Subgroups — #13029128

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617154	C₂	1	1	yes	maximal, characteristic
2	C₄×#4131	C₂	1	1	yes	maximal, characteristic
3	#10611184	C₂	1	1	yes	maximal, characteristic
4	#10604737	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604735	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#170⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#10604013	C₂	1	1	yes	maximal, characteristic, complemented
9	#10604011	C₂	1	1	yes	maximal, characteristic, complemented
10	#10603895	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603893	C₂	1	1	yes	maximal, characteristic, complemented
12	#10603893	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603892	C₂	1	1	yes	maximal, characteristic, complemented
14	#10603864	C₂	1	1	yes	maximal, characteristic, complemented
15	#10603862	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4131	C₄	1	2	yes	—
17	C₄×#711	C₂²	1	1	yes	characteristic
18	#65773	C₄	1	2	yes	—
19	#65754	C₂²	1	1	yes	characteristic
20	C₄×#704	C₂²	1	1	yes	characteristic
21	C₄×#704	C₂²	1	1	yes	characteristic
22	C₄×#704	C₂²	1	1	yes	characteristic
23	#65748	C₂²	1	1	yes	characteristic
24	C₂×C₄×#170	C₂²	1	1	yes	characteristic
25	C₂×C₄×#170	C₂²	1	1	yes	characteristic
26	C₂×C₄×#170	C₂²	1	1	yes	characteristic
27	#65707	C₄	1	2	yes	—
28	#65701	C₄	1	2	yes	—
29	#65695	C₄	1	2	yes	—
30	#65693	C₄	1	2	yes	—
31	#65691	C₄	1	2	yes	—
32	#65691	C₄	1	2	yes	—
33	#65678	C₂²	1	1	yes	characteristic
34	C₄×#700	C₂²	1	1	yes	characteristic
35	C₄×#700	C₂²	1	1	yes	characteristic
36	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×#435	C₄	1	1	yes	characteristic
38	#65417	C₄	1	1	yes	characteristic
39	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
40	#65400	C₄	1	1	yes	characteristic
41	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
42	#65300	C₄	1	1	yes	characteristic
43	#65122	C₂²	1	1	yes	characteristic
44	#65117	C₄	1	1	yes	characteristic
45	#65019	C₄	1	1	yes	characteristic
46	#65018	C₄	1	1	yes	characteristic
47	#65007	C₂²	1	1	yes	characteristic
48	#65007	C₂²	1	1	yes	characteristic
49	#64996	C₂²	1	1	yes	characteristic
50	#64990	C₄	1	1	yes	characteristic
51	#170⋊C₈	C₂²	1	1	yes	characteristic
52	#170⋊C₈	C₂²	1	1	yes	characteristic
53	#170⋊C₈	C₂²	1	1	yes	characteristic
54	#170⋊C₈	C₂²	1	1	yes	characteristic
55	#170⋊C₈	C₂²	1	1	yes	characteristic
56	#170⋊C₈	C₂²	1	1	yes	characteristic
57	#170⋊C₈	C₂²	1	1	yes	characteristic
58	#170⋊C₈	C₂²	1	1	yes	characteristic
59	#170⋊C₈	C₂²	1	1	yes	characteristic
60	#170⋊C₈	C₂²	1	1	yes	characteristic
61	#64879	C₂²	1	1	yes	characteristic
62	#64879	C₂²	1	1	yes	characteristic
63	#64879	C₂²	1	1	yes	characteristic
64	#64879	C₂²	1	1	yes	characteristic
65	C₈×#170	C₂²	1	1	yes	characteristic
66	C₈×#170	C₂²	1	1	yes	characteristic
67	#17336	—	5	1	no	maximal, Sylow
68	C₂×#711	C₂×C₄	1	1	yes	characteristic
69	C₂×#704	C₂×C₄	1	2	yes	—
70	C₂×#704	C₂×C₄	1	2	yes	—
71	C₂×#704	C₂×C₄	1	2	yes	—
72	C₂²×#170	C₂×C₄	1	2	yes	—
73	C₂²×#170	C₂×C₄	1	2	yes	—
74	C₂²×#170	C₂×C₄	1	2	yes	—
75	#4131	—	2	8	no	—
76	C₂×#700	C₂×C₄	1	2	yes	—
77	C₂×#700	C₂×C₄	1	2	yes	—
78	C₂×D₅⋊C₈	C₂×C₄	1	2	yes	—
79	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
82	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
87	C₂×#681	C₂×C₄	1	1	yes	characteristic
88	C₂²×#168	C₂×C₄	1	1	yes	characteristic
89	C₂×#676	C₂×C₄	1	1	yes	characteristic
90	C₂×#676	C₂×C₄	1	1	yes	characteristic
91	#4038	C₂×C₄	1	1	yes	characteristic
92	#4033	C₂×C₄	1	1	yes	characteristic
93	#4027	C₂×C₄	1	1	yes	characteristic
94	#4027	C₂×C₄	1	1	yes	characteristic
95	#4023	C₂×C₄	1	1	yes	characteristic
96	#4023	C₂×C₄	1	1	yes	characteristic
97	C₄²×D₅	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊#170	C₂×C₄	1	2	yes	—
100	C₂²⋊#170	C₂×C₄	1	2	yes	—
101	#4004	C₂×C₄	1	2	yes	—
102	#4004	C₂×C₄	1	2	yes	—
103	#4003	C₂×C₄	1	2	yes	—
104	#4002	C₂×C₄	1	2	yes	—
105	#4002	C₂×C₄	1	2	yes	—
106	#4002	C₂×C₄	1	2	yes	—
107	#4002	C₂×C₄	1	2	yes	—
108	#4002	C₂×C₄	1	2	yes	—
109	C₄⋊#170	C₂×C₄	1	2	yes	—
110	C₄×#170	C₂×C₄	1	2	yes	—
111	C₄×#170	C₂×C₄	1	2	yes	—
112	C₄×#170	C₂×C₄	1	2	yes	—
113	C₄×#170	C₂×C₄	1	2	yes	—
114	C₄×#170	C₂³	1	1	yes	characteristic
115	C₄×#170	C₂³	1	1	yes	characteristic
116	C₄×#170	C₂³	1	1	yes	characteristic
117	C₄×#170	C₂³	1	1	yes	characteristic
118	C₄×#170	C₂³	1	1	yes	characteristic
119	C₄×#170	C₂³	1	1	yes	characteristic
120	C₄×#170	C₂³	1	1	yes	characteristic
121	C₄×#170	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
123	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₅×#97	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
127	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
128	#3952	C₂×C₄	1	1	yes	characteristic
129	#3952	C₂×C₄	1	1	yes	characteristic
130	#3947	C₂×C₄	1	1	yes	characteristic
131	#3947	C₂×C₄	1	1	yes	characteristic
132	#3946	C₂×C₄	1	1	yes	characteristic
133	#3946	C₂×C₄	1	1	yes	characteristic
134	#3946	C₂×C₄	1	1	yes	characteristic
135	#3946	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
138	C₈×Dic₅	C₂³	1	1	yes	characteristic
139	C₈×Dic₅	C₂³	1	1	yes	characteristic
140	C₈×Dic₅	C₂³	1	1	yes	characteristic
141	C₈×Dic₅	C₂³	1	1	yes	characteristic
142	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
143	#3935	C₂×C₄	1	1	yes	characteristic
144	#2965	—	5	1	no	—
145	#2965	—	5	1	no	—
146	C₄×#131	—	5	1	no	—
147	#1455	—	5	1	no	—
148	#1455	—	5	1	no	—
149	#1453	—	5	1	no	—
150	#1453	—	5	1	no	—
151	#1451	—	5	1	no	—
152	#1451	—	5	1	no	—
153	#1451	—	5	1	no	—
154	#1451	—	5	1	no	—
155	#1451	—	5	1	no	—
156	#1451	—	5	1	no	—
157	#1450	—	5	1	no	—
158	C₂×#322	—	5	1	no	—
159	C₂×C₅×D₄	C₄²	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
163	C₂×C₂²⋊D₅	C₄²	1	1	yes	characteristic
164	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
167	C₂²×Dic₅	C₂²×C₄	1	1	yes	characteristic
168	#711	—	2	4	no	—
169	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×Dic₁₀	C₄²	1	1	yes	characteristic
173	#704	—	2	4	no	—
174	#704	—	2	4	no	—
175	#704	—	4	2	no	—
176	C₂×#170	—	2	4	no	—
177	C₂×#170	—	4	2	no	—
178	C₂×#170	M₁₆	1	8	yes	complemented
179	C₂×#170	C₂²×C₄	1	2	yes	—
180	C₂×#170	C₂²×C₄	1	2	yes	—
181	C₂×#170	C₂²×C₄	1	2	yes	—
182	C₂×#170	C₂²×C₄	1	2	yes	—
183	C₂×#170	C₂²×C₄	1	2	yes	—
184	C₂×#170	C₂²×C₄	1	2	yes	—
185	C₂×#170	C₂²×C₄	1	2	yes	—
186	C₂×#170	C₂²×C₄	1	2	yes	—
187	#700	—	2	4	no	—
188	#700	—	4	2	no	—
189	D₅⋊C₈	—	2	4	no	—
190	C₅×M₁₆	—	4	1	no	—
191	C₂×C₅×C₈	—	4	1	no	—
192	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
197	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
198	C₅×C₂²⋊C₄	C₄²	1	1	yes	characteristic
199	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
201	C₂²⋊Dic₅	C₄²	1	1	yes	characteristic
202	#685	C₄²	1	1	yes	characteristic
203	#685	C₄²	1	1	yes	characteristic
204	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
205	#683	C₄²	1	1	yes	characteristic
206	#683	C₄²	1	1	yes	characteristic
207	#683	C₄²	1	1	yes	characteristic
208	#683	C₄²	1	1	yes	characteristic
209	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
214	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
217	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
218	#681	—	4	1	no	—
219	C₂×#168	—	4	1	no	—
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂²×C₄	1	1	yes	characteristic
222	C₂×#168	C₂²×C₄	1	1	yes	characteristic
223	C₂×#168	C₂²×C₄	1	1	yes	characteristic
224	#676	—	4	1	no	—
225	#676	—	4	1	no	—
226	C₂×#131	—	5	2	no	—
227	C₄×#41	—	5	1	no	—
228	#446	—	5	2	no	—
229	#446	—	5	1	no	—
230	#446	—	5	1	no	—
231	#436	—	5	2	no	—
232	#436	—	5	1	no	—
233	#436	—	5	1	no	—
234	#435	—	5	2	no	—
235	#435	—	5	2	no	—
236	#435	—	5	1	no	—
237	#435	—	5	1	no	—
238	#435	—	5	1	no	—
239	#435	AGL(1,𝔽₅)	1	1	yes	characteristic
240	#431	—	5	1	no	—
241	#431	—	5	1	no	—
242	#431	—	5	1	no	—
243	#431	—	5	1	no	—
244	#431	—	5	1	no	—
245	#431	—	5	1	no	—
246	#405	—	5	2	no	—
247	#405	—	5	2	no	—
248	#405	—	5	2	no	—
249	C₄×M₁₆	—	5	1	no	—
250	C₄×M₁₆	—	5	1	no	—
251	C₄×M₁₆	—	5	1	no	—
252	C₄×M₁₆	—	5	1	no	—
253	C₄×M₁₆	—	5	1	no	—
254	C₄×M₁₆	—	5	1	no	—
255	C₄×M₁₆	—	5	1	no	—
256	C₂×C₄×C₈	—	5	1	no	—
257	C₂×C₄×C₈	—	5	1	no	—
258	C₂×C₄×C₈	—	5	1	no	—
259	C₂×C₄×C₈	—	5	1	no	—
260	C₂×C₄×C₈	—	5	1	no	—
261	#322	—	5	1	no	—
262	#322	—	5	1	no	—
263	#322	—	5	1	no	—
264	#322	—	5	1	no	—
265	#322	—	5	1	no	—
266	#322	—	5	1	no	—
267	#322	—	5	1	no	—
268	#322	—	5	1	no	—
269	#322	—	5	1	no	—
270	#322	—	5	1	no	—
271	#322	—	5	1	no	—
272	#322	—	5	1	no	—
273	#322	—	5	1	no	—
274	#322	—	5	1	no	—
275	C₈²	—	5	1	no	—
276	C₈²	—	5	1	no	—
277	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
278	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
279	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
280	C₅×D₄	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
290	C₂²⋊D₅	—	2	2	no	—
291	C₂²⋊D₅	—	2	2	no	—
292	C₂×Dic₅	—	2	2	no	—
293	C₂×Dic₅	—	2	2	no	—
294	C₂×Dic₅	—	2	2	no	—
295	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
296	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
297	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
298	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
299	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
300	C₂×Dic₅	C₂×M₁₆	1	4	yes	—
301	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
302	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
303	C₄×D₅	—	2	1	no	—
304	C₄×D₅	—	2	1	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	2	2	no	—
307	Dic₁₀	—	2	2	no	—
308	#170	—	2	2	no	—
309	#170	—	2	2	no	—
310	#170	—	2	2	no	—
311	#170	—	2	2	no	—
312	#170	—	2	2	no	—
313	#170	—	2	2	no	—
314	#170	C₂×M₁₆	1	4	yes	—
315	#170	C₂×M₁₆	1	4	yes	—
316	C₅×C₈	—	2	1	no	—
317	C₅×C₈	—	2	1	no	—
318	C₅×C₈	—	2	1	no	—
319	C₅×C₈	—	2	1	no	—
320	#168	—	2	1	no	—
321	#168	—	2	1	no	—
322	#168	—	2	1	no	—
323	#168	—	2	1	no	—
324	C₂×#41	—	5	1	no	—
325	#131	—	10	8	no	—
326	C₂×M₁₆	—	5	2	no	—
327	C₂×M₁₆	—	5	2	no	—
328	C₂×M₁₆	—	5	2	no	—
329	C₂×M₁₆	—	5	2	no	—
330	C₂×M₁₆	—	5	2	no	—
331	C₂×M₁₆	—	5	1	no	—
332	C₂×M₁₆	—	5	1	no	—
333	C₂×M₁₆	—	5	1	no	—
334	C₂×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₂²×C₈	—	5	2	no	—
336	C₂²×C₈	—	5	2	no	—
337	C₂²×C₈	—	5	2	no	—
338	C₂²×C₈	—	5	2	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₄×Q₈	—	5	1	no	—
342	C₄×Q₈	—	5	1	no	—
343	C₄×D₄	—	5	1	no	—
344	C₄×D₄	—	5	1	no	—
345	C₄×D₄	—	5	1	no	—
346	C₄×D₄	—	5	1	no	—
347	C₄×D₄	—	5	1	no	—
348	C₄×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
349	#117	—	5	1	no	—
350	#117	—	5	1	no	—
351	#117	—	5	1	no	—
352	C₂×C₄²	—	5	1	no	—
353	C₂×C₄²	—	5	1	no	—
354	C₂×C₄²	—	5	1	no	—
355	C₄⋊C₈	—	5	2	no	—
356	C₄⋊C₈	—	5	2	no	—
357	C₄⋊C₈	—	5	2	no	—
358	C₄⋊C₈	—	5	1	no	—
359	C₄⋊C₈	—	5	1	no	—
360	C₄⋊C₈	—	5	1	no	—
361	C₄⋊C₈	—	5	1	no	—
362	C₄⋊C₈	—	5	1	no	—
363	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₂²⋊C₈	—	5	2	no	—
365	C₂²⋊C₈	—	5	2	no	—
366	C₂²⋊C₈	—	5	2	no	—
367	C₂²⋊C₈	—	5	1	no	—
368	C₂²⋊C₈	—	5	1	no	—
369	C₂²⋊C₈	—	5	1	no	—
370	C₂²⋊C₈	—	5	1	no	—
371	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
372	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
373	#97	—	5	2	no	—
374	#97	—	5	2	no	—
375	#97	—	5	2	no	—
376	#97	—	5	2	no	—
377	#97	—	5	2	no	—
378	#97	—	5	1	no	—
379	#97	—	5	1	no	—
380	#97	—	5	1	no	—
381	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₄×C₈	—	5	1	no	—
383	C₄×C₈	—	5	1	no	—
384	C₄×C₈	—	5	1	no	—
385	C₄×C₈	—	5	1	no	—
386	C₄×C₈	—	5	1	no	—
387	C₄×C₈	—	5	1	no	—
388	C₄×C₈	—	5	1	no	—
389	C₄×C₈	—	5	1	no	—
390	C₄×C₈	—	5	2	no	—
391	C₄×C₈	—	5	2	no	—
392	C₄×C₈	—	5	2	no	—
393	C₄×C₈	—	5	2	no	—
394	C₄×C₈	—	5	1	no	—
395	C₄×C₈	—	5	1	no	—
396	C₄×C₈	—	5	1	no	—
397	C₄×C₈	—	5	1	no	—
398	C₄×C₈	—	5	1	no	—
399	C₄×C₈	—	5	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	C₄×M₁₆	1	2	yes	—
406	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
407	C₂×D₅	—	2	1	no	—
408	C₂×D₅	—	2	1	no	—
409	C₂×D₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	#568	1	1	yes	characteristic
415	C₄×C₅	#568	1	1	yes	characteristic
416	Dic₅	—	2	1	no	—
417	Dic₅	—	2	1	no	—
418	Dic₅	—	2	1	no	—
419	Dic₅	—	2	1	no	—
420	Dic₅	C₄×M₁₆	1	2	yes	—
421	Dic₅	C₂²×M₁₆	1	2	yes	—
422	Dic₅	#568	1	2	yes	—
423	#41	—	10	4	no	—
424	C₂×Q₈	—	5	1	no	—
425	C₂×D₄	—	5	1	no	—
426	C₂×D₄	—	5	1	no	—
427	C₂×D₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
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	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
436	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
437	M₁₆	—	4	1	no	—
438	M₁₆	—	10	4	no	—
439	M₁₆	—	10	4	no	—
440	M₁₆	—	10	4	no	—
441	M₁₆	—	20	1	no	—
442	M₁₆	—	20	1	no	—
443	M₁₆	—	20	1	no	—
444	M₁₆	—	20	2	no	—
445	M₁₆	—	20	2	no	—
446	C₂×C₈	—	4	1	no	—
447	C₂×C₈	—	5	2	no	—
448	C₂×C₈	—	5	2	no	—
449	C₂×C₈	—	5	8	no	—
450	C₂×C₈	—	5	2	no	—
451	C₂×C₈	—	5	2	no	—
452	C₂×C₈	—	5	2	no	—
453	C₂×C₈	—	5	2	no	—
454	C₂×C₈	—	5	2	no	—
455	C₂×C₈	—	5	2	no	—
456	C₂×C₈	—	5	1	no	—
457	C₂×C₈	—	5	1	no	—
458	C₂×C₈	—	5	1	no	—
459	C₂×C₈	—	5	1	no	—
460	C₂×C₈	—	10	4	no	—
461	C₂×C₈	—	10	4	no	—
462	C₂×C₈	—	20	1	no	—
463	C₂×C₈	—	20	2	no	—
464	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
465	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
466	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₄⋊C₄	—	5	1	no	—
471	C₄⋊C₄	—	5	1	no	—
472	C₄⋊C₄	—	5	1	no	—
473	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
474	C₂²⋊C₄	—	5	1	no	—
475	C₂²⋊C₄	—	5	1	no	—
476	C₂²⋊C₄	—	5	1	no	—
477	C₂²⋊C₄	—	5	1	no	—
478	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₂²⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
480	C₄²	—	5	1	no	—
481	C₄²	—	5	1	no	—
482	C₄²	—	5	1	no	—
483	C₄²	—	5	1	no	—
484	C₄²	—	5	1	no	—
485	C₄²	—	5	1	no	—
486	C₄²	—	5	1	no	—
487	C₄²	—	5	1	no	—
488	C₄²	—	5	1	no	—
489	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
490	C₂×C₅	—	2	2	no	—
491	C₂×C₅	—	4	1	no	—
492	C₂×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic
493	C₂×C₅	#2875	1	1	yes	characteristic
494	C₂×C₅	#2875	1	1	yes	characteristic
495	D₅	—	4	1	no	—
496	C₂³	—	5	1	no	—
497	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
498	C₂³	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
499	Q₈	—	10	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	10	2	no	—
502	D₄	—	10	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	5	4	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	—	10	2	no	—
516	C₂×C₄	—	10	2	no	—
517	C₂×C₄	—	10	2	no	—
518	C₂×C₄	—	10	2	no	—
519	C₂×C₄	—	10	2	no	—
520	C₂×C₄	—	10	1	no	—
521	C₂×C₄	—	10	1	no	—
522	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
523	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
524	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
526	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	5	4	no	—
532	C₈	—	5	4	no	—
533	C₈	—	10	2	no	—
534	C₈	—	10	2	no	—
535	C₈	—	10	2	no	—
536	C₈	—	10	2	no	—
537	C₈	—	10	2	no	—
538	C₈	—	10	2	no	—
539	C₈	—	10	1	no	—
540	C₈	—	10	1	no	—
541	C₈	—	10	1	no	—
542	C₈	—	10	1	no	—
543	C₅	#17336	1	1	yes	characteristic, complemented, Sylow
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	10	1	no	—
550	C₂²	—	10	1	no	—
551	C₂²	—	10	1	no	—
552	C₂²	M₁₆×AGL(1,𝔽₅)	1	2	yes	—
553	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	5	2	no	—
559	C₄	—	5	2	no	—
560	C₄	—	5	2	no	—
561	C₄	—	10	1	no	—
562	C₄	—	10	1	no	—
563	C₄	—	10	1	no	—
564	C₄	—	10	1	no	—
565	C₄	#66256	1	1	yes	characteristic
566	C₄	#66264	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	20	1	no	—
570	C₂	#10617136	1	1	yes	characteristic
571	C₂	C₂×M₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic
572	C₂	#10617415	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#435	C₄
prime radical	C₂×#711	C₂×C₄
cosocle	C₄×Dic₅	C₂⁴
hypercenter	#435	AGL(1,𝔽₅)
hypocenter	C₅	#17336
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
4. #10604737	C₂	semidirect
5. #10604735	C₂	semidirect
6. #10604688	C₂	semidirect
7. C₂×#170⋊C₈	C₂	semidirect
8. #10604013	C₂	semidirect
9. #10604011	C₂	semidirect
10. #10603895	C₂	semidirect
11. #10603893	C₂	semidirect
12. #10603893	C₂	semidirect
13. #10603892	C₂	semidirect
14. #10603864	C₂	semidirect
15. #10603862	C₂	semidirect
178. C₂×#170	M₁₆	semidirect
543. C₅	#17336	semidirect

Maximal subgroups

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

subgroup	index
#10617154	2
C₄×#4131	2
#10611184	2
#10604737	2
#10604735	2
#10604688	2
C₂×#170⋊C₈	2
#10604013	2
#10604011	2
#10603895	2
#10603893	2
#10603892	2
#10603864	2
#10603862	2
#17336	5