Subgroups — C₃×#10617150 #14415696

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅⋊M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#700	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#65773	C₂	1	2	yes	maximal, complemented
5	C₃×#65756	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65756	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65704	C₂	1	2	yes	maximal, complemented
8	C₃×#65695	C₂	1	2	yes	maximal, complemented
9	C₃×#65692	C₂	1	2	yes	maximal, complemented
10	C₃×#65682	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#700	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617150	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#704	C₂²	1	2	yes	complemented
17	C₂²×C₃×#170	C₂²	1	2	yes	complemented
18	C₃×D₅⋊M₁₆	—	2	4	no	—
19	C₂×C₃×#700	—	2	4	no	—
20	C₂×C₃×#700	C₂²	1	1	yes	characteristic
21	C₂×C₃×#700	C₂²	1	1	yes	characteristic
22	C₂×C₃×#700	C₂²	1	1	yes	characteristic
23	C₂×C₃×#700	C₂²	1	1	yes	characteristic
24	C₂×C₃×#700	C₂²	1	2	yes	complemented
25	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	complemented
26	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
27	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
29	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic
30	C₃×#4039	C₂²	1	1	yes	characteristic
31	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
32	C₃×#4027	C₂²	1	1	yes	characteristic
33	C₃×#4027	C₂²	1	1	yes	characteristic
34	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
35	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
36	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
37	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
38	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
39	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
40	C₃×#4004	C₂²	1	2	yes	complemented
41	C₃×#4004	C₂²	1	2	yes	complemented
42	C₃×#4003	C₂²	1	2	yes	complemented
43	C₃×#4003	C₂²	1	2	yes	complemented
44	C₃×#4002	C₂²	1	2	yes	complemented
45	C₃×C₄×#170	C₂²	1	2	yes	complemented
46	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
47	C₂×D₅⋊M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×#700	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
50	#65773	C₂×C₃	1	2	yes	complemented
51	#65756	C₂×C₃	1	1	yes	characteristic, complemented
52	#65756	C₂×C₃	1	1	yes	characteristic, complemented
53	#65704	C₂×C₃	1	2	yes	complemented
54	#65695	C₂×C₃	1	2	yes	complemented
55	#65692	C₂×C₃	1	2	yes	complemented
56	#65682	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×#700	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
67	C₃×D₄×D₅	—	2	4	no	—
68	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	—	2	2	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×C₄×D₅	—	2	2	no	—
72	C₂×C₃×C₄×D₅	—	2	2	no	—
73	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
82	C₃×#704	—	2	4	no	—
83	C₂×C₃×#170	—	2	4	no	—
84	C₂×C₃×#170	C₂³	1	2	yes	—
85	C₂×C₃×#170	C₂³	1	2	yes	—
86	C₂×C₃×#170	C₂³	1	2	yes	—
87	C₂×C₃×#170	C₂³	1	2	yes	—
88	C₃×#700	—	2	2	no	—
89	C₃×#700	—	2	2	no	—
90	C₃×#700	—	2	2	no	—
91	C₃×#700	—	2	4	no	—
92	C₃×#700	D₄	1	4	yes	complemented
93	C₃×D₅⋊C₈	—	2	4	no	—
94	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
98	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₃×#685	C₂×C₄	1	1	yes	characteristic
101	C₃×#685	C₂×C₄	1	1	yes	characteristic
102	C₃×#685	C₂×C₄	1	1	yes	characteristic
103	C₃×#685	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
105	C₃×#683	C₂×C₄	1	1	yes	characteristic
106	C₃×#683	C₂×C₄	1	1	yes	characteristic
107	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
109	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×M₁₆	—	5	1	no	—
111	C₂²×C₃×M₁₆	—	5	1	no	—
112	C₂×C₃×C₄×D₄	—	5	1	no	—
113	C₃×#436	—	5	2	no	—
114	C₃×#435	—	5	2	no	—
115	C₃×#435	—	5	2	no	—
116	C₃×C₈×D₄	—	5	2	no	—
117	C₃×#423	—	5	1	no	—
118	C₃×#407	—	5	1	no	—
119	C₃×#407	—	5	1	no	—
120	C₃×C₄×M₁₆	—	5	1	no	—
121	C₂×D₄×D₅	C₃×C₄	1	1	yes	characteristic
122	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
124	C₂×#704	C₂²×C₃	1	2	yes	complemented
125	C₂²×#170	C₂²×C₃	1	2	yes	complemented
126	D₅⋊M₁₆	—	2	4	no	—
127	C₂×#700	—	2	4	no	—
128	C₂×#700	C₂²×C₃	1	1	yes	characteristic
129	C₂×#700	C₂²×C₃	1	1	yes	characteristic
130	C₂×#700	C₂²×C₃	1	1	yes	characteristic
131	C₂×#700	C₂²×C₃	1	1	yes	characteristic
132	C₂×#700	C₂²×C₃	1	2	yes	complemented
133	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	complemented
134	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
135	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
136	C₄×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic
137	C₄×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic
138	#4039	C₂²×C₃	1	1	yes	characteristic
139	D₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
140	#4027	C₂²×C₃	1	1	yes	characteristic
141	#4027	C₂²×C₃	1	1	yes	characteristic
142	D₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
143	D₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
144	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic
145	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
146	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
147	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
148	#4004	C₂²×C₃	1	2	yes	complemented
149	#4004	C₂²×C₃	1	2	yes	complemented
150	#4003	C₂²×C₃	1	2	yes	complemented
151	#4003	C₂²×C₃	1	2	yes	complemented
152	#4002	C₂²×C₃	1	2	yes	complemented
153	C₄×#170	C₂²×C₃	1	2	yes	complemented
154	D₄×M₁₆	—	5	1	no	Sylow
155	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₃×D₅	—	2	2	no	—
158	C₂²×C₃×D₅	—	2	2	no	—
159	C₂²×C₃×D₅	—	2	2	no	—
160	C₂²×C₃×D₅	—	2	2	no	—
161	C₂²×C₃×D₅	—	4	1	no	—
162	C₂²×C₃×D₅	—	4	1	no	—
163	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
166	C₃×C₅×D₄	—	2	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₃×C₂²⋊D₅	—	2	2	no	—
175	C₃×C₂²⋊D₅	M₁₆	1	4	yes	complemented
176	C₂×C₃×Dic₅	—	2	1	no	—
177	C₂×C₃×Dic₅	—	2	1	no	—
178	C₂×C₃×Dic₅	—	2	1	no	—
179	C₂×C₃×Dic₅	—	2	1	no	—
180	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
185	C₃×D₂₀	—	2	2	no	—
186	C₃×C₄×D₅	—	2	2	no	—
187	C₃×C₄×D₅	—	2	2	no	—
188	C₃×C₄×D₅	—	2	2	no	—
189	C₃×C₄×D₅	—	2	2	no	—
190	C₃×C₄×D₅	—	2	2	no	—
191	C₃×C₄×D₅	—	2	1	no	—
192	C₃×C₄×D₅	—	2	1	no	—
193	C₃×C₄×D₅	—	2	1	no	—
194	C₃×C₄×D₅	—	2	1	no	—
195	C₃×C₄×D₅	—	4	1	no	—
196	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
197	C₃×C₄×D₅	#41	1	2	yes	—
198	C₃×#170	—	2	2	no	—
199	C₃×#170	—	2	2	no	—
200	C₃×#170	—	2	2	no	—
201	C₃×#170	C₂×D₄	1	4	yes	complemented
202	C₂²×C₃×D₄	—	5	1	no	—
203	C₂³×C₃×C₄	—	5	1	no	—
204	C₂³×C₃×C₄	—	5	1	no	—
205	C₂×C₃×M₁₆	—	5	1	no	—
206	C₂×C₃×M₁₆	—	5	1	no	—
207	C₂×C₃×M₁₆	—	5	1	no	—
208	C₂×C₃×M₁₆	—	5	2	no	—
209	C₂×C₃×M₁₆	—	5	2	no	—
210	C₂×C₃×M₁₆	—	5	1	no	—
211	C₂×C₃×M₁₆	—	10	4	no	—
212	C₂×C₃×M₁₆	—	10	4	no	—
213	C₂²×C₃×C₈	—	5	2	no	—
214	C₂²×C₃×C₈	—	5	2	no	—
215	C₃×C₄×D₄	—	5	1	no	—
216	C₃×C₄×D₄	—	5	1	no	—
217	C₃×C₄×D₄	—	5	1	no	—
218	C₃×C₄×D₄	—	5	1	no	—
219	C₃×C₄×D₄	—	5	1	no	—
220	C₃×C₄×D₄	—	5	1	no	—
221	C₃×C₄×D₄	—	5	1	no	—
222	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
223	C₂×C₃×C₄⋊C₄	—	5	1	no	—
224	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
225	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
226	C₂×C₃×C₄²	—	5	1	no	—
227	C₃×C₄⋊C₈	—	5	2	no	—
228	C₃×C₄⋊C₈	—	5	2	no	—
229	C₃×C₂²⋊C₈	—	5	2	no	—
230	C₃×C₂²⋊C₈	—	5	2	no	—
231	C₃×C₂²⋊C₈	—	5	2	no	—
232	C₃×C₂²⋊C₈	—	5	2	no	—
233	C₃×#97	—	5	2	no	—
234	C₃×C₄×C₈	—	5	2	no	—
235	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
236	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
237	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
240	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
241	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
242	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
243	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
244	D₄×D₅	—	2	4	no	—
245	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
246	C₂×C₄×D₅	—	2	2	no	—
247	C₂×C₄×D₅	—	2	2	no	—
248	C₂×C₄×D₅	—	2	2	no	—
249	C₂×C₄×D₅	—	2	2	no	—
250	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
251	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
252	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
253	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
254	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
255	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
256	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
259	#704	—	2	4	no	—
260	C₂×#170	—	2	4	no	—
261	C₂×#170	C₂³×C₃	1	2	yes	—
262	C₂×#170	C₂³×C₃	1	2	yes	—
263	C₂×#170	C₂³×C₃	1	2	yes	—
264	C₂×#170	C₂³×C₃	1	2	yes	—
265	#700	—	2	2	no	—
266	#700	—	2	2	no	—
267	#700	—	2	2	no	—
268	#700	—	2	4	no	—
269	#700	C₃×D₄	1	4	yes	complemented
270	D₅⋊C₈	—	2	4	no	—
271	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
272	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
273	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
274	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
275	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
276	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
277	#685	C₂×C₃×C₄	1	1	yes	characteristic
278	#685	C₂×C₃×C₄	1	1	yes	characteristic
279	#685	C₂×C₃×C₄	1	1	yes	characteristic
280	#685	C₂×C₃×C₄	1	1	yes	characteristic
281	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
282	#683	C₂×C₃×C₄	1	1	yes	characteristic
283	#683	C₂×C₃×C₄	1	1	yes	characteristic
284	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
285	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
286	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
287	C₂²×M₁₆	—	5	1	no	—
288	C₂²×M₁₆	—	5	1	no	—
289	C₂×C₄×D₄	—	5	1	no	—
290	#436	—	5	2	no	—
291	#435	—	5	2	no	—
292	#435	—	5	2	no	—
293	C₈×D₄	—	5	2	no	—
294	#423	—	5	1	no	—
295	#407	—	5	1	no	—
296	#407	—	5	1	no	—
297	C₄×M₁₆	—	5	1	no	—
298	C₂²×C₃×C₅	—	2	1	no	—
299	C₂²×C₃×C₅	—	2	1	no	—
300	C₂²×C₃×C₅	—	2	1	no	—
301	C₂²×C₃×C₅	—	2	1	no	—
302	C₂²×C₃×C₅	—	2	1	no	—
303	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
304	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₃×D₅	—	2	1	no	—
306	C₂×C₃×D₅	—	2	1	no	—
307	C₂×C₃×D₅	—	2	1	no	—
308	C₂×C₃×D₅	—	2	1	no	—
309	C₂×C₃×D₅	—	2	1	no	—
310	C₂×C₃×D₅	—	2	1	no	—
311	C₂×C₃×D₅	—	2	1	no	—
312	C₂×C₃×D₅	—	4	4	no	—
313	C₂×C₃×D₅	—	4	4	no	—
314	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
315	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	complemented
316	C₃×C₄×C₅	—	2	1	no	—
317	C₃×C₄×C₅	—	2	1	no	—
318	C₃×C₄×C₅	—	2	1	no	—
319	C₃×C₄×C₅	—	2	1	no	—
320	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
321	C₃×Dic₅	—	2	1	no	—
322	C₃×Dic₅	—	2	1	no	—
323	C₃×Dic₅	—	2	1	no	—
324	C₃×Dic₅	C₂×M₁₆	1	2	yes	complemented
325	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
326	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
327	C₂⁴×C₃	—	5	1	no	—
328	C₂⁴×C₃	—	5	1	no	—
329	C₂×C₃×D₄	—	5	1	no	—
330	C₂×C₃×D₄	—	5	1	no	—
331	C₂×C₃×D₄	—	5	1	no	—
332	C₂×C₃×D₄	—	10	4	no	—
333	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₂²×C₃×C₄	—	5	1	no	—
335	C₂²×C₃×C₄	—	5	1	no	—
336	C₂²×C₃×C₄	—	5	1	no	—
337	C₂²×C₃×C₄	—	5	1	no	—
338	C₂²×C₃×C₄	—	5	1	no	—
339	C₂²×C₃×C₄	—	5	1	no	—
340	C₂²×C₃×C₄	—	5	1	no	—
341	C₂²×C₃×C₄	—	5	1	no	—
342	C₂²×C₃×C₄	—	5	1	no	—
343	C₂²×C₃×C₄	—	5	1	no	—
344	C₂²×C₃×C₄	—	5	1	no	—
345	C₂²×C₃×C₄	—	10	2	no	—
346	C₂²×C₃×C₄	—	10	2	no	—
347	C₂²×C₃×C₄	—	10	2	no	—
348	C₂²×C₃×C₄	—	10	2	no	—
349	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₃×M₁₆	—	5	4	no	—
352	C₃×M₁₆	—	10	4	no	—
353	C₃×M₁₆	—	10	4	no	—
354	C₃×M₁₆	—	10	2	no	—
355	C₃×M₁₆	—	10	2	no	—
356	C₃×M₁₆	—	10	2	no	—
357	C₂×C₃×C₈	—	5	2	no	—
358	C₂×C₃×C₈	—	5	2	no	—
359	C₂×C₃×C₈	—	5	2	no	—
360	C₂×C₃×C₈	—	5	2	no	—
361	C₂×C₃×C₈	—	10	4	no	—
362	C₂×C₃×C₈	—	10	4	no	—
363	C₃×C₄⋊C₄	—	5	1	no	—
364	C₃×C₄⋊C₄	—	5	1	no	—
365	C₃×C₄⋊C₄	—	5	1	no	—
366	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₃×C₂²⋊C₄	—	5	1	no	—
368	C₃×C₂²⋊C₄	—	5	1	no	—
369	C₃×C₂²⋊C₄	—	5	1	no	—
370	C₃×C₂²⋊C₄	—	5	1	no	—
371	C₃×C₂²⋊C₄	—	5	1	no	—
372	C₃×C₂²⋊C₄	—	5	1	no	—
373	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₃×C₄²	—	5	1	no	—
376	C₃×C₄²	—	5	1	no	—
377	C₃×C₄²	—	5	1	no	—
378	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
380	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
381	C₂²×D₅	—	2	2	no	—
382	C₂²×D₅	—	2	2	no	—
383	C₂²×D₅	—	2	2	no	—
384	C₂²×D₅	—	2	2	no	—
385	C₂²×D₅	—	4	1	no	—
386	C₂²×D₅	—	4	1	no	—
387	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
388	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
389	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
390	C₅×D₄	—	2	2	no	—
391	C₂×C₄×C₅	—	2	2	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
394	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
395	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
396	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
397	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
398	C₂²⋊D₅	—	2	2	no	—
399	C₂²⋊D₅	C₃×M₁₆	1	4	yes	complemented
400	C₂×Dic₅	—	2	1	no	—
401	C₂×Dic₅	—	2	1	no	—
402	C₂×Dic₅	—	2	1	no	—
403	C₂×Dic₅	—	2	1	no	—
404	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
405	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
407	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
409	D₂₀	—	2	2	no	—
410	C₄×D₅	—	2	2	no	—
411	C₄×D₅	—	2	2	no	—
412	C₄×D₅	—	2	2	no	—
413	C₄×D₅	—	2	2	no	—
414	C₄×D₅	—	2	2	no	—
415	C₄×D₅	—	2	1	no	—
416	C₄×D₅	—	2	1	no	—
417	C₄×D₅	—	2	1	no	—
418	C₄×D₅	—	2	1	no	—
419	C₄×D₅	—	4	1	no	—
420	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
421	C₄×D₅	C₃×#41	1	2	yes	—
422	#170	—	2	2	no	—
423	#170	—	2	2	no	—
424	#170	—	2	2	no	—
425	#170	C₂×C₃×D₄	1	4	yes	complemented
426	C₂²×D₄	—	5	1	no	—
427	C₂³×C₄	—	5	1	no	—
428	C₂³×C₄	—	5	1	no	—
429	C₂×M₁₆	—	5	1	no	—
430	C₂×M₁₆	—	5	1	no	—
431	C₂×M₁₆	—	5	1	no	—
432	C₂×M₁₆	—	5	1	no	—
433	C₂×M₁₆	—	5	2	no	—
434	C₂×M₁₆	—	5	2	no	—
435	C₂×M₁₆	—	10	4	no	—
436	C₂×M₁₆	—	10	4	no	—
437	C₂²×C₈	—	5	2	no	—
438	C₂²×C₈	—	5	2	no	—
439	C₄×D₄	—	5	1	no	—
440	C₄×D₄	—	5	1	no	—
441	C₄×D₄	—	5	1	no	—
442	C₄×D₄	—	5	1	no	—
443	C₄×D₄	—	5	1	no	—
444	C₄×D₄	—	5	1	no	—
445	C₄×D₄	—	5	1	no	—
446	C₄×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	5	1	no	—
448	C₂×C₂²⋊C₄	—	5	1	no	—
449	C₂×C₂²⋊C₄	—	5	1	no	—
450	C₂×C₄²	—	5	1	no	—
451	C₄⋊C₈	—	5	2	no	—
452	C₄⋊C₈	—	5	2	no	—
453	C₂²⋊C₈	—	5	2	no	—
454	C₂²⋊C₈	—	5	2	no	—
455	C₂²⋊C₈	—	5	2	no	—
456	C₂²⋊C₈	—	5	2	no	—
457	#97	—	5	2	no	—
458	C₄×C₈	—	5	2	no	—
459	C₂×C₃×C₅	—	2	2	no	—
460	C₂×C₃×C₅	—	4	1	no	—
461	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
462	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
463	C₂×C₃×C₅	#568	1	1	yes	characteristic
464	C₃×D₅	—	2	2	no	—
465	C₃×D₅	—	2	2	no	—
466	C₃×D₅	—	4	1	no	—
467	C₂³×C₃	—	5	1	no	—
468	C₂³×C₃	—	5	1	no	—
469	C₂³×C₃	—	5	1	no	—
470	C₂³×C₃	—	10	2	no	—
471	C₂³×C₃	—	10	2	no	—
472	C₂³×C₃	—	10	2	no	—
473	C₂³×C₃	—	10	2	no	—
474	C₂³×C₃	—	20	1	no	—
475	C₂³×C₃	—	20	1	no	—
476	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₃×D₄	—	2	2	no	—
479	C₃×D₄	—	5	4	no	—
480	C₃×D₄	—	10	2	no	—
481	C₃×D₄	—	10	2	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	5	1	no	—
485	C₂×C₃×C₄	—	5	1	no	—
486	C₂×C₃×C₄	—	5	2	no	—
487	C₂×C₃×C₄	—	5	2	no	—
488	C₂×C₃×C₄	—	5	1	no	—
489	C₂×C₃×C₄	—	5	1	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	10	1	no	—
492	C₂×C₃×C₄	—	10	1	no	—
493	C₂×C₃×C₄	—	10	1	no	—
494	C₂×C₃×C₄	—	10	1	no	—
495	C₂×C₃×C₄	—	10	2	no	—
496	C₂×C₃×C₄	—	10	2	no	—
497	C₂×C₃×C₄	—	10	2	no	—
498	C₂×C₃×C₄	—	10	1	no	—
499	C₂×C₃×C₄	—	10	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	—	10	2	no	—
503	C₂×C₃×C₄	—	10	2	no	—
504	C₂×C₃×C₄	—	20	1	no	—
505	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
509	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
510	C₃×C₈	—	5	4	no	—
511	C₃×C₈	—	10	2	no	—
512	C₃×C₈	—	10	2	no	—
513	C₃×C₈	—	10	2	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	2	1	no	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
520	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
521	C₂×D₅	—	2	1	no	—
522	C₂×D₅	—	2	1	no	—
523	C₂×D₅	—	2	1	no	—
524	C₂×D₅	—	2	1	no	—
525	C₂×D₅	—	2	1	no	—
526	C₂×D₅	—	2	1	no	—
527	C₂×D₅	—	2	1	no	—
528	C₂×D₅	—	4	4	no	—
529	C₂×D₅	—	4	4	no	—
530	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
531	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	complemented
532	C₄×C₅	—	2	1	no	—
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	2	1	no	—
535	C₄×C₅	—	2	1	no	—
536	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
537	Dic₅	—	2	1	no	—
538	Dic₅	—	2	1	no	—
539	Dic₅	—	2	1	no	—
540	Dic₅	C₂×C₃×M₁₆	1	2	yes	complemented
541	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
542	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
543	C₂⁴	—	5	1	no	—
544	C₂⁴	—	5	1	no	—
545	C₂×D₄	—	5	1	no	—
546	C₂×D₄	—	5	1	no	—
547	C₂×D₄	—	5	1	no	—
548	C₂×D₄	—	10	4	no	—
549	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
550	C₂²×C₄	—	5	1	no	—
551	C₂²×C₄	—	5	1	no	—
552	C₂²×C₄	—	5	1	no	—
553	C₂²×C₄	—	5	1	no	—
554	C₂²×C₄	—	5	1	no	—
555	C₂²×C₄	—	5	1	no	—
556	C₂²×C₄	—	5	1	no	—
557	C₂²×C₄	—	5	1	no	—
558	C₂²×C₄	—	5	1	no	—
559	C₂²×C₄	—	5	1	no	—
560	C₂²×C₄	—	5	1	no	—
561	C₂²×C₄	—	10	2	no	—
562	C₂²×C₄	—	10	2	no	—
563	C₂²×C₄	—	10	2	no	—
564	C₂²×C₄	—	10	2	no	—
565	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
566	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
567	M₁₆	—	5	4	no	—
568	M₁₆	—	10	4	no	—
569	M₁₆	—	10	4	no	—
570	M₁₆	—	10	2	no	—
571	M₁₆	—	10	2	no	—
572	M₁₆	—	10	2	no	—
573	C₂×C₈	—	5	2	no	—
574	C₂×C₈	—	5	2	no	—
575	C₂×C₈	—	5	2	no	—
576	C₂×C₈	—	5	2	no	—
577	C₂×C₈	—	10	4	no	—
578	C₂×C₈	—	10	4	no	—
579	C₄⋊C₄	—	5	1	no	—
580	C₄⋊C₄	—	5	1	no	—
581	C₄⋊C₄	—	5	1	no	—
582	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
583	C₂²⋊C₄	—	5	1	no	—
584	C₂²⋊C₄	—	5	1	no	—
585	C₂²⋊C₄	—	5	1	no	—
586	C₂²⋊C₄	—	5	1	no	—
587	C₂²⋊C₄	—	5	1	no	—
588	C₂²⋊C₄	—	5	1	no	—
589	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
590	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
591	C₄²	—	5	1	no	—
592	C₄²	—	5	1	no	—
593	C₄²	—	5	1	no	—
594	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
595	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	5	2	no	—
602	C₂²×C₃	—	5	2	no	—
603	C₂²×C₃	—	10	1	no	—
604	C₂²×C₃	—	10	1	no	—
605	C₂²×C₃	—	10	1	no	—
606	C₂²×C₃	—	10	1	no	—
607	C₂²×C₃	—	10	1	no	—
608	C₂²×C₃	—	10	1	no	—
609	C₂²×C₃	—	10	1	no	—
610	C₂²×C₃	—	20	4	no	—
611	C₂²×C₃	—	20	4	no	—
612	C₂²×C₃	D₅⋊M₁₆	1	2	yes	complemented
613	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
614	C₃×C₄	—	2	1	no	—
615	C₃×C₄	—	2	1	no	—
616	C₃×C₄	—	2	1	no	—
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	5	2	no	—
619	C₃×C₄	—	5	1	no	—
620	C₃×C₄	—	5	1	no	—
621	C₃×C₄	—	10	1	no	—
622	C₃×C₄	—	10	1	no	—
623	C₃×C₄	—	10	1	no	—
624	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
625	C₂×C₅	—	2	2	no	—
626	C₂×C₅	—	4	1	no	—
627	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
628	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
629	C₂×C₅	C₃×#568	1	1	yes	characteristic
630	D₅	—	2	2	no	—
631	D₅	—	2	2	no	—
632	D₅	—	4	1	no	—
633	C₂³	—	5	1	no	—
634	C₂³	—	5	1	no	—
635	C₂³	—	5	1	no	—
636	C₂³	—	10	2	no	—
637	C₂³	—	10	2	no	—
638	C₂³	—	10	2	no	—
639	C₂³	—	10	2	no	—
640	C₂³	—	20	1	no	—
641	C₂³	—	20	1	no	—
642	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
643	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
644	D₄	—	2	2	no	—
645	D₄	—	5	4	no	—
646	D₄	—	10	2	no	—
647	D₄	—	10	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	5	1	no	—
651	C₂×C₄	—	5	1	no	—
652	C₂×C₄	—	5	2	no	—
653	C₂×C₄	—	5	2	no	—
654	C₂×C₄	—	5	1	no	—
655	C₂×C₄	—	5	1	no	—
656	C₂×C₄	—	5	1	no	—
657	C₂×C₄	—	10	1	no	—
658	C₂×C₄	—	10	1	no	—
659	C₂×C₄	—	10	1	no	—
660	C₂×C₄	—	10	1	no	—
661	C₂×C₄	—	10	2	no	—
662	C₂×C₄	—	10	2	no	—
663	C₂×C₄	—	10	2	no	—
664	C₂×C₄	—	10	1	no	—
665	C₂×C₄	—	10	1	no	—
666	C₂×C₄	—	10	1	no	—
667	C₂×C₄	—	10	1	no	—
668	C₂×C₄	—	10	2	no	—
669	C₂×C₄	—	10	2	no	—
670	C₂×C₄	—	20	1	no	—
671	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
672	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
673	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
674	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
675	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
676	C₈	—	5	4	no	—
677	C₈	—	10	2	no	—
678	C₈	—	10	2	no	—
679	C₈	—	10	2	no	—
680	C₂×C₃	—	2	2	no	—
681	C₂×C₃	—	4	1	no	—
682	C₂×C₃	—	10	2	no	—
683	C₂×C₃	—	10	2	no	—
684	C₂×C₃	—	20	1	no	—
685	C₂×C₃	C₂×D₅⋊M₁₆	1	1	yes	characteristic
686	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
687	C₂×C₃	#66264	1	1	yes	characteristic
688	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	5	2	no	—
695	C₂²	—	5	2	no	—
696	C₂²	—	10	1	no	—
697	C₂²	—	10	1	no	—
698	C₂²	—	10	1	no	—
699	C₂²	—	10	1	no	—
700	C₂²	—	10	1	no	—
701	C₂²	—	10	1	no	—
702	C₂²	—	10	1	no	—
703	C₂²	—	20	4	no	—
704	C₂²	—	20	4	no	—
705	C₂²	C₃×D₅⋊M₁₆	1	2	yes	complemented
706	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	5	2	no	—
712	C₄	—	5	1	no	—
713	C₄	—	5	1	no	—
714	C₄	—	10	1	no	—
715	C₄	—	10	1	no	—
716	C₄	—	10	1	no	—
717	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
718	C₃	#10617150	1	1	yes	characteristic, direct product factor, Sylow
719	C₂	—	2	2	no	—
720	C₂	—	4	1	no	—
721	C₂	—	10	2	no	—
722	C₂	—	10	2	no	—
723	C₂	—	20	1	no	—
724	C₂	C₂×C₃×D₅⋊M₁₆	1	1	yes	characteristic
725	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
726	C₂	C₃×#66264	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₄×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×D₄×D₅	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₄×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅⋊M₁₆	C₂	semidirect
2. C₂²×C₃×#700	C₂	semidirect
4. C₃×#65773	C₂	semidirect
5. C₃×#65756	C₂	semidirect
6. C₃×#65756	C₂	semidirect
7. C₃×#65704	C₂	semidirect
8. C₃×#65695	C₂	semidirect
9. C₃×#65692	C₂	semidirect
10. C₃×#65682	C₂	semidirect
11. C₃×C₄×#700	C₂	semidirect
12. #10617150	C₃	direct (N × H)
16. C₂×C₃×#704	C₂²	semidirect
17. C₂²×C₃×#170	C₂²	semidirect
24. C₂×C₃×#700	C₂²	semidirect
25. C₂×C₃×D₅⋊C₈	C₂²	semidirect
38. C₃×C₂²⋊#170	C₂²	semidirect
39. C₃×C₂²⋊#170	C₂²	semidirect
40. C₃×#4004	C₂²	semidirect
41. C₃×#4004	C₂²	semidirect
42. C₃×#4003	C₂²	semidirect
43. C₃×#4003	C₂²	semidirect
44. C₃×#4002	C₂²	semidirect
45. C₃×C₄×#170	C₂²	semidirect
47. C₂×D₅⋊M₁₆	C₂×C₃	semidirect
48. C₂²×#700	C₂×C₃	semidirect
50. #65773	C₂×C₃	semidirect
51. #65756	C₂×C₃	semidirect
52. #65756	C₂×C₃	semidirect
53. #65704	C₂×C₃	semidirect
54. #65695	C₂×C₃	semidirect
55. #65692	C₂×C₃	semidirect
56. #65682	C₂×C₃	semidirect
57. C₄×#700	C₂×C₃	semidirect
92. C₃×#700	D₄	semidirect
124. C₂×#704	C₂²×C₃	semidirect
125. C₂²×#170	C₂²×C₃	semidirect
132. C₂×#700	C₂²×C₃	semidirect
133. C₂×D₅⋊C₈	C₂²×C₃	semidirect
146. C₂²⋊#170	C₂²×C₃	semidirect
147. C₂²⋊#170	C₂²×C₃	semidirect
148. #4004	C₂²×C₃	semidirect
149. #4004	C₂²×C₃	semidirect
150. #4003	C₂²×C₃	semidirect
151. #4003	C₂²×C₃	semidirect
152. #4002	C₂²×C₃	semidirect
153. C₄×#170	C₂²×C₃	semidirect
175. C₃×C₂²⋊D₅	M₁₆	semidirect
201. C₃×#170	C₂×D₄	semidirect
269. #700	C₃×D₄	semidirect
303. C₂²×C₃×C₅	C₂×M₁₆	semidirect
315. C₂×C₃×D₅	C₂×M₁₆	semidirect
324. C₃×Dic₅	C₂×M₁₆	semidirect
399. C₂²⋊D₅	C₃×M₁₆	semidirect
425. #170	C₂×C₃×D₄	semidirect
519. C₂²×C₅	C₂×C₃×M₁₆	semidirect
531. C₂×D₅	C₂×C₃×M₁₆	semidirect
540. Dic₅	C₂×C₃×M₁₆	semidirect
595. C₃×C₅	D₄×M₁₆	semidirect
612. C₂²×C₃	D₅⋊M₁₆	semidirect
688. C₅	C₃×D₄×M₁₆	semidirect
705. C₂²	C₃×D₅⋊M₁₆	semidirect
718. C₃	#10617150	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×D₅⋊M₁₆	2
C₂²×C₃×#700	2
C₃×C₄×D₄×D₅	2
C₃×#65773	2
C₃×#65756	2
C₃×#65704	2
C₃×#65695	2
C₃×#65692	2
C₃×#65682	2
C₃×C₄×#700	2
#10617150	3
C₃×D₄×M₁₆	5

Subgroups — C3×#10617150 #14415696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617150 #14415696