₄	C₂²×C₃×D₅²	1	2	yes	—
695	C₃	#13107821	1	1	yes	characteristic, direct product factor, Sylow
696	C₂	—	2	1	no	—
697	C₂	—	2	4	no	—
698	C₂	—	10	8	no	—
699	C₂	—	25	2	no	—
700	C₂	—	50	1	no	—
701	C₂	—	50	4	no	—
702	C₂	C₂³×C₃×D₅²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂³×D₅²
commutator, cosocle	C₂×C₅²	C₂⁵×C₃
Frattini	C₂	C₂³×C₃×D₅²
Fitting	C₂×C₃×C₅²×D₄	C₂²
socle	C₂×C₃×C₅²	C₂⁵
hypercenter	C₂×C₃×D₄	D₅²
hypocenter	C₅²	C₂×C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×#11717473	C₂	semidirect
2. C₃×#11717479	C₂	semidirect
3. C₃×#11717495	C₂	semidirect
4. C₃×C₅×#4144	C₂	semidirect
5. C₃×#11717477	C₂	semidirect
6. C₃×D₄×D₅²	C₂	semidirect
7. C₂×C₃×#87886	C₂	semidirect
8. C₃×#11717471	C₂	semidirect
9. C₂×C₃×D₄×C₅⋊D₅	C₂	semidirect
10. #13107821	C₃	direct (N × H)
11. C₂³×C₃×C₅⋊D₅	C₂²	semidirect
12. C₂²×C₃×D₅²	C₂²	semidirect
13. C₂×C₃×C₅²×D₄	C₂²	semidirect
14. C₂×C₃×C₂²⋊(C₅⋊D₅)	C₂²	semidirect
15. C₃×D₄×C₅⋊D₅	C₂²	semidirect
16. C₃×D₄×C₅⋊D₅	C₂²	semidirect
17. C₂×C₃×C₄⋊(C₅⋊D₅)	C₂²	semidirect
18. C₂×C₃×C₄×C₅⋊D₅	C₂²	semidirect
19. C₂×C₃×C₅×C₂²⋊D₅	C₂²	semidirect
20. C₃×C₅×#711	C₂²	semidirect
21. C₃×C₅×D₄×D₅	C₂²	semidirect
22. C₃×C₅×#709	C₂²	semidirect
23. C₃×#87886	C₂²	semidirect
24. C₃×#87886	C₂²	semidirect
25. C₃×#87886	C₂²	semidirect
26. C₃×#87886	C₂²	semidirect
27. C₃×D₅×C₂²⋊D₅	C₂²	semidirect
28. C₂×C₃×#6038	C₂²	semidirect
29. C₂×C₃×#6036	C₂²	semidirect
30. C₃×#87880	C₂²	semidirect
31. C₃×#87879	C₂²	semidirect
32. C₃×#87877	C₂²	semidirect
33. C₃×D₅×D₂₀	C₂²	semidirect
34. C₃×C₄×D₅²	C₂²	semidirect
35. C₃×#87874	C₂²	semidirect
36. C₃×#87873	C₂²	semidirect
37. C₃×#87872	C₂²	semidirect
38. C₃×#87871	C₂²	semidirect
40. C₂×D₄×C₅⋊D₅	C₂×C₃	semidirect
41. C₅×#4144	C₂×C₃	semidirect
42. #11717495	C₂×C₃	semidirect
43. C₂×#87886	C₂×C₃	semidirect
44. #11717479	C₂×C₃	semidirect
45. #11717477	C₂×C₃	semidirect
46. D₄×D₅²	C₂×C₃	semidirect
47. #11717473	C₂×C₃	semidirect
48. #11717471	C₂×C₃	semidirect
49. C₂³×C₃×C₅²	C₂³	semidirect
53. C₂²×C₃×C₅⋊D₅	C₂³	semidirect
54. C₂²×C₃×C₅⋊D₅	C₂³	semidirect
55. C₂²×C₃×C₅×D₅	C₂³	semidirect
58. C₂×C₃×D₅²	C₂³	semidirect
59. C₃×C₅²×D₄	C₂³	semidirect
60. C₂×C₃×C₄×C₅²	C₂³	semidirect
61. C₃×C₂²⋊(C₅⋊D₅)	C₂³	semidirect
62. C₂×C₃×#1039	C₂³	semidirect
63. C₃×C₄⋊(C₅⋊D₅)	C₂³	semidirect
65. C₃×C₄×C₅⋊D₅	C₂³	semidirect
66. C₃×C₅×C₂²⋊D₅	C₂³	semidirect
67. C₃×C₅×C₂²⋊D₅	C₂³	semidirect
68. C₂×C₃×C₅×Dic₅	C₂³	semidirect
69. C₃×C₅×D₂₀	C₂³	semidirect
70. C₃×C₄×C₅×D₅	C₂³	semidirect
71. C₃×C₅×Dic₁₀	C₂³	semidirect
72. C₃×#6039	C₂³	semidirect
73. C₃×#6038	C₂³	semidirect
74. C₃×#6038	C₂³	semidirect
75. C₃×#6037	C₂³	semidirect
77. C₃×#6036	C₂³	semidirect
78. C₃×D₅×Dic₅	C₂³	semidirect
86. C₃×#4144	D₅	semidirect
91. C₂³×C₅⋊D₅	C₂²×C₃	semidirect
92. C₂²×D₅²	C₂²×C₃	semidirect
93. C₂×C₅²×D₄	C₂²×C₃	semidirect
94. C₂×C₂²⋊(C₅⋊D₅)	C₂²×C₃	semidirect
95. D₄×C₅⋊D₅	C₂²×C₃	semidirect
96. D₄×C₅⋊D₅	C₂²×C₃	semidirect
97. C₂×C₄⋊(C₅⋊D₅)	C₂²×C₃	semidirect
98. C₂×C₄×C₅⋊D₅	C₂²×C₃	semidirect
99. C₂×C₅×C₂²⋊D₅	C₂²×C₃	semidirect
100. C₅×#711	C₂²×C₃	semidirect
101. C₅×D₄×D₅	C₂²×C₃	semidirect
102. C₅×#709	C₂²×C₃	semidirect
103. #87886	C₂²×C₃	semidirect
104. #87886	C₂²×C₃	semidirect
105. #87886	C₂²×C₃	semidirect
106. #87886	C₂²×C₃	semidirect
107. D₅×C₂²⋊D₅	C₂²×C₃	semidirect
108. C₂×#6038	C₂²×C₃	semidirect
109. C₂×#6036	C₂²×C₃	semidirect
110. #87880	C₂²×C₃	semidirect
111. #87879	C₂²×C₃	semidirect
112. #87877	C₂²×C₃	semidirect
113. D₅×D₂₀	C₂²×C₃	semidirect
114. C₄×D₅²	C₂²×C₃	semidirect
115. #87874	C₂²×C₃	semidirect
116. #87873	C₂²×C₃	semidirect
117. #87872	C₂²×C₃	semidirect
118. #87871	C₂²×C₃	semidirect
145. C₂×C₃×C₅×D₄	C₂×D₅	semidirect
150. C₂×C₃×C₂²⋊D₅	C₂×D₅	semidirect
157. C₃×#711	C₂×D₅	semidirect
169. C₃×D₄×D₅	C₂×D₅	semidirect
173. C₃×#709	C₂×D₅	semidirect
182. C₂³×C₅²	C₂³×C₃	semidirect
186. C₂²×C₅⋊D₅	C₂³×C₃	semidirect
187. C₂²×C₅⋊D₅	C₂³×C₃	semidirect
188. C₂²×C₅×D₅	C₂³×C₃	semidirect
191. C₂×D₅²	C₂³×C₃	semidirect
192. C₅²×D₄	C₂³×C₃	semidirect
193. C₂×C₄×C₅²	C₂³×C₃	semidirect
194. C₂²⋊(C₅⋊D₅)	C₂³×C₃	semidirect
195. C₂×#1039	C₂³×C₃	semidirect
196. C₄⋊(C₅⋊D₅)	C₂³×C₃	semidirect
198. C₄×C₅⋊D₅	C₂³×C₃	semidirect
199. C₅×C₂²⋊D₅	C₂³×C₃	semidirect
200. C₅×C₂²⋊D₅	C₂³×C₃	semidirect
201. C₂×C₅×Dic₅	C₂³×C₃	semidirect
202. C₅×D₂₀	C₂³×C₃	semidirect
203. C₄×C₅×D₅	C₂³×C₃	semidirect
204. C₅×Dic₁₀	C₂³×C₃	semidirect
205. #6039	C₂³×C₃	semidirect
206. #6038	C₂³×C₃	semidirect
207. #6038	C₂³×C₃	semidirect
208. #6037	C₂³×C₃	semidirect
210. #6036	C₂³×C₃	semidirect
211. D₅×Dic₅	C₂³×C₃	semidirect
220. #4144	C₃×D₅	semidirect
230. C₃×C₅⋊D₅	H(5,𝔽₂)	semidirect
234. C₂³×C₃×C₅	C₂²×D₅	semidirect
249. C₂²×C₃×D₅	C₂²×D₅	semidirect
255. C₃×C₅×D₄	C₂²×D₅	semidirect
259. C₂×C₃×C₄×C₅	C₂²×D₅	semidirect
265. C₃×C₂²⋊D₅	C₂²×D₅	semidirect
266. C₃×C₂²⋊D₅	C₂²×D₅	semidirect
270. C₂×C₃×Dic₅	C₂²×D₅	semidirect
275. C₃×D₂₀	C₂²×D₅	semidirect
283. C₃×C₄×D₅	C₂²×D₅	semidirect
285. C₃×Dic₁₀	C₂²×D₅	semidirect
320. C₂×C₅×D₄	C₂×C₃×D₅	semidirect
325. C₂×C₂²⋊D₅	C₂×C₃×D₅	semidirect
332. #711	C₂×C₃×D₅	semidirect
344. D₄×D₅	C₂×C₃×D₅	semidirect
348. #709	C₂×C₃×D₅	semidirect
357. C₃×C₅²	C₂×H(5,𝔽₂)	semidirect
400. C₅⋊D₅	C₃×H(5,𝔽₂)	semidirect
426. C₂×C₃×D₄	D₅²	semidirect
432. C₂³×C₅	C₂²×C₃×D₅	semidirect
447. C₂²×D₅	C₂²×C₃×D₅	semidirect
453. C₅×D₄	C₂²×C₃×D₅	semidirect
457. C₂×C₄×C₅	C₂²×C₃×D₅	semidirect
463. C₂²⋊D₅	C₂²×C₃×D₅	semidirect
464. C₂²⋊D₅	C₂²×C₃×D₅	semidirect
468. C₂×Dic₅	C₂²×C₃×D₅	semidirect
473. D₂₀	C₂²×C₃×D₅	semidirect
481. C₄×D₅	C₂²×C₃×D₅	semidirect
483. Dic₁₀	C₂²×C₃×D₅	semidirect
509. C₅²	C₂×C₃×H(5,𝔽₂)	semidirect
519. C₂³×C₃	C₂×D₅²	semidirect
530. C₃×D₄	C₂×D₅²	semidirect
539. C₂×C₃×C₄	C₂×D₅²	semidirect
600. C₂×D₄	C₃×D₅²	semidirect
605. C₃×C₅	D₅×H(5,𝔽₂)	semidirect
648. C₂³	C₂×C₃×D₅²	semidirect
659. D₄	C₂×C₃×D₅²	semidirect
668. C₂×C₄	C₂×C₃×D₅²	semidirect
677. C₅	C₃×D₅×H(5,𝔽₂)	semidirect
695. C₃	#13107821	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×#11717473	2
C₃×#11717479	2
C₃×#11717495	2
C₃×C₅×#4144	2
C₃×#11717477	2
C₃×D₄×D₅²	2
C₂×C₃×#87886	2
C₃×#11717471	2
C₂×C₃×D₄×C₅⋊D₅	2
#13107821	3
C₃×D₅×H(5,𝔽₂)	5

Subgroups — C3×#13107821 #72231629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#13107821 #72231629