Subgroups — #11989249

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×#65214	C₂	1	1	yes	maximal, characteristic
3	C₂×#65213	C₂	1	1	yes	maximal, characteristic
4	#10598202	C₂	1	4	yes	maximal, complemented
5	C₂²×C₅×M₁₆	—	2	1	no	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂²×#681	—	2	1	no	—
8	C₅×#423	—	2	1	no	—
9	C₅×#423	—	2	1	no	—
10	C₅×#423	C₄	1	2	yes	—
11	C₅×#423	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₈	—	2	1	no	—
13	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	—
14	C₂×C₂²⋊#168	C₄	1	2	yes	—
15	#65214	—	2	1	no	—
16	#65214	—	2	1	no	—
17	#65214	—	2	1	no	—
18	#65214	—	2	1	no	—
19	#65213	—	2	1	no	—
20	#65213	—	2	1	no	—
21	#65213	C₄	1	2	yes	—
22	#65213	C₂²	1	2	yes	—
23	C₂×C₄⋊#168	—	2	1	no	—
24	C₂×C₄⋊#168	C₄	1	2	yes	—
25	C₂×C₄⋊#168	C₂²	1	2	yes	—
26	C₂×C₄×#168	C₄	1	2	yes	—
27	#8001	—	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	Q₈	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	4	2	no	—
34	C₂×C₅×M₁₆	—	4	2	no	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₂×#681	—	2	2	no	—
49	C₂×#681	—	2	2	no	—
50	C₂×#681	—	4	2	no	—
51	C₂×#681	—	4	2	no	—
52	C₂²×#168	—	2	2	no	—
53	C₂²×#168	C₂×C₄	1	4	yes	—
54	C₅×C₄⋊C₈	—	2	2	no	—
55	C₅×C₄⋊C₈	—	2	2	no	—
56	C₅×C₄⋊C₈	—	2	2	no	—
57	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
58	C₂²⋊#168	—	2	2	no	—
59	C₂²⋊#168	—	2	2	no	—
60	C₄⋊#168	—	2	2	no	—
61	C₄⋊#168	—	2	2	no	—
62	C₄⋊#168	—	2	2	no	—
63	C₄⋊#168	—	2	2	no	—
64	C₄⋊#168	—	2	2	no	—
65	C₄⋊#168	C₂×C₄	1	4	yes	—
66	C₄×#168	—	2	2	no	—
67	C₄×#168	—	2	2	no	—
68	C₂×#431	—	5	1	no	—
69	C₂×#423	—	5	1	no	—
70	C₂×#423	D₅	1	1	yes	characteristic
71	#1292	—	5	4	no	—
72	C₂⁴×C₅	C₄⋊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	C₄⋊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×Q₈	1	1	yes	characteristic
97	C₅×M₁₆	—	4	4	no	—
98	C₅×M₁₆	—	4	2	no	—
99	C₅×M₁₆	—	4	2	no	—
100	C₂×C₅×C₈	—	2	4	no	—
101	C₂×C₅×C₈	—	4	4	no	—
102	C₄²×C₅	C₄²	1	1	yes	characteristic
103	C₄²×C₅	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
118	#681	—	4	4	no	—
119	#681	—	4	2	no	—
120	#681	—	4	2	no	—
121	C₂×#168	—	2	4	no	—
122	C₂×#168	—	2	4	no	—
123	C₂×#168	—	4	4	no	—
124	C₂×#168	—	4	4	no	—
125	C₂²×M₁₆	—	2	1	no	—
126	C₂²×M₁₆	—	10	1	no	—
127	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
128	#431	—	10	1	no	—
129	#431	—	10	1	no	—
130	#431	—	10	1	no	—
131	#431	—	10	1	no	—
132	#423	—	2	1	no	—
133	#423	—	2	1	no	—
134	#423	—	5	2	no	—
135	#423	—	5	2	no	—
136	#423	—	10	1	no	—
137	#423	—	10	1	no	—
138	#423	Dic₅	1	2	yes	—
139	#423	C₂×D₅	1	2	yes	—
140	C₂×C₄⋊C₈	—	2	1	no	—
141	C₂×C₄⋊C₈	—	5	2	no	—
142	C₂×C₄⋊C₈	—	5	2	no	—
143	C₂×C₄⋊C₈	—	10	1	no	—
144	C₂×C₄⋊C₈	Dic₅	1	2	yes	—
145	C₂×C₂²⋊C₈	—	5	2	no	—
146	C₂×C₄×C₈	—	5	2	no	—
147	C₂³×C₅	—	4	1	no	—
148	C₂³×C₅	—	4	1	no	—
149	C₂³×C₅	#95	1	1	yes	characteristic
150	C₂³×C₅	#95	1	1	yes	characteristic
151	C₂³×C₅	#106	1	2	yes	—
152	C₂³×C₅	#107	1	2	yes	—
153	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
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	—	4	1	no	—
161	C₂×C₄×C₅	—	4	1	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	#95	1	1	yes	characteristic
167	C₂×C₄×C₅	#95	1	1	yes	characteristic
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	#102	1	2	yes	—
173	C₂×C₄×C₅	#102	1	2	yes	—
174	C₂×C₄×C₅	#102	1	2	yes	—
175	C₂×C₄×C₅	#102	1	2	yes	—
176	C₂×C₄×C₅	#103	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	#107	1	2	yes	—
182	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
192	C₅×C₈	—	4	4	no	—
193	#168	—	4	4	no	—
194	#168	—	4	4	no	—
195	C₂³×C₄	Dic₁₀	1	1	yes	characteristic
196	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
197	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	4	2	no	—
201	C₂×M₁₆	—	4	2	no	—
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	—	5	4	no	—
208	C₂²×C₈	—	10	2	no	—
209	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
210	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
211	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
212	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₂×C₄²	D₂₀	1	1	yes	characteristic
214	C₂×C₄²	D₂₀	1	1	yes	characteristic
215	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
216	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
217	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
218	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
219	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
220	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	5	4	no	—
225	C₄⋊C₈	—	10	2	no	—
226	C₄⋊C₈	—	10	2	no	—
227	C₄⋊C₈	—	10	2	no	—
228	C₄⋊C₈	—	10	2	no	—
229	C₄⋊C₈	—	10	2	no	—
230	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
231	C₂²⋊C₈	—	10	2	no	—
232	C₂²⋊C₈	—	10	2	no	—
233	C₄×C₈	—	10	2	no	—
234	C₄×C₈	—	10	2	no	—
235	C₂²×C₅	—	2	1	no	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	2	1	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	4	2	no	—
242	C₂²×C₅	—	4	2	no	—
243	C₂²×C₅	#340	1	2	yes	—
244	C₂²×C₅	#340	1	2	yes	—
245	C₂²×C₅	C₂×#95	1	1	yes	characteristic
246	C₂²×C₅	C₂×#106	1	1	yes	characteristic
247	C₂²×C₅	C₂×#107	1	1	yes	characteristic
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	—	2	1	no	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	#338	1	2	yes	—
255	C₄×C₅	#340	1	2	yes	—
256	C₄×C₅	#340	1	2	yes	—
257	C₄×C₅	#413	1	2	yes	—
258	C₄×C₅	C₂×#102	1	1	yes	characteristic
259	C₄×C₅	C₂×#102	1	1	yes	characteristic
260	C₄×C₅	C₂×#103	1	1	yes	characteristic
261	C₄×C₅	C₂×#103	1	1	yes	characteristic
262	C₂⁴	#683	1	1	yes	characteristic
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
266	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
267	C₂²×C₄	#683	1	1	yes	characteristic
268	C₂²×C₄	#683	1	1	yes	characteristic
269	C₂²×C₄	#683	1	1	yes	characteristic
270	C₂²×C₄	#683	1	1	yes	characteristic
271	C₂²×C₄	#683	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
274	C₂²×C₄	#685	1	1	yes	characteristic
275	C₂²×C₄	#685	1	1	yes	characteristic
276	C₂²×C₄	#685	1	1	yes	characteristic
277	C₂²×C₄	#685	1	1	yes	characteristic
278	C₂²×C₄	#686	1	2	yes	—
279	C₂²×C₄	#687	1	2	yes	—
280	C₂²×C₄	#688	1	2	yes	—
281	C₂²×C₄	#689	1	2	yes	—
282	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
284	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	M₁₆	—	4	4	no	—
288	M₁₆	—	4	2	no	—
289	M₁₆	—	4	2	no	—
290	M₁₆	—	20	4	no	—
291	M₁₆	—	20	2	no	—
292	M₁₆	—	20	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	4	4	no	—
295	C₂×C₈	—	10	4	no	—
296	C₂×C₈	—	10	4	no	—
297	C₂×C₈	—	20	4	no	—
298	C₂×C₈	—	20	4	no	—
299	C₄²	C₄×Dic₅	1	1	yes	characteristic
300	C₄²	C₄×Dic₅	1	1	yes	characteristic
301	C₄²	#683	1	1	yes	characteristic
302	C₄²	#683	1	1	yes	characteristic
303	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
304	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
305	C₄²	#685	1	1	yes	characteristic
306	C₄²	#685	1	1	yes	characteristic
307	C₄²	#685	1	1	yes	characteristic
308	C₄²	#685	1	1	yes	characteristic
309	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
310	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
311	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
312	C₄²	C₂×D₂₀	1	1	yes	characteristic
313	C₄²	C₂²×Dic₅	1	1	yes	characteristic
314	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	2	2	no	—
317	C₂×C₅	—	2	1	no	—
318	C₂×C₅	—	2	1	no	—
319	C₂×C₅	C₂×#338	1	1	yes	characteristic
320	C₂×C₅	C₂×#340	1	1	yes	characteristic
321	C₂×C₅	#1742	1	1	yes	characteristic
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	#3939	1	2	yes	—
325	C₂³	#3940	1	2	yes	—
326	C₂³	#3963	1	1	yes	characteristic
327	C₂³	#3963	1	1	yes	characteristic
328	C₂³	C₂×#683	1	1	yes	characteristic
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	#3939	1	2	yes	—
342	C₂×C₄	#3940	1	2	yes	—
343	C₂×C₄	#3941	1	2	yes	—
344	C₂×C₄	#3941	1	2	yes	—
345	C₂×C₄	#3942	1	2	yes	—
346	C₂×C₄	#3942	1	2	yes	—
347	C₂×C₄	#3963	1	1	yes	characteristic
348	C₂×C₄	#3963	1	1	yes	characteristic
349	C₂×C₄	#3963	1	1	yes	characteristic
350	C₂×C₄	#3963	1	1	yes	characteristic
351	C₂×C₄	#3963	1	1	yes	characteristic
352	C₂×C₄	#3963	1	1	yes	characteristic
353	C₂×C₄	#3964	1	2	yes	—
354	C₂×C₄	#3964	1	2	yes	—
355	C₂×C₄	#3967	1	2	yes	—
356	C₂×C₄	#3967	1	2	yes	—
357	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
358	C₂×C₄	C₂×#683	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
360	C₂×C₄	C₂×#685	1	1	yes	characteristic
361	C₂×C₄	C₂×#685	1	1	yes	characteristic
362	C₂×C₄	C₂×#686	1	1	yes	characteristic
363	C₂×C₄	C₂×#687	1	1	yes	characteristic
364	C₂×C₄	C₂×#688	1	1	yes	characteristic
365	C₂×C₄	C₂×#689	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
367	C₈	—	4	4	no	—
368	C₈	—	20	4	no	—
369	C₈	—	20	4	no	—
370	C₅	#8001	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	#64749	1	2	yes	—
380	C₂²	#64749	1	2	yes	—
381	C₂²	C₂×#3939	1	1	yes	characteristic
382	C₂²	C₂×#3940	1	1	yes	characteristic
383	C₂²	C₂×#3963	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	#64749	1	2	yes	—
391	C₄	#64749	1	2	yes	—
392	C₄	#64780	1	2	yes	—
393	C₄	C₂×#3941	1	1	yes	characteristic
394	C₄	C₂×#3942	1	1	yes	characteristic
395	C₄	#65421	1	2	yes	—
396	C₄	C₂×#3964	1	1	yes	characteristic
397	C₄	C₂×#3967	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	C₂×#64749	1	1	yes	characteristic
403	C₂	#10602780	1	1	yes	characteristic
404	C₂	C₂×#64780	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3963
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×#423	C₂
socle	C₂²×C₅	C₂×#95
prime radical	C₂⁴×C₅	C₄⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×#423	D₅
hypocenter	C₅	#8001
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
4. #10598202	C₂	semidirect
370. C₅	#8001	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₂×#65214	2
C₂×#65213	2
#10598202	2
#8001	5