Subgroups — C₃×#10617407 #14411396

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4130	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₅⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#65728	C₂	1	4	yes	maximal, complemented
5	C₃×M₁₆×AGL(1,𝔽₅)	C₂	1	4	yes	maximal, complemented
6	C₃×#65718	C₂	1	4	yes	maximal, complemented
7	#10617407	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
10	C₂×C₃×#704	C₄	1	2	yes	complemented
11	C₃×#4130	C₄	1	2	yes	—
12	C₃×#4130	C₄	1	2	yes	—
13	C₃×#4130	C₂²	1	2	yes	—
14	C₃×#4130	C₂²	1	2	yes	—
15	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	1	2	yes	—
16	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
17	C₃×D₅⋊M₁₆	C₄	1	2	yes	complemented
18	C₃×D₅⋊M₁₆	C₄	1	2	yes	complemented
19	C₃×D₅⋊M₁₆	C₂²	1	2	yes	—
20	C₃×D₅⋊M₁₆	C₂²	1	2	yes	—
21	C₂×C₃×#700	C₄	1	2	yes	complemented
22	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
24	C₂×C₃×#681	C₄	1	1	yes	characteristic, complemented
25	C₃×D₅×M₁₆	C₄	1	2	yes	complemented
26	C₃×D₅×M₁₆	C₄	1	2	yes	complemented
27	C₃×D₅×M₁₆	C₂²	1	2	yes	—
28	C₃×D₅×M₁₆	C₂²	1	2	yes	—
29	C₂×C₃×#676	C₄	1	2	yes	complemented
30	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
31	C₃×#3992	C₂²	1	8	yes	complemented
32	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
33	C₃×#2873	—	5	1	no	maximal, Hall
34	C₂×#4130	C₂×C₃	1	1	yes	characteristic
35	C₂×D₅⋊M₁₆	C₂×C₃	1	1	yes	characteristic
36	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
37	#65728	C₂×C₃	1	4	yes	complemented
38	M₁₆×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	complemented
39	#65718	C₂×C₃	1	4	yes	complemented
40	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
56	C₃×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
57	C₃×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
58	C₃×#704	C₂×C₄	1	4	yes	—
59	C₃×#704	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×#170	C₂×C₄	1	4	yes	complemented
61	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
62	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
63	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
64	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	4	yes	—
65	C₃×#700	C₂×C₄	1	4	yes	—
66	C₃×#700	C₂×C₄	1	4	yes	complemented
67	C₃×D₅⋊C₈	C₂×C₄	1	4	yes	complemented
68	C₃×D₅⋊C₈	C₂³	1	4	yes	—
69	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
70	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
71	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
72	C₃×#681	C₂×C₄	1	2	yes	—
73	C₃×#681	C₂×C₄	1	2	yes	complemented
74	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
75	C₃×#676	C₂×C₄	1	4	yes	—
76	C₃×#676	C₂×C₄	1	4	yes	complemented
77	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
78	C₃×C₈×D₅	C₂³	1	4	yes	—
79	C₂²×C₃×M₁₆	—	5	1	no	—
80	C₂²×C₃×M₁₆	—	5	1	no	—
81	C₂×C₃×#117	—	5	1	no	—
82	C₃×#405	—	5	4	no	—
83	C₃×#405	—	5	4	no	—
84	C₃×C₄×M₁₆	—	5	4	no	—
85	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₂²⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
87	C₂×#704	C₃×C₄	1	2	yes	complemented
88	#4130	C₃×C₄	1	2	yes	—
89	#4130	C₃×C₄	1	2	yes	—
90	#4130	C₂²×C₃	1	2	yes	—
91	#4130	C₂²×C₃	1	2	yes	—
92	C₂×C₄⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
93	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
94	D₅⋊M₁₆	C₃×C₄	1	2	yes	complemented
95	D₅⋊M₁₆	C₃×C₄	1	2	yes	complemented
96	D₅⋊M₁₆	C₂²×C₃	1	2	yes	—
97	D₅⋊M₁₆	C₂²×C₃	1	2	yes	—
98	C₂×#700	C₃×C₄	1	2	yes	complemented
99	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
100	C₂×C₅×M₁₆	C₃×C₄	1	1	yes	characteristic, complemented
101	C₂×#681	C₃×C₄	1	1	yes	characteristic, complemented
102	D₅×M₁₆	C₃×C₄	1	2	yes	complemented
103	D₅×M₁₆	C₃×C₄	1	2	yes	complemented
104	D₅×M₁₆	C₂²×C₃	1	2	yes	—
105	D₅×M₁₆	C₂²×C₃	1	2	yes	—
106	C₂×#676	C₃×C₄	1	2	yes	complemented
107	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
108	#3992	C₂²×C₃	1	8	yes	complemented
109	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
110	#2873	—	5	1	no	Sylow
111	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
112	C₂²×C₃×D₅	—	4	2	no	—
113	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
114	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
115	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
116	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
120	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	—
121	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
128	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
129	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
130	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
133	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
134	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
135	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
136	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
137	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
138	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
139	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
141	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
142	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
143	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
144	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
145	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
146	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
148	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
149	C₃×#170	C₂²×C₄	1	8	yes	—
150	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
151	C₃×#168	C₂²×C₄	1	4	yes	—
152	C₂³×C₃×C₄	—	5	1	no	—
153	C₂×C₃×M₁₆	—	5	2	no	—
154	C₂×C₃×M₁₆	—	5	2	no	—
155	C₂×C₃×M₁₆	—	5	2	no	—
156	C₂×C₃×M₁₆	—	5	2	no	—
157	C₂×C₃×M₁₆	—	5	2	no	—
158	C₂×C₃×M₁₆	—	5	2	no	—
159	C₂×C₃×M₁₆	—	5	1	no	—
160	C₂×C₃×M₁₆	—	5	2	no	—
161	C₂×C₃×M₁₆	—	5	2	no	—
162	C₂×C₃×M₁₆	—	5	2	no	—
163	C₂×C₃×M₁₆	—	5	2	no	—
164	C₂×C₃×M₁₆	—	5	2	no	—
165	C₂×C₃×M₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
166	C₂²×C₃×C₈	—	5	2	no	—
167	C₂²×C₃×C₈	—	5	2	no	—
168	C₃×#117	—	5	2	no	—
169	C₃×#117	—	5	2	no	—
170	C₃×#117	—	5	2	no	—
171	C₃×#117	—	5	2	no	—
172	C₂×C₃×C₄⋊C₄	—	5	2	no	—
173	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
174	C₂×C₃×C₄²	—	5	2	no	—
175	C₃×#97	—	5	8	no	—
176	C₃×C₄×C₈	—	5	8	no	—
177	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
179	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
180	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
181	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
185	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
189	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
190	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
193	C₂²⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
194	C₂²⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
195	#704	C₂×C₃×C₄	1	4	yes	—
196	#704	C₂×C₃×C₄	1	4	yes	complemented
197	C₂×#170	C₂×C₃×C₄	1	4	yes	complemented
198	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
199	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
200	C₄×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
201	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
202	#700	C₂×C₃×C₄	1	4	yes	—
203	#700	C₂×C₃×C₄	1	4	yes	complemented
204	D₅⋊C₈	C₂×C₃×C₄	1	4	yes	complemented
205	D₅⋊C₈	C₂³×C₃	1	4	yes	—
206	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	—
207	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	complemented
208	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	complemented
209	#681	C₂×C₃×C₄	1	2	yes	—
210	#681	C₂×C₃×C₄	1	2	yes	complemented
211	C₂×#168	C₂×C₃×C₄	1	2	yes	complemented
212	#676	C₂×C₃×C₄	1	4	yes	—
213	#676	C₂×C₃×C₄	1	4	yes	complemented
214	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
215	C₈×D₅	C₂³×C₃	1	4	yes	—
216	C₂²×M₁₆	—	5	1	no	—
217	C₂²×M₁₆	—	5	1	no	—
218	C₂×#117	—	5	1	no	—
219	#405	—	5	4	no	—
220	#405	—	5	4	no	—
221	C₄×M₁₆	—	5	4	no	—
222	C₂²×C₃×C₅	—	4	1	no	—
223	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
225	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
226	C₂×C₃×D₅	—	2	2	no	—
227	C₂×C₃×D₅	—	2	2	no	—
228	C₂×C₃×D₅	—	2	2	no	—
229	C₂×C₃×D₅	—	4	1	no	—
230	C₂×C₃×D₅	—	4	1	no	—
231	C₂×C₃×D₅	—	4	1	no	—
232	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
233	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
234	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
235	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
236	C₃×AGL(1,𝔽₅)	—	2	8	no	—
237	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
238	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
241	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
242	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
243	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
244	C₃×Dic₅	C₂³×C₄	1	1	yes	characteristic
245	C₂⁴×C₃	—	5	1	no	—
246	C₂²×C₃×C₄	—	5	1	no	—
247	C₂²×C₃×C₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	1	no	—
251	C₂²×C₃×C₄	—	5	1	no	—
252	C₂²×C₃×C₄	—	5	1	no	—
253	C₂²×C₃×C₄	—	5	1	no	—
254	C₂²×C₃×C₄	—	5	1	no	—
255	C₂²×C₃×C₄	—	5	1	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	5	1	no	—
258	C₂²×C₃×C₄	—	5	1	no	—
259	C₂²×C₃×C₄	—	5	4	no	—
260	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
261	C₃×M₁₆	—	5	4	no	—
262	C₃×M₁₆	—	5	4	no	—
263	C₃×M₁₆	—	5	4	no	—
264	C₃×M₁₆	—	5	4	no	—
265	C₃×M₁₆	—	5	2	no	—
266	C₃×M₁₆	—	5	2	no	—
267	C₃×M₁₆	—	5	4	no	—
268	C₃×M₁₆	—	5	4	no	—
269	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	—
270	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
271	C₂×C₃×C₈	—	5	4	no	—
272	C₂×C₃×C₈	—	5	4	no	—
273	C₂×C₃×C₈	—	5	4	no	—
274	C₂×C₃×C₈	—	5	2	no	—
275	C₂×C₃×C₈	—	5	4	no	—
276	C₂×C₃×C₈	—	5	4	no	—
277	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
278	C₃×C₄⋊C₄	—	5	4	no	—
279	C₃×C₄⋊C₄	—	5	4	no	—
280	C₃×C₂²⋊C₄	—	5	4	no	—
281	C₃×C₂²⋊C₄	—	5	4	no	—
282	C₃×C₄²	—	5	4	no	—
283	C₃×C₄²	—	5	4	no	—
284	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
285	C₂²×D₅	—	4	2	no	—
286	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
287	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
288	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
289	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
290	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
291	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
292	C₂×AGL(1,𝔽₅)	—	4	4	no	—
293	C₂×AGL(1,𝔽₅)	C₂²×C₃×C₄	1	8	yes	—
294	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
295	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
296	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
300	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
301	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
302	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
303	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
304	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
306	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
307	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
308	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
309	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
310	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
311	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
312	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
313	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
314	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
316	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
317	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
318	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
322	#170	C₂²×C₃×C₄	1	8	yes	—
323	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
324	#168	C₂²×C₃×C₄	1	4	yes	—
325	C₂³×C₄	—	5	1	no	—
326	C₂×M₁₆	—	5	2	no	—
327	C₂×M₁₆	—	5	2	no	—
328	C₂×M₁₆	—	5	2	no	—
329	C₂×M₁₆	—	5	2	no	—
330	C₂×M₁₆	—	5	2	no	—
331	C₂×M₁₆	—	5	2	no	—
332	C₂×M₁₆	—	5	1	no	—
333	C₂×M₁₆	—	5	2	no	—
334	C₂×M₁₆	—	5	2	no	—
335	C₂×M₁₆	—	5	2	no	—
336	C₂×M₁₆	—	5	2	no	—
337	C₂×M₁₆	—	5	2	no	—
338	C₂×M₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
339	C₂²×C₈	—	5	2	no	—
340	C₂²×C₈	—	5	2	no	—
341	#117	—	5	2	no	—
342	#117	—	5	2	no	—
343	#117	—	5	2	no	—
344	#117	—	5	2	no	—
345	C₂×C₄⋊C₄	—	5	2	no	—
346	C₂×C₂²⋊C₄	—	5	2	no	—
347	C₂×C₄²	—	5	2	no	—
348	#97	—	5	8	no	—
349	C₄×C₈	—	5	8	no	—
350	C₂×C₃×C₅	—	2	1	no	—
351	C₂×C₃×C₅	—	2	1	no	—
352	C₂×C₃×C₅	—	2	1	no	—
353	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
354	C₃×D₅	—	2	1	no	—
355	C₃×D₅	—	2	1	no	—
356	C₃×D₅	—	2	1	no	—
357	C₃×D₅	#568	1	2	yes	—
358	C₂³×C₃	—	5	1	no	—
359	C₂³×C₃	—	5	1	no	—
360	C₂³×C₃	—	5	1	no	—
361	C₂³×C₃	—	5	1	no	—
362	C₂³×C₃	—	5	1	no	—
363	C₂³×C₃	—	5	1	no	—
364	C₂³×C₃	—	20	2	no	—
365	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₂×C₃×C₄	—	5	1	no	—
367	C₂×C₃×C₄	—	5	1	no	—
368	C₂×C₃×C₄	—	5	1	no	—
369	C₂×C₃×C₄	—	5	1	no	—
370	C₂×C₃×C₄	—	5	1	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	5	1	no	—
373	C₂×C₃×C₄	—	5	1	no	—
374	C₂×C₃×C₄	—	5	1	no	—
375	C₂×C₃×C₄	—	5	1	no	—
376	C₂×C₃×C₄	—	5	1	no	—
377	C₂×C₃×C₄	—	5	1	no	—
378	C₂×C₃×C₄	—	5	1	no	—
379	C₂×C₃×C₄	—	5	1	no	—
380	C₂×C₃×C₄	—	5	1	no	—
381	C₂×C₃×C₄	—	5	1	no	—
382	C₂×C₃×C₄	—	5	1	no	—
383	C₂×C₃×C₄	—	5	1	no	—
384	C₂×C₃×C₄	—	5	1	no	—
385	C₂×C₃×C₄	—	5	1	no	—
386	C₂×C₃×C₄	—	5	1	no	—
387	C₂×C₃×C₄	—	5	1	no	—
388	C₂×C₃×C₄	—	5	8	no	—
389	C₂×C₃×C₄	—	20	4	no	—
390	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
396	C₃×C₈	—	5	8	no	—
397	C₃×C₈	—	5	4	no	—
398	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	4	yes	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
401	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
402	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
403	C₂×D₅	—	2	2	no	—
404	C₂×D₅	—	2	2	no	—
405	C₂×D₅	—	2	2	no	—
406	C₂×D₅	—	4	1	no	—
407	C₂×D₅	—	4	1	no	—
408	C₂×D₅	—	4	1	no	—
409	C₂×D₅	C₂×C₃×C₄²	1	1	yes	characteristic
410	C₂×D₅	C₂×C₃×C₄²	1	1	yes	characteristic
411	C₂×D₅	C₂×C₃×C₄²	1	1	yes	characteristic
412	C₂×D₅	C₂³×C₃×C₄	1	1	yes	characteristic
413	AGL(1,𝔽₅)	—	2	8	no	—
414	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
415	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
416	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
417	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
418	Dic₅	C₂×C₃×C₄²	1	1	yes	characteristic
419	Dic₅	C₂×C₃×C₄²	1	1	yes	characteristic
420	Dic₅	C₂×C₃×C₄²	1	1	yes	characteristic
421	Dic₅	C₂³×C₃×C₄	1	1	yes	characteristic
422	C₂⁴	—	5	1	no	—
423	C₂²×C₄	—	5	1	no	—
424	C₂²×C₄	—	5	1	no	—
425	C₂²×C₄	—	5	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	5	1	no	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	1	no	—
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	1	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	1	no	—
435	C₂²×C₄	—	5	1	no	—
436	C₂²×C₄	—	5	4	no	—
437	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
438	M₁₆	—	5	4	no	—
439	M₁₆	—	5	4	no	—
440	M₁₆	—	5	4	no	—
441	M₁₆	—	5	4	no	—
442	M₁₆	—	5	2	no	—
443	M₁₆	—	5	2	no	—
444	M₁₆	—	5	4	no	—
445	M₁₆	—	5	4	no	—
446	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
447	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
448	C₂×C₈	—	5	4	no	—
449	C₂×C₈	—	5	4	no	—
450	C₂×C₈	—	5	4	no	—
451	C₂×C₈	—	5	2	no	—
452	C₂×C₈	—	5	4	no	—
453	C₂×C₈	—	5	4	no	—
454	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
455	C₄⋊C₄	—	5	4	no	—
456	C₄⋊C₄	—	5	4	no	—
457	C₂²⋊C₄	—	5	4	no	—
458	C₂²⋊C₄	—	5	4	no	—
459	C₄²	—	5	4	no	—
460	C₄²	—	5	4	no	—
461	C₃×C₅	#2873	1	1	yes	characteristic, complemented, Hall
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	5	1	no	—
464	C₂²×C₃	—	5	1	no	—
465	C₂²×C₃	—	5	1	no	—
466	C₂²×C₃	—	5	1	no	—
467	C₂²×C₃	—	10	2	no	—
468	C₂²×C₃	—	10	2	no	—
469	C₂²×C₃	—	10	2	no	—
470	C₂²×C₃	—	20	1	no	—
471	C₂²×C₃	—	20	1	no	—
472	C₂²×C₃	—	20	1	no	—
473	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
474	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
476	C₃×C₄	—	5	1	no	—
477	C₃×C₄	—	5	1	no	—
478	C₃×C₄	—	5	1	no	—
479	C₃×C₄	—	5	1	no	—
480	C₃×C₄	—	10	8	no	—
481	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
482	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
483	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
484	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
485	C₂×C₅	—	2	1	no	—
486	C₂×C₅	—	2	1	no	—
487	C₂×C₅	—	2	1	no	—
488	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
489	D₅	—	2	1	no	—
490	D₅	—	2	1	no	—
491	D₅	—	2	1	no	—
492	D₅	C₃×#568	1	2	yes	—
493	C₂³	—	5	1	no	—
494	C₂³	—	5	1	no	—
495	C₂³	—	5	1	no	—
496	C₂³	—	5	1	no	—
497	C₂³	—	5	1	no	—
498	C₂³	—	5	1	no	—
499	C₂³	—	20	2	no	—
500	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	5	1	no	—
507	C₂×C₄	—	5	1	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	5	1	no	—
512	C₂×C₄	—	5	1	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	1	no	—
516	C₂×C₄	—	5	1	no	—
517	C₂×C₄	—	5	1	no	—
518	C₂×C₄	—	5	1	no	—
519	C₂×C₄	—	5	1	no	—
520	C₂×C₄	—	5	1	no	—
521	C₂×C₄	—	5	1	no	—
522	C₂×C₄	—	5	1	no	—
523	C₂×C₄	—	5	8	no	—
524	C₂×C₄	—	20	4	no	—
525	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
526	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
527	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
529	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
530	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
531	C₈	—	5	8	no	—
532	C₈	—	5	4	no	—
533	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
534	C₂×C₃	—	2	1	no	—
535	C₂×C₃	—	2	1	no	—
536	C₂×C₃	—	2	1	no	—
537	C₂×C₃	—	5	2	no	—
538	C₂×C₃	—	10	1	no	—
539	C₂×C₃	—	10	1	no	—
540	C₂×C₃	—	10	1	no	—
541	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
542	C₅	C₃×#2873	1	1	yes	characteristic, complemented, Sylow
543	C₂²	—	4	1	no	—
544	C₂²	—	5	1	no	—
545	C₂²	—	5	1	no	—
546	C₂²	—	5	1	no	—
547	C₂²	—	5	1	no	—
548	C₂²	—	10	2	no	—
549	C₂²	—	10	2	no	—
550	C₂²	—	10	2	no	—
551	C₂²	—	20	1	no	—
552	C₂²	—	20	1	no	—
553	C₂²	—	20	1	no	—
554	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
555	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
556	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
557	C₄	—	5	1	no	—
558	C₄	—	5	1	no	—
559	C₄	—	5	1	no	—
560	C₄	—	5	1	no	—
561	C₄	—	10	8	no	—
562	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
563	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
564	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
565	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
566	C₃	#10617407	1	1	yes	characteristic, direct product factor, Sylow
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	5	2	no	—
571	C₂	—	10	1	no	—
572	C₂	—	10	1	no	—
573	C₂	—	10	1	no	—
574	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂³×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×M₁₆	C₄
socle	C₂×C₃×C₅	C₂²×C₄²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×M₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2873
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×#65728	C₂	semidirect
5. C₃×M₁₆×AGL(1,𝔽₅)	C₂	semidirect
6. C₃×#65718	C₂	semidirect
7. #10617407	C₃	direct (N × H)
10. C₂×C₃×#704	C₄	semidirect
17. C₃×D₅⋊M₁₆	C₄	semidirect
18. C₃×D₅⋊M₁₆	C₄	semidirect
21. C₂×C₃×#700	C₄	semidirect
23. C₂×C₃×C₅×M₁₆	C₄	semidirect
24. C₂×C₃×#681	C₄	semidirect
25. C₃×D₅×M₁₆	C₄	semidirect
26. C₃×D₅×M₁₆	C₄	semidirect
29. C₂×C₃×#676	C₄	semidirect
31. C₃×#3992	C₂²	semidirect
32. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
37. #65728	C₂×C₃	semidirect
38. M₁₆×AGL(1,𝔽₅)	C₂×C₃	semidirect
39. #65718	C₂×C₃	semidirect
59. C₃×#704	C₂×C₄	semidirect
60. C₂×C₃×#170	C₂×C₄	semidirect
66. C₃×#700	C₂×C₄	semidirect
67. C₃×D₅⋊C₈	C₂×C₄	semidirect
70. C₃×C₅×M₁₆	C₂×C₄	semidirect
71. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
73. C₃×#681	C₂×C₄	semidirect
74. C₂×C₃×#168	C₂×C₄	semidirect
76. C₃×#676	C₂×C₄	semidirect
77. C₃×C₈×D₅	C₂×C₄	semidirect
87. C₂×#704	C₃×C₄	semidirect
94. D₅⋊M₁₆	C₃×C₄	semidirect
95. D₅⋊M₁₆	C₃×C₄	semidirect
98. C₂×#700	C₃×C₄	semidirect
100. C₂×C₅×M₁₆	C₃×C₄	semidirect
101. C₂×#681	C₃×C₄	semidirect
102. D₅×M₁₆	C₃×C₄	semidirect
103. D₅×M₁₆	C₃×C₄	semidirect
106. C₂×#676	C₃×C₄	semidirect
108. #3992	C₂²×C₃	semidirect
109. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
165. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
196. #704	C₂×C₃×C₄	semidirect
197. C₂×#170	C₂×C₃×C₄	semidirect
203. #700	C₂×C₃×C₄	semidirect
204. D₅⋊C₈	C₂×C₃×C₄	semidirect
207. C₅×M₁₆	C₂×C₃×C₄	semidirect
208. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
210. #681	C₂×C₃×C₄	semidirect
211. C₂×#168	C₂×C₃×C₄	semidirect
213. #676	C₂×C₃×C₄	semidirect
214. C₈×D₅	C₂×C₃×C₄	semidirect
270. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
277. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
338. C₂×M₁₆	C₃×AGL(1,𝔽₅)	semidirect
447. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
454. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
461. C₃×C₅	#2873	semidirect
542. C₅	C₃×#2873	semidirect
566. C₃	#10617407	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×#4130	2
C₂×C₃×D₅⋊M₁₆	2
C₂×C₃×D₅×M₁₆	2
C₃×#65728	2
C₃×M₁₆×AGL(1,𝔽₅)	2
C₃×#65718	2
#10617407	3
C₃×#2873	5

Subgroups — C3×#10617407 #14411396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617407 #14411396