Subgroups — C₂×#11746523 #14294473

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊#208	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4130	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
4	#11746523	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64862	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂²×D₅×Dic₃	—	2	1	no	—
8	C₂×#6762	—	2	1	no	—
9	D₅⋊#208	—	2	1	no	—
10	D₅⋊#208	—	2	1	no	—
11	D₅⋊#208	C₄	1	2	yes	complemented
12	D₅⋊#208	C₂²	1	2	yes	—
13	C₂×#6758	C₄	1	2	yes	complemented
14	C₂×D₅⋊(C₃⋊C₈)	—	2	1	no	—
15	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
16	C₃×#4130	—	2	1	no	—
17	C₃×#4130	—	2	1	no	—
18	C₃×#4130	C₄	1	2	yes	complemented
19	C₃×#4130	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	1	2	yes	complemented
21	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
22	C₂×C₄×Dic₁₅	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic, complemented
24	C₂×Dic₃×Dic₅	—	2	1	no	—
25	C₄×D₅×Dic₃	—	2	1	no	—
26	C₄×D₅×Dic₃	—	2	1	no	—
27	C₄×D₅×Dic₃	C₄	1	2	yes	complemented
28	C₄×D₅×Dic₃	C₂²	1	2	yes	—
29	C₂×#4532	—	5	1	no	maximal, Hall
30	C₂×#4130	D₃	1	1	yes	characteristic
31	C₂×D₅⋊M₁₆	—	3	1	no	—
32	C₂×C₄²×D₅	—	3	1	no	—
33	#64862	—	3	4	no	—
34	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×C₅×Dic₃	—	2	1	no	—
39	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₂×D₅×Dic₃	—	2	8	no	—
53	C₂×D₅×Dic₃	—	2	2	no	—
54	C₂×D₅×Dic₃	—	2	2	no	—
55	#6762	—	2	2	no	—
56	#6762	—	2	2	no	—
57	C₂×C₃⋊#170	—	2	2	no	—
58	#6758	—	2	2	no	—
59	#6758	C₂×C₄	1	4	yes	complemented
60	D₅⋊(C₃⋊C₈)	—	2	2	no	—
61	D₅⋊(C₃⋊C₈)	—	2	2	no	—
62	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
63	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
64	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
65	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	complemented
66	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
67	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
68	C₄×Dic₁₅	—	2	1	no	—
69	C₄×Dic₁₅	C₂×C₄	1	2	yes	complemented
70	C₄×C₅×Dic₃	—	2	1	no	—
71	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
72	Dic₃×Dic₅	—	2	2	no	—
73	Dic₃×Dic₅	—	2	2	no	—
74	C₂×C₃×#117	—	5	1	no	—
75	C₂²×C₄×Dic₃	—	5	1	no	—
76	C₂²×#208	—	5	1	no	—
77	#4532	—	5	4	no	—
78	C₂²×C₄×D₅	—	6	1	no	—
79	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
80	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
81	C₂×#704	—	6	1	no	—
82	#4130	—	2	1	no	—
83	#4130	—	2	1	no	—
84	#4130	Dic₃	1	2	yes	complemented
85	#4130	C₂×D₃	1	2	yes	—
86	C₂×C₄⋊AGL(1,𝔽₅)	Dic₃	1	2	yes	complemented
87	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
88	D₅⋊M₁₆	—	3	2	no	—
89	D₅⋊M₁₆	—	3	2	no	—
90	D₅⋊M₁₆	—	6	1	no	—
91	D₅⋊M₁₆	—	6	1	no	—
92	C₂×#700	—	3	2	no	—
93	C₂×D₅⋊C₈	—	6	1	no	—
94	C₂×C₄²×C₅	—	3	1	no	—
95	C₂×C₄×Dic₅	—	3	1	no	—
96	C₂×C₄×Dic₅	—	6	1	no	—
97	C₄²×D₅	—	3	2	no	—
98	C₄²×D₅	—	3	2	no	—
99	C₄²×D₅	—	6	1	no	—
100	C₄²×D₅	—	6	1	no	—
101	C₂×#339	—	15	1	no	Sylow
102	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₃×D₅	—	2	4	no	—
104	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
111	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
112	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×Dic₁₅	—	2	4	no	—
119	C₂×Dic₁₅	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	4	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
128	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
129	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
130	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
131	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
132	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
133	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
134	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
135	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
136	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
137	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
138	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
139	C₃×C₄×D₅	C₄⋊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	C₂×D₄	1	1	yes	characteristic
143	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
144	D₅×Dic₃	—	2	8	no	—
145	D₅×Dic₃	—	2	8	no	—
146	C₃⋊#170	—	2	4	no	—
147	C₂³×C₃×C₄	—	5	1	no	—
148	C₂³×Dic₃	—	10	1	no	—
149	C₃×#117	—	5	2	no	—
150	C₃×#117	—	5	2	no	—
151	C₃×#117	—	10	1	no	—
152	C₃×#117	—	10	1	no	—
153	C₂×C₃×C₄⋊C₄	—	5	2	no	—
154	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
155	C₂×C₃×C₄²	—	10	1	no	—
156	C₂×C₄×Dic₃	—	5	1	no	—
157	C₂×C₄×Dic₃	—	5	2	no	—
158	C₂×C₄×Dic₃	—	5	2	no	—
159	C₂×C₄×Dic₃	—	10	1	no	—
160	C₂×C₄×Dic₃	—	10	1	no	—
161	C₂×C₄×Dic₃	—	10	1	no	—
162	C₂×C₄×Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
163	C₂×#208	—	5	2	no	—
164	C₂×#208	—	5	2	no	—
165	C₂×#208	—	5	2	no	—
166	C₂×#208	—	10	1	no	—
167	C₂×#208	—	10	1	no	—
168	C₂×#208	—	10	1	no	—
169	C₂²×C₃⋊C₈	—	10	1	no	—
170	C₂³×D₅	#67	1	1	yes	characteristic
171	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
172	C₂²×C₄×C₅	—	6	1	no	—
173	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
174	C₂²×Dic₅	—	6	1	no	—
175	C₂²×Dic₅	D₁₂	1	1	yes	characteristic
176	C₂×C₄×D₅	—	6	8	no	—
177	C₂×C₄×D₅	—	6	2	no	—
178	C₂×C₄×D₅	—	6	2	no	—
179	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
180	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
181	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
182	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
183	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
184	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
185	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
186	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
187	C₂×C₄×D₅	#67	1	1	yes	characteristic
188	C₂×C₄×D₅	#67	1	1	yes	characteristic
189	C₂×C₄×D₅	#67	1	1	yes	characteristic
190	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
191	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
192	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
193	#704	—	6	2	no	—
194	#704	—	6	2	no	—
195	C₂×#170	—	6	2	no	—
196	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
197	C₄⋊AGL(1,𝔽₅)	C₂×Dic₃	1	4	yes	complemented
198	C₄×AGL(1,𝔽₅)	—	2	2	no	—
199	C₄×AGL(1,𝔽₅)	—	2	2	no	—
200	#700	—	3	4	no	—
201	#700	—	6	2	no	—
202	D₅⋊C₈	—	6	2	no	—
203	D₅⋊C₈	—	6	2	no	—
204	C₄²×C₅	—	3	2	no	—
205	C₄²×C₅	—	6	1	no	—
206	C₄×Dic₅	—	3	2	no	—
207	C₄×Dic₅	—	6	1	no	—
208	C₄×Dic₅	—	6	2	no	—
209	C₄×Dic₅	—	6	2	no	—
210	C₂²×M₁₆	—	15	1	no	—
211	C₂×#117	—	5	1	no	—
212	C₂²×C₄²	—	15	1	no	—
213	#339	—	15	4	no	—
214	C₂²×C₃×C₅	—	2	2	no	—
215	C₂²×C₃×C₅	#95	1	1	yes	characteristic
216	C₂²×C₃×C₅	#95	1	1	yes	characteristic
217	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₃×D₅	—	2	2	no	—
219	C₂×C₃×D₅	—	2	2	no	—
220	C₂×C₃×D₅	—	2	2	no	—
221	C₂×C₃×D₅	—	2	2	no	—
222	C₂×C₃×D₅	—	2	2	no	—
223	C₂×C₃×D₅	#95	1	1	yes	characteristic
224	C₂×C₃×D₅	#95	1	1	yes	characteristic
225	C₂×C₃×D₅	#104	1	4	yes	—
226	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₃×AGL(1,𝔽₅)	—	4	4	no	—
229	C₃×C₄×C₅	#95	1	1	yes	characteristic
230	C₃×C₄×C₅	#95	1	1	yes	characteristic
231	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
233	Dic₁₅	—	2	4	no	—
234	C₃×Dic₅	#95	1	1	yes	characteristic
235	C₃×Dic₅	#95	1	1	yes	characteristic
236	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₅×Dic₃	—	2	4	no	—
239	C₂⁴×C₃	—	5	1	no	—
240	C₂²×C₃×C₄	—	5	1	no	—
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂²×C₃×C₄	—	5	1	no	—
243	C₂²×C₃×C₄	—	5	1	no	—
244	C₂²×C₃×C₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	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	—	10	2	no	—
254	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
255	C₂²×Dic₃	—	2	1	no	—
256	C₂²×Dic₃	—	10	2	no	—
257	C₂²×Dic₃	—	10	2	no	—
258	C₂²×Dic₃	—	10	8	no	—
259	C₂²×Dic₃	—	10	1	no	—
260	C₃×C₄⋊C₄	—	5	4	no	—
261	C₃×C₄⋊C₄	—	10	2	no	—
262	C₃×C₂²⋊C₄	—	10	2	no	—
263	C₃×C₂²⋊C₄	—	10	2	no	—
264	C₃×C₄²	—	10	2	no	—
265	C₃×C₄²	—	10	2	no	—
266	C₄×Dic₃	—	2	1	no	—
267	C₄×Dic₃	—	5	2	no	—
268	C₄×Dic₃	—	10	2	no	—
269	C₄×Dic₃	—	10	2	no	—
270	C₄×Dic₃	—	10	1	no	—
271	C₄×Dic₃	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
272	#208	—	5	4	no	—
273	#208	—	10	2	no	—
274	#208	—	10	2	no	—
275	#208	—	10	2	no	—
276	C₂×C₃⋊C₈	—	10	2	no	—
277	C₂×C₃⋊C₈	—	10	2	no	—
278	C₂×C₃⋊C₈	—	10	2	no	—
279	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
280	C₂²×D₅	—	2	4	no	—
281	C₂²×D₅	Dic₃⋊C₄	1	1	yes	characteristic
282	C₂²×D₅	Dic₃⋊C₄	1	1	yes	characteristic
283	C₂²×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
284	C₂²×D₅	#217	1	1	yes	characteristic
285	C₂²×D₅	#217	1	1	yes	characteristic
286	C₂²×D₅	C₂×#67	1	1	yes	characteristic
287	C₂×AGL(1,𝔽₅)	—	2	4	no	—
288	C₂×AGL(1,𝔽₅)	—	4	4	no	—
289	C₂×C₄×C₅	—	6	4	no	—
290	C₂×C₄×C₅	—	6	2	no	—
291	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
292	C₂×C₄×C₅	C₄×Dic₃	1	1	yes	characteristic
293	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
297	C₂×Dic₅	—	6	4	no	—
298	C₂×Dic₅	—	6	2	no	—
299	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
300	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
301	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
302	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
303	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
304	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
305	C₄×D₅	—	6	8	no	—
306	C₄×D₅	—	6	8	no	—
307	C₄×D₅	C₄×Dic₃	1	1	yes	characteristic
308	C₄×D₅	C₄×Dic₃	1	1	yes	characteristic
309	C₄×D₅	Dic₃⋊C₄	1	1	yes	characteristic
310	C₄×D₅	Dic₃⋊C₄	1	1	yes	characteristic
311	C₄×D₅	Dic₃⋊C₄	1	1	yes	characteristic
312	C₄×D₅	Dic₃⋊C₄	1	1	yes	characteristic
313	C₄×D₅	C₄⋊Dic₃	1	1	yes	characteristic
314	C₄×D₅	C₄⋊Dic₃	1	1	yes	characteristic
315	C₄×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
316	C₄×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
317	C₄×D₅	#217	1	1	yes	characteristic
318	C₄×D₅	#217	1	1	yes	characteristic
319	C₄×D₅	C₂×Dic₆	1	1	yes	characteristic
320	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
321	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
322	C₄×D₅	C₂×#67	1	1	yes	characteristic
323	#170	—	6	4	no	—
324	C₂³×C₄	—	5	1	no	—
325	C₂³×C₄	—	30	1	no	—
326	C₂×M₁₆	—	15	2	no	—
327	C₂×M₁₆	—	15	2	no	—
328	C₂×M₁₆	—	15	2	no	—
329	C₂×M₁₆	—	30	1	no	—
330	C₂×M₁₆	—	30	1	no	—
331	C₂×M₁₆	—	30	1	no	—
332	C₂²×C₈	—	30	1	no	—
333	#117	—	5	2	no	—
334	#117	—	5	2	no	—
335	#117	—	10	1	no	—
336	#117	—	10	1	no	—
337	C₂×C₄⋊C₄	—	5	2	no	—
338	C₂×C₂²⋊C₄	—	10	1	no	—
339	C₂×C₄²	—	3	1	no	—
340	C₂×C₄²	—	10	1	no	—
341	C₂×C₄²	—	15	2	no	—
342	C₂×C₄²	—	15	2	no	—
343	C₂×C₄²	—	15	1	no	—
344	C₂×C₄²	—	30	1	no	—
345	C₂×C₄²	—	30	1	no	—
346	C₂×C₄²	—	30	1	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	#339	1	2	yes	complemented
350	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
351	C₃×D₅	—	2	1	no	—
352	C₃×D₅	—	2	1	no	—
353	C₃×D₅	#339	1	2	yes	complemented
354	C₃×D₅	C₂×#104	1	2	yes	—
355	C₂³×C₃	—	5	1	no	—
356	C₂³×C₃	—	5	1	no	—
357	C₂³×C₃	—	5	1	no	—
358	C₂³×C₃	—	5	1	no	—
359	C₂³×C₃	—	5	1	no	—
360	C₂³×C₃	—	5	1	no	—
361	C₂³×C₃	—	10	4	no	—
362	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
363	C₂×C₃×C₄	—	5	1	no	—
364	C₂×C₃×C₄	—	5	1	no	—
365	C₂×C₃×C₄	—	5	1	no	—
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	—	10	4	no	—
386	C₂×C₃×C₄	—	20	4	no	—
387	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
388	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
389	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₂×Dic₃	—	2	4	no	—
394	C₂×Dic₃	—	2	2	no	—
395	C₂×Dic₃	—	10	8	no	—
396	C₂×Dic₃	—	10	8	no	—
397	C₂×Dic₃	—	10	4	no	—
398	C₂×Dic₃	—	10	2	no	—
399	C₃⋊C₈	—	10	4	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	C₃⋊#95	1	1	yes	characteristic
402	C₂²×C₅	C₃⋊#95	1	1	yes	characteristic
403	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
404	C₂×D₅	—	2	2	no	—
405	C₂×D₅	—	2	2	no	—
406	C₂×D₅	—	2	2	no	—
407	C₂×D₅	—	2	2	no	—
408	C₂×D₅	—	2	2	no	—
409	C₂×D₅	C₃⋊#95	1	1	yes	characteristic
410	C₂×D₅	C₃⋊#95	1	1	yes	characteristic
411	C₂×D₅	#837	1	4	yes	—
412	C₂×D₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
413	C₂×D₅	C₂×#217	1	1	yes	characteristic
414	AGL(1,𝔽₅)	—	4	4	no	—
415	C₄×C₅	—	6	4	no	—
416	C₄×C₅	C₃⋊#95	1	1	yes	characteristic
417	C₄×C₅	C₃⋊#95	1	1	yes	characteristic
418	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
419	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
420	Dic₅	—	6	4	no	—
421	Dic₅	C₃⋊#95	1	1	yes	characteristic
422	Dic₅	C₃⋊#95	1	1	yes	characteristic
423	Dic₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
424	Dic₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
425	C₂⁴	—	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	1	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	6	1	no	—
440	C₂²×C₄	—	10	2	no	—
441	C₂²×C₄	—	30	2	no	—
442	C₂²×C₄	—	30	2	no	—
443	C₂²×C₄	—	30	8	no	—
444	C₂²×C₄	—	30	1	no	—
445	C₂²×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
446	M₁₆	—	15	4	no	—
447	M₁₆	—	30	2	no	—
448	M₁₆	—	30	2	no	—
449	M₁₆	—	30	2	no	—
450	C₂×C₈	—	30	2	no	—
451	C₂×C₈	—	30	2	no	—
452	C₂×C₈	—	30	2	no	—
453	C₄⋊C₄	—	5	4	no	—
454	C₄⋊C₄	—	10	2	no	—
455	C₂²⋊C₄	—	10	2	no	—
456	C₂²⋊C₄	—	10	2	no	—
457	C₄²	—	3	2	no	—
458	C₄²	—	6	1	no	—
459	C₄²	—	10	2	no	—
460	C₄²	—	10	2	no	—
461	C₄²	—	15	2	no	—
462	C₄²	—	30	2	no	—
463	C₄²	—	30	2	no	—
464	C₄²	—	30	1	no	—
465	C₃×C₅	C₂×#339	1	1	yes	characteristic, complemented, Hall
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	5	4	no	—
468	C₂²×C₃	—	5	1	no	—
469	C₂²×C₃	—	5	1	no	—
470	C₂²×C₃	—	5	1	no	—
471	C₂²×C₃	—	5	1	no	—
472	C₂²×C₃	—	10	2	no	—
473	C₂²×C₃	—	10	2	no	—
474	C₂²×C₃	—	10	2	no	—
475	C₂²×C₃	—	10	2	no	—
476	C₂²×C₃	—	10	2	no	—
477	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
478	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
479	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
480	C₃×C₄	—	5	1	no	—
481	C₃×C₄	—	5	1	no	—
482	C₃×C₄	—	5	1	no	—
483	C₃×C₄	—	5	1	no	—
484	C₃×C₄	—	20	4	no	—
485	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
486	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
487	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
488	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
489	Dic₃	—	2	4	no	—
490	Dic₃	—	10	4	no	—
491	C₂×C₅	—	2	1	no	—
492	C₂×C₅	—	2	1	no	—
493	C₂×C₅	#4532	1	2	yes	complemented
494	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
495	D₅	—	2	1	no	—
496	D₅	—	2	1	no	—
497	D₅	#4532	1	2	yes	complemented
498	D₅	C₂×#837	1	2	yes	—
499	C₂³	—	5	1	no	—
500	C₂³	—	5	1	no	—
501	C₂³	—	5	1	no	—
502	C₂³	—	5	1	no	—
503	C₂³	—	5	1	no	—
504	C₂³	—	5	1	no	—
505	C₂³	—	10	4	no	—
506	C₂³	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
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	1	no	—
524	C₂×C₄	—	5	1	no	—
525	C₂×C₄	—	5	1	no	—
526	C₂×C₄	—	5	1	no	—
527	C₂×C₄	—	5	1	no	—
528	C₂×C₄	—	5	1	no	—
529	C₂×C₄	—	6	4	no	—
530	C₂×C₄	—	6	2	no	—
531	C₂×C₄	—	10	4	no	—
532	C₂×C₄	—	20	4	no	—
533	C₂×C₄	—	30	8	no	—
534	C₂×C₄	—	30	8	no	—
535	C₂×C₄	—	30	4	no	—
536	C₂×C₄	—	30	2	no	—
537	C₂×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
538	C₂×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
539	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
540	C₂×C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
541	C₂×C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
542	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
543	C₈	—	30	4	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	5	2	no	—
547	C₂×C₃	—	5	2	no	—
548	C₂×C₃	—	10	1	no	—
549	C₂×C₃	—	10	1	no	—
550	C₂×C₃	#64862	1	2	yes	complemented
551	C₂×C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
552	C₅	C₂×#4532	1	1	yes	characteristic, complemented, Sylow
553	C₂²	—	2	2	no	—
554	C₂²	—	5	1	no	—
555	C₂²	—	5	1	no	—
556	C₂²	—	5	4	no	—
557	C₂²	—	5	1	no	—
558	C₂²	—	5	1	no	—
559	C₂²	—	10	2	no	—
560	C₂²	—	10	2	no	—
561	C₂²	—	10	2	no	—
562	C₂²	—	10	2	no	—
563	C₂²	—	10	2	no	—
564	C₂²	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
565	C₂²	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
566	C₂²	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
567	C₄	—	5	1	no	—
568	C₄	—	5	1	no	—
569	C₄	—	5	1	no	—
570	C₄	—	5	1	no	—
571	C₄	—	6	4	no	—
572	C₄	—	20	4	no	—
573	C₄	—	30	4	no	—
574	C₄	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
575	C₄	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
576	C₄	C₂×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
577	C₄	C₂×Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
578	C₃	C₂×#64862	1	1	yes	characteristic, complemented, Sylow
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	5	2	no	—
582	C₂	—	5	2	no	—
583	C₂	—	10	1	no	—
584	C₂	—	10	1	no	—
585	C₂	#11746523	1	2	yes	direct product factor
586	C₂	C₂×(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	Dic₃⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₄×C₅	C₂×C₄
socle	C₂²×C₃×C₅	#95
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂²×C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#339
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
4. #11746523	C₂	direct (N × H)
11. D₅⋊#208	C₄	semidirect
13. C₂×#6758	C₄	semidirect
18. C₃×#4130	C₄	semidirect
20. C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	semidirect
22. C₂×C₄×Dic₁₅	C₄	semidirect
23. C₂×C₄×C₅×Dic₃	C₄	semidirect
27. C₄×D₅×Dic₃	C₄	semidirect
59. #6758	C₂×C₄	semidirect
65. C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	semidirect
69. C₄×Dic₁₅	C₂×C₄	semidirect
71. C₄×C₅×Dic₃	C₂×C₄	semidirect
84. #4130	Dic₃	semidirect
86. C₂×C₄⋊AGL(1,𝔽₅)	Dic₃	semidirect
162. C₂×C₄×Dic₃	AGL(1,𝔽₅)	semidirect
197. C₄⋊AGL(1,𝔽₅)	C₂×Dic₃	semidirect
271. C₄×Dic₃	C₂×AGL(1,𝔽₅)	semidirect
349. C₂×C₃×C₅	#339	semidirect
353. C₃×D₅	#339	semidirect
465. C₃×C₅	C₂×#339	semidirect
493. C₂×C₅	#4532	semidirect
497. D₅	#4532	semidirect
550. C₂×C₃	#64862	semidirect
552. C₅	C₂×#4532	semidirect
578. C₃	C₂×#64862	semidirect
585. C₂	#11746523	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×D₅⋊#208	2
C₂×C₃×#4130	2
C₂×C₄×D₅×Dic₃	2
#11746523	2
C₂×#64862	3
C₂×#4532	5

Subgroups — C2×#11746523 #14294473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746523 #14294473