Subgroups — #11989604

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
2	#10613793	C₂	1	1	yes	maximal, characteristic
3	C₂×#65213	C₂	1	1	yes	maximal, characteristic
4	#10598237	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₂×#4072	—	2	1	no	—
7	C₂²×#681	—	2	1	no	—
8	C₅×#431	—	2	1	no	—
9	C₅×#431	—	2	1	no	—
10	C₅×#431	C₄	1	2	yes	complemented
11	C₅×#431	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
13	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
14	C₂×C₄×C₅×C₈	—	2	1	no	—
15	#65501	—	2	1	no	—
16	#65501	C₄	1	2	yes	—
17	#65225	C₄	1	2	yes	—
18	#65224	—	2	1	no	—
19	C₄×C₄⋊Dic₅	—	2	1	no	—
20	C₄×C₄⋊Dic₅	C₂²	1	2	yes	—
21	#65213	—	2	1	no	—
22	#65213	—	2	1	no	—
23	#65213	C₄	1	2	yes	complemented
24	#65213	C₂²	1	2	yes	—
25	C₂×C₄⋊#168	—	2	1	no	—
26	C₂×C₄⋊#168	C₄	1	2	yes	complemented
27	#8095	—	5	1	no	maximal, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂²×C₅×C₈	—	2	2	no	—
32	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊Dic₅	—	2	2	no	—
45	#4072	—	4	2	no	—
46	#4072	—	4	2	no	—
47	C₂×C₄⋊Dic₅	—	2	2	no	—
48	C₂×C₄⋊Dic₅	—	2	2	no	—
49	C₂×C₄⋊Dic₅	—	2	2	no	—
50	C₂×C₄×Dic₅	—	2	2	no	—
51	C₂×#681	—	2	2	no	—
52	C₂×#681	—	2	2	no	—
53	C₂×#681	—	4	2	no	—
54	C₂×#681	—	4	2	no	—
55	C₂²×#168	—	2	2	no	—
56	C₅×C₄⋊C₈	—	2	2	no	—
57	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₅×C₂²⋊C₈	—	2	2	no	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₄×C₅×C₈	—	2	2	no	—
61	C₄×C₅×C₈	—	2	2	no	—
62	#3963	—	2	2	no	—
63	#3963	C₂×C₄	1	4	yes	—
64	C₄⋊#168	—	2	2	no	—
65	C₄⋊#168	—	2	2	no	—
66	C₄⋊#168	—	2	2	no	—
67	C₄⋊#168	C₂×C₄	1	4	yes	—
68	C₂×#431	D₅	1	1	yes	characteristic
69	C₂×#423	—	5	1	no	—
70	#2285	—	5	1	no	—
71	#1303	—	5	4	no	—
72	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅	—	4	2	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	D₈	1	2	yes	—
91	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×Dic₅	—	2	4	no	—
98	C₂×C₅×C₈	—	2	4	no	—
99	C₂×C₅×C₈	—	4	4	no	—
100	C₄²×C₅	C₄²	1	1	yes	characteristic
101	C₄²×C₅	C₄²	1	1	yes	characteristic
102	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
116	C₂²⋊Dic₅	—	4	4	no	—
117	C₄⋊Dic₅	—	4	4	no	—
118	C₄⋊Dic₅	—	4	4	no	—
119	C₄⋊Dic₅	—	4	4	no	—
120	C₄×Dic₅	—	4	2	no	—
121	C₄×Dic₅	—	4	2	no	—
122	#681	—	4	4	no	—
123	#681	—	4	2	no	—
124	#681	—	4	2	no	—
125	C₂×#168	—	2	4	no	—
126	C₂×#168	—	4	4	no	—
127	C₂²×M₁₆	—	10	1	no	—
128	C₂×#117	—	10	1	no	—
129	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
130	#431	—	2	1	no	—
131	#431	—	2	1	no	—
132	#431	Dic₅	1	2	yes	complemented
133	#431	C₂×D₅	1	2	yes	—
134	#423	—	5	2	no	—
135	#423	—	5	2	no	—
136	#423	—	10	1	no	—
137	#423	—	10	1	no	—
138	C₂×C₄⋊C₈	—	5	2	no	—
139	C₂×C₄⋊C₈	—	10	1	no	—
140	C₂×C₄⋊C₈	Dic₅	1	2	yes	complemented
141	C₂×C₂²⋊C₈	—	2	1	no	—
142	C₂×C₄×C₈	—	2	1	no	—
143	#384	—	10	1	no	—
144	#382	—	5	2	no	—
145	#380	—	5	2	no	—
146	#380	—	10	1	no	—
147	C₄×C₄⋊C₄	—	5	2	no	—
148	C₄×C₄⋊C₄	—	10	1	no	—
149	C₂³×C₅	—	4	1	no	—
150	C₂³×C₅	—	4	1	no	—
151	C₂³×C₅	#95	1	1	yes	characteristic
152	C₂³×C₅	#95	1	1	yes	characteristic
153	C₂³×C₅	#102	1	2	yes	—
154	C₂³×C₅	#103	1	2	yes	—
155	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	4	1	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	—	4	1	no	—
165	C₂×C₄×C₅	—	4	1	no	—
166	C₂×C₄×C₅	—	4	1	no	—
167	C₂×C₄×C₅	—	4	1	no	—
168	C₂×C₄×C₅	#95	1	1	yes	characteristic
169	C₂×C₄×C₅	#95	1	1	yes	characteristic
170	C₂×C₄×C₅	#95	1	1	yes	characteristic
171	C₂×C₄×C₅	#95	1	1	yes	characteristic
172	C₂×C₄×C₅	#95	1	1	yes	characteristic
173	C₂×C₄×C₅	#95	1	1	yes	characteristic
174	C₂×C₄×C₅	#102	1	2	yes	—
175	C₂×C₄×C₅	#102	1	2	yes	—
176	C₂×C₄×C₅	#102	1	2	yes	—
177	C₂×C₄×C₅	#103	1	2	yes	—
178	C₂×C₄×C₅	#103	1	2	yes	—
179	C₂×C₄×C₅	#103	1	2	yes	—
180	C₂×C₄×C₅	#106	1	2	yes	—
181	C₂×C₄×C₅	#106	1	2	yes	—
182	C₂×C₄×C₅	#107	1	2	yes	—
183	C₂×C₄×C₅	#107	1	2	yes	—
184	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
194	C₂×Dic₅	—	4	4	no	—
195	C₂×Dic₅	—	4	4	no	—
196	C₂×Dic₅	—	4	4	no	—
197	C₅×C₈	—	4	4	no	—
198	#168	—	4	4	no	—
199	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
200	C₂³×C₄	D₂₀	1	1	yes	characteristic
201	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
202	C₂×M₁₆	—	10	2	no	—
203	C₂×M₁₆	—	10	2	no	—
204	C₂×M₁₆	—	20	2	no	—
205	C₂×M₁₆	—	20	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	10	2	no	—
208	#117	—	20	2	no	—
209	#117	—	20	2	no	—
210	C₂×C₄⋊C₄	—	10	2	no	—
211	C₂×C₄⋊C₄	—	10	2	no	—
212	C₂×C₄⋊C₄	—	10	2	no	—
213	C₂×C₂²⋊C₄	—	10	2	no	—
214	C₂×C₄²	—	10	2	no	—
215	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
216	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
217	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
218	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
219	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
220	C₂×C₄²	D₂₀	1	1	yes	characteristic
221	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
222	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
223	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
225	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
226	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	—	5	4	no	—
229	C₄⋊C₈	—	10	2	no	—
230	C₄⋊C₈	—	10	2	no	—
231	C₄⋊C₈	—	10	2	no	—
232	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	2	no	—
235	C₄×C₈	—	2	2	no	—
236	C₄×C₈	—	2	2	no	—
237	#95	—	5	4	no	—
238	#95	—	10	2	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	—	2	1	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	4	2	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	#340	1	2	yes	—
248	C₂²×C₅	#340	1	2	yes	—
249	C₂²×C₅	C₂×#95	1	1	yes	characteristic
250	C₂²×C₅	C₂×#102	1	1	yes	characteristic
251	C₂²×C₅	C₂×#103	1	1	yes	characteristic
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	1	no	—
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	#340	1	2	yes	—
259	C₄×C₅	#340	1	2	yes	—
260	C₄×C₅	#344	1	2	yes	—
261	C₄×C₅	C₂×#102	1	1	yes	characteristic
262	C₄×C₅	C₂×#103	1	1	yes	characteristic
263	C₄×C₅	#421	1	2	yes	—
264	C₄×C₅	C₂×#106	1	1	yes	characteristic
265	C₄×C₅	C₂×#107	1	1	yes	characteristic
266	Dic₅	—	8	4	no	—
267	C₂⁴	#685	1	1	yes	characteristic
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	10	4	no	—
271	C₂²×C₄	#677	1	2	yes	—
272	C₂²×C₄	#677	1	2	yes	—
273	C₂²×C₄	D₄₀	1	2	yes	—
274	C₂²×C₄	Dic₂₀	1	2	yes	—
275	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
276	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
277	C₂²×C₄	#683	1	1	yes	characteristic
278	C₂²×C₄	#683	1	1	yes	characteristic
279	C₂²×C₄	#683	1	1	yes	characteristic
280	C₂²×C₄	#683	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
283	C₂²×C₄	#685	1	1	yes	characteristic
284	C₂²×C₄	#685	1	1	yes	characteristic
285	C₂²×C₄	#685	1	1	yes	characteristic
286	C₂²×C₄	#685	1	1	yes	characteristic
287	C₂²×C₄	#685	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
289	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
293	M₁₆	—	20	4	no	—
294	M₁₆	—	20	2	no	—
295	M₁₆	—	20	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	4	no	—
298	C₂×C₈	—	10	4	no	—
299	C₂×C₈	—	20	4	no	—
300	C₄⋊C₄	—	20	4	no	—
301	C₄⋊C₄	—	20	4	no	—
302	C₄⋊C₄	—	20	4	no	—
303	C₂²⋊C₄	—	20	4	no	—
304	C₄²	—	20	2	no	—
305	C₄²	—	20	2	no	—
306	C₄²	C₄×Dic₅	1	1	yes	characteristic
307	C₄²	C₄×Dic₅	1	1	yes	characteristic
308	C₄²	#683	1	1	yes	characteristic
309	C₄²	#683	1	1	yes	characteristic
310	C₄²	#683	1	1	yes	characteristic
311	C₄²	#683	1	1	yes	characteristic
312	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
313	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
314	C₄²	#685	1	1	yes	characteristic
315	C₄²	#685	1	1	yes	characteristic
316	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
317	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
318	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
320	C₄²	C₂²×Dic₅	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	2	1	no	—
326	C₂×C₅	#1733	1	1	yes	characteristic
327	C₂×C₅	C₂×#340	1	1	yes	characteristic
328	C₂×C₅	C₂×#344	1	1	yes	characteristic
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	#3948	1	2	yes	—
332	C₂³	#3953	1	2	yes	—
333	C₂³	#3963	1	1	yes	characteristic
334	C₂³	#3963	1	1	yes	characteristic
335	C₂³	C₂×#685	1	1	yes	characteristic
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	20	4	no	—
349	C₂×C₄	—	20	4	no	—
350	C₂×C₄	—	20	4	no	—
351	C₂×C₄	#3948	1	2	yes	—
352	C₂×C₄	#3948	1	2	yes	—
353	C₂×C₄	#3948	1	2	yes	—
354	C₂×C₄	#3949	1	2	yes	—
355	C₂×C₄	#3949	1	2	yes	—
356	C₂×C₄	#3950	1	2	yes	—
357	C₂×C₄	#3950	1	2	yes	—
358	C₂×C₄	#3953	1	2	yes	—
359	C₂×C₄	#3953	1	2	yes	—
360	C₂×C₄	#3953	1	2	yes	—
361	C₂×C₄	#3963	1	1	yes	characteristic
362	C₂×C₄	#3963	1	1	yes	characteristic
363	C₂×C₄	#3963	1	1	yes	characteristic
364	C₂×C₄	#3963	1	1	yes	characteristic
365	C₂×C₄	#3963	1	1	yes	characteristic
366	C₂×C₄	#3963	1	1	yes	characteristic
367	C₂×C₄	C₂×#677	1	1	yes	characteristic
368	C₂×C₄	C₂×#677	1	1	yes	characteristic
369	C₂×C₄	C₂×D₄₀	1	1	yes	characteristic
370	C₂×C₄	C₂×Dic₂₀	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
372	C₂×C₄	C₂×#683	1	1	yes	characteristic
373	C₂×C₄	C₂×#683	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
375	C₂×C₄	C₂×#685	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
377	C₈	—	4	4	no	—
378	C₈	—	20	4	no	—
379	C₅	#8095	1	1	yes	characteristic, complemented, Sylow
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	#64771	1	2	yes	—
389	C₂²	#64771	1	2	yes	—
390	C₂²	C₂×#3948	1	1	yes	characteristic
391	C₂²	C₂×#3953	1	1	yes	characteristic
392	C₂²	C₂×#3963	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	40	4	no	—
400	C₄	#64771	1	2	yes	—
401	C₄	#64771	1	2	yes	—
402	C₄	#64779	1	2	yes	—
403	C₄	C₂×#3948	1	1	yes	characteristic
404	C₄	C₂×#3949	1	1	yes	characteristic
405	C₄	C₂×#3950	1	1	yes	characteristic
406	C₄	C₂×#3953	1	1	yes	characteristic
407	C₄	#65525	1	2	yes	—
408	C₂	—	2	1	no	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	1	no	—
412	C₂	#10602367	1	1	yes	characteristic
413	C₂	C₂×#64771	1	1	yes	characteristic
414	C₂	C₂×#64779	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#685
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×#431	C₂
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁴×C₅	C₂²⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×#431	D₅
hypocenter	C₅	#8095
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
4. #10598237	C₂	semidirect
10. C₅×#431	C₄	semidirect
12. C₂×C₅×C₄⋊C₈	C₄	semidirect
23. #65213	C₄	semidirect
26. C₂×C₄⋊#168	C₄	semidirect
132. #431	Dic₅	semidirect
140. C₂×C₄⋊C₈	Dic₅	semidirect
379. C₅	#8095	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#431	2
#10613793	2
C₂×#65213	2
#10598237	2
#8095	5