Subgroups — #11989402

Order 1280.

790 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65126	C₂	1	1	yes	maximal, characteristic
2	C₂×#65122	C₂	1	1	yes	maximal, characteristic
3	D₅×#384	C₂	1	1	yes	maximal, characteristic
4	C₅×#1296	C₂	1	1	yes	maximal, characteristic, complemented
5	#10598193	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598193	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#676	—	2	1	no	—
9	C₂×D₅×C₄⋊C₄	—	2	1	no	—
10	C₂×D₅×C₄⋊C₄	—	2	1	no	—
11	C₂×D₅×C₄⋊C₄	C₄	1	2	yes	—
12	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₅×#384	C₂²	1	1	yes	characteristic
16	C₂×#3952	—	2	1	no	—
17	C₂×#3946	—	2	1	no	—
18	C₂×C₈×Dic₅	—	2	1	no	—
19	#65265	—	2	1	no	—
20	#65265	—	2	1	no	—
21	#65265	C₄	1	2	yes	—
22	#65224	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
25	#65126	—	2	2	no	—
26	#65126	C₄	1	4	yes	complemented
27	#65122	—	2	2	no	—
28	#65122	C₄	1	4	yes	complemented
29	#8043	—	5	1	no	maximal, Sylow
30	C₂²×C₄×D₅	—	2	2	no	—
31	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂²×C₅×C₈	—	2	1	no	—
36	C₂×C₅×C₄⋊C₄	—	2	1	no	—
37	C₂×C₅×C₄⋊C₄	—	2	1	no	—
38	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊Dic₅	—	2	1	no	—
41	C₂×C₄⋊Dic₅	—	2	1	no	—
42	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
43	C₂×#683	—	2	2	no	—
44	C₂×#683	—	2	2	no	—
45	C₂×#683	—	2	2	no	—
46	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
49	C₂²×#168	—	2	1	no	—
50	C₂²×#168	—	2	1	no	—
51	C₂×#676	—	2	4	no	—
52	C₂×#676	—	4	2	no	—
53	C₂×#676	—	4	2	no	—
54	D₅×C₄⋊C₄	—	4	2	no	—
55	D₅×C₄⋊C₄	—	4	2	no	—
56	D₅×C₄⋊C₄	—	4	2	no	—
57	D₅×C₄⋊C₄	—	4	2	no	—
58	D₅×C₄⋊C₄	—	4	4	no	—
59	C₄²×D₅	C₂×C₄	1	2	yes	—
60	C₄²×D₅	C₂×C₄	1	2	yes	—
61	C₄²×D₅	D₄	1	2	yes	—
62	C₄²×D₅	Q₈	1	2	yes	—
63	C₅×C₄⋊C₈	—	2	1	no	—
64	C₅×C₄⋊C₈	—	2	1	no	—
65	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
66	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
67	#3952	—	2	4	no	—
68	#3946	—	2	4	no	—
69	C₈×Dic₅	—	2	4	no	—
70	C₄⋊#168	—	2	1	no	—
71	C₄⋊#168	—	2	1	no	—
72	C₄⋊#168	C₂×C₄	1	2	yes	complemented
73	C₄⋊#168	C₂×C₄	1	2	yes	complemented
74	C₂×#431	—	5	1	no	—
75	C₂×#423	—	5	1	no	—
76	C₂×#384	—	5	1	no	—
77	#1296	—	5	1	no	—
78	#1296	—	5	1	no	—
79	#1296	—	5	1	no	—
80	#1296	D₅	1	1	yes	characteristic, complemented
81	C₂³×D₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	—	2	2	no	—
83	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×Dic₅	—	2	2	no	—
87	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₅	—	2	1	no	—
91	C₂×C₄×D₅	—	2	1	no	—
92	C₂×C₄×D₅	—	2	1	no	—
93	C₂×C₄×D₅	—	2	1	no	—
94	C₂×C₄×D₅	—	2	2	no	—
95	C₂×C₄×D₅	—	2	2	no	—
96	C₂×C₄×D₅	—	4	4	no	—
97	C₂×C₄×D₅	—	4	4	no	—
98	C₂×C₄×D₅	—	4	4	no	—
99	C₂×C₄×D₅	C₄²	1	2	yes	—
100	C₂×C₄×D₅	C₂²⋊C₄	1	2	yes	—
101	C₂×C₄×D₅	C₂²⋊C₄	1	2	yes	—
102	C₂×C₄×D₅	C₄⋊C₄	1	2	yes	—
103	C₂×C₄×D₅	C₄⋊C₄	1	2	yes	—
104	C₂×C₄×D₅	C₄⋊C₄	1	2	yes	—
105	C₂×C₄×D₅	D₈	1	2	yes	—
106	C₂×C₄×D₅	SD₁₆	1	2	yes	—
107	C₂×C₄×D₅	SD₁₆	1	2	yes	—
108	C₂×C₄×D₅	Q₁₆	1	2	yes	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	4	1	no	—
112	C₂×C₅×C₈	—	4	1	no	—
113	C₂×C₅×C₈	—	4	1	no	—
114	C₂×C₅×C₈	—	4	1	no	—
115	C₅×C₄⋊C₄	—	4	2	no	—
116	C₅×C₄⋊C₄	—	4	1	no	—
117	C₅×C₄⋊C₄	—	4	1	no	—
118	C₅×C₄⋊C₄	—	4	1	no	—
119	C₅×C₄⋊C₄	—	4	1	no	—
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
124	C₄⋊Dic₅	—	4	1	no	—
125	C₄⋊Dic₅	—	4	1	no	—
126	C₄⋊Dic₅	—	4	1	no	—
127	C₄⋊Dic₅	—	4	1	no	—
128	C₄⋊Dic₅	—	4	2	no	—
129	#683	—	4	4	no	—
130	#683	—	4	4	no	—
131	#683	—	4	4	no	—
132	C₄×Dic₅	C₄²	1	2	yes	—
133	C₄×Dic₅	C₂²⋊C₄	1	2	yes	—
134	C₄×Dic₅	C₂²⋊C₄	1	2	yes	—
135	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
136	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
137	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	2	2	no	—
140	C₂×#168	—	4	1	no	—
141	C₂×#168	—	4	1	no	—
142	C₂×#168	—	4	1	no	—
143	C₂×#168	—	4	1	no	—
144	#676	—	4	8	no	—
145	C₂²×M₁₆	—	10	1	no	—
146	C₂²×C₄⋊C₄	—	5	2	no	—
147	C₂²×C₄⋊C₄	—	10	1	no	—
148	C₂²×C₄⋊C₄	—	10	1	no	—
149	C₂²×C₄²	—	5	1	no	—
150	#431	—	5	4	no	—
151	#431	—	10	2	no	—
152	#423	—	5	4	no	—
153	#423	—	10	2	no	—
154	C₂×C₄⋊C₈	—	5	1	no	—
155	C₂×C₄⋊C₈	—	5	1	no	—
156	C₂×C₄⋊C₈	—	10	1	no	—
157	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
159	C₂×C₂²⋊C₈	—	10	1	no	—
160	C₂×C₄×C₈	—	10	1	no	—
161	#384	—	5	2	no	—
162	#384	—	5	1	no	—
163	#384	—	10	1	no	—
164	#384	—	10	1	no	—
165	#384	C₂×D₅	1	1	yes	characteristic
166	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×D₅	—	2	1	no	—
168	C₂²×D₅	—	2	1	no	—
169	C₂²×D₅	—	2	1	no	—
170	C₂²×D₅	—	2	1	no	—
171	C₂²×D₅	#95	1	2	yes	—
172	C₂²×D₅	#102	1	2	yes	—
173	C₂²×D₅	#103	1	2	yes	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	4	2	no	—
177	C₂×C₄×C₅	—	4	2	no	—
178	C₂×C₄×C₅	—	4	2	no	—
179	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
189	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×C₄×C₅	#137	1	1	yes	characteristic
192	C₂×C₄×C₅	#137	1	1	yes	characteristic
193	C₂×Dic₅	—	2	1	no	—
194	C₂×Dic₅	—	2	1	no	—
195	C₂×Dic₅	—	4	2	no	—
196	C₂×Dic₅	—	4	2	no	—
197	C₂×Dic₅	—	4	2	no	—
198	C₂×Dic₅	#95	1	2	yes	—
199	C₂×Dic₅	#95	1	2	yes	—
200	C₂×Dic₅	#95	1	2	yes	—
201	C₂×Dic₅	#100	1	2	yes	—
202	C₂×Dic₅	#101	1	2	yes	—
203	C₂×Dic₅	#102	1	2	yes	—
204	C₂×Dic₅	#103	1	2	yes	—
205	C₄×D₅	—	2	2	no	—
206	C₄×D₅	—	2	2	no	—
207	C₄×D₅	—	2	2	no	—
208	C₄×D₅	—	2	2	no	—
209	C₄×D₅	—	2	4	no	—
210	C₄×D₅	—	2	4	no	—
211	C₄×D₅	—	8	8	no	—
212	C₄×D₅	#102	1	4	yes	—
213	C₄×D₅	#103	1	4	yes	—
214	C₄×D₅	#106	1	4	yes	—
215	C₄×D₅	#107	1	4	yes	—
216	C₅×C₈	—	4	2	no	—
217	C₅×C₈	—	4	2	no	—
218	#168	—	4	2	no	—
219	#168	—	4	2	no	—
220	C₂³×C₄	—	5	1	no	—
221	C₂³×C₄	—	5	1	no	—
222	C₂³×C₄	—	5	1	no	—
223	C₂³×C₄	—	10	2	no	—
224	C₂×M₁₆	—	10	4	no	—
225	C₂×M₁₆	—	20	2	no	—
226	C₂×M₁₆	—	20	2	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	10	1	no	—
230	C₂²×C₈	—	10	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	5	2	no	—
234	C₂×C₄⋊C₄	—	10	2	no	—
235	C₂×C₄⋊C₄	—	10	2	no	—
236	C₂×C₄⋊C₄	—	10	2	no	—
237	C₂×C₄⋊C₄	—	10	1	no	—
238	C₂×C₄⋊C₄	—	10	1	no	—
239	C₂×C₄⋊C₄	—	20	2	no	—
240	C₂×C₄⋊C₄	—	20	2	no	—
241	C₂×C₄⋊C₄	—	20	2	no	—
242	C₂×C₄⋊C₄	—	20	2	no	—
243	C₂×C₄⋊C₄	—	20	4	no	—
244	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
245	C₂×C₄²	—	5	1	no	—
246	C₂×C₄²	—	5	1	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₂×C₄²	—	5	2	no	—
249	C₂×C₄²	—	5	2	no	—
250	C₂×C₄²	—	5	2	no	—
251	C₂×C₄²	—	5	2	no	—
252	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	5	2	no	—
256	C₄⋊C₈	—	5	2	no	—
257	C₄⋊C₈	—	10	4	no	—
258	C₄⋊C₈	—	10	1	no	—
259	C₄⋊C₈	—	10	1	no	—
260	C₄⋊C₈	C₄×D₅	1	2	yes	complemented
261	C₄⋊C₈	C₄×D₅	1	2	yes	complemented
262	C₂²⋊C₈	—	10	4	no	—
263	C₄×C₈	—	10	4	no	—
264	C₂²×C₅	C₂×#95	1	1	yes	characteristic
265	C₂²×C₅	C₂×#100	1	1	yes	characteristic
266	C₂²×C₅	C₂×#101	1	1	yes	characteristic
267	C₂²×C₅	C₂×#102	1	1	yes	characteristic
268	C₂²×C₅	C₂×#103	1	1	yes	characteristic
269	C₂²×C₅	#418	1	1	yes	characteristic
270	C₂²×C₅	#419	1	1	yes	characteristic
271	C₂×D₅	—	2	2	no	—
272	C₂×D₅	—	2	2	no	—
273	C₂×D₅	—	2	2	no	—
274	C₂×D₅	—	2	2	no	—
275	C₂×D₅	—	2	2	no	—
276	C₂×D₅	—	2	2	no	—
277	C₂×D₅	#340	1	4	yes	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	8	2	no	—
281	C₄×C₅	C₂×#102	1	1	yes	characteristic
282	C₄×C₅	C₂×#103	1	1	yes	characteristic
283	C₄×C₅	#417	1	1	yes	characteristic
284	C₄×C₅	#417	1	1	yes	characteristic
285	C₄×C₅	C₂×#106	1	1	yes	characteristic
286	C₄×C₅	C₂×#107	1	1	yes	characteristic
287	C₄×C₅	#428	1	1	yes	characteristic
288	C₄×C₅	#428	1	1	yes	characteristic
289	Dic₅	—	2	2	no	—
290	Dic₅	—	8	2	no	—
291	Dic₅	#340	1	4	yes	—
292	Dic₅	#343	1	4	yes	—
293	C₂⁴	—	5	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	2	no	—
298	C₂²×C₄	—	5	2	no	—
299	C₂²×C₄	—	5	2	no	—
300	C₂²×C₄	—	5	2	no	—
301	C₂²×C₄	—	5	2	no	—
302	C₂²×C₄	—	5	2	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	2	no	—
305	C₂²×C₄	—	5	2	no	—
306	C₂²×C₄	—	5	2	no	—
307	C₂²×C₄	—	5	2	no	—
308	C₂²×C₄	—	10	2	no	—
309	C₂²×C₄	—	10	2	no	—
310	C₂²×C₄	—	10	1	no	—
311	C₂²×C₄	—	10	1	no	—
312	C₂²×C₄	—	10	1	no	—
313	C₂²×C₄	—	10	1	no	—
314	C₂²×C₄	—	10	2	no	—
315	C₂²×C₄	—	20	4	no	—
316	C₂²×C₄	—	20	4	no	—
317	C₂²×C₄	—	20	4	no	—
318	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
321	M₁₆	—	20	8	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	10	2	no	—
329	C₂×C₈	—	10	2	no	—
330	C₂×C₈	—	20	1	no	—
331	C₂×C₈	—	20	1	no	—
332	C₂×C₈	—	20	1	no	—
333	C₂×C₈	—	20	1	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	20	2	no	—
340	C₄⋊C₄	—	20	4	no	—
341	C₄⋊C₄	—	20	4	no	—
342	C₄⋊C₄	—	20	4	no	—
343	C₄⋊C₄	—	20	1	no	—
344	C₄⋊C₄	—	20	1	no	—
345	C₄⋊C₄	—	20	1	no	—
346	C₄⋊C₄	—	20	1	no	—
347	C₄²	—	5	2	no	—
348	C₄²	—	5	2	no	—
349	C₄²	—	5	2	no	—
350	C₄²	—	5	2	no	—
351	C₄²	—	5	2	no	—
352	C₄²	—	5	2	no	—
353	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
354	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
355	C₄²	D₄×D₅	1	1	yes	characteristic
356	C₄²	Q₈×D₅	1	1	yes	characteristic
357	C₂×C₅	#1545	1	1	yes	characteristic
358	C₂×C₅	#1546	1	1	yes	characteristic
359	C₂×C₅	#1548	1	1	yes	characteristic
360	C₂×C₅	#1549	1	1	yes	characteristic
361	C₂×C₅	C₂×#340	1	1	yes	characteristic
362	C₂×C₅	#1736	1	1	yes	characteristic
363	C₂×C₅	C₂×#343	1	1	yes	characteristic
364	D₅	—	2	4	no	—
365	C₂³	—	5	2	no	—
366	C₂³	—	5	2	no	—
367	C₂³	—	5	2	no	—
368	C₂³	—	10	1	no	—
369	C₂³	—	10	1	no	—
370	C₂³	—	10	1	no	—
371	C₂³	—	10	1	no	—
372	C₂³	D₅×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	5	2	no	—
379	C₂×C₄	—	5	2	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	2	no	—
382	C₂×C₄	—	5	2	no	—
383	C₂×C₄	—	5	2	no	—
384	C₂×C₄	—	5	4	no	—
385	C₂×C₄	—	5	4	no	—
386	C₂×C₄	—	5	4	no	—
387	C₂×C₄	—	5	4	no	—
388	C₂×C₄	—	5	2	no	—
389	C₂×C₄	—	10	4	no	—
390	C₂×C₄	—	10	4	no	—
391	C₂×C₄	—	10	1	no	—
392	C₂×C₄	—	10	1	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	2	no	—
395	C₂×C₄	—	10	2	no	—
396	C₂×C₄	—	10	2	no	—
397	C₂×C₄	—	20	2	no	—
398	C₂×C₄	—	20	2	no	—
399	C₂×C₄	—	20	2	no	—
400	C₂×C₄	—	40	8	no	—
401	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
402	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
405	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
406	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
407	C₂×C₄	D₅×D₈	1	1	yes	characteristic
408	C₂×C₄	#4057	1	1	yes	characteristic
409	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
410	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
411	C₂×C₄	#4060	1	1	yes	characteristic
412	C₂×C₄	#4061	1	1	yes	characteristic
413	C₂×C₄	D₅×Q₁₆	1	1	yes	characteristic
414	C₂×C₄	#4064	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	20	2	no	—
418	C₈	—	20	2	no	—
419	C₅	#8043	1	1	yes	characteristic, complemented, Sylow
420	C₂²	—	5	4	no	—
421	C₂²	—	10	2	no	—
422	C₂²	—	10	2	no	—
423	C₂²	—	10	2	no	—
424	C₂²	—	10	2	no	—
425	C₂²	—	10	2	no	—
426	C₂²	—	10	2	no	—
427	C₂²	D₅×#95	1	1	yes	characteristic
428	C₂²	D₅×#100	1	1	yes	characteristic
429	C₂²	D₅×#101	1	1	yes	characteristic
430	C₂²	D₅×#102	1	1	yes	characteristic
431	C₂²	#65059	1	1	yes	characteristic
432	C₂²	D₅×#103	1	1	yes	characteristic
433	C₂²	#65091	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	5	4	no	—
437	C₄	—	5	4	no	—
438	C₄	—	8	2	no	—
439	C₄	—	10	2	no	—
440	C₄	—	40	2	no	—
441	C₄	D₅×#102	1	1	yes	characteristic
442	C₄	#65060	1	1	yes	characteristic
443	C₄	D₅×#103	1	1	yes	characteristic
444	C₄	#65092	1	1	yes	characteristic
445	C₄	D₅×#106	1	1	yes	characteristic
446	C₄	#65150	1	1	yes	characteristic
447	C₄	D₅×#107	1	1	yes	characteristic
448	C₄	#65170	1	1	yes	characteristic
449	C₂	—	10	4	no	—
450	C₂	#10599176	1	1	yes	characteristic
451	C₂	#10599213	1	1	yes	characteristic
452	C₂	#10599215	1	1	yes	characteristic
453	C₂	#10599276	1	1	yes	characteristic
454	C₂	D₅×#340	1	1	yes	characteristic
455	C₂	#10599660	1	1	yes	characteristic
456	C₂	D₅×#343	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₅×C₂²⋊C₄
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₅×#1296	C₂
socle	C₂³×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×D₅	C₂²⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	#1296	D₅
hypocenter	C₅	#8043
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. C₅×#1296	C₂	semidirect
5. #10598193	C₂	semidirect
6. #10598193	C₂	semidirect
7. #10598125	C₂	semidirect
26. #65126	C₄	semidirect
28. #65122	C₄	semidirect
65. C₅×C₄⋊C₈	C₂×C₄	semidirect
66. C₅×C₄⋊C₈	C₂×C₄	semidirect
72. C₄⋊#168	C₂×C₄	semidirect
73. C₄⋊#168	C₂×C₄	semidirect
80. #1296	D₅	semidirect
260. C₄⋊C₈	C₄×D₅	semidirect
261. C₄⋊C₈	C₄×D₅	semidirect
419. C₅	#8043	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65126	2
C₂×#65122	2
D₅×#384	2
C₅×#1296	2
#10598193	2
#10598125	2
#8043	5