Subgroups — C₂×#11746527 #14294476

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91989	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×#208	C₂	1	1	yes	maximal, characteristic
4	#11746527	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64900	—	3	1	no	maximal, Hall
6	C₂³×C₃×AGL(1,𝔽₅)	—	2	1	no	—
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×#6763	—	2	1	no	—
9	#91989	—	2	1	no	—
10	#91989	—	2	1	no	—
11	#91989	C₄	1	2	yes	complemented
12	#91989	C₂²	1	2	yes	—
13	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₄	1	2	yes	complemented
14	C₂×C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
15	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
16	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
17	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
18	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	complemented
19	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	complemented
20	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
21	C₂×#6710	C₄	1	1	yes	characteristic, complemented
22	C₂×C₅×#208	C₄	1	1	yes	characteristic, complemented
23	C₂×#6649	—	2	1	no	—
24	D₅×#208	—	2	1	no	—
25	D₅×#208	—	2	1	no	—
26	D₅×#208	C₄	1	2	yes	complemented
27	D₅×#208	C₂²	1	2	yes	—
28	C₂×D₅×C₃⋊C₈	—	2	1	no	—
29	C₂×#4523	—	5	1	no	maximal, Hall
30	C₂×#4130	—	3	1	no	—
31	C₂²×C₄×AGL(1,𝔽₅)	D₃	1	1	yes	characteristic
32	C₂×D₅×M₁₆	—	3	1	no	—
33	#64900	—	3	4	no	—
34	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
35	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
36	C₂²×C₃×AGL(1,𝔽₅)	—	2	8	no	—
37	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
38	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
39	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	Q₈	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	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂×C₄	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	D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
52	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
54	#6763	—	2	2	no	—
55	#6763	—	2	2	no	—
56	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
57	C₄⋊ΓL(1,𝔽₁₆)	C₂×C₄	1	4	yes	complemented
58	C₄×ΓL(1,𝔽₁₆)	—	2	2	no	—
59	C₄×ΓL(1,𝔽₁₆)	—	2	2	no	—
60	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
61	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
62	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
63	C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	complemented
64	#6710	—	2	1	no	—
65	#6710	C₂×C₄	1	2	yes	complemented
66	C₂×C₃⋊#168	—	2	1	no	—
67	C₅×#208	—	2	1	no	—
68	C₅×#208	C₂×C₄	1	2	yes	complemented
69	C₂×C₅×C₃⋊C₈	—	2	1	no	—
70	#6649	—	2	2	no	—
71	#6649	—	2	2	no	—
72	D₅×C₃⋊C₈	—	2	2	no	—
73	D₅×C₃⋊C₈	—	2	2	no	—
74	C₂²×C₃×C₄²	—	5	1	no	—
75	C₂×#926	—	5	1	no	—
76	C₂²×#208	—	5	1	no	—
77	#4523	—	5	4	no	—
78	C₂³×AGL(1,𝔽₅)	—	2	1	no	—
79	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
80	C₂×C₂²⋊AGL(1,𝔽₅)	—	6	1	no	—
81	#4130	—	3	2	no	—
82	#4130	—	3	2	no	—
83	#4130	—	6	1	no	—
84	#4130	—	6	1	no	—
85	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
86	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
87	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
88	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
89	C₂×C₄×AGL(1,𝔽₅)	—	6	1	no	—
90	C₂×C₄×AGL(1,𝔽₅)	Dic₃	1	2	yes	complemented
91	C₂×C₄×AGL(1,𝔽₅)	Dic₃	1	2	yes	complemented
92	C₂×C₄×AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
93	C₂×C₅×M₁₆	—	3	1	no	—
94	C₂×#681	—	3	1	no	—
95	D₅×M₁₆	—	3	2	no	—
96	D₅×M₁₆	—	3	2	no	—
97	D₅×M₁₆	—	6	1	no	—
98	D₅×M₁₆	—	6	1	no	—
99	C₂×#676	—	6	1	no	—
100	C₂×C₈×D₅	—	6	1	no	—
101	C₂×#339	—	15	1	no	Sylow
102	C₂³×C₃×C₅	C₄⋊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	C₂²⋊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×ΓL(1,𝔽₁₆)	—	2	4	no	—
111	C₂×ΓL(1,𝔽₁₆)	—	4	4	no	—
112	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
113	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
114	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
115	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
116	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₄⋊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×Q₈	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	C₂²⋊C₄	1	1	yes	characteristic
135	C₃×C₄×D₅	C₂²⋊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×D₄	1	1	yes	characteristic
144	C₃⋊#168	—	2	2	no	—
145	C₅×C₃⋊C₈	—	2	2	no	—
146	C₂³×C₃×C₄	—	5	1	no	—
147	C₂³×C₃×C₄	—	10	1	no	—
148	C₂×C₃×C₄²	—	5	2	no	—
149	C₂×C₃×C₄²	—	5	2	no	—
150	C₂×C₃×C₄²	—	5	2	no	—
151	C₂×C₃×C₄²	—	10	1	no	—
152	C₂×C₃×C₄²	—	10	1	no	—
153	C₂×C₃×C₄²	—	10	1	no	—
154	C₂×#217	—	10	1	no	—
155	#926	—	5	2	no	—
156	#926	—	5	2	no	—
157	#926	—	10	1	no	—
158	#926	—	10	1	no	—
159	C₂×C₄⋊Dic₃	—	5	2	no	—
160	C₂×C₄×Dic₃	—	10	1	no	—
161	C₂×#208	—	5	1	no	—
162	C₂×#208	—	5	2	no	—
163	C₂×#208	—	5	2	no	—
164	C₂×#208	—	10	1	no	—
165	C₂×#208	—	10	1	no	—
166	C₂×#208	—	10	1	no	—
167	C₂×#208	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
168	C₂²×C₃⋊C₈	—	10	1	no	—
169	C₂³×D₅	#67	1	1	yes	characteristic
170	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
171	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
172	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
173	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
174	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
175	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
176	C₂²×Dic₅	Dic₆	1	1	yes	characteristic
177	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
178	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
179	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
180	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
181	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
182	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
183	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
184	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
185	C₂×C₄×D₅	#67	1	1	yes	characteristic
186	C₂×C₄×D₅	#67	1	1	yes	characteristic
187	C₂×C₄×D₅	#67	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
189	C₂²⋊AGL(1,𝔽₅)	—	6	2	no	—
190	C₂²⋊AGL(1,𝔽₅)	—	6	2	no	—
191	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
192	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
193	C₄×AGL(1,𝔽₅)	—	2	2	no	—
194	C₄×AGL(1,𝔽₅)	—	2	2	no	—
195	C₄×AGL(1,𝔽₅)	—	2	2	no	—
196	C₄×AGL(1,𝔽₅)	—	6	2	no	—
197	C₄×AGL(1,𝔽₅)	—	6	2	no	—
198	C₄×AGL(1,𝔽₅)	C₂×Dic₃	1	4	yes	complemented
199	C₅×M₁₆	—	3	2	no	—
200	C₅×M₁₆	—	6	1	no	—
201	C₂×C₅×C₈	—	6	1	no	—
202	#681	—	3	2	no	—
203	#681	—	6	1	no	—
204	C₂×#168	—	6	1	no	—
205	#676	—	6	2	no	—
206	#676	—	6	2	no	—
207	C₈×D₅	—	6	2	no	—
208	C₈×D₅	—	6	2	no	—
209	C₂²×M₁₆	—	15	1	no	—
210	C₂×#117	—	15	1	no	—
211	C₂²×C₄²	—	5	1	no	—
212	#339	—	15	4	no	—
213	C₂²×C₃×C₅	—	2	2	no	—
214	C₂²×C₃×C₅	#95	1	1	yes	characteristic
215	C₂²×C₃×C₅	#95	1	1	yes	characteristic
216	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂×C₃×D₅	—	2	2	no	—
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	#95	1	1	yes	characteristic
223	C₂×C₃×D₅	#95	1	1	yes	characteristic
224	C₂×C₃×D₅	#104	1	4	yes	—
225	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	ΓL(1,𝔽₁₆)	—	4	4	no	—
228	C₃×AGL(1,𝔽₅)	—	2	8	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×C₂²⋊C₄	1	1	yes	characteristic
233	C₃×Dic₅	#95	1	1	yes	characteristic
234	C₃×Dic₅	#95	1	1	yes	characteristic
235	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂⁴×C₃	—	5	1	no	—
238	C₂²×C₃×C₄	—	5	1	no	—
239	C₂²×C₃×C₄	—	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	—	10	2	no	—
252	C₂²×C₃×C₄	—	10	2	no	—
253	C₂²×C₃×C₄	—	10	2	no	—
254	C₂²×C₃×C₄	—	10	8	no	—
255	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
256	C₂²×Dic₃	—	10	2	no	—
257	C₃×C₄²	—	5	4	no	—
258	C₃×C₄²	—	10	2	no	—
259	C₃×C₄²	—	10	2	no	—
260	C₃×C₄²	—	10	2	no	—
261	#217	—	10	2	no	—
262	#217	—	10	2	no	—
263	C₄⋊Dic₃	—	5	4	no	—
264	C₄⋊Dic₃	—	10	2	no	—
265	C₄×Dic₃	—	10	2	no	—
266	C₄×Dic₃	—	10	2	no	—
267	#208	—	2	1	no	—
268	#208	—	5	2	no	—
269	#208	—	10	2	no	—
270	#208	—	10	2	no	—
271	#208	—	10	1	no	—
272	#208	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
273	C₂×C₃⋊C₈	—	2	1	no	—
274	C₂×C₃⋊C₈	—	10	2	no	—
275	C₂×C₃⋊C₈	—	10	2	no	—
276	C₂×C₃⋊C₈	—	10	1	no	—
277	C₂³×C₅	Dic₃⋊C₄	1	1	yes	characteristic
278	C₂²×D₅	—	2	4	no	—
279	C₂²×D₅	Dic₃⋊C₄	1	1	yes	characteristic
280	C₂²×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
281	C₂²×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
282	C₂²×D₅	#217	1	1	yes	characteristic
283	C₂²×D₅	#217	1	1	yes	characteristic
284	C₂²×D₅	C₂×#67	1	1	yes	characteristic
285	C₂×AGL(1,𝔽₅)	—	2	8	no	—
286	C₂×AGL(1,𝔽₅)	—	2	8	no	—
287	C₂×AGL(1,𝔽₅)	—	2	8	no	—
288	C₂×AGL(1,𝔽₅)	—	2	4	no	—
289	C₂×AGL(1,𝔽₅)	—	6	4	no	—
290	C₂×AGL(1,𝔽₅)	—	12	4	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	(C₂×D₃)⋊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	Dic₃⋊C₄	1	1	yes	characteristic
298	C₂×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
299	C₂×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
300	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
301	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
302	C₂×Dic₅	C₂×Dic₆	1	1	yes	characteristic
303	C₄×D₅	C₄×Dic₃	1	1	yes	characteristic
304	C₄×D₅	C₄×Dic₃	1	1	yes	characteristic
305	C₄×D₅	Dic₃⋊C₄	1	1	yes	characteristic
306	C₄×D₅	Dic₃⋊C₄	1	1	yes	characteristic
307	C₄×D₅	C₄⋊Dic₃	1	1	yes	characteristic
308	C₄×D₅	C₄⋊Dic₃	1	1	yes	characteristic
309	C₄×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
310	C₄×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
311	C₄×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
312	C₄×D₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
313	C₄×D₅	#217	1	1	yes	characteristic
314	C₄×D₅	#217	1	1	yes	characteristic
315	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
316	C₄×D₅	C₂×D₁₂	1	1	yes	characteristic
317	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
318	C₄×D₅	C₂×#67	1	1	yes	characteristic
319	C₅×C₈	—	6	2	no	—
320	#168	—	6	2	no	—
321	C₂³×C₄	—	5	1	no	—
322	C₂³×C₄	—	10	1	no	—
323	C₂×M₁₆	—	3	1	no	—
324	C₂×M₁₆	—	15	2	no	—
325	C₂×M₁₆	—	15	2	no	—
326	C₂×M₁₆	—	15	1	no	—
327	C₂×M₁₆	—	30	1	no	—
328	C₂×M₁₆	—	30	1	no	—
329	C₂×M₁₆	—	30	1	no	—
330	C₂²×C₈	—	30	1	no	—
331	#117	—	15	2	no	—
332	#117	—	15	2	no	—
333	#117	—	30	1	no	—
334	#117	—	30	1	no	—
335	C₂×C₄⋊C₄	—	15	2	no	—
336	C₂×C₂²⋊C₄	—	30	1	no	—
337	C₂×C₄²	—	5	2	no	—
338	C₂×C₄²	—	5	2	no	—
339	C₂×C₄²	—	5	2	no	—
340	C₂×C₄²	—	10	1	no	—
341	C₂×C₄²	—	10	1	no	—
342	C₂×C₄²	—	10	1	no	—
343	C₂×C₄²	—	30	1	no	—
344	C₂×C₃×C₅	—	2	1	no	—
345	C₂×C₃×C₅	—	2	1	no	—
346	C₂×C₃×C₅	#339	1	2	yes	complemented
347	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
348	C₃×D₅	—	2	1	no	—
349	C₃×D₅	—	2	1	no	—
350	C₃×D₅	#339	1	2	yes	complemented
351	C₃×D₅	C₂×#104	1	2	yes	—
352	C₂³×C₃	—	5	1	no	—
353	C₂³×C₃	—	5	1	no	—
354	C₂³×C₃	—	5	1	no	—
355	C₂³×C₃	—	5	1	no	—
356	C₂³×C₃	—	5	1	no	—
357	C₂³×C₃	—	5	1	no	—
358	C₂³×C₃	—	10	4	no	—
359	C₂³×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂×C₃×C₄	—	5	1	no	—
361	C₂×C₃×C₄	—	5	1	no	—
362	C₂×C₃×C₄	—	5	1	no	—
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	—	10	4	no	—
383	C₂×C₃×C₄	—	10	8	no	—
384	C₂×C₃×C₄	—	10	8	no	—
385	C₂×C₃×C₄	—	10	8	no	—
386	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
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	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×Dic₃	—	10	4	no	—
393	C₂×Dic₃	—	20	4	no	—
394	C₃⋊C₈	—	2	2	no	—
395	C₃⋊C₈	—	10	2	no	—
396	C₂²×C₅	—	2	2	no	—
397	C₂²×C₅	C₃⋊#95	1	1	yes	characteristic
398	C₂²×C₅	C₃⋊#95	1	1	yes	characteristic
399	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
400	C₂×D₅	—	2	2	no	—
401	C₂×D₅	—	2	2	no	—
402	C₂×D₅	—	2	2	no	—
403	C₂×D₅	—	2	2	no	—
404	C₂×D₅	—	2	2	no	—
405	C₂×D₅	#805	1	4	yes	—
406	C₂×D₅	C₃⋊#95	1	1	yes	characteristic
407	C₂×D₅	C₃⋊#95	1	1	yes	characteristic
408	C₂×D₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
409	C₂×D₅	C₂×#217	1	1	yes	characteristic
410	AGL(1,𝔽₅)	—	2	8	no	—
411	AGL(1,𝔽₅)	—	12	4	no	—
412	C₄×C₅	C₃⋊#95	1	1	yes	characteristic
413	C₄×C₅	C₃⋊#95	1	1	yes	characteristic
414	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
415	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
416	Dic₅	C₃⋊#95	1	1	yes	characteristic
417	Dic₅	C₃⋊#95	1	1	yes	characteristic
418	Dic₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
419	Dic₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
420	C₂⁴	—	5	1	no	—
421	C₂²×C₄	—	5	1	no	—
422	C₂²×C₄	—	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	—	10	2	no	—
435	C₂²×C₄	—	10	2	no	—
436	C₂²×C₄	—	10	2	no	—
437	C₂²×C₄	—	10	8	no	—
438	C₂²×C₄	—	30	2	no	—
439	C₂²×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
440	M₁₆	—	3	2	no	—
441	M₁₆	—	6	1	no	—
442	M₁₆	—	15	2	no	—
443	M₁₆	—	30	2	no	—
444	M₁₆	—	30	2	no	—
445	M₁₆	—	30	1	no	—
446	C₂×C₈	—	6	1	no	—
447	C₂×C₈	—	30	2	no	—
448	C₂×C₈	—	30	2	no	—
449	C₂×C₈	—	30	1	no	—
450	C₄⋊C₄	—	15	4	no	—
451	C₄⋊C₄	—	30	2	no	—
452	C₂²⋊C₄	—	30	2	no	—
453	C₂²⋊C₄	—	30	2	no	—
454	C₄²	—	5	4	no	—
455	C₄²	—	10	2	no	—
456	C₄²	—	10	2	no	—
457	C₄²	—	10	2	no	—
458	C₄²	—	30	2	no	—
459	C₄²	—	30	2	no	—
460	C₃×C₅	C₂×#339	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	5	4	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	—	10	2	no	—
471	C₂²×C₃	—	10	2	no	—
472	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
473	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
474	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₃×C₄	—	5	1	no	—
476	C₃×C₄	—	5	1	no	—
477	C₃×C₄	—	5	1	no	—
478	C₃×C₄	—	5	1	no	—
479	C₃×C₄	—	10	8	no	—
480	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
481	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
482	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
483	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
484	Dic₃	—	20	4	no	—
485	C₂×C₅	—	2	1	no	—
486	C₂×C₅	—	2	1	no	—
487	C₂×C₅	#4523	1	2	yes	complemented
488	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
489	D₅	—	2	1	no	—
490	D₅	—	2	1	no	—
491	D₅	#4523	1	2	yes	complemented
492	D₅	C₂×#805	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	—	10	4	no	—
500	C₂³	Dic₃⋊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	—	10	4	no	—
524	C₂×C₄	—	10	8	no	—
525	C₂×C₄	—	10	8	no	—
526	C₂×C₄	—	10	8	no	—
527	C₂×C₄	—	30	4	no	—
528	C₂×C₄	—	60	4	no	—
529	C₂×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
530	C₂×C₄	Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
531	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
532	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
533	C₂×C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
534	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
535	C₈	—	6	2	no	—
536	C₈	—	30	2	no	—
537	C₂×C₃	—	2	1	no	—
538	C₂×C₃	—	2	1	no	—
539	C₂×C₃	—	5	2	no	—
540	C₂×C₃	—	5	2	no	—
541	C₂×C₃	—	10	1	no	—
542	C₂×C₃	—	10	1	no	—
543	C₂×C₃	#64900	1	2	yes	complemented
544	C₂×C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
545	C₅	C₂×#4523	1	1	yes	characteristic, complemented, Sylow
546	C₂²	—	2	2	no	—
547	C₂²	—	5	1	no	—
548	C₂²	—	5	1	no	—
549	C₂²	—	5	4	no	—
550	C₂²	—	5	1	no	—
551	C₂²	—	5	1	no	—
552	C₂²	—	10	2	no	—
553	C₂²	—	10	2	no	—
554	C₂²	—	10	2	no	—
555	C₂²	—	10	2	no	—
556	C₂²	—	10	2	no	—
557	C₂²	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
558	C₂²	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
559	C₂²	C₂×Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
560	C₄	—	5	1	no	—
561	C₄	—	5	1	no	—
562	C₄	—	5	1	no	—
563	C₄	—	5	1	no	—
564	C₄	—	10	8	no	—
565	C₄	—	60	4	no	—
566	C₄	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
567	C₄	(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic
568	C₄	C₂×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
569	C₄	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
570	C₃	C₂×#64900	1	1	yes	characteristic, complemented, Sylow
571	C₂	—	2	1	no	—
572	C₂	—	2	1	no	—
573	C₂	—	5	2	no	—
574	C₂	—	5	2	no	—
575	C₂	—	10	1	no	—
576	C₂	—	10	1	no	—
577	C₂	#11746527	1	2	yes	direct product factor
578	C₂	C₂×(C₂×AGL(1,𝔽₅))⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₃)⋊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. #11746527	C₂	direct (N × H)
11. #91989	C₄	semidirect
13. C₂×C₄⋊ΓL(1,𝔽₁₆)	C₄	semidirect
18. C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	semidirect
19. C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	semidirect
21. C₂×#6710	C₄	semidirect
22. C₂×C₅×#208	C₄	semidirect
26. D₅×#208	C₄	semidirect
57. C₄⋊ΓL(1,𝔽₁₆)	C₂×C₄	semidirect
63. C₃×C₄×AGL(1,𝔽₅)	C₂×C₄	semidirect
65. #6710	C₂×C₄	semidirect
68. C₅×#208	C₂×C₄	semidirect
90. C₂×C₄×AGL(1,𝔽₅)	Dic₃	semidirect
91. C₂×C₄×AGL(1,𝔽₅)	Dic₃	semidirect
167. C₂×#208	AGL(1,𝔽₅)	semidirect
198. C₄×AGL(1,𝔽₅)	C₂×Dic₃	semidirect
272. #208	C₂×AGL(1,𝔽₅)	semidirect
346. C₂×C₃×C₅	#339	semidirect
350. C₃×D₅	#339	semidirect
460. C₃×C₅	C₂×#339	semidirect
487. C₂×C₅	#4523	semidirect
491. D₅	#4523	semidirect
543. C₂×C₃	#64900	semidirect
545. C₅	C₂×#4523	semidirect
570. C₃	C₂×#64900	semidirect
577. C₂	#11746527	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×#91989	2
C₂²×C₃×C₄×AGL(1,𝔽₅)	2
C₂×D₅×#208	2
#11746527	2
C₂×#64900	3
C₂×#4523	5

Subgroups — C2×#11746527 #14294476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11746527 #14294476