Subgroups — #11989410

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 448 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×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#10606049	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	C₂²×C₈×D₅	—	2	1	no	—
10	C₂×#4038	—	2	1	no	—
11	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₅×#384	C₂²	1	1	yes	characteristic
15	C₂×#3946	—	2	1	no	—
16	C₂×#3946	—	2	1	no	—
17	#65276	—	2	1	no	—
18	#65276	C₄	1	2	yes	—
19	#65266	—	2	1	no	—
20	C₄⋊C₄×Dic₅	—	2	1	no	—
21	C₄⋊C₄×Dic₅	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	D₅×C₄⋊C₈	—	2	2	no	—
28	D₅×C₄⋊C₈	C₄	1	4	yes	complemented
29	#8045	—	5	1	no	maximal, Sylow
30	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂×C₅×C₄⋊C₄	—	2	1	no	—
36	C₂×C₅×C₄⋊C₄	—	2	1	no	—
37	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
39	C₂×#685	—	2	2	no	—
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×C₄×Dic₅	—	2	2	no	—
44	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
47	C₂²×#168	—	2	1	no	—
48	C₂²×#168	—	2	1	no	—
49	C₂×#676	—	2	4	no	—
50	C₂×#676	—	4	2	no	—
51	C₂×#676	—	4	2	no	—
52	C₂×C₈×D₅	—	2	4	no	—
53	C₂×C₈×D₅	—	4	2	no	—
54	C₂×C₈×D₅	—	4	2	no	—
55	#4038	—	4	2	no	—
56	#4038	—	4	2	no	—
57	C₄²×D₅	C₂×C₄	1	2	yes	—
58	C₄²×D₅	C₂×C₄	1	2	yes	—
59	C₄²×D₅	D₄	1	2	yes	—
60	C₄²×D₅	Q₈	1	2	yes	—
61	C₅×C₄⋊C₈	—	2	1	no	—
62	C₅×C₄⋊C₈	—	2	1	no	—
63	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	#3963	—	2	2	no	—
66	#3963	—	2	2	no	—
67	#3946	—	2	4	no	—
68	#3946	—	2	4	no	—
69	C₄⋊#168	—	2	1	no	—
70	C₄⋊#168	—	2	1	no	—
71	C₄⋊#168	C₂×C₄	1	2	yes	—
72	C₄⋊#168	C₂×C₄	1	2	yes	—
73	C₂×#423	—	5	1	no	—
74	C₂²×C₄⋊C₈	—	5	1	no	—
75	#2285	—	5	1	no	—
76	#1296	—	5	1	no	—
77	#1296	—	5	1	no	—
78	#1296	—	5	1	no	—
79	#1296	D₅	1	1	yes	characteristic, complemented
80	C₂³×D₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	2	2	no	—
82	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₅	—	2	2	no	—
86	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₅	—	2	1	no	—
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	—	4	1	no	—
94	C₂×C₄×D₅	—	4	1	no	—
95	C₂×C₄×D₅	C₄²	1	2	yes	—
96	C₂×C₄×D₅	C₂²⋊C₄	1	2	yes	—
97	C₂×C₄×D₅	C₂²⋊C₄	1	2	yes	—
98	C₂×C₄×D₅	C₄⋊C₄	1	2	yes	—
99	C₂×C₄×D₅	C₄⋊C₄	1	2	yes	—
100	C₂×C₄×D₅	C₄⋊C₄	1	2	yes	—
101	C₂×C₄×D₅	D₈	1	2	yes	—
102	C₂×C₄×D₅	SD₁₆	1	2	yes	—
103	C₂×C₄×D₅	SD₁₆	1	2	yes	—
104	C₂×C₄×D₅	Q₁₆	1	2	yes	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	4	1	no	—
108	C₂×C₅×C₈	—	4	1	no	—
109	C₂×C₅×C₈	—	4	1	no	—
110	C₂×C₅×C₈	—	4	1	no	—
111	C₅×C₄⋊C₄	—	4	2	no	—
112	C₅×C₄⋊C₄	—	4	1	no	—
113	C₅×C₄⋊C₄	—	4	1	no	—
114	C₅×C₄⋊C₄	—	4	1	no	—
115	C₅×C₄⋊C₄	—	4	1	no	—
116	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
120	#685	—	4	4	no	—
121	C₄⋊Dic₅	—	4	1	no	—
122	C₄⋊Dic₅	—	4	1	no	—
123	C₄⋊Dic₅	—	4	1	no	—
124	C₄⋊Dic₅	—	4	1	no	—
125	C₄⋊Dic₅	—	4	2	no	—
126	C₄×Dic₅	—	4	4	no	—
127	C₄×Dic₅	C₄²	1	2	yes	—
128	C₄×Dic₅	C₂²⋊C₄	1	2	yes	—
129	C₄×Dic₅	C₂²⋊C₄	1	2	yes	—
130	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
131	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
132	C₄×Dic₅	C₄⋊C₄	1	2	yes	—
133	C₂×#168	—	2	2	no	—
134	C₂×#168	—	2	2	no	—
135	C₂×#168	—	4	1	no	—
136	C₂×#168	—	4	1	no	—
137	C₂×#168	—	4	1	no	—
138	C₂×#168	—	4	1	no	—
139	#676	—	4	8	no	—
140	C₈×D₅	—	4	8	no	—
141	C₂²×M₁₆	—	10	1	no	—
142	C₂³×C₈	—	10	1	no	—
143	C₂×#117	—	10	1	no	—
144	C₂²×C₄²	—	5	1	no	—
145	#423	—	5	4	no	—
146	#423	—	10	2	no	—
147	C₂×C₄⋊C₈	—	5	1	no	—
148	C₂×C₄⋊C₈	—	5	1	no	—
149	C₂×C₄⋊C₈	—	5	4	no	—
150	C₂×C₄⋊C₈	—	10	2	no	—
151	C₂×C₄⋊C₈	—	10	1	no	—
152	C₂×C₄⋊C₈	—	10	1	no	—
153	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
155	#384	—	5	1	no	—
156	#384	C₂×D₅	1	1	yes	characteristic
157	#382	—	10	1	no	—
158	#380	—	5	2	no	—
159	#380	—	10	1	no	—
160	C₄×C₄⋊C₄	—	5	2	no	—
161	C₄×C₄⋊C₄	—	10	1	no	—
162	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×D₅	—	2	1	no	—
164	C₂²×D₅	—	2	1	no	—
165	C₂²×D₅	—	2	1	no	—
166	C₂²×D₅	—	2	1	no	—
167	C₂²×D₅	#95	1	2	yes	—
168	C₂²×D₅	#102	1	2	yes	—
169	C₂²×D₅	#103	1	2	yes	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	4	2	no	—
173	C₂×C₄×C₅	—	4	2	no	—
174	C₂×C₄×C₅	—	4	2	no	—
175	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
185	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₅	#137	1	1	yes	characteristic
188	C₂×C₄×C₅	#137	1	1	yes	characteristic
189	C₂×Dic₅	—	2	1	no	—
190	C₂×Dic₅	—	2	1	no	—
191	C₂×Dic₅	—	2	1	no	—
192	C₂×Dic₅	—	2	1	no	—
193	C₂×Dic₅	—	4	2	no	—
194	C₂×Dic₅	—	4	2	no	—
195	C₂×Dic₅	—	4	2	no	—
196	C₂×Dic₅	#95	1	2	yes	—
197	C₂×Dic₅	#95	1	2	yes	—
198	C₂×Dic₅	#95	1	2	yes	—
199	C₂×Dic₅	#102	1	2	yes	—
200	C₂×Dic₅	#103	1	2	yes	—
201	C₄×D₅	—	2	2	no	—
202	C₄×D₅	—	2	2	no	—
203	C₄×D₅	—	2	2	no	—
204	C₄×D₅	—	2	2	no	—
205	C₄×D₅	—	4	2	no	—
206	C₄×D₅	—	4	2	no	—
207	C₄×D₅	#102	1	4	yes	—
208	C₄×D₅	#103	1	4	yes	—
209	C₄×D₅	#106	1	4	yes	—
210	C₄×D₅	#107	1	4	yes	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	—	4	2	no	—
213	#168	—	4	2	no	—
214	#168	—	4	2	no	—
215	C₂³×C₄	—	5	1	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂³×C₄	—	5	1	no	—
218	C₂×M₁₆	—	10	4	no	—
219	C₂×M₁₆	—	20	2	no	—
220	C₂×M₁₆	—	20	2	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₂²×C₈	—	10	4	no	—
224	C₂²×C₈	—	10	1	no	—
225	C₂²×C₈	—	10	1	no	—
226	C₂²×C₈	—	20	2	no	—
227	C₂²×C₈	—	20	2	no	—
228	#117	—	20	2	no	—
229	#117	—	20	2	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	5	2	no	—
233	C₂×C₄⋊C₄	—	10	1	no	—
234	C₂×C₄⋊C₄	—	10	1	no	—
235	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
236	C₂×C₂²⋊C₄	—	10	2	no	—
237	C₂×C₄²	—	5	1	no	—
238	C₂×C₄²	—	5	1	no	—
239	C₂×C₄²	—	5	1	no	—
240	C₂×C₄²	—	5	2	no	—
241	C₂×C₄²	—	5	2	no	—
242	C₂×C₄²	—	5	2	no	—
243	C₂×C₄²	—	5	2	no	—
244	C₂×C₄²	—	10	2	no	—
245	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	5	2	no	—
249	C₄⋊C₈	—	5	2	no	—
250	C₄⋊C₈	—	10	4	no	—
251	C₄⋊C₈	—	10	4	no	—
252	C₄⋊C₈	—	10	1	no	—
253	C₄⋊C₈	—	10	1	no	—
254	C₄⋊C₈	C₄×D₅	1	2	yes	—
255	C₄⋊C₈	C₄×D₅	1	2	yes	—
256	#95	—	10	2	no	—
257	#95	—	10	2	no	—
258	C₂²×C₅	C₂×#95	1	1	yes	characteristic
259	C₂²×C₅	#413	1	1	yes	characteristic
260	C₂²×C₅	#413	1	1	yes	characteristic
261	C₂²×C₅	C₂×#102	1	1	yes	characteristic
262	C₂²×C₅	C₂×#103	1	1	yes	characteristic
263	C₂²×C₅	#417	1	1	yes	characteristic
264	C₂²×C₅	#417	1	1	yes	characteristic
265	C₂×D₅	—	2	2	no	—
266	C₂×D₅	—	2	2	no	—
267	C₂×D₅	—	2	2	no	—
268	C₂×D₅	—	2	2	no	—
269	C₂×D₅	—	2	2	no	—
270	C₂×D₅	—	2	2	no	—
271	C₂×D₅	#340	1	4	yes	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	8	2	no	—
275	C₄×C₅	C₂×#102	1	1	yes	characteristic
276	C₄×C₅	C₂×#103	1	1	yes	characteristic
277	C₄×C₅	#418	1	1	yes	characteristic
278	C₄×C₅	#419	1	1	yes	characteristic
279	C₄×C₅	C₂×#106	1	1	yes	characteristic
280	C₄×C₅	C₂×#107	1	1	yes	characteristic
281	C₄×C₅	#428	1	1	yes	characteristic
282	C₄×C₅	#428	1	1	yes	characteristic
283	Dic₅	—	2	2	no	—
284	Dic₅	—	2	2	no	—
285	Dic₅	—	8	2	no	—
286	Dic₅	#340	1	4	yes	—
287	C₂⁴	—	5	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	5	1	no	—
290	C₂²×C₄	—	5	2	no	—
291	C₂²×C₄	—	5	2	no	—
292	C₂²×C₄	—	5	2	no	—
293	C₂²×C₄	—	5	2	no	—
294	C₂²×C₄	—	5	2	no	—
295	C₂²×C₄	—	5	2	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	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	—	10	1	no	—
303	C₂²×C₄	—	10	1	no	—
304	C₂²×C₄	—	10	1	no	—
305	C₂²×C₄	—	10	1	no	—
306	C₂²×C₄	—	10	2	no	—
307	C₂²×C₄	—	20	1	no	—
308	C₂²×C₄	—	20	1	no	—
309	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
312	M₁₆	—	20	8	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	10	2	no	—
320	C₂×C₈	—	10	2	no	—
321	C₂×C₈	—	20	8	no	—
322	C₂×C₈	—	20	1	no	—
323	C₂×C₈	—	20	1	no	—
324	C₂×C₈	—	20	1	no	—
325	C₂×C₈	—	20	1	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	20	2	no	—
332	C₄⋊C₄	—	20	1	no	—
333	C₄⋊C₄	—	20	1	no	—
334	C₄⋊C₄	—	20	1	no	—
335	C₄⋊C₄	—	20	1	no	—
336	C₂²⋊C₄	—	20	4	no	—
337	C₄²	—	5	2	no	—
338	C₄²	—	5	2	no	—
339	C₄²	—	5	2	no	—
340	C₄²	—	5	2	no	—
341	C₄²	—	5	2	no	—
342	C₄²	—	5	2	no	—
343	C₄²	—	20	4	no	—
344	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
345	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
346	C₄²	D₄×D₅	1	1	yes	characteristic
347	C₄²	Q₈×D₅	1	1	yes	characteristic
348	C₂×C₅	#1547	1	1	yes	characteristic
349	C₂×C₅	#1547	1	1	yes	characteristic
350	C₂×C₅	#1550	1	1	yes	characteristic
351	C₂×C₅	#1550	1	1	yes	characteristic
352	C₂×C₅	C₂×#340	1	1	yes	characteristic
353	C₂×C₅	#1736	1	1	yes	characteristic
354	C₂×C₅	#1742	1	1	yes	characteristic
355	D₅	—	2	4	no	—
356	C₂³	—	5	2	no	—
357	C₂³	—	5	2	no	—
358	C₂³	—	5	2	no	—
359	C₂³	—	10	1	no	—
360	C₂³	—	10	1	no	—
361	C₂³	—	10	1	no	—
362	C₂³	—	10	1	no	—
363	C₂³	D₅×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	5	2	no	—
370	C₂×C₄	—	5	2	no	—
371	C₂×C₄	—	5	2	no	—
372	C₂×C₄	—	5	4	no	—
373	C₂×C₄	—	5	4	no	—
374	C₂×C₄	—	5	4	no	—
375	C₂×C₄	—	5	4	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	10	1	no	—
379	C₂×C₄	—	10	1	no	—
380	C₂×C₄	—	10	1	no	—
381	C₂×C₄	—	10	1	no	—
382	C₂×C₄	—	10	2	no	—
383	C₂×C₄	—	10	2	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	20	2	no	—
387	C₂×C₄	—	20	2	no	—
388	C₂×C₄	—	20	2	no	—
389	C₂×C₄	—	20	2	no	—
390	C₂×C₄	—	20	2	no	—
391	C₂×C₄	C₄²×D₅	1	1	yes	characteristic
392	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
393	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
395	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
396	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
397	C₂×C₄	D₅×D₈	1	1	yes	characteristic
398	C₂×C₄	#4057	1	1	yes	characteristic
399	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
400	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
401	C₂×C₄	#4060	1	1	yes	characteristic
402	C₂×C₄	#4061	1	1	yes	characteristic
403	C₂×C₄	D₅×Q₁₆	1	1	yes	characteristic
404	C₂×C₄	#4064	1	1	yes	characteristic
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	20	2	no	—
408	C₈	—	20	2	no	—
409	C₅	#8045	1	1	yes	characteristic, complemented, Sylow
410	C₂²	—	5	4	no	—
411	C₂²	—	10	2	no	—
412	C₂²	—	10	2	no	—
413	C₂²	—	10	2	no	—
414	C₂²	—	10	2	no	—
415	C₂²	—	10	2	no	—
416	C₂²	—	10	2	no	—
417	C₂²	D₅×#95	1	1	yes	characteristic
418	C₂²	#65034	1	1	yes	characteristic
419	C₂²	#65040	1	1	yes	characteristic
420	C₂²	D₅×#102	1	1	yes	characteristic
421	C₂²	#65060	1	1	yes	characteristic
422	C₂²	D₅×#103	1	1	yes	characteristic
423	C₂²	#65092	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	5	4	no	—
427	C₄	—	8	2	no	—
428	C₄	—	10	2	no	—
429	C₄	—	10	2	no	—
430	C₄	—	40	2	no	—
431	C₄	D₅×#102	1	1	yes	characteristic
432	C₄	#65059	1	1	yes	characteristic
433	C₄	D₅×#103	1	1	yes	characteristic
434	C₄	#65091	1	1	yes	characteristic
435	C₄	D₅×#106	1	1	yes	characteristic
436	C₄	#65150	1	1	yes	characteristic
437	C₄	D₅×#107	1	1	yes	characteristic
438	C₄	#65170	1	1	yes	characteristic
439	C₂	—	10	4	no	—
440	C₂	#10599177	1	1	yes	characteristic
441	C₂	#10599214	1	1	yes	characteristic
442	C₂	#10599216	1	1	yes	characteristic
443	C₂	#10599277	1	1	yes	characteristic
444	C₂	D₅×#340	1	1	yes	characteristic
445	C₂	#10599660	1	1	yes	characteristic
446	C₂	#10599782	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	#8045
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. D₅×C₄⋊C₈	C₄	semidirect
79. #1296	D₅	semidirect
409. C₅	#8045	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×D₅×C₄⋊C₈	2
#10606049	2
C₅×#1296	2
#10598193	2
#10598125	2
#8045	5