Subgroups — #13043664

Order 1280.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611097	C₂	1	1	yes	maximal, characteristic
2	#10604368	C₂	1	1	yes	maximal, characteristic, complemented
3	#10604366	C₂	1	1	yes	maximal, characteristic, complemented
4	#10604026	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604024	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604022	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604021	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603906	C₂	1	1	yes	maximal, characteristic, complemented
9	#10603905	C₂	1	1	yes	maximal, characteristic, complemented
10	#10603903	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603903	C₂	1	1	yes	maximal, characteristic, complemented
12	#10603870	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603868	C₂	1	1	yes	maximal, characteristic, complemented
14	#10603830	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₅⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	#65862	C₄	1	1	yes	characteristic
17	C₂×#3998	C₂²	1	1	yes	characteristic
18	C₂²×#674	C₂²	1	1	yes	characteristic
19	C₂×#3990	C₂²	1	1	yes	characteristic
20	C₂×D₅⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×D₅⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×D₅⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₅×#433	C₄	1	1	yes	characteristic
24	#65286	C₂²	1	1	yes	characteristic
25	#65125	C₄	1	1	yes	characteristic
26	#65123	C₂²	1	1	yes	characteristic
27	#65119	C₂²	1	1	yes	characteristic
28	#65117	C₄	1	1	yes	characteristic
29	#65018	C₄	1	1	yes	characteristic
30	#65017	C₄	1	1	yes	characteristic
31	#65014	C₂²	1	1	yes	characteristic
32	#65014	C₂²	1	1	yes	characteristic
33	#64997	C₂²	1	1	yes	characteristic
34	#64994	C₄	1	1	yes	characteristic
35	#64979	C₄	1	1	yes	characteristic
36	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
37	C₂²⋊#674	C₂²	1	1	yes	characteristic
38	C₂²⋊#674	C₂²	1	1	yes	characteristic
39	#64888	C₂²	1	1	yes	characteristic
40	#64888	C₂²	1	1	yes	characteristic
41	#64888	C₂²	1	1	yes	characteristic
42	#64888	C₂²	1	1	yes	characteristic
43	#64887	C₂²	1	1	yes	characteristic
44	#64887	C₂²	1	1	yes	characteristic
45	#64887	C₂²	1	1	yes	characteristic
46	#64887	C₂²	1	1	yes	characteristic
47	#64886	C₂²	1	1	yes	characteristic
48	#64885	C₂²	1	1	yes	characteristic
49	#64885	C₂²	1	1	yes	characteristic
50	#64885	C₂²	1	1	yes	characteristic
51	#64859	C₂²	1	1	yes	characteristic
52	#64859	C₂²	1	1	yes	characteristic
53	#64859	C₂²	1	1	yes	characteristic
54	C₄⋊#674	C₂²	1	1	yes	characteristic
55	C₄⋊#674	C₂²	1	1	yes	characteristic
56	C₄×#674	C₂²	1	1	yes	characteristic
57	C₄×#674	C₂²	1	1	yes	characteristic
58	C₄×#674	C₂²	1	1	yes	characteristic
59	#33480	—	5	1	no	maximal, Sylow
60	C₅×#117	C₂×C₄	1	1	yes	characteristic
61	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
62	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×#681	C₂×C₄	1	1	yes	characteristic
64	C₂²×#168	C₂³	1	1	yes	characteristic
65	C₂×#676	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
69	#4044	C₈	1	1	yes	characteristic
70	#4042	C₈	1	1	yes	characteristic
71	#4040	C₈	1	1	yes	characteristic
72	#4035	C₈	1	1	yes	characteristic
73	#4031	C₈	1	1	yes	characteristic
74	#4030	C₈	1	1	yes	characteristic
75	#4029	C₈	1	1	yes	characteristic
76	#4025	C₈	1	1	yes	characteristic
77	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
78	#4018	C₂×C₄	1	1	yes	characteristic
79	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
81	#3998	—	2	2	no	—
82	C₂×#674	—	2	2	no	—
83	C₂×#674	C₂³	1	1	yes	characteristic
84	C₂×#674	C₂³	1	1	yes	characteristic
85	C₂×#674	C₂³	1	1	yes	characteristic
86	C₂×#674	C₂³	1	1	yes	characteristic
87	C₂×#674	C₂³	1	1	yes	characteristic
88	C₂×#674	C₂³	1	1	yes	characteristic
89	C₂×#674	C₂³	1	1	yes	characteristic
90	C₂×#674	C₂³	1	1	yes	characteristic
91	#3990	—	2	2	no	—
92	D₅⋊C₁₆	—	2	2	no	—
93	D₅⋊C₁₆	—	2	2	no	—
94	D₅⋊C₁₆	—	2	2	no	—
95	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₅×#97	C₂×C₄	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
101	#3952	C₂×C₄	1	1	yes	characteristic
102	#3952	C₂×C₄	1	1	yes	characteristic
103	#3952	C₂×C₄	1	1	yes	characteristic
104	#3952	C₂×C₄	1	1	yes	characteristic
105	#3947	C₂×C₄	1	1	yes	characteristic
106	#3946	C₂×C₄	1	1	yes	characteristic
107	#3946	C₂×C₄	1	1	yes	characteristic
108	#3946	C₂×C₄	1	1	yes	characteristic
109	#3946	C₂×C₄	1	1	yes	characteristic
110	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
111	C₈×Dic₅	C₂³	1	1	yes	characteristic
112	C₈×Dic₅	C₂³	1	1	yes	characteristic
113	#3935	C₂×C₄	1	1	yes	characteristic
114	#3935	C₂×C₄	1	1	yes	characteristic
115	C₄×#168	C₂³	1	1	yes	characteristic
116	C₄×#168	C₂³	1	1	yes	characteristic
117	#2966	—	5	1	no	—
118	#2183	—	5	1	no	—
119	Q₈×C₁₆	—	5	1	no	—
120	#2169	—	5	1	no	—
121	#2168	—	5	1	no	—
122	#2168	—	5	1	no	—
123	D₄×C₁₆	—	5	1	no	—
124	D₄×C₁₆	—	5	1	no	—
125	D₄×C₁₆	—	5	1	no	—
126	#2164	—	5	1	no	—
127	#2164	—	5	1	no	—
128	#2163	—	5	1	no	—
129	#2108	—	5	1	no	—
130	#2108	—	5	1	no	—
131	C₂×C₄×C₁₆	—	5	1	no	—
132	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
135	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₁₀	C₂×C₈	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
146	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
148	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
149	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
152	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
153	#685	C₂×C₈	1	1	yes	characteristic
154	#685	C₂×C₈	1	1	yes	characteristic
155	#685	C₂×C₈	1	1	yes	characteristic
156	#685	C₂×C₈	1	1	yes	characteristic
157	#685	C₂×C₈	1	1	yes	characteristic
158	#685	C₂×C₈	1	1	yes	characteristic
159	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
160	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
161	#683	C₂×C₈	1	1	yes	characteristic
162	#683	C₂×C₈	1	1	yes	characteristic
163	#683	C₂×C₈	1	1	yes	characteristic
164	#683	C₂×C₈	1	1	yes	characteristic
165	#683	C₂×C₈	1	1	yes	characteristic
166	#683	C₂×C₈	1	1	yes	characteristic
167	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
168	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
169	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
171	#681	—	2	2	no	—
172	C₂×#168	—	2	1	no	—
173	C₂×#168	—	2	1	no	—
174	C₂×#168	C₂²×C₄	1	1	yes	characteristic
175	C₂×#168	C₂²×C₄	1	1	yes	characteristic
176	C₂×#168	C₂²×C₄	1	1	yes	characteristic
177	C₂×#168	C₂⁴	1	1	yes	characteristic
178	#676	—	2	2	no	—
179	C₈×D₅	—	2	2	no	—
180	C₈×D₅	—	2	1	no	—
181	C₈×D₅	—	2	1	no	—
182	C₈×D₅	—	2	1	no	—
183	C₈×D₅	—	2	1	no	—
184	#674	—	2	1	no	—
185	#674	—	2	1	no	—
186	#674	—	2	1	no	—
187	#674	—	2	1	no	—
188	#674	—	2	1	no	—
189	#674	—	2	1	no	—
190	#674	#41	1	2	yes	—
191	#674	#41	1	2	yes	—
192	#529	—	5	1	no	—
193	C₂×M₃₂	—	5	1	no	—
194	C₂×M₃₂	—	5	1	no	—
195	C₂²×C₁₆	—	5	1	no	—
196	C₂²×C₁₆	—	5	1	no	—
197	C₂²×C₁₆	—	5	1	no	—
198	C₂²×C₁₆	—	5	1	no	—
199	#446	—	5	1	no	—
200	C₈×Q₈	—	5	1	no	—
201	#436	—	5	1	no	—
202	#435	—	5	1	no	—
203	#435	—	5	1	no	—
204	C₈×D₄	—	5	1	no	—
205	C₈×D₄	—	5	1	no	—
206	C₈×D₄	—	5	1	no	—
207	#433	—	5	1	no	—
208	#433	AGL(1,𝔽₅)	1	1	yes	characteristic
209	#432	—	5	1	no	—
210	#405	—	5	1	no	—
211	#405	—	5	1	no	—
212	C₂×C₄×C₈	—	5	1	no	—
213	C₄⋊C₁₆	—	5	1	no	—
214	C₄⋊C₁₆	—	5	1	no	—
215	C₄⋊C₁₆	—	5	1	no	—
216	C₄⋊C₁₆	—	5	1	no	—
217	C₄⋊C₁₆	—	5	1	no	—
218	C₄⋊C₁₆	—	5	1	no	—
219	C₂²⋊C₁₆	—	5	1	no	—
220	C₂²⋊C₁₆	—	5	1	no	—
221	C₂²⋊C₁₆	—	5	1	no	—
222	C₂²⋊C₁₆	—	5	1	no	—
223	C₂²⋊C₁₆	—	5	1	no	—
224	C₂²⋊C₁₆	—	5	1	no	—
225	#346	—	5	1	no	—
226	#346	—	5	1	no	—
227	#346	—	5	1	no	—
228	#346	—	5	1	no	—
229	C₄×C₁₆	—	5	1	no	—
230	C₄×C₁₆	—	5	1	no	—
231	C₄×C₁₆	—	5	1	no	—
232	C₄×C₁₆	—	5	1	no	—
233	C₄×C₁₆	—	5	1	no	—
234	C₄×C₁₆	—	5	1	no	—
235	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
236	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
237	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
246	C₂²⋊D₅	—	2	2	no	—
247	C₂²⋊D₅	—	2	2	no	—
248	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
249	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
250	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
251	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
252	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
253	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
254	D₂₀	—	2	2	no	—
255	C₄×D₅	—	2	2	no	—
256	C₄×D₅	—	2	1	no	—
257	C₄×D₅	—	2	1	no	—
258	C₄×D₅	—	2	1	no	—
259	C₄×D₅	—	2	1	no	—
260	C₄×D₅	—	2	2	no	—
261	Dic₁₀	—	2	2	no	—
262	C₅×C₈	—	2	1	no	—
263	C₅×C₈	—	2	1	no	—
264	C₅×C₈	—	2	1	no	—
265	C₅×C₈	—	2	1	no	—
266	#168	—	2	1	no	—
267	#168	—	2	1	no	—
268	#168	#131	1	2	yes	—
269	#168	C₂×#41	1	1	yes	characteristic
270	#168	C₂×#41	1	1	yes	characteristic
271	C₂×M₁₆	—	5	1	no	—
272	C₂×M₁₆	—	5	1	no	—
273	C₂²×C₈	—	5	1	no	—
274	C₂²×C₈	—	5	1	no	—
275	C₂²×C₈	—	5	1	no	—
276	C₂²×C₈	—	5	1	no	—
277	#126	—	5	1	no	—
278	#126	—	5	1	no	—
279	#125	—	5	1	no	—
280	#124	—	5	1	no	—
281	#123	—	5	1	no	—
282	#123	—	5	1	no	—
283	C₂²⋊Q₈	—	5	1	no	—
284	#121	—	5	1	no	—
285	C₄×Q₈	—	5	1	no	—
286	C₄×D₄	—	5	1	no	—
287	C₄×D₄	—	5	1	no	—
288	C₄×D₄	—	5	1	no	—
289	#117	—	5	1	no	—
290	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
291	C₂×C₄²	—	5	1	no	—
292	M₃₂	—	10	2	no	—
293	M₃₂	—	10	2	no	—
294	C₂×C₁₆	—	5	1	no	—
295	C₂×C₁₆	—	5	1	no	—
296	C₂×C₁₆	—	5	1	no	—
297	C₂×C₁₆	—	5	1	no	—
298	C₂×C₁₆	—	5	1	no	—
299	C₂×C₁₆	—	5	1	no	—
300	C₂×C₁₆	—	5	1	no	—
301	C₂×C₁₆	—	5	1	no	—
302	C₂×C₁₆	—	10	2	no	—
303	C₂×C₁₆	—	10	2	no	—
304	C₂×C₁₆	—	10	2	no	—
305	C₂×C₁₆	—	10	2	no	—
306	C₄⋊C₈	—	5	1	no	—
307	C₄⋊C₈	—	5	1	no	—
308	C₄⋊C₈	—	5	1	no	—
309	C₄⋊C₈	—	5	1	no	—
310	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
311	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
312	C₂²⋊C₈	—	5	1	no	—
313	C₂²⋊C₈	—	5	1	no	—
314	C₂²⋊C₈	—	5	1	no	—
315	C₂²⋊C₈	—	5	1	no	—
316	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
318	#97	—	5	1	no	—
319	#97	—	5	1	no	—
320	#97	—	5	1	no	—
321	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₄×C₈	—	5	1	no	—
323	C₄×C₈	—	5	1	no	—
324	C₄×C₈	—	5	1	no	—
325	C₄×C₈	—	5	1	no	—
326	C₄×C₈	—	5	1	no	—
327	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
332	C₂×D₅	—	2	1	no	—
333	C₂×D₅	—	2	1	no	—
334	C₂×D₅	—	2	1	no	—
335	C₂×D₅	—	2	1	no	—
336	C₂×D₅	—	2	1	no	—
337	C₂×D₅	#504	1	2	yes	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	C₄×#41	1	1	yes	characteristic
344	C₄×C₅	C₂×#131	1	1	yes	characteristic
345	Dic₅	—	2	1	no	—
346	Dic₅	—	2	1	no	—
347	Dic₅	—	2	1	no	—
348	Dic₅	—	2	1	no	—
349	Dic₅	—	2	1	no	—
350	Dic₅	#504	1	2	yes	—
351	C₂×Q₈	—	5	1	no	—
352	C₂×D₄	—	5	1	no	—
353	C₂×D₄	—	5	1	no	—
354	C₂×D₄	—	5	1	no	—
355	C₂²×C₄	—	5	1	no	—
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	5	1	no	—
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
360	M₁₆	—	10	2	no	—
361	M₁₆	—	10	2	no	—
362	C₂×C₈	—	5	1	no	—
363	C₂×C₈	—	5	1	no	—
364	C₂×C₈	—	5	1	no	—
365	C₂×C₈	—	5	1	no	—
366	C₂×C₈	—	10	1	no	—
367	C₂×C₈	—	10	1	no	—
368	C₂×C₈	—	10	1	no	—
369	C₂×C₈	—	10	1	no	—
370	C₂×C₈	—	10	2	no	—
371	C₂×C₈	—	10	1	no	—
372	C₂×C₈	—	10	1	no	—
373	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
376	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
377	C₄⋊C₄	—	5	1	no	—
378	C₄⋊C₄	—	5	1	no	—
379	C₄⋊C₄	—	5	1	no	—
380	C₄⋊C₄	—	5	1	no	—
381	C₄⋊C₄	—	5	1	no	—
382	C₄⋊C₄	—	5	1	no	—
383	C₄⋊C₄	—	5	1	no	—
384	C₄⋊C₄	—	5	1	no	—
385	C₄⋊C₄	D₅⋊C₈	1	1	yes	characteristic
386	C₄⋊C₄	D₅⋊C₈	1	1	yes	characteristic
387	C₂²⋊C₄	—	5	1	no	—
388	C₂²⋊C₄	—	5	1	no	—
389	C₂²⋊C₄	—	5	1	no	—
390	C₂²⋊C₄	—	5	1	no	—
391	C₂²⋊C₄	—	5	1	no	—
392	C₂²⋊C₄	—	5	1	no	—
393	C₂²⋊C₄	—	5	1	no	—
394	C₂²⋊C₄	—	5	1	no	—
395	C₂²⋊C₄	D₅⋊C₈	1	1	yes	characteristic
396	C₂²⋊C₄	D₅⋊C₈	1	1	yes	characteristic
397	C₄²	—	5	1	no	—
398	C₄²	—	5	1	no	—
399	C₄²	—	5	1	no	—
400	C₄²	—	5	1	no	—
401	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
402	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₁₆	—	5	2	no	—
404	C₁₆	—	5	2	no	—
405	C₁₆	—	10	1	no	—
406	C₁₆	—	10	1	no	—
407	C₁₆	—	10	1	no	—
408	C₁₆	—	10	1	no	—
409	C₁₆	—	10	1	no	—
410	C₁₆	—	10	1	no	—
411	C₂×C₅	—	4	1	no	—
412	C₂×C₅	C₈×#41	1	1	yes	characteristic
413	C₂×C₅	C₂×#504	1	1	yes	characteristic
414	C₂×C₅	C₂×#504	1	1	yes	characteristic
415	D₅	—	2	2	no	—
416	D₅	—	4	1	no	—
417	C₂³	—	5	1	no	—
418	C₂³	—	5	1	no	—
419	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
420	Q₈	—	10	2	no	—
421	D₄	—	10	2	no	—
422	D₄	—	10	2	no	—
423	D₄	—	10	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	5	1	no	—
427	C₂×C₄	—	5	1	no	—
428	C₂×C₄	—	5	1	no	—
429	C₂×C₄	—	5	1	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	5	1	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	1	no	—
435	C₂×C₄	—	10	1	no	—
436	C₂×C₄	—	10	1	no	—
437	C₂×C₄	—	10	1	no	—
438	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
439	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
440	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
441	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
442	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
443	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	5	2	no	—
449	C₈	—	5	1	no	—
450	C₈	—	5	1	no	—
451	C₈	—	10	1	no	—
452	C₈	—	10	1	no	—
453	C₅	#33480	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	5	2	no	—
458	C₂²	—	10	1	no	—
459	C₂²	—	10	1	no	—
460	C₂²	—	10	1	no	—
461	C₂²	—	10	1	no	—
462	C₂²	—	10	1	no	—
463	C₂²	C₂²×D₅⋊C₈	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	5	2	no	—
470	C₄	—	10	1	no	—
471	C₄	—	10	1	no	—
472	C₄	—	10	1	no	—
473	C₄	—	10	1	no	—
474	C₄	—	10	1	no	—
475	C₄	D₅⋊#131	1	1	yes	characteristic
476	C₄	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	10	2	no	—
479	C₂	—	20	1	no	—
480	C₂	#10617114	1	1	yes	characteristic
481	C₂	D₅⋊#504	1	1	yes	characteristic
482	C₂	D₅⋊#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#433	C₄
prime radical	#4030	C₈
cosocle	C₂×#168	C₂⁴
hypercenter	#433	AGL(1,𝔽₅)
hypocenter	C₅	#33480
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
2. #10604368	C₂	semidirect
3. #10604366	C₂	semidirect
4. #10604026	C₂	semidirect
5. #10604024	C₂	semidirect
6. #10604022	C₂	semidirect
7. #10604021	C₂	semidirect
8. #10603906	C₂	semidirect
9. #10603905	C₂	semidirect
10. #10603903	C₂	semidirect
11. #10603903	C₂	semidirect
12. #10603870	C₂	semidirect
13. #10603868	C₂	semidirect
14. #10603830	C₂	semidirect
15. C₄×D₅⋊C₁₆	C₂	semidirect
453. C₅	#33480	semidirect

Maximal subgroups

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

subgroup	index
#10611097	2
#10604368	2
#10604366	2
#10604026	2
#10604024	2
#10604022	2
#10604021	2
#10603906	2
#10603905	2
#10603903	2
#10603870	2
#10603868	2
#10603830	2
C₄×D₅⋊C₁₆	2
#33480	5