Subgroups — #12005194

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#106	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3949	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#10602356	C₂	1	2	yes	maximal
5	C₂×#64749	C₂	1	2	yes	maximal
6	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₅	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₅	C₂²	1	1	yes	characteristic
10	C₂³×#168	C₂²	1	1	yes	characteristic
11	C₂×C₅×#106	—	2	2	no	—
12	C₂×C₅×#106	—	2	2	no	—
13	C₂×C₅×#106	C₄	1	4	yes	complemented
14	C₂×#3963	—	2	4	no	—
15	C₂×#3949	—	2	2	no	—
16	C₂×#3949	—	2	2	no	—
17	C₂×#3949	C₄	1	4	yes	complemented
18	C₂×C₈×Dic₅	—	2	2	no	—
19	C₂×C₈×Dic₅	—	2	2	no	—
20	C₂×C₈×Dic₅	C₄	1	4	yes	complemented
21	#64749	—	2	4	no	—
22	#10861	—	5	1	no	maximal, Sylow
23	C₂³×C₄×C₅	—	2	2	no	—
24	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₂³×Dic₅	—	2	2	no	—
26	C₂³×Dic₅	D₄	1	2	yes	—
27	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
28	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
30	C₂²×C₅×C₈	D₄	1	2	yes	—
31	C₂²×C₅×C₈	D₄	1	2	yes	—
32	C₂²×C₅×C₈	D₄	1	2	yes	—
33	C₂²×C₅×C₈	Q₈	1	2	yes	—
34	C₂×C₅×C₄⋊C₄	—	2	2	no	—
35	C₂×C₅×C₄⋊C₄	—	2	2	no	—
36	C₂×C₅×C₄⋊C₄	—	2	2	no	—
37	C₂×C₅×C₄⋊C₄	—	2	2	no	—
38	C₂×C₅×C₄⋊C₄	—	2	2	no	—
39	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
40	C₂×C₄⋊Dic₅	—	2	2	no	—
41	C₂×C₄⋊Dic₅	—	2	2	no	—
42	C₂×C₄⋊Dic₅	—	2	2	no	—
43	C₂×C₄⋊Dic₅	—	2	2	no	—
44	C₂×C₄⋊Dic₅	—	2	2	no	—
45	C₂×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
46	C₂×C₄×Dic₅	—	2	1	no	—
47	C₂×C₄×Dic₅	—	2	1	no	—
48	C₂×C₄×Dic₅	—	2	1	no	—
49	C₂×C₄×Dic₅	—	2	1	no	—
50	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₅	Q₈	1	2	yes	—
52	C₂²×#168	—	2	1	no	—
53	C₂²×#168	—	2	1	no	—
54	C₂²×#168	—	2	1	no	—
55	C₂²×#168	—	2	1	no	—
56	C₂²×#168	C₂×C₄	1	2	yes	—
57	C₂²×#168	D₄	1	2	yes	—
58	C₂²×#168	Q₈	1	2	yes	—
59	C₅×#106	—	2	8	no	—
60	#3963	—	4	8	no	—
61	#3949	—	2	8	no	—
62	C₈×Dic₅	—	2	8	no	—
63	C₂²×#106	—	5	1	no	—
64	C₂²×#106	D₅	1	1	yes	characteristic
65	C₂²×C₄×C₈	—	5	1	no	—
66	C₂×#340	—	5	2	no	—
67	C₄⋊#95	—	5	2	no	—
68	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₅	—	2	4	no	—
70	C₂²×C₄×C₅	—	4	2	no	—
71	C₂²×C₄×C₅	—	4	2	no	—
72	C₂²×C₄×C₅	—	4	4	no	—
73	C₂²×C₄×C₅	—	4	4	no	—
74	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₅	#41	1	1	yes	characteristic
85	C₂²×C₄×C₅	#41	1	1	yes	characteristic
86	C₂²×C₄×C₅	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅	#41	1	1	yes	characteristic
88	C₂²×Dic₅	—	2	2	no	—
89	C₂²×Dic₅	—	2	2	no	—
90	C₂²×Dic₅	—	2	4	no	—
91	C₂²×Dic₅	—	2	4	no	—
92	C₂²×Dic₅	—	4	2	no	—
93	C₂²×Dic₅	—	4	2	no	—
94	C₂²×Dic₅	—	4	4	no	—
95	C₂²×Dic₅	—	4	4	no	—
96	C₂²×Dic₅	C₄⋊C₄	1	4	yes	—
97	C₂²×Dic₅	SD₁₆	1	8	yes	—
98	C₂×C₅×C₈	C₄²	1	4	yes	—
99	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
100	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
101	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
102	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
103	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
104	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
105	C₅×C₄⋊C₄	—	2	4	no	—
106	C₅×C₄⋊C₄	—	2	4	no	—
107	C₅×C₄⋊C₄	—	4	2	no	—
108	C₅×C₄⋊C₄	—	4	2	no	—
109	C₄⋊Dic₅	—	2	4	no	—
110	C₄⋊Dic₅	—	2	4	no	—
111	C₄⋊Dic₅	—	4	2	no	—
112	C₄⋊Dic₅	—	4	2	no	—
113	C₄×Dic₅	—	2	2	no	—
114	C₄×Dic₅	—	2	2	no	—
115	C₄×Dic₅	—	2	2	no	—
116	C₄×Dic₅	—	2	2	no	—
117	C₂×#168	—	2	2	no	—
118	C₂×#168	—	2	2	no	—
119	C₂×#168	—	2	2	no	—
120	C₂×#168	—	2	2	no	—
121	C₂×#168	—	2	2	no	—
122	C₂×#168	—	2	2	no	—
123	C₂×#168	C₄⋊C₄	1	4	yes	—
124	C₂³×C₈	—	5	1	no	—
125	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
126	C₂²×C₄⋊C₄	—	5	2	no	—
127	C₂²×C₄⋊C₄	C₂×D₅	1	2	yes	—
128	C₂²×C₄²	—	5	1	no	—
129	C₂×#106	—	2	2	no	—
130	C₂×#106	—	2	2	no	—
131	C₂×#106	—	5	4	no	—
132	C₂×#106	—	10	2	no	—
133	C₂×#106	—	10	2	no	—
134	C₂×#106	Dic₅	1	4	yes	complemented
135	C₂×C₄×C₈	—	5	4	no	—
136	C₂×C₄×C₈	—	10	2	no	—
137	C₂×C₄×C₈	—	10	2	no	—
138	C₂×#95	—	10	4	no	—
139	#340	—	10	4	no	—
140	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
142	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
143	C₂³×C₅	#121	1	1	yes	characteristic
144	C₂³×C₅	#121	1	1	yes	characteristic
145	C₂³×C₅	#127	1	1	yes	characteristic
146	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
147	C₂³×C₅	C₂×SD₁₆	1	4	yes	—
148	C₂³×C₅	#135	1	4	yes	—
149	C₂×C₄×C₅	—	4	4	no	—
150	C₂×C₄×C₅	—	4	8	no	—
151	C₂×C₄×C₅	—	8	4	no	—
152	C₂×C₄×C₅	—	8	2	no	—
153	C₂×C₄×C₅	—	8	2	no	—
154	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	#117	1	1	yes	characteristic
163	C₂×C₄×C₅	#117	1	1	yes	characteristic
164	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅	#121	1	1	yes	characteristic
171	C₂×C₄×C₅	#121	1	1	yes	characteristic
172	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₅	#124	1	1	yes	characteristic
177	C₂×C₄×C₅	#124	1	1	yes	characteristic
178	C₂×C₄×C₅	#125	1	1	yes	characteristic
179	C₂×C₄×C₅	#125	1	1	yes	characteristic
180	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
182	C₂×Dic₅	—	2	4	no	—
183	C₂×Dic₅	—	2	4	no	—
184	C₂×Dic₅	—	2	8	no	—
185	C₂×Dic₅	—	2	8	no	—
186	C₂×Dic₅	—	4	4	no	—
187	C₂×Dic₅	—	4	8	no	—
188	C₂×Dic₅	—	8	4	no	—
189	C₂×Dic₅	—	8	2	no	—
190	C₂×Dic₅	—	8	2	no	—
191	C₂×Dic₅	#106	1	8	yes	complemented
192	C₅×C₈	#95	1	8	yes	complemented
193	#168	—	2	4	no	—
194	C₂³×C₄	—	2	2	no	—
195	C₂³×C₄	—	5	2	no	—
196	C₂³×C₄	—	10	2	no	—
197	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
198	C₂²×C₈	—	5	2	no	—
199	C₂²×C₈	—	5	2	no	—
200	C₂²×C₈	—	5	2	no	—
201	C₂²×C₈	—	10	1	no	—
202	C₂²×C₈	—	10	1	no	—
203	C₂²×C₈	—	10	1	no	—
204	C₂²×C₈	—	10	1	no	—
205	C₂²×C₈	Dic₁₀	1	2	yes	—
206	C₂²×C₈	C₄×D₅	1	2	yes	—
207	C₂²×C₈	C₄×D₅	1	2	yes	—
208	C₂²×C₈	D₂₀	1	2	yes	—
209	C₂²×C₈	C₂×Dic₅	1	2	yes	—
210	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
211	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	5	4	no	—
218	C₂×C₄⋊C₄	—	10	2	no	—
219	C₂×C₄⋊C₄	—	10	2	no	—
220	C₂×C₄⋊C₄	—	10	2	no	—
221	C₂×C₄⋊C₄	—	10	2	no	—
222	C₂×C₄⋊C₄	—	10	2	no	—
223	C₂×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
224	C₂×C₄²	—	5	2	no	—
225	C₂×C₄²	—	5	2	no	—
226	C₂×C₄²	—	10	1	no	—
227	C₂×C₄²	—	10	1	no	—
228	C₂×C₄²	—	10	1	no	—
229	C₂×C₄²	—	10	1	no	—
230	#106	—	2	8	no	—
231	#106	—	10	8	no	—
232	C₄×C₈	—	10	8	no	—
233	#95	—	20	8	no	—
234	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₅	#380	1	1	yes	characteristic
236	C₂²×C₅	#384	1	1	yes	characteristic
237	C₂²×C₅	#389	1	1	yes	characteristic
238	C₂²×C₅	#389	1	1	yes	characteristic
239	C₂²×C₅	#390	1	1	yes	characteristic
240	C₂²×C₅	#390	1	1	yes	characteristic
241	C₂²×C₅	C₂×#106	1	2	yes	—
242	C₂²×C₅	#427	1	2	yes	—
243	C₂²×C₅	C₄×SD₁₆	1	4	yes	—
244	C₂²×C₅	C₄×SD₁₆	1	4	yes	—
245	C₂²×C₅	#465	1	4	yes	—
246	C₂²×C₅	#465	1	4	yes	—
247	C₂²×C₅	#492	1	2	yes	—
248	C₂²×C₅	#495	1	2	yes	—
249	C₂²×C₅	#498	1	2	yes	—
250	C₂²×C₅	#499	1	2	yes	—
251	C₄×C₅	—	8	4	no	—
252	C₄×C₅	C₂×#95	1	1	yes	characteristic
253	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
254	C₄×C₅	#380	1	1	yes	characteristic
255	C₄×C₅	#382	1	1	yes	characteristic
256	C₄×C₅	#389	1	1	yes	characteristic
257	C₄×C₅	#389	1	1	yes	characteristic
258	C₄×C₅	#391	1	1	yes	characteristic
259	C₄×C₅	#391	1	1	yes	characteristic
260	Dic₅	—	2	8	no	—
261	Dic₅	—	8	4	no	—
262	C₂⁴	D₄×D₅	1	1	yes	characteristic
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	5	4	no	—
269	C₂²×C₄	—	5	8	no	—
270	C₂²×C₄	—	10	2	no	—
271	C₂²×C₄	—	10	4	no	—
272	C₂²×C₄	—	10	2	no	—
273	C₂²×C₄	—	10	4	no	—
274	C₂²×C₄	—	20	2	no	—
275	C₂²×C₄	—	20	4	no	—
276	C₂²×C₄	—	20	4	no	—
277	C₂²×C₄	—	20	2	no	—
278	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
282	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
283	C₂²×C₄	#711	1	1	yes	characteristic
284	C₂²×C₄	#711	1	1	yes	characteristic
285	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
286	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
287	C₂²×C₄	#713	1	1	yes	characteristic
288	C₂²×C₄	#713	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
292	C₂×C₈	—	5	4	no	—
293	C₂×C₈	—	10	2	no	—
294	C₂×C₈	—	10	2	no	—
295	C₂×C₈	—	10	2	no	—
296	C₂×C₈	—	10	2	no	—
297	C₂×C₈	—	10	2	no	—
298	C₂×C₈	—	10	2	no	—
299	C₂×C₈	C₄×Dic₅	1	4	yes	—
300	C₂×C₈	#683	1	4	yes	—
301	C₂×C₈	#683	1	4	yes	—
302	C₂×C₈	C₄⋊Dic₅	1	4	yes	—
303	C₂×C₈	#685	1	4	yes	—
304	C₂×C₈	#685	1	4	yes	—
305	C₂×C₈	C₂²⋊Dic₅	1	4	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	10	4	no	—
311	C₄⋊C₄	—	10	4	no	—
312	C₄⋊C₄	—	20	2	no	—
313	C₄⋊C₄	—	20	2	no	—
314	C₄²	—	10	2	no	—
315	C₄²	—	10	2	no	—
316	C₄²	—	10	2	no	—
317	C₄²	—	10	2	no	—
318	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
319	C₂×C₅	C₄×#106	1	2	yes	—
320	C₂×C₅	#1807	1	2	yes	—
321	C₂×C₅	#1844	1	1	yes	characteristic
322	C₂×C₅	#1846	1	1	yes	characteristic
323	C₂×C₅	#1941	1	2	yes	—
324	C₂×C₅	#1941	1	2	yes	—
325	C₂×C₅	#1968	1	2	yes	—
326	C₂×C₅	#1968	1	2	yes	—
327	C₂³	#4034	1	1	yes	characteristic
328	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
329	C₂³	#4039	1	1	yes	characteristic
330	C₂³	#4041	1	1	yes	characteristic
331	C₂³	D₅×SD₁₆	1	4	yes	—
332	C₂³	#4062	1	4	yes	—
333	C₂³	D₄×Dic₅	1	1	yes	characteristic
334	C₂³	#4084	1	1	yes	characteristic
335	C₂³	#4086	1	1	yes	characteristic
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	5	8	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	10	4	no	—
343	C₂×C₄	—	10	8	no	—
344	C₂×C₄	—	10	8	no	—
345	C₂×C₄	—	10	4	no	—
346	C₂×C₄	—	20	8	no	—
347	C₂×C₄	—	20	4	no	—
348	C₂×C₄	—	40	4	no	—
349	C₂×C₄	—	40	2	no	—
350	C₂×C₄	—	40	2	no	—
351	C₂×C₄	#4033	1	1	yes	characteristic
352	C₂×C₄	#4033	1	1	yes	characteristic
353	C₂×C₄	#4034	1	1	yes	characteristic
354	C₂×C₄	#4036	1	1	yes	characteristic
355	C₂×C₄	#4036	1	1	yes	characteristic
356	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₄	#4038	1	1	yes	characteristic
358	C₂×C₄	#4038	1	1	yes	characteristic
359	C₂×C₄	#4039	1	1	yes	characteristic
360	C₂×C₄	#4041	1	1	yes	characteristic
361	C₂×C₄	#4043	1	1	yes	characteristic
362	C₂×C₄	#4043	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
364	C₂×C₄	C₂×#683	1	1	yes	characteristic
365	C₂×C₄	C₂×#683	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
367	C₂×C₄	C₂×#685	1	1	yes	characteristic
368	C₂×C₄	C₂×#685	1	1	yes	characteristic
369	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
370	C₂×C₄	#4082	1	1	yes	characteristic
371	C₂×C₄	#4084	1	1	yes	characteristic
372	C₂×C₄	#4090	1	1	yes	characteristic
373	C₂×C₄	Q₈×Dic₅	1	1	yes	characteristic
374	C₂×C₄	Q₈×Dic₅	1	1	yes	characteristic
375	C₂×C₄	#4092	1	1	yes	characteristic
376	C₂×C₄	#4092	1	1	yes	characteristic
377	C₂×C₄	#4093	1	1	yes	characteristic
378	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
379	C₈	—	10	4	no	—
380	C₈	#3963	1	8	yes	complemented
381	C₅	#10861	1	1	yes	characteristic, complemented, Sylow
382	C₂²	#65141	1	4	yes	—
383	C₂²	#65144	1	2	yes	—
384	C₂²	#65147	1	2	yes	—
385	C₂²	D₅×#106	1	2	yes	—
386	C₂²	#65149	1	2	yes	—
387	C₂²	#65153	1	4	yes	—
388	C₂²	#65262	1	1	yes	characteristic
389	C₂²	C₄⋊C₄×Dic₅	1	1	yes	characteristic
390	C₂²	#65265	1	1	yes	characteristic
391	C₂²	#65274	1	1	yes	characteristic
392	C₂²	#65276	1	1	yes	characteristic
393	C₂²	#65277	1	1	yes	characteristic
394	C₂²	SD₁₆×Dic₅	1	4	yes	—
395	C₂²	#65457	1	2	yes	—
396	C₂²	#65460	1	4	yes	—
397	C₂²	#65464	1	2	yes	—
398	C₂²	#65510	1	1	yes	characteristic
399	C₄	—	8	4	no	—
400	C₄	—	10	8	no	—
401	C₄	—	40	4	no	—
402	C₄	#65262	1	1	yes	characteristic
403	C₄	#65263	1	1	yes	characteristic
404	C₄	C₄⋊C₄×Dic₅	1	1	yes	characteristic
405	C₄	#65266	1	1	yes	characteristic
406	C₄	#65274	1	1	yes	characteristic
407	C₄	#65276	1	1	yes	characteristic
408	C₄	C₂×#3963	1	1	yes	characteristic
409	C₄	#65519	1	1	yes	characteristic
410	C₂	Dic₅×#106	1	2	yes	—
411	C₂	#10601347	1	1	yes	characteristic
412	C₂	#10601348	1	1	yes	characteristic
413	C₂	#10601352	1	2	yes	—
414	C₂	#10601353	1	2	yes	—
415	C₂	#10601367	1	2	yes	—
416	C₂	#10601370	1	2	yes	—
417	C₂	#10602356	1	1	yes	characteristic
418	C₂	#10602842	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₅
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅
Fitting	C₂²×C₅×#106	C₂
socle, prime radical	C₂⁴×C₅	C₂×D₄
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂²×#106	D₅
hypocenter	C₅	#10861
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#106

Complements

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

N	H ≅ G/N	type
13. C₂×C₅×#106	C₄	semidirect
17. C₂×#3949	C₄	semidirect
20. C₂×C₈×Dic₅	C₄	semidirect
134. C₂×#106	Dic₅	semidirect
191. C₂×Dic₅	#106	semidirect
192. C₅×C₈	#95	semidirect
380. C₈	#3963	semidirect
381. C₅	#10861	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#106	2
C₂²×#3949	2
C₂²×C₈×Dic₅	2
#10602356	2
C₂×#64749	2
#10861	5