Subgroups — C₃×#10617538 #14411979

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic
2	C₃×#66258	C₂	1	2	yes	maximal, complemented
3	C₃×#65785	C₂	1	2	yes	maximal, complemented
4	C₃×D₅⋊#99	C₂	1	4	yes	maximal, complemented
5	C₃×#65745	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3999	C₂	1	4	yes	maximal, complemented
7	#10617538	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic, complemented
9	C₃×#4149	—	2	8	no	—
10	C₂×C₃×#713	C₄	1	1	yes	characteristic, complemented
11	C₂×C₃×#713	C₂²	1	1	yes	characteristic
12	C₂×C₃×D₄×D₅	C₄	1	2	yes	complemented
13	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#709	C₄	1	2	yes	complemented
17	C₂×C₃×#709	C₂²	1	1	yes	characteristic
18	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic, complemented
19	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
20	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
21	C₃×D₄×AGL(1,𝔽₅)	—	2	8	no	—
22	C₃×#4130	C₂²	1	4	yes	complemented
23	C₃×#4011	C₂²	1	4	yes	complemented
24	C₃×#3999	C₂²	1	4	yes	complemented
25	C₃×#3999	C₂²	1	8	yes	complemented
26	C₃×#2883	—	5	1	no	maximal, Hall
27	C₂×#4149	C₂×C₃	1	1	yes	characteristic
28	#66258	C₂×C₃	1	2	yes	complemented
29	#65785	C₂×C₃	1	2	yes	complemented
30	D₅⋊#99	C₂×C₃	1	4	yes	complemented
31	#65745	C₂×C₃	1	2	yes	complemented
32	C₂×#3999	C₂×C₃	1	4	yes	complemented
33	C₂³×C₃×D₅	C₂×C₄	1	2	yes	complemented
34	C₂³×C₃×D₅	C₂×C₄	1	2	yes	complemented
35	C₂³×C₃×D₅	C₂³	1	2	yes	—
36	C₂²×C₃×AGL(1,𝔽₅)	—	2	8	no	—
37	C₃×C₅×#41	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic, complemented
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	complemented
43	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	complemented
45	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
47	C₃×#713	—	2	4	no	—
48	C₃×#713	—	2	4	no	—
49	C₃×D₄×D₅	—	2	8	no	—
50	C₃×D₄×D₅	—	2	4	no	—
51	C₃×D₄×D₅	—	2	8	no	—
52	C₃×D₄×D₅	D₄	1	8	yes	—
53	C₃×#709	—	2	8	no	—
54	C₃×#709	—	2	4	no	—
55	C₂×C₃×D₂₀	—	2	8	no	—
56	C₂×C₃×D₂₀	—	2	4	no	—
57	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	complemented
59	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	complemented
61	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
62	C₂×C₃×D₂₀	C₂³	1	2	yes	—
63	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	complemented
64	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	complemented
65	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
68	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	8	no	—
69	C₃×C₂²⋊AGL(1,𝔽₅)	C₂³	1	8	yes	—
70	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
71	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
72	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
73	C₃×#518	—	5	2	no	—
74	C₃×#410	—	5	2	no	—
75	C₃×#410	—	5	2	no	—
76	C₂×C₃×#99	—	5	4	no	—
77	C₂×C₃×#99	—	5	4	no	—
78	C₂×C₅×#41	C₃×C₄	1	1	yes	characteristic, complemented
79	#4149	—	2	8	no	—
80	C₂×#713	C₃×C₄	1	1	yes	characteristic, complemented
81	C₂×#713	C₂²×C₃	1	1	yes	characteristic
82	C₂×D₄×D₅	C₃×C₄	1	2	yes	complemented
83	C₂×D₄×D₅	C₃×C₄	1	1	yes	characteristic, complemented
84	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
85	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
86	C₂×#709	C₃×C₄	1	2	yes	complemented
87	C₂×#709	C₂²×C₃	1	1	yes	characteristic
88	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
89	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
90	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
91	D₄×AGL(1,𝔽₅)	—	2	8	no	—
92	#4130	C₂²×C₃	1	4	yes	complemented
93	#4011	C₂²×C₃	1	4	yes	complemented
94	#3999	C₂²×C₃	1	4	yes	complemented
95	#3999	C₂²×C₃	1	8	yes	complemented
96	#2883	—	5	1	no	Sylow
97	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
99	C₂²×C₃×D₅	—	2	4	no	—
100	C₂²×C₃×D₅	—	2	4	no	—
101	C₂²×C₃×D₅	—	8	2	no	—
102	C₂²×C₃×D₅	—	8	2	no	—
103	C₂²×C₃×D₅	—	8	2	no	—
104	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
105	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
108	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
110	C₂×C₃×AGL(1,𝔽₅)	—	8	8	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×D₄	—	2	4	no	—
113	C₃×C₅×D₄	C₂²⋊C₄	1	4	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	1	yes	characteristic
119	C₃×C₂²⋊D₅	—	2	4	no	—
120	C₃×C₂²⋊D₅	—	2	2	no	—
121	C₃×C₂²⋊D₅	—	2	2	no	—
122	C₃×C₂²⋊D₅	C₂²⋊C₄	1	8	yes	—
123	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
125	C₃×D₂₀	—	2	4	no	—
126	C₃×D₂₀	—	2	4	no	—
127	C₃×D₂₀	—	2	2	no	—
128	C₃×D₂₀	—	2	4	no	—
129	C₃×D₂₀	—	2	2	no	—
130	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
131	C₃×C₄×D₅	—	2	4	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×C₄×D₅	—	2	4	no	—
134	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
135	C₃×Dic₁₀	—	2	2	no	—
136	C₃×H(5,𝔽₂)	—	10	8	no	—
137	C₂×C₃×#41	—	5	1	no	—
138	C₂×C₃×#41	—	5	1	no	—
139	C₂×C₃×#41	—	5	2	no	—
140	C₂×C₃×#41	—	5	1	no	—
141	C₂×C₃×#41	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
142	C₂²×C₃×D₄	—	5	1	no	—
143	C₂²×C₃×D₄	—	5	1	no	—
144	C₂²×C₃×D₄	—	5	2	no	—
145	C₂²×C₃×D₄	—	5	2	no	—
146	C₂²×C₃×D₄	—	5	1	no	—
147	C₂²×C₃×D₄	—	5	2	no	—
148	C₃×C₄×D₄	—	10	8	no	—
149	C₃×#117	—	5	4	no	—
150	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
151	C₃×#99	—	5	4	no	—
152	C₃×#99	—	5	8	no	—
153	C₃×#99	—	5	4	no	—
154	C₂³×D₅	C₂×C₃×C₄	1	2	yes	complemented
155	C₂³×D₅	C₂×C₃×C₄	1	2	yes	complemented
156	C₂³×D₅	C₂³×C₃	1	2	yes	—
157	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
158	C₅×#41	—	2	4	no	—
159	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
160	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	complemented
162	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
163	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	complemented
164	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
165	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	complemented
166	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
168	#713	—	2	4	no	—
169	#713	—	2	4	no	—
170	D₄×D₅	—	2	8	no	—
171	D₄×D₅	—	2	4	no	—
172	D₄×D₅	—	2	8	no	—
173	D₄×D₅	C₃×D₄	1	8	yes	—
174	#709	—	2	8	no	—
175	#709	—	2	4	no	—
176	C₂×D₂₀	—	2	8	no	—
177	C₂×D₂₀	—	2	4	no	—
178	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
179	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	complemented
180	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
181	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	complemented
182	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
183	C₂×D₂₀	C₂³×C₃	1	2	yes	—
184	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	complemented
185	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	complemented
186	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
187	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
188	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
189	C₂²⋊AGL(1,𝔽₅)	—	2	8	no	—
190	C₂²⋊AGL(1,𝔽₅)	C₂³×C₃	1	8	yes	—
191	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
192	C₄×AGL(1,𝔽₅)	—	2	4	no	—
193	C₂×H(5,𝔽₂)	—	5	1	no	—
194	#518	—	5	2	no	—
195	#410	—	5	2	no	—
196	#410	—	5	2	no	—
197	C₂×#99	—	5	4	no	—
198	C₂×#99	—	5	4	no	—
199	C₂²×C₃×C₅	—	2	1	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	4	1	no	—
202	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
203	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₃×D₅	—	2	1	no	—
205	C₂×C₃×D₅	—	2	2	no	—
206	C₂×C₃×D₅	—	4	8	no	—
207	C₂×C₃×D₅	—	4	2	no	—
208	C₂×C₃×D₅	—	4	1	no	—
209	C₂×C₃×D₅	—	4	2	no	—
210	C₂×C₃×D₅	—	4	1	no	—
211	C₂×C₃×D₅	—	8	4	no	—
212	C₂×C₃×D₅	—	8	4	no	—
213	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	4	yes	—
214	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
215	C₃×AGL(1,𝔽₅)	—	4	8	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	2	no	—
218	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
219	C₃×Dic₅	—	2	1	no	—
220	C₃×Dic₅	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂⁴×C₃	—	5	2	no	—
222	C₂⁴×C₃	—	5	2	no	—
223	C₂⁴×C₃	—	5	2	no	—
224	C₃×#41	—	2	4	no	—
225	C₃×#41	—	10	4	no	—
226	C₃×#41	—	10	8	no	—
227	C₃×#41	—	10	4	no	—
228	C₃×#41	—	10	4	no	—
229	C₂×C₃×Q₈	—	5	1	no	—
230	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
231	C₂×C₃×D₄	—	5	2	no	—
232	C₂×C₃×D₄	—	5	8	no	—
233	C₂×C₃×D₄	—	5	1	no	—
234	C₂×C₃×D₄	—	5	1	no	—
235	C₂×C₃×D₄	—	5	2	no	—
236	C₂×C₃×D₄	—	5	1	no	—
237	C₂×C₃×D₄	—	5	2	no	—
238	C₂×C₃×D₄	—	5	1	no	—
239	C₂×C₃×D₄	—	5	2	no	—
240	C₂×C₃×D₄	—	5	2	no	—
241	C₂×C₃×D₄	—	5	1	no	—
242	C₂×C₃×D₄	—	10	4	no	—
243	C₂×C₃×D₄	—	10	8	no	—
244	C₂×C₃×D₄	—	10	8	no	—
245	C₂×C₃×D₄	—	10	8	no	—
246	C₂×C₃×D₄	—	10	4	no	—
247	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
248	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	2	no	—
251	C₂²×C₃×C₄	—	5	2	no	—
252	C₂²×C₃×C₄	—	5	1	no	—
253	C₂²×C₃×C₄	—	10	8	no	—
254	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
255	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
256	C₃×C₄⋊C₄	—	10	4	no	—
257	C₃×C₂²⋊C₄	—	5	8	no	—
258	C₃×C₂²⋊C₄	—	10	8	no	—
259	C₃×C₄²	—	10	4	no	—
260	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂²×D₅	—	2	4	no	—
263	C₂²×D₅	—	2	4	no	—
264	C₂²×D₅	—	8	2	no	—
265	C₂²×D₅	—	8	2	no	—
266	C₂²×D₅	—	8	2	no	—
267	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
268	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
270	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
271	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
272	C₂×AGL(1,𝔽₅)	—	2	8	no	—
273	C₂×AGL(1,𝔽₅)	—	8	8	no	—
274	C₅×Q₈	—	2	2	no	—
275	C₅×D₄	—	2	4	no	—
276	C₅×D₄	C₃×C₂²⋊C₄	1	4	yes	—
277	C₂×C₄×C₅	—	2	4	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
281	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₂²⋊D₅	—	2	4	no	—
283	C₂²⋊D₅	—	2	2	no	—
284	C₂²⋊D₅	—	2	2	no	—
285	C₂²⋊D₅	C₃×C₂²⋊C₄	1	8	yes	—
286	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
287	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
288	D₂₀	—	2	4	no	—
289	D₂₀	—	2	4	no	—
290	D₂₀	—	2	2	no	—
291	D₂₀	—	2	4	no	—
292	D₂₀	—	2	2	no	—
293	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
294	C₄×D₅	—	2	4	no	—
295	C₄×D₅	—	2	2	no	—
296	C₄×D₅	—	2	4	no	—
297	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
298	Dic₁₀	—	2	2	no	—
299	H(5,𝔽₂)	—	10	8	no	—
300	C₂×#41	—	5	1	no	—
301	C₂×#41	—	5	1	no	—
302	C₂×#41	—	5	2	no	—
303	C₂×#41	—	5	1	no	—
304	C₂×#41	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
305	C₂²×D₄	—	5	1	no	—
306	C₂²×D₄	—	5	1	no	—
307	C₂²×D₄	—	5	2	no	—
308	C₂²×D₄	—	5	2	no	—
309	C₂²×D₄	—	5	1	no	—
310	C₂²×D₄	—	5	2	no	—
311	C₄×D₄	—	10	8	no	—
312	#117	—	5	4	no	—
313	C₂×C₂²⋊C₄	—	5	8	no	—
314	#99	—	5	4	no	—
315	#99	—	5	8	no	—
316	#99	—	5	4	no	—
317	C₂×C₃×C₅	—	2	1	no	—
318	C₂×C₃×C₅	—	2	4	no	—
319	C₂×C₃×C₅	—	4	1	no	—
320	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₃×D₅	—	2	2	no	—
322	C₃×D₅	—	2	4	no	—
323	C₃×D₅	—	4	2	no	—
324	C₃×D₅	—	4	1	no	—
325	C₂³×C₃	—	5	8	no	—
326	C₂³×C₃	—	5	2	no	—
327	C₂³×C₃	—	5	1	no	—
328	C₂³×C₃	—	5	2	no	—
329	C₂³×C₃	—	5	1	no	—
330	C₂³×C₃	—	10	4	no	—
331	C₂³×C₃	—	10	4	no	—
332	C₂³×C₃	—	40	2	no	—
333	C₂³×C₃	—	40	2	no	—
334	C₂³×C₃	—	40	2	no	—
335	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
337	C₃×Q₈	—	2	2	no	—
338	C₃×Q₈	—	10	2	no	—
339	C₃×D₄	—	2	4	no	—
340	C₃×D₄	—	5	8	no	—
341	C₃×D₄	—	5	4	no	—
342	C₃×D₄	—	10	4	no	—
343	C₃×D₄	—	10	2	no	—
344	C₃×D₄	—	10	4	no	—
345	C₃×D₄	—	10	4	no	—
346	C₃×D₄	—	10	2	no	—
347	C₃×D₄	—	10	2	no	—
348	C₃×D₄	—	10	4	no	—
349	C₃×D₄	—	10	2	no	—
350	C₃×D₄	C₂²⋊AGL(1,𝔽₅)	1	4	yes	—
351	C₂×C₃×C₄	—	2	4	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	5	1	no	—
354	C₂×C₃×C₄	—	5	4	no	—
355	C₂×C₃×C₄	—	5	1	no	—
356	C₂×C₃×C₄	—	10	4	no	—
357	C₂×C₃×C₄	—	10	4	no	—
358	C₂×C₃×C₄	—	10	2	no	—
359	C₂×C₃×C₄	—	10	8	no	—
360	C₂×C₃×C₄	—	40	8	no	—
361	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
362	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	—	4	2	no	—
366	C₂²×C₅	—	4	1	no	—
367	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
368	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
369	C₂×D₅	—	2	1	no	—
370	C₂×D₅	—	2	2	no	—
371	C₂×D₅	—	4	8	no	—
372	C₂×D₅	—	4	2	no	—
373	C₂×D₅	—	4	1	no	—
374	C₂×D₅	—	4	2	no	—
375	C₂×D₅	—	4	1	no	—
376	C₂×D₅	—	8	4	no	—
377	C₂×D₅	—	8	4	no	—
378	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
379	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
380	AGL(1,𝔽₅)	—	4	8	no	—
381	C₄×C₅	—	2	1	no	—
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
384	Dic₅	—	2	1	no	—
385	Dic₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
386	C₂⁴	—	5	2	no	—
387	C₂⁴	—	5	2	no	—
388	C₂⁴	—	5	2	no	—
389	#41	—	2	4	no	—
390	#41	—	10	4	no	—
391	#41	—	10	8	no	—
392	#41	—	10	4	no	—
393	#41	—	10	4	no	—
394	C₂×Q₈	—	5	1	no	—
395	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
396	C₂×D₄	—	5	2	no	—
397	C₂×D₄	—	5	8	no	—
398	C₂×D₄	—	5	1	no	—
399	C₂×D₄	—	5	1	no	—
400	C₂×D₄	—	5	2	no	—
401	C₂×D₄	—	5	1	no	—
402	C₂×D₄	—	5	2	no	—
403	C₂×D₄	—	5	1	no	—
404	C₂×D₄	—	5	2	no	—
405	C₂×D₄	—	5	2	no	—
406	C₂×D₄	—	5	1	no	—
407	C₂×D₄	—	10	4	no	—
408	C₂×D₄	—	10	8	no	—
409	C₂×D₄	—	10	8	no	—
410	C₂×D₄	—	10	8	no	—
411	C₂×D₄	—	10	4	no	—
412	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
414	C₂²×C₄	—	5	1	no	—
415	C₂²×C₄	—	5	2	no	—
416	C₂²×C₄	—	5	2	no	—
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	10	8	no	—
419	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
420	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
421	C₄⋊C₄	—	10	4	no	—
422	C₂²⋊C₄	—	5	8	no	—
423	C₂²⋊C₄	—	10	8	no	—
424	C₄²	—	10	4	no	—
425	C₃×C₅	#2883	1	1	yes	characteristic, complemented, Hall
426	C₂²×C₃	—	2	1	no	—
427	C₂²×C₃	—	4	2	no	—
428	C₂²×C₃	—	4	1	no	—
429	C₂²×C₃	—	5	4	no	—
430	C₂²×C₃	—	5	2	no	—
431	C₂²×C₃	—	10	2	no	—
432	C₂²×C₃	—	10	1	no	—
433	C₂²×C₃	—	20	8	no	—
434	C₂²×C₃	—	20	1	no	—
435	C₂²×C₃	—	20	2	no	—
436	C₂²×C₃	—	20	1	no	—
437	C₂²×C₃	—	20	2	no	—
438	C₂²×C₃	—	40	4	no	—
439	C₂²×C₃	—	40	4	no	—
440	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	4	yes	—
441	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	2	2	no	—
444	C₃×C₄	—	5	2	no	—
445	C₃×C₄	—	10	1	no	—
446	C₃×C₄	—	20	8	no	—
447	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
448	C₂×C₅	—	2	1	no	—
449	C₂×C₅	—	2	4	no	—
450	C₂×C₅	—	4	1	no	—
451	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
452	D₅	—	2	2	no	—
453	D₅	—	2	4	no	—
454	D₅	—	4	2	no	—
455	D₅	—	4	1	no	—
456	C₂³	—	5	8	no	—
457	C₂³	—	5	1	no	—
458	C₂³	—	5	2	no	—
459	C₂³	—	5	2	no	—
460	C₂³	—	5	1	no	—
461	C₂³	—	10	4	no	—
462	C₂³	—	10	4	no	—
463	C₂³	—	40	2	no	—
464	C₂³	—	40	2	no	—
465	C₂³	—	40	2	no	—
466	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
468	Q₈	—	2	2	no	—
469	Q₈	—	10	2	no	—
470	D₄	—	2	4	no	—
471	D₄	—	5	8	no	—
472	D₄	—	5	4	no	—
473	D₄	—	10	2	no	—
474	D₄	—	10	4	no	—
475	D₄	—	10	4	no	—
476	D₄	—	10	4	no	—
477	D₄	—	10	2	no	—
478	D₄	—	10	2	no	—
479	D₄	—	10	4	no	—
480	D₄	—	10	2	no	—
481	D₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	4	yes	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	5	4	no	—
486	C₂×C₄	—	5	1	no	—
487	C₂×C₄	—	10	4	no	—
488	C₂×C₄	—	10	4	no	—
489	C₂×C₄	—	10	2	no	—
490	C₂×C₄	—	10	8	no	—
491	C₂×C₄	—	40	8	no	—
492	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
493	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
494	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	2	4	no	—
497	C₂×C₃	—	4	1	no	—
498	C₂×C₃	—	10	2	no	—
499	C₂×C₃	—	10	4	no	—
500	C₂×C₃	—	20	1	no	—
501	C₂×C₃	—	20	2	no	—
502	C₂×C₃	C₂²×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
503	C₅	C₃×#2883	1	1	yes	characteristic, complemented, Sylow
504	C₂²	—	2	1	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	5	2	no	—
508	C₂²	—	5	4	no	—
509	C₂²	—	10	2	no	—
510	C₂²	—	10	1	no	—
511	C₂²	—	20	8	no	—
512	C₂²	—	20	1	no	—
513	C₂²	—	20	2	no	—
514	C₂²	—	20	1	no	—
515	C₂²	—	20	2	no	—
516	C₂²	—	40	4	no	—
517	C₂²	—	40	4	no	—
518	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	4	yes	—
519	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	5	2	no	—
523	C₄	—	10	1	no	—
524	C₄	—	20	8	no	—
525	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
526	C₃	#10617538	1	1	yes	characteristic, direct product factor, Sylow
527	C₂	—	2	1	no	—
528	C₂	—	2	4	no	—
529	C₂	—	4	1	no	—
530	C₂	—	10	2	no	—
531	C₂	—	10	4	no	—
532	C₂	—	20	1	no	—
533	C₂	—	20	2	no	—
534	C₂	C₂²×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×C₂²⋊AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×#41	C₄
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₃×#4149	C₂
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×#41	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2883
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×D₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₃×#66258	C₂	semidirect
3. C₃×#65785	C₂	semidirect
4. C₃×D₅⋊#99	C₂	semidirect
5. C₃×#65745	C₂	semidirect
6. C₂×C₃×#3999	C₂	semidirect
7. #10617538	C₃	direct (N × H)
8. C₂×C₃×C₅×#41	C₄	semidirect
10. C₂×C₃×#713	C₄	semidirect
12. C₂×C₃×D₄×D₅	C₄	semidirect
13. C₂×C₃×D₄×D₅	C₄	semidirect
16. C₂×C₃×#709	C₄	semidirect
18. C₂²×C₃×D₂₀	C₄	semidirect
20. C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	semidirect
22. C₃×#4130	C₂²	semidirect
23. C₃×#4011	C₂²	semidirect
24. C₃×#3999	C₂²	semidirect
25. C₃×#3999	C₂²	semidirect
28. #66258	C₂×C₃	semidirect
29. #65785	C₂×C₃	semidirect
30. D₅⋊#99	C₂×C₃	semidirect
31. #65745	C₂×C₃	semidirect
32. C₂×#3999	C₂×C₃	semidirect
33. C₂³×C₃×D₅	C₂×C₄	semidirect
34. C₂³×C₃×D₅	C₂×C₄	semidirect
38. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
40. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
41. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
42. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
44. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
45. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
58. C₂×C₃×D₂₀	C₂×C₄	semidirect
59. C₂×C₃×D₂₀	C₂×C₄	semidirect
60. C₂×C₃×D₂₀	C₂×C₄	semidirect
63. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
64. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
65. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
67. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
78. C₂×C₅×#41	C₃×C₄	semidirect
80. C₂×#713	C₃×C₄	semidirect
82. C₂×D₄×D₅	C₃×C₄	semidirect
83. C₂×D₄×D₅	C₃×C₄	semidirect
86. C₂×#709	C₃×C₄	semidirect
88. C₂²×D₂₀	C₃×C₄	semidirect
90. C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	semidirect
92. #4130	C₂²×C₃	semidirect
93. #4011	C₂²×C₃	semidirect
94. #3999	C₂²×C₃	semidirect
95. #3999	C₂²×C₃	semidirect
141. C₂×C₃×#41	AGL(1,𝔽₅)	semidirect
154. C₂³×D₅	C₂×C₃×C₄	semidirect
155. C₂³×D₅	C₂×C₃×C₄	semidirect
159. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
161. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
162. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
163. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
165. C₂×C₂²⋊D₅	C₂×C₃×C₄	semidirect
166. C₂×C₂²⋊D₅	C₂×C₃×C₄	semidirect
179. C₂×D₂₀	C₂×C₃×C₄	semidirect
180. C₂×D₂₀	C₂×C₃×C₄	semidirect
181. C₂×D₂₀	C₂×C₃×C₄	semidirect
184. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
185. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
186. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
188. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
230. C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	semidirect
248. C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
254. C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	semidirect
255. C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	semidirect
304. C₂×#41	C₃×AGL(1,𝔽₅)	semidirect
395. C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
413. C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
419. C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
420. C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
425. C₃×C₅	#2883	semidirect
503. C₅	C₃×#2883	semidirect
526. C₃	#10617538	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×#4149	2
C₃×#66258	2
C₃×#65785	2
C₃×D₅⋊#99	2
C₃×#65745	2
C₂×C₃×#3999	2
#10617538	3
C₃×#2883	5

Subgroups — C3×#10617538 #14411979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617538 #14411979