Subgroups — C₃×#10617084 #14415694

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 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	2	yes	maximal, complemented
2	C₂×C₃×#4039	C₂	1	1	yes	maximal, characteristic
3	C₃×#65758	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65755	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65705	C₂	1	2	yes	maximal, complemented
7	C₃×#65704	C₂	1	4	yes	maximal, complemented
8	C₃×#65702	C₂	1	2	yes	maximal, complemented
9	#10617084	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
12	C₂×C₃×#704	C₂²	1	1	yes	characteristic
13	C₂×C₃×#704	C₂²	1	2	yes	—
14	C₂×C₃×#704	C₂²	1	1	yes	characteristic
15	C₃×D₅⋊M₁₆	—	2	8	no	—
16	C₂×C₃×#700	C₂²	1	4	yes	complemented
17	C₂×C₃×D₅⋊C₈	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
19	C₂×C₃×#685	C₄	1	2	yes	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₃×#4039	C₄	1	2	yes	—
22	C₃×#4039	C₄	1	1	yes	characteristic
23	C₃×#4039	C₄	1	1	yes	characteristic
24	C₃×#4039	C₂²	1	1	yes	characteristic
25	C₃×#4039	C₂²	1	2	yes	—
26	C₃×#4039	C₂²	1	1	yes	characteristic
27	C₃×#4004	C₂²	1	2	yes	complemented
28	C₃×#4003	C₂²	1	4	yes	complemented
29	C₃×#4003	C₂²	1	4	yes	complemented
30	C₃×#4002	C₂²	1	2	yes	complemented
31	C₃×C₄⋊#170	C₂²	1	2	yes	complemented
32	C₃×C₄×#170	C₂²	1	2	yes	complemented
33	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
34	C₂×D₅⋊M₁₆	C₂×C₃	1	2	yes	complemented
35	C₂×#4039	C₂×C₃	1	1	yes	characteristic
36	#65758	C₂×C₃	1	1	yes	characteristic, complemented
37	#65755	C₂×C₃	1	2	yes	complemented
38	C₄×#704	C₂×C₃	1	1	yes	characteristic, complemented
39	#65705	C₂×C₃	1	2	yes	complemented
40	#65704	C₂×C₃	1	4	yes	complemented
41	#65702	C₂×C₃	1	2	yes	complemented
42	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×D₂₀	—	2	4	no	—
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	—	2	4	no	—
52	C₂×C₃×C₄×D₅	—	2	4	no	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
57	C₃×#704	—	2	4	no	—
58	C₃×#704	—	2	2	no	—
59	C₃×#704	D₄	1	4	yes	complemented
60	C₂×C₃×#170	C₂³	1	4	yes	—
61	C₂×C₃×#170	C₂³	1	2	yes	—
62	C₂×C₃×#170	C₂³	1	2	yes	—
63	C₃×#700	—	2	8	no	—
64	C₃×D₅⋊C₈	—	2	8	no	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×#685	C₂×C₄	1	2	yes	—
70	C₃×#685	C₂×C₄	1	2	yes	—
71	C₃×#685	C₂×C₄	1	2	yes	—
72	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×M₁₆	—	5	2	no	—
77	C₂×C₃×C₄×D₄	—	5	1	no	—
78	C₃×#436	—	5	2	no	—
79	C₃×#435	—	5	4	no	—
80	C₃×C₈×D₄	—	5	2	no	—
81	C₃×#423	—	5	1	no	—
82	C₃×#407	—	5	2	no	—
83	C₃×C₄×M₁₆	—	5	1	no	—
84	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic
85	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
86	C₂×#704	C₂²×C₃	1	2	yes	—
87	C₂×#704	C₂²×C₃	1	1	yes	characteristic
88	C₂×#704	C₂²×C₃	1	1	yes	characteristic
89	D₅⋊M₁₆	—	2	8	no	—
90	C₂×#700	C₂²×C₃	1	4	yes	complemented
91	C₂×D₅⋊C₈	C₂²×C₃	1	4	yes	complemented
92	C₂×C₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
93	C₂×#685	C₃×C₄	1	2	yes	—
94	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
95	#4039	C₃×C₄	1	2	yes	—
96	#4039	C₃×C₄	1	1	yes	characteristic
97	#4039	C₃×C₄	1	1	yes	characteristic
98	#4039	C₂²×C₃	1	1	yes	characteristic
99	#4039	C₂²×C₃	1	2	yes	—
100	#4039	C₂²×C₃	1	1	yes	characteristic
101	#4004	C₂²×C₃	1	2	yes	complemented
102	#4003	C₂²×C₃	1	4	yes	complemented
103	#4003	C₂²×C₃	1	4	yes	complemented
104	#4002	C₂²×C₃	1	2	yes	complemented
105	C₄⋊#170	C₂²×C₃	1	2	yes	complemented
106	C₄×#170	C₂²×C₃	1	2	yes	complemented
107	D₄×M₁₆	—	5	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₃×D₅	—	2	4	no	—
110	C₂²×C₃×D₅	—	2	4	no	—
111	C₂²×C₃×D₅	—	4	2	no	—
112	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
113	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	—	2	4	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	—	4	1	no	—
121	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×Dic₅	#41	1	2	yes	—
126	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
127	C₃×D₂₀	—	2	4	no	—
128	C₃×D₂₀	—	2	2	no	—
129	C₃×D₂₀	M₁₆	1	4	yes	complemented
130	C₃×C₄×D₅	—	2	4	no	—
131	C₃×C₄×D₅	—	2	4	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	—	2	2	no	—
134	C₃×C₄×D₅	—	2	2	no	—
135	C₃×C₄×D₅	—	2	2	no	—
136	C₃×#170	—	2	4	no	—
137	C₃×#170	—	2	2	no	—
138	C₃×#170	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×D₄	—	5	1	no	—
140	C₂³×C₃×C₄	—	5	2	no	—
141	C₂×C₃×M₁₆	—	5	1	no	—
142	C₂×C₃×M₁₆	—	5	4	no	—
143	C₂×C₃×M₁₆	—	5	2	no	—
144	C₂×C₃×M₁₆	—	5	1	no	—
145	C₂×C₃×M₁₆	—	10	8	no	—
146	C₂²×C₃×C₈	—	5	4	no	—
147	C₃×C₄×D₄	—	5	1	no	—
148	C₃×C₄×D₄	—	5	2	no	—
149	C₃×C₄×D₄	—	5	1	no	—
150	C₃×C₄×D₄	—	5	1	no	—
151	C₃×C₄×D₄	—	5	2	no	—
152	C₃×C₄×D₄	—	5	1	no	—
153	C₂×C₃×C₄⋊C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
155	C₂×C₃×C₄²	—	5	1	no	—
156	C₃×C₄⋊C₈	—	5	2	no	—
157	C₃×C₄⋊C₈	—	5	2	no	—
158	C₃×C₂²⋊C₈	—	5	4	no	—
159	C₃×C₂²⋊C₈	—	5	4	no	—
160	C₃×#97	—	5	2	no	—
161	C₃×C₄×C₈	—	5	2	no	—
162	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
163	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
164	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
167	C₂×D₂₀	—	2	4	no	—
168	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
169	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
170	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	—	2	4	no	—
172	C₂×C₄×D₅	—	2	4	no	—
173	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
174	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
175	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
176	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
177	#704	—	2	4	no	—
178	#704	—	2	2	no	—
179	#704	C₃×D₄	1	4	yes	complemented
180	C₂×#170	C₂³×C₃	1	4	yes	—
181	C₂×#170	C₂³×C₃	1	2	yes	—
182	C₂×#170	C₂³×C₃	1	2	yes	—
183	#700	—	2	8	no	—
184	D₅⋊C₈	—	2	8	no	—
185	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
186	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
187	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
188	#685	C₂×C₃×C₄	1	2	yes	—
189	#685	C₂×C₃×C₄	1	2	yes	—
190	#685	C₂×C₃×C₄	1	2	yes	—
191	#685	C₂×C₃×C₄	1	2	yes	—
192	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
193	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
194	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
195	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²×M₁₆	—	5	2	no	—
197	C₂×C₄×D₄	—	5	1	no	—
198	#436	—	5	2	no	—
199	#435	—	5	4	no	—
200	C₈×D₄	—	5	2	no	—
201	#423	—	5	1	no	—
202	#407	—	5	2	no	—
203	C₄×M₁₆	—	5	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	2	no	—
210	C₂×C₃×D₅	—	2	2	no	—
211	C₂×C₃×D₅	—	2	2	no	—
212	C₂×C₃×D₅	—	2	2	no	—
213	C₂×C₃×D₅	—	4	8	no	—
214	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	complemented
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	2	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
219	C₃×Dic₅	—	2	1	no	—
220	C₃×Dic₅	—	2	1	no	—
221	C₃×Dic₅	C₄×D₄	1	2	yes	—
222	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
223	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
224	C₂⁴×C₃	—	5	2	no	—
225	C₂×C₃×D₄	—	5	1	no	—
226	C₂×C₃×D₄	—	5	2	no	—
227	C₂×C₃×D₄	—	5	1	no	—
228	C₂×C₃×D₄	—	10	4	no	—
229	C₂²×C₃×C₄	—	5	1	no	—
230	C₂²×C₃×C₄	—	5	1	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	10	4	no	—
236	C₂²×C₃×C₄	—	10	4	no	—
237	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
239	C₃×M₁₆	—	5	4	no	—
240	C₃×M₁₆	—	10	8	no	—
241	C₃×M₁₆	—	10	2	no	—
242	C₃×M₁₆	—	10	4	no	—
243	C₂×C₃×C₈	—	5	2	no	—
244	C₂×C₃×C₈	—	5	2	no	—
245	C₂×C₃×C₈	—	5	4	no	—
246	C₂×C₃×C₈	—	10	8	no	—
247	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
248	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
249	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₃×C₂²⋊C₄	—	5	2	no	—
251	C₃×C₂²⋊C₄	—	5	2	no	—
252	C₃×C₂²⋊C₄	—	5	2	no	—
253	C₃×C₂²⋊C₄	—	5	2	no	—
254	C₃×C₄²	—	5	1	no	—
255	C₃×C₄²	—	5	1	no	—
256	C₃×C₄²	—	5	1	no	—
257	C₃×C₄²	—	5	1	no	—
258	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
259	C₂²×D₅	—	2	4	no	—
260	C₂²×D₅	—	2	4	no	—
261	C₂²×D₅	—	4	2	no	—
262	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
263	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
264	C₂×C₄×C₅	—	2	4	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
268	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
269	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
270	C₂×Dic₅	—	4	1	no	—
271	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
272	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
274	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
275	C₂×Dic₅	C₃×#41	1	2	yes	—
276	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
277	D₂₀	—	2	4	no	—
278	D₂₀	—	2	2	no	—
279	D₂₀	C₃×M₁₆	1	4	yes	complemented
280	C₄×D₅	—	2	4	no	—
281	C₄×D₅	—	2	4	no	—
282	C₄×D₅	—	2	2	no	—
283	C₄×D₅	—	2	2	no	—
284	C₄×D₅	—	2	2	no	—
285	C₄×D₅	—	2	2	no	—
286	#170	—	2	4	no	—
287	#170	—	2	2	no	—
288	#170	C₂×C₃×D₄	1	4	yes	complemented
289	C₂²×D₄	—	5	1	no	—
290	C₂³×C₄	—	5	2	no	—
291	C₂×M₁₆	—	5	1	no	—
292	C₂×M₁₆	—	5	4	no	—
293	C₂×M₁₆	—	5	2	no	—
294	C₂×M₁₆	—	5	1	no	—
295	C₂×M₁₆	—	10	8	no	—
296	C₂²×C₈	—	5	4	no	—
297	C₄×D₄	—	5	1	no	—
298	C₄×D₄	—	5	2	no	—
299	C₄×D₄	—	5	1	no	—
300	C₄×D₄	—	5	1	no	—
301	C₄×D₄	—	5	2	no	—
302	C₄×D₄	—	5	1	no	—
303	C₂×C₄⋊C₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	5	2	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₄⋊C₈	—	5	2	no	—
307	C₄⋊C₈	—	5	2	no	—
308	C₂²⋊C₈	—	5	4	no	—
309	C₂²⋊C₈	—	5	4	no	—
310	#97	—	5	2	no	—
311	C₄×C₈	—	5	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#568	1	1	yes	characteristic
316	C₃×D₅	—	2	4	no	—
317	C₃×D₅	—	4	2	no	—
318	C₂³×C₃	—	5	2	no	—
319	C₂³×C₃	—	5	2	no	—
320	C₂³×C₃	—	10	4	no	—
321	C₂³×C₃	—	10	4	no	—
322	C₂³×C₃	—	20	2	no	—
323	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₃×D₄	—	5	4	no	—
325	C₃×D₄	—	10	4	no	—
326	C₃×D₄	—	10	2	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	2	no	—
331	C₂×C₃×C₄	—	5	1	no	—
332	C₂×C₃×C₄	—	5	1	no	—
333	C₂×C₃×C₄	—	5	1	no	—
334	C₂×C₃×C₄	—	5	1	no	—
335	C₂×C₃×C₄	—	10	2	no	—
336	C₂×C₃×C₄	—	10	2	no	—
337	C₂×C₃×C₄	—	10	4	no	—
338	C₂×C₃×C₄	—	10	4	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	—	10	2	no	—
341	C₂×C₃×C₄	—	20	1	no	—
342	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
344	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
345	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
346	C₃×C₈	—	5	4	no	—
347	C₃×C₈	—	10	4	no	—
348	C₃×C₈	—	10	2	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
352	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
353	C₂×D₅	—	2	2	no	—
354	C₂×D₅	—	2	2	no	—
355	C₂×D₅	—	2	2	no	—
356	C₂×D₅	—	2	2	no	—
357	C₂×D₅	—	2	2	no	—
358	C₂×D₅	—	4	8	no	—
359	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	complemented
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	2	no	—
362	C₄×C₅	—	2	2	no	—
363	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
364	Dic₅	—	2	1	no	—
365	Dic₅	—	2	1	no	—
366	Dic₅	C₃×C₄×D₄	1	2	yes	—
367	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
368	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
369	C₂⁴	—	5	2	no	—
370	C₂×D₄	—	5	1	no	—
371	C₂×D₄	—	5	2	no	—
372	C₂×D₄	—	5	1	no	—
373	C₂×D₄	—	10	4	no	—
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	1	no	—
376	C₂²×C₄	—	5	2	no	—
377	C₂²×C₄	—	5	2	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	5	2	no	—
380	C₂²×C₄	—	10	4	no	—
381	C₂²×C₄	—	10	4	no	—
382	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
384	M₁₆	—	5	4	no	—
385	M₁₆	—	10	8	no	—
386	M₁₆	—	10	4	no	—
387	M₁₆	—	10	2	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	5	4	no	—
391	C₂×C₈	—	10	8	no	—
392	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
393	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
395	C₂²⋊C₄	—	5	2	no	—
396	C₂²⋊C₄	—	5	2	no	—
397	C₂²⋊C₄	—	5	2	no	—
398	C₂²⋊C₄	—	5	2	no	—
399	C₄²	—	5	1	no	—
400	C₄²	—	5	1	no	—
401	C₄²	—	5	1	no	—
402	C₄²	—	5	1	no	—
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	—	5	4	no	—
407	C₂²×C₃	—	10	2	no	—
408	C₂²×C₃	—	10	2	no	—
409	C₂²×C₃	—	10	2	no	—
410	C₂²×C₃	—	10	2	no	—
411	C₂²×C₃	—	10	2	no	—
412	C₂²×C₃	—	20	8	no	—
413	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
414	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	5	2	no	—
419	C₃×C₄	—	5	1	no	—
420	C₃×C₄	—	5	1	no	—
421	C₃×C₄	—	10	1	no	—
422	C₃×C₄	—	10	1	no	—
423	C₃×C₄	D₅⋊M₁₆	1	2	yes	complemented
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
426	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
427	C₂×C₅	C₃×#568	1	1	yes	characteristic
428	D₅	—	2	4	no	—
429	D₅	—	4	2	no	—
430	C₂³	—	5	2	no	—
431	C₂³	—	5	2	no	—
432	C₂³	—	10	4	no	—
433	C₂³	—	10	4	no	—
434	C₂³	—	20	2	no	—
435	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
436	D₄	—	5	4	no	—
437	D₄	—	10	4	no	—
438	D₄	—	10	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	5	2	no	—
442	C₂×C₄	—	5	2	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	1	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	1	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	4	no	—
452	C₂×C₄	—	10	4	no	—
453	C₂×C₄	—	20	1	no	—
454	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
456	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
457	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
458	C₈	—	5	4	no	—
459	C₈	—	10	4	no	—
460	C₈	—	10	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	10	4	no	—
463	C₂×C₃	—	20	2	no	—
464	C₂×C₃	C₂×D₅⋊M₁₆	1	1	yes	characteristic
465	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
466	C₂×C₃	#66260	1	1	yes	characteristic
467	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	5	4	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	10	2	no	—
473	C₂²	—	10	2	no	—
474	C₂²	—	10	2	no	—
475	C₂²	—	10	2	no	—
476	C₂²	—	20	8	no	—
477	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
478	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	5	1	no	—
483	C₄	—	5	1	no	—
484	C₄	—	5	2	no	—
485	C₄	—	10	1	no	—
486	C₄	—	10	1	no	—
487	C₄	C₃×D₅⋊M₁₆	1	2	yes	complemented
488	C₃	#10617084	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	10	4	no	—
491	C₂	—	20	2	no	—
492	C₂	C₂×C₃×D₅⋊M₁₆	1	1	yes	characteristic
493	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
494	C₂	C₃×#66260	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	C₂×C₃×C₅×C₄⋊C₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₂₀	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅⋊M₁₆	C₂	semidirect
3. C₃×#65758	C₂	semidirect
4. C₃×#65755	C₂	semidirect
5. C₃×C₄×#704	C₂	semidirect
6. C₃×#65705	C₂	semidirect
7. C₃×#65704	C₂	semidirect
8. C₃×#65702	C₂	semidirect
9. #10617084	C₃	direct (N × H)
16. C₂×C₃×#700	C₂²	semidirect
17. C₂×C₃×D₅⋊C₈	C₂²	semidirect
27. C₃×#4004	C₂²	semidirect
28. C₃×#4003	C₂²	semidirect
29. C₃×#4003	C₂²	semidirect
30. C₃×#4002	C₂²	semidirect
31. C₃×C₄⋊#170	C₂²	semidirect
32. C₃×C₄×#170	C₂²	semidirect
34. C₂×D₅⋊M₁₆	C₂×C₃	semidirect
36. #65758	C₂×C₃	semidirect
37. #65755	C₂×C₃	semidirect
38. C₄×#704	C₂×C₃	semidirect
39. #65705	C₂×C₃	semidirect
40. #65704	C₂×C₃	semidirect
41. #65702	C₂×C₃	semidirect
59. C₃×#704	D₄	semidirect
90. C₂×#700	C₂²×C₃	semidirect
91. C₂×D₅⋊C₈	C₂²×C₃	semidirect
101. #4004	C₂²×C₃	semidirect
102. #4003	C₂²×C₃	semidirect
103. #4003	C₂²×C₃	semidirect
104. #4002	C₂²×C₃	semidirect
105. C₄⋊#170	C₂²×C₃	semidirect
106. C₄×#170	C₂²×C₃	semidirect
129. C₃×D₂₀	M₁₆	semidirect
138. C₃×#170	C₂×D₄	semidirect
179. #704	C₃×D₄	semidirect
214. C₂×C₃×D₅	C₂×M₁₆	semidirect
218. C₃×C₄×C₅	C₂×M₁₆	semidirect
279. D₂₀	C₃×M₁₆	semidirect
288. #170	C₂×C₃×D₄	semidirect
359. C₂×D₅	C₂×C₃×M₁₆	semidirect
363. C₄×C₅	C₂×C₃×M₁₆	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
423. C₃×C₄	D₅⋊M₁₆	semidirect
467. C₅	C₃×D₄×M₁₆	semidirect
487. C₄	C₃×D₅⋊M₁₆	semidirect
488. C₃	#10617084	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
C₂×C₃×#4039	2
C₃×#65758	2
C₃×#65755	2
C₃×C₄×#704	2
C₃×#65705	2
C₃×#65704	2
C₃×#65702	2
#10617084	3
C₃×D₄×M₁₆	5

Subgroups — C3×#10617084 #14415694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617084 #14415694