Subgroups — #14411572

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756835	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#907	C₂	1	1	yes	maximal, characteristic
3	D₅×#901	C₂	1	1	yes	maximal, characteristic
4	C₂×#91221	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65718	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751698	C₂	1	1	yes	maximal, characteristic, complemented
7	#11751697	C₂	1	1	yes	maximal, characteristic, complemented
8	#11751671	C₂	1	2	yes	maximal, complemented
9	#11751656	C₂	1	2	yes	maximal, complemented
10	D₃×#3992	C₂	1	2	yes	maximal, complemented
11	AGL(1,𝔽₅)×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
12	#10617415	—	3	1	no	maximal, Hall
13	D₅×#235	C₂²	1	1	yes	characteristic
14	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
15	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₃×#4130	C₂²	1	1	yes	characteristic
17	C₃×D₅⋊M₁₆	C₂²	1	1	yes	characteristic
18	#67⋊AGL(1,𝔽₅)	C₄	1	4	yes	—
19	#91929	C₄	1	4	yes	complemented
20	#91921	C₄	1	2	yes	—
21	C₄×D₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
22	D₅⋊ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	#91916	C₄	1	2	yes	complemented
24	#91913	C₄	1	2	yes	complemented
25	D₃×D₅⋊C₈	C₂²	1	2	yes	—
26	#91909	C₂²	1	2	yes	—
27	ΓL(1,𝔽₁₆)⋊Q₈	C₄	1	2	yes	—
28	#91790	C₄	1	1	yes	characteristic, complemented
29	C₅×#901	C₄	1	1	yes	characteristic, complemented
30	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
31	#91290	C₄	1	1	yes	characteristic, complemented
32	#91286	C₄	1	1	yes	characteristic, complemented
33	D₅×#208	C₂²	1	1	yes	characteristic
34	#91266	C₄	1	2	yes	complemented
35	#91265	C₄	1	2	yes	complemented
36	D₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
37	D₃×C₈×D₅	C₂²	1	2	yes	—
38	#91221	C₂²	1	1	yes	characteristic
39	#91221	C₂²	1	1	yes	characteristic
40	#91221	C₂²	1	1	yes	characteristic
41	#91221	C₂²	1	1	yes	characteristic
42	C₃×#3992	C₂²	1	2	yes	—
43	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	2	yes	—
44	#91150	C₂²	1	2	yes	—
45	#91149	C₂²	1	2	yes	—
46	ΓL(1,𝔽₁₆)⋊C₈	C₂²	1	2	yes	—
47	AGL(1,𝔽₅)×C₃⋊C₈	C₂²	1	2	yes	—
48	#78550	—	5	1	no	maximal, Hall
49	#41×AGL(1,𝔽₅)	—	3	1	no	—
50	D₅⋊#131	—	3	1	no	—
51	D₅×#131	—	3	1	no	—
52	#65728	—	3	2	no	—
53	#65728	—	3	1	no	—
54	M₁₆×AGL(1,𝔽₅)	—	3	2	no	—
55	M₁₆×AGL(1,𝔽₅)	—	3	1	no	—
56	#65718	—	3	2	no	—
57	#65718	D₃	1	1	yes	characteristic, complemented
58	C₂×#3992	—	3	1	no	—
59	C₂×#3992	—	3	2	no	—
60	C₂²×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
61	C₂×D₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
62	#6817	C₂×C₄	1	1	yes	characteristic
63	C₅×#235	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
65	D₅×#67	C₂×C₄	1	2	yes	—
66	#6782	C₂×C₄	1	2	yes	—
67	D₅×D₁₂	C₂×C₄	1	1	yes	characteristic
68	C₄×D₃×D₅	C₂³	1	2	yes	—
69	#6773	C₂×C₄	1	1	yes	characteristic
70	#6772	C₂×C₄	1	1	yes	characteristic
71	#6771	C₂×C₄	1	2	yes	—
72	D₅×Dic₆	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃⋊#170	C₂×C₄	1	2	yes	complemented
74	C₄×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
75	C₄×ΓL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
76	C₄×ΓL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
77	D₅⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	complemented
78	D₅⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
79	D₅⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
80	C₃×C₂²⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
81	C₃×#704	C₂×C₄	1	2	yes	complemented
82	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	2	yes	—
83	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
84	C₃×#700	C₂×C₄	1	2	yes	complemented
85	C₃×D₅⋊C₈	C₂³	1	2	yes	—
86	#6740	C₂×C₄	1	4	yes	complemented
87	#6739	C₂×C₄	1	4	yes	complemented
88	#6738	C₂×C₄	1	4	yes	complemented
89	D₃×#170	C₂×C₄	1	4	yes	complemented
90	Dic₃⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
91	(C₂×D₃)⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
92	Dic₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
93	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
94	#6710	C₂×C₄	1	1	yes	characteristic, complemented
95	#6705	C₂×C₄	1	2	yes	complemented
96	C₈×D₁₅	C₂×C₄	1	2	yes	complemented
97	C₅×#208	C₂×C₄	1	1	yes	characteristic, complemented
98	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	complemented
99	C₅×D₃×C₈	C₂×C₄	1	2	yes	complemented
100	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic, complemented
101	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
102	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
103	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
104	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
105	#6651	C₂×C₄	1	2	yes	complemented
106	#6650	C₂×C₄	1	2	yes	complemented
107	#6649	C₂×C₄	1	2	yes	complemented
108	#6648	C₂×C₄	1	2	yes	complemented
109	D₃×#168	C₂×C₄	1	2	yes	complemented
110	D₅×C₃⋊C₈	C₂³	1	2	yes	—
111	C₂×#907	—	5	1	no	—
112	C₂×#901	—	5	1	no	—
113	#5522	—	5	1	no	—
114	C₃×#405	—	5	1	no	—
115	Dic₃×M₁₆	—	5	1	no	—
116	C₂×#815	—	5	1	no	—
117	#4997	—	5	1	no	—
118	#4708	—	5	2	no	—
119	D₃×#97	—	5	2	no	—
120	#4689	—	5	2	no	—
121	C₄×ΓL(1,𝔽₂₅)	—	5	2	no	—
122	D₅×#41	—	3	1	no	—
123	Q₈×AGL(1,𝔽₅)	—	3	2	no	—
124	#4133	—	3	2	no	—
125	D₄×AGL(1,𝔽₅)	—	3	4	no	—
126	D₄×AGL(1,𝔽₅)	—	3	2	no	—
127	#4131	—	3	4	no	—
128	#4131	—	3	2	no	—
129	#4130	—	3	2	no	—
130	#4130	C₂×D₃	1	1	yes	characteristic
131	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
132	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
133	D₅⋊M₁₆	—	3	2	no	—
134	D₅⋊M₁₆	C₂×D₃	1	1	yes	characteristic
135	C₂×D₅⋊C₈	—	3	1	no	—
136	C₂×D₅⋊C₈	—	3	2	no	—
137	C₅×#131	—	3	1	no	—
138	#4094	—	3	1	no	—
139	#4053	—	3	1	no	—
140	#4053	—	3	2	no	—
141	D₅×M₁₆	—	3	1	no	—
142	D₅×M₁₆	—	3	2	no	—
143	#4047	—	3	1	no	—
144	#4047	—	3	2	no	—
145	C₂×C₈×D₅	—	3	2	no	—
146	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
147	#3992	—	3	2	no	—
148	#3992	—	3	2	no	—
149	#3992	—	3	1	no	—
150	#3992	—	3	1	no	—
151	#3992	—	3	1	no	—
152	#3992	—	3	1	no	—
153	#3992	C₂×D₃	1	2	yes	—
154	C₈×AGL(1,𝔽₅)	—	3	2	no	—
155	C₈×AGL(1,𝔽₅)	—	3	2	no	—
156	C₈×AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
157	#2875	—	15	1	no	Sylow
158	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₃×D₅	C₂²×C₄	1	2	yes	—
160	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
161	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	2	yes	—
162	C₂×ΓL(1,𝔽₁₆)	C₂²×C₄	1	2	yes	—
163	C₂×C₃×AGL(1,𝔽₅)	C₂²×C₄	1	4	yes	—
164	D₃×AGL(1,𝔽₅)	—	4	4	no	—
165	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	#1220	C₄²	1	2	yes	—
167	D₆₀	C₄²	1	1	yes	characteristic
168	C₄×D₁₅	C₂²×C₄	1	2	yes	—
169	Dic₃₀	C₄²	1	1	yes	characteristic
170	C₅×#67	C₄²	1	2	yes	—
171	C₅×D₁₂	C₄²	1	1	yes	characteristic
172	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
173	C₅×Dic₆	C₄²	1	1	yes	characteristic
174	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
175	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
176	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
177	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
178	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
179	#1204	C₄²	1	2	yes	—
180	#1203	C₄²	1	2	yes	—
181	#1202	C₄²	1	2	yes	—
182	#1201	C₄²	1	2	yes	—
183	#1200	C₂²×C₄	1	2	yes	—
184	D₃×Dic₅	C₂²×C₄	1	2	yes	—
185	D₅×Dic₃	C₂²×C₄	1	2	yes	—
186	C₃⋊#170	C₂²×C₄	1	2	yes	—
187	C₃⋊#170	C₂²×C₄	1	2	yes	—
188	C₃×#170	C₂²×C₄	1	4	yes	—
189	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₃⋊#168	C₂²×C₄	1	2	yes	—
192	C₃×#168	C₂²×C₄	1	1	yes	characteristic
193	C₃×#168	C₂²×C₄	1	1	yes	characteristic
194	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
195	C₂×#235	—	5	1	no	—
196	C₂×C₃×M₁₆	—	5	1	no	—
197	C₂²×C₃×C₈	—	5	1	no	—
198	C₃×#117	—	5	1	no	—
199	C₂×C₄×Dic₃	—	5	1	no	—
200	C₂×#208	—	5	1	no	—
201	C₂²×C₃⋊C₈	—	5	1	no	—
202	#907	—	5	2	no	—
203	#907	—	5	2	no	—
204	#907	—	5	4	no	—
205	#901	—	5	1	no	—
206	#901	—	5	1	no	—
207	#901	—	5	1	no	—
208	#901	—	5	2	no	—
209	#901	—	5	2	no	—
210	#901	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
211	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
212	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
213	C₂×D₃×C₈	—	5	2	no	—
214	C₂×D₃×C₈	—	5	2	no	—
215	#893	—	5	2	no	—
216	#887	—	5	2	no	—
217	#67⋊C₄	—	5	4	no	—
218	#872	—	5	2	no	—
219	C₄²×D₃	—	5	2	no	—
220	C₃×#97	—	5	2	no	—
221	C₃×C₄×C₈	—	5	2	no	—
222	#815	—	5	2	no	—
223	#815	—	5	1	no	—
224	#815	—	5	1	no	—
225	#815	—	5	1	no	—
226	#815	—	5	1	no	—
227	C₈×Dic₃	—	5	2	no	—
228	#803	—	5	2	no	—
229	C₄×C₃⋊C₈	—	5	2	no	—
230	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
231	C₂²×AGL(1,𝔽₅)	—	3	4	no	—
232	C₅×#41	—	3	1	no	—
233	#713	—	3	1	no	—
234	Q₈×D₅	—	3	1	no	—
235	#711	—	3	2	no	—
236	#711	—	3	1	no	—
237	D₄×D₅	—	3	2	no	—
238	D₄×D₅	—	3	1	no	—
239	#709	—	3	1	no	—
240	#709	—	3	2	no	—
241	C₂×C₄×D₅	—	3	2	no	—
242	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
243	C₂²⋊AGL(1,𝔽₅)	—	3	4	no	—
244	C₂²⋊AGL(1,𝔽₅)	C₄×D₃	1	2	yes	—
245	#704	—	3	4	no	—
246	#704	C₄×D₃	1	2	yes	complemented
247	C₂×#170	—	3	2	no	—
248	C₂×#170	—	3	4	no	—
249	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
250	C₄⋊AGL(1,𝔽₅)	C₄×D₃	1	2	yes	—
251	C₄×AGL(1,𝔽₅)	—	3	4	no	—
252	C₄×AGL(1,𝔽₅)	—	3	2	no	—
253	C₄×AGL(1,𝔽₅)	—	3	1	no	—
254	C₄×AGL(1,𝔽₅)	—	3	1	no	—
255	C₄×AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
256	#700	—	3	4	no	—
257	#700	C₄×D₃	1	2	yes	complemented
258	D₅⋊C₈	—	3	2	no	—
259	D₅⋊C₈	—	3	1	no	—
260	D₅⋊C₈	—	3	1	no	—
261	D₅⋊C₈	—	3	4	no	—
262	D₅⋊C₈	C₂²×D₃	1	2	yes	—
263	C₅×M₁₆	—	3	1	no	—
264	C₅×M₁₆	—	3	2	no	—
265	C₂×C₅×C₈	—	3	2	no	—
266	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic, complemented
267	#681	—	3	1	no	—
268	#681	—	3	2	no	—
269	C₂×#168	—	3	2	no	—
270	C₂×#168	C₄×D₃	1	1	yes	characteristic, complemented
271	#676	—	3	2	no	—
272	#676	—	3	2	no	—
273	#676	—	3	2	no	—
274	C₈×D₅	—	3	2	no	—
275	C₈×D₅	—	3	2	no	—
276	C₈×D₅	—	3	2	no	—
277	C₈×D₅	C₄×D₃	1	1	yes	characteristic, complemented
278	C₈×D₅	C₄×D₃	1	1	yes	characteristic, complemented
279	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
280	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
281	C₂×#131	—	15	1	no	—
282	C₂×#131	—	15	1	no	—
283	C₄×#41	—	15	1	no	—
284	#405	—	5	1	no	—
285	#405	—	15	2	no	—
286	#405	—	15	2	no	—
287	#405	—	15	1	no	—
288	C₄×M₁₆	—	15	2	no	—
289	C₄×M₁₆	—	15	1	no	—
290	C₂×#97	—	15	2	no	—
291	C₂×#97	—	15	1	no	—
292	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
293	C₂×D₁₅	C₂×C₄²	1	2	yes	—
294	C₂×C₅×D₃	C₂×C₄²	1	2	yes	—
295	C₂×C₃×D₅	—	2	2	no	—
296	C₂×C₃×D₅	C₂×C₄²	1	1	yes	characteristic
297	C₂×C₃×D₅	C₂³×C₄	1	1	yes	characteristic
298	D₃×D₅	—	2	4	no	—
299	ΓL(1,𝔽₁₆)	—	2	2	no	—
300	ΓL(1,𝔽₁₆)	—	2	2	no	—
301	C₃×AGL(1,𝔽₅)	—	2	4	no	—
302	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
303	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
304	Dic₁₅	C₂×C₄²	1	2	yes	—
305	C₃×Dic₅	C₂×C₄²	1	1	yes	characteristic
306	C₃×Dic₅	C₂³×C₄	1	1	yes	characteristic
307	C₅×Dic₃	C₂×C₄²	1	2	yes	—
308	C₂²×C₃×C₄	—	5	1	no	—
309	C₂×#67	—	5	2	no	—
310	C₂²×Dic₃	—	5	2	no	—
311	#235	—	5	1	no	—
312	#235	—	5	2	no	—
313	#235	—	5	1	no	—
314	#235	—	5	2	no	—
315	#235	—	5	1	no	—
316	#235	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂×D₁₂	—	5	1	no	—
318	C₂×C₄×D₃	—	5	2	no	—
319	C₂×C₄×D₃	—	5	4	no	—
320	C₂×Dic₆	—	5	1	no	—
321	C₃×M₁₆	—	5	2	no	—
322	C₃×M₁₆	—	5	2	no	—
323	C₂×C₃×C₈	—	5	2	no	—
324	C₂×C₃×C₈	—	5	1	no	—
325	C₂×C₃×C₈	—	5	1	no	—
326	C₂×C₃×C₈	—	5	1	no	—
327	C₂×C₃×C₈	—	5	1	no	—
328	C₂×C₃×C₈	—	5	1	no	—
329	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
330	C₃×C₄⋊C₄	—	5	2	no	—
331	C₃×C₂²⋊C₄	—	5	2	no	—
332	C₃×C₄²	—	5	2	no	—
333	(C₂×D₃)⋊C₄	—	5	4	no	—
334	Dic₃⋊C₄	—	5	4	no	—
335	C₄×Dic₃	—	5	1	no	—
336	C₄×Dic₃	—	5	1	no	—
337	C₄×Dic₃	—	5	4	no	—
338	C₄×Dic₃	—	5	2	no	—
339	#208	—	5	1	no	—
340	#208	—	5	2	no	—
341	#208	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
342	C₂×C₃⋊C₈	—	5	1	no	—
343	C₂×C₃⋊C₈	—	5	1	no	—
344	C₂×C₃⋊C₈	—	5	2	no	—
345	C₂×C₃⋊C₈	—	5	2	no	—
346	C₂×C₃⋊C₈	—	5	2	no	—
347	ΓL(1,𝔽₂₅)	—	5	4	no	—
348	ΓL(1,𝔽₂₅)	—	5	4	no	—
349	ΓL(1,𝔽₂₅)	—	5	2	no	—
350	ΓL(1,𝔽₂₅)	—	5	2	no	—
351	ΓL(1,𝔽₂₅)	—	5	2	no	—
352	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
353	D₃×C₈	—	5	4	no	—
354	D₃×C₈	—	5	4	no	—
355	D₃×C₈	—	5	2	no	—
356	D₃×C₈	—	5	2	no	—
357	D₃×C₈	—	5	2	no	—
358	D₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
359	C₂²×D₅	—	3	2	no	—
360	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
361	C₂×AGL(1,𝔽₅)	—	3	2	no	—
362	C₂×AGL(1,𝔽₅)	—	3	2	no	—
363	C₂×AGL(1,𝔽₅)	—	12	4	no	—
364	C₂×AGL(1,𝔽₅)	—	12	2	no	—
365	C₂×AGL(1,𝔽₅)	C₂×C₄×D₃	1	4	yes	—
366	C₅×Q₈	—	3	1	no	—
367	C₅×D₄	—	3	2	no	—
368	C₅×D₄	—	3	1	no	—
369	C₂×C₄×C₅	—	3	2	no	—
370	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
371	C₂²⋊D₅	—	3	2	no	—
372	C₂²⋊D₅	—	3	2	no	—
373	C₂²⋊D₅	—	3	2	no	—
374	C₂×Dic₅	—	3	2	no	—
375	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
376	D₂₀	—	3	2	no	—
377	D₂₀	—	3	1	no	—
378	C₄×D₅	—	3	2	no	—
379	C₄×D₅	—	3	2	no	—
380	C₄×D₅	—	3	2	no	—
381	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
382	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
383	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
384	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
385	Dic₁₀	—	3	1	no	—
386	Dic₁₀	—	3	2	no	—
387	#170	—	3	2	no	—
388	#170	—	3	2	no	—
389	#170	C₂×C₄×D₃	1	4	yes	—
390	C₅×C₈	—	3	2	no	—
391	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
392	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
393	#168	—	3	2	no	—
394	#168	C₂×C₄×D₃	1	1	yes	characteristic
395	#168	C₂×C₄×D₃	1	1	yes	characteristic
396	C₂×#41	—	15	1	no	—
397	#131	—	3	1	no	—
398	#131	—	15	2	no	—
399	#131	—	15	1	no	—
400	#131	—	15	2	no	—
401	#131	—	15	1	no	—
402	#131	—	15	4	no	—
403	#131	—	15	2	no	—
404	#131	—	15	2	no	—
405	#131	—	15	1	no	—
406	C₂×M₁₆	—	5	1	no	—
407	C₂×M₁₆	—	15	2	no	—
408	C₂×M₁₆	—	15	2	no	—
409	C₂×M₁₆	—	15	1	no	—
410	C₂²×C₈	—	5	1	no	—
411	C₂²×C₈	—	15	2	no	—
412	C₂²×C₈	—	15	2	no	—
413	C₂²×C₈	—	15	1	no	—
414	C₄×Q₈	—	15	2	no	—
415	C₄×D₄	—	15	4	no	—
416	C₄×D₄	—	15	2	no	—
417	#117	—	5	1	no	—
418	#117	—	15	2	no	—
419	C₂×C₄²	—	15	2	no	—
420	C₂×C₄²	—	15	1	no	—
421	#97	—	5	2	no	—
422	#97	—	15	2	no	—
423	#97	—	15	1	no	—
424	#97	—	15	2	no	—
425	#97	—	15	1	no	—
426	#97	—	15	1	no	—
427	#97	—	15	1	no	—
428	C₄×C₈	—	5	2	no	—
429	C₄×C₈	—	15	2	no	—
430	C₄×C₈	—	15	2	no	—
431	C₂×C₃×C₅	—	2	1	no	—
432	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
433	D₁₅	—	2	2	no	—
434	C₃×D₅	—	2	1	no	—
435	C₃×D₅	#568	1	2	yes	—
436	C₅×D₃	—	2	2	no	—
437	C₂³×C₃	—	5	1	no	—
438	C₂²×D₃	—	5	2	no	—
439	C₂×C₃×C₄	—	5	1	no	—
440	C₂×C₃×C₄	—	5	1	no	—
441	C₂×C₃×C₄	—	5	1	no	—
442	C₂×C₃×C₄	—	5	1	no	—
443	C₂×C₃×C₄	—	5	1	no	—
444	C₂×C₃×C₄	—	5	4	no	—
445	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
446	#67	—	5	2	no	—
447	#67	—	5	2	no	—
448	#67	—	5	2	no	—
449	#67	C₄×AGL(1,𝔽₅)	1	2	yes	—
450	C₂×Dic₃	—	5	2	no	—
451	C₂×Dic₃	—	5	2	no	—
452	C₂×Dic₃	—	5	2	no	—
453	C₂×Dic₃	—	20	2	no	—
454	D₁₂	—	5	2	no	—
455	D₁₂	—	5	1	no	—
456	D₁₂	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
457	C₄×D₃	—	5	2	no	—
458	C₄×D₃	—	5	2	no	—
459	C₄×D₃	—	5	2	no	—
460	C₄×D₃	—	20	4	no	—
461	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
462	Dic₆	—	5	1	no	—
463	Dic₆	—	5	2	no	—
464	Dic₆	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
465	C₃×C₈	—	5	4	no	—
466	C₃×C₈	—	5	1	no	—
467	C₃×C₈	—	5	1	no	—
468	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
469	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
470	C₃⋊C₈	—	5	2	no	—
471	C₃⋊C₈	—	5	2	no	—
472	C₃⋊C₈	—	5	2	no	—
473	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
474	C₂²×C₅	—	3	2	no	—
475	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
476	C₂×D₅	—	2	2	no	—
477	C₂×D₅	—	3	2	no	—
478	C₂×D₅	—	6	4	no	—
479	C₂×D₅	C₄²×D₃	1	1	yes	characteristic
480	C₂×D₅	C₂²×C₄×D₃	1	1	yes	characteristic
481	AGL(1,𝔽₅)	—	2	4	no	—
482	AGL(1,𝔽₅)	—	6	2	no	—
483	AGL(1,𝔽₅)	—	6	2	no	—
484	C₄×C₅	—	3	2	no	—
485	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
486	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
487	Dic₅	—	3	2	no	—
488	Dic₅	C₄²×D₃	1	1	yes	characteristic
489	Dic₅	C₂²×C₄×D₃	1	1	yes	characteristic
490	#41	—	3	1	no	—
491	#41	—	15	2	no	—
492	#41	—	15	2	no	—
493	#41	—	15	1	no	—
494	#41	—	15	1	no	—
495	#41	—	15	1	no	—
496	C₂×Q₈	—	15	1	no	—
497	C₂×D₄	—	15	1	no	—
498	C₂×D₄	—	15	2	no	—
499	C₂²×C₄	—	5	1	no	—
500	C₂²×C₄	—	15	2	no	—
501	C₂²×C₄	—	15	4	no	—
502	C₂²×C₄	—	15	2	no	—
503	M₁₆	—	3	1	no	—
504	M₁₆	—	3	2	no	—
505	M₁₆	—	5	2	no	—
506	M₁₆	—	5	2	no	—
507	M₁₆	—	15	2	no	—
508	M₁₆	—	15	2	no	—
509	M₁₆	—	15	2	no	—
510	M₁₆	—	15	4	no	—
511	M₁₆	—	15	4	no	—
512	M₁₆	—	15	1	no	—
513	M₁₆	—	15	2	no	—
514	C₂×C₈	—	3	2	no	—
515	C₂×C₈	—	5	2	no	—
516	C₂×C₈	—	5	1	no	—
517	C₂×C₈	—	5	1	no	—
518	C₂×C₈	—	5	1	no	—
519	C₂×C₈	—	5	1	no	—
520	C₂×C₈	—	5	1	no	—
521	C₂×C₈	—	15	2	no	—
522	C₂×C₈	—	15	2	no	—
523	C₂×C₈	—	15	2	no	—
524	C₂×C₈	—	15	4	no	—
525	C₂×C₈	—	15	4	no	—
526	C₂×C₈	—	15	1	no	—
527	C₂×C₈	—	15	1	no	—
528	C₂×C₈	—	15	2	no	—
529	C₂×C₈	—	15	2	no	—
530	C₂×C₈	—	15	2	no	—
531	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
532	C₄⋊C₄	—	5	2	no	—
533	C₄⋊C₄	—	15	4	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	15	4	no	—
536	C₄²	—	5	2	no	—
537	C₄²	—	15	1	no	—
538	C₄²	—	15	1	no	—
539	C₄²	—	15	2	no	—
540	C₄²	—	15	4	no	—
541	C₃×C₅	#2875	1	1	yes	characteristic, complemented, Hall
542	C₂²×C₃	—	5	1	no	—
543	C₂²×C₃	—	5	1	no	—
544	C₂²×C₃	—	10	2	no	—
545	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
546	C₂×D₃	—	5	2	no	—
547	C₂×D₃	—	10	4	no	—
548	C₂×D₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
549	C₃×C₄	—	5	1	no	—
550	C₃×C₄	—	5	1	no	—
551	C₃×C₄	—	10	4	no	—
552	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
553	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
554	Dic₃	—	5	2	no	—
555	Dic₃	—	10	2	no	—
556	Dic₃	—	10	2	no	—
557	Dic₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
558	C₂×C₅	—	2	1	no	—
559	C₂×C₅	—	6	2	no	—
560	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
561	D₅	—	2	1	no	—
562	D₅	—	6	2	no	—
563	D₅	#5750	1	2	yes	—
564	C₂³	—	5	1	no	—
565	C₂³	—	15	2	no	—
566	Q₈	—	3	1	no	—
567	Q₈	—	15	2	no	—
568	Q₈	—	15	1	no	—
569	D₄	—	3	2	no	—
570	D₄	—	3	1	no	—
571	D₄	—	15	2	no	—
572	D₄	—	15	2	no	—
573	D₄	—	15	2	no	—
574	D₄	—	15	2	no	—
575	D₄	—	15	1	no	—
576	C₂×C₄	—	3	2	no	—
577	C₂×C₄	—	5	1	no	—
578	C₂×C₄	—	5	1	no	—
579	C₂×C₄	—	5	1	no	—
580	C₂×C₄	—	5	1	no	—
581	C₂×C₄	—	5	1	no	—
582	C₂×C₄	—	5	4	no	—
583	C₂×C₄	—	15	2	no	—
584	C₂×C₄	—	15	2	no	—
585	C₂×C₄	—	15	2	no	—
586	C₂×C₄	—	15	2	no	—
587	C₂×C₄	—	15	2	no	—
588	C₂×C₄	—	15	2	no	—
589	C₂×C₄	—	60	4	no	—
590	C₂×C₄	—	60	2	no	—
591	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
592	C₈	—	3	2	no	—
593	C₈	—	5	4	no	—
594	C₈	—	5	1	no	—
595	C₈	—	5	1	no	—
596	C₈	—	15	2	no	—
597	C₈	—	15	2	no	—
598	C₈	—	15	2	no	—
599	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
600	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
601	C₂×C₃	—	2	1	no	—
602	C₂×C₃	—	5	2	no	—
603	C₂×C₃	—	10	1	no	—
604	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
605	D₃	—	2	2	no	—
606	D₃	—	10	2	no	—
607	C₅	#78550	1	1	yes	characteristic, complemented, Sylow
608	C₂²	—	3	2	no	—
609	C₂²	—	5	1	no	—
610	C₂²	—	5	1	no	—
611	C₂²	—	10	2	no	—
612	C₂²	—	15	2	no	—
613	C₂²	—	30	4	no	—
614	C₂²	C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
615	C₄	—	3	2	no	—
616	C₄	—	5	1	no	—
617	C₄	—	5	1	no	—
618	C₄	—	10	4	no	—
619	C₄	—	15	2	no	—
620	C₄	—	30	2	no	—
621	C₄	—	30	2	no	—
622	C₄	C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
623	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
624	C₃	#10617415	1	1	yes	characteristic, complemented, Sylow
625	C₂	—	2	1	no	—
626	C₂	—	5	2	no	—
627	C₂	—	6	2	no	—
628	C₂	—	10	1	no	—
629	C₂	—	30	2	no	—
630	C₂	C₂×C₄×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
prime radical	D₅×#235	C₂²
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#2875
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×#91221	C₂	semidirect
5. C₃×#65718	C₂	semidirect
6. #11751698	C₂	semidirect
7. #11751697	C₂	semidirect
8. #11751671	C₂	semidirect
9. #11751656	C₂	semidirect
10. D₃×#3992	C₂	semidirect
11. AGL(1,𝔽₅)×ΓL(1,𝔽₂₅)	C₂	semidirect
19. #91929	C₄	semidirect
23. #91916	C₄	semidirect
24. #91913	C₄	semidirect
28. #91790	C₄	semidirect
29. C₅×#901	C₄	semidirect
31. #91290	C₄	semidirect
32. #91286	C₄	semidirect
34. #91266	C₄	semidirect
35. #91265	C₄	semidirect
57. #65718	D₃	semidirect
73. C₂×C₃⋊#170	C₂×C₄	semidirect
77. D₅⋊(C₃⋊C₈)	C₂×C₄	semidirect
81. C₃×#704	C₂×C₄	semidirect
84. C₃×#700	C₂×C₄	semidirect
86. #6740	C₂×C₄	semidirect
87. #6739	C₂×C₄	semidirect
88. #6738	C₂×C₄	semidirect
89. D₃×#170	C₂×C₄	semidirect
93. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
94. #6710	C₂×C₄	semidirect
95. #6705	C₂×C₄	semidirect
96. C₈×D₁₅	C₂×C₄	semidirect
97. C₅×#208	C₂×C₄	semidirect
98. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
99. C₅×D₃×C₈	C₂×C₄	semidirect
100. C₂×C₃×#168	C₂×C₄	semidirect
101. C₃×C₈×D₅	C₂×C₄	semidirect
102. C₃×C₈×D₅	C₂×C₄	semidirect
105. #6651	C₂×C₄	semidirect
106. #6650	C₂×C₄	semidirect
107. #6649	C₂×C₄	semidirect
108. #6648	C₂×C₄	semidirect
109. D₃×#168	C₂×C₄	semidirect
210. #901	AGL(1,𝔽₅)	semidirect
246. #704	C₄×D₃	semidirect
257. #700	C₄×D₃	semidirect
266. C₂×C₅×C₈	C₄×D₃	semidirect
270. C₂×#168	C₄×D₃	semidirect
277. C₈×D₅	C₄×D₃	semidirect
278. C₈×D₅	C₄×D₃	semidirect
329. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
341. #208	C₂×AGL(1,𝔽₅)	semidirect
352. ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	semidirect
358. D₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
531. C₂×C₈	D₃×AGL(1,𝔽₅)	semidirect
541. C₃×C₅	#2875	semidirect
607. C₅	#78550	semidirect
624. C₃	#10617415	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11756835	2
D₅⋊#907	2
D₅×#901	2
C₂×#91221	2
C₃×#65718	2
#11751698	2
#11751697	2
#11751671	2
#11751656	2
D₃×#3992	2
AGL(1,𝔽₅)×ΓL(1,𝔽₂₅)	2
#10617415	3
#78550	5