Subgroups — #12252408

Order 1280.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64978	C₂	1	1	yes	maximal, characteristic
2	C₅×#2163	C₂	1	1	yes	maximal, characteristic, complemented
3	#10600537	C₂	1	1	yes	maximal, characteristic, complemented
4	#10600078	C₂	1	2	yes	maximal, complemented
5	#10600069	C₂	1	2	yes	maximal, complemented
6	#10599899	C₂	1	1	yes	maximal, characteristic
7	D₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
8	#10599886	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599885	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599867	C₂	1	2	yes	maximal, complemented
11	#10599865	C₂	1	2	yes	maximal, complemented
12	C₂²×#676	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
14	C₂×#4018	C₄	1	1	yes	characteristic
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×#3947	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×#3935	C₄	1	1	yes	characteristic
19	C₂×#3930	C₂²	1	2	yes	—
20	C₂×D₅×C₁₆	C₂²	1	2	yes	—
21	#64978	C₄	1	1	yes	characteristic
22	#64978	C₄	1	1	yes	characteristic
23	#64978	C₄	1	1	yes	characteristic
24	#64978	C₄	1	1	yes	characteristic
25	#64978	C₂²	1	1	yes	characteristic
26	#64978	C₂²	1	1	yes	characteristic
27	#64978	C₂²	1	1	yes	characteristic
28	#64978	C₂²	1	1	yes	characteristic
29	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
30	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₅×#346	C₂²	1	2	yes	complemented
33	C₂²⋊#672	C₂²	1	1	yes	characteristic
34	C₂²⋊#672	C₂²	1	1	yes	characteristic
35	#64727	C₂²	1	2	yes	—
36	#64727	C₂²	1	2	yes	—
37	#64722	C₂²	1	2	yes	complemented
38	#64721	C₂²	1	2	yes	complemented
39	#64721	C₂²	1	2	yes	complemented
40	C₁₆×Dic₅	C₂²	1	2	yes	complemented
41	C₄⋊#672	C₂²	1	2	yes	complemented
42	C₄×#672	C₂²	1	2	yes	complemented
43	#33422	—	5	1	no	maximal, Sylow
44	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂×#685	C₈	1	1	yes	characteristic
49	C₂×#685	C₈	1	1	yes	characteristic
50	C₂×#683	C₈	1	1	yes	characteristic
51	C₂×#683	C₈	1	1	yes	characteristic
52	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×#168	C₂×C₄	1	1	yes	characteristic
54	C₂²×#168	C₂×C₄	1	1	yes	characteristic
55	C₂×#676	—	2	4	no	—
56	C₂×#676	C₂×C₄	1	1	yes	characteristic
57	C₂×#676	C₂×C₄	1	1	yes	characteristic
58	C₂×#676	C₂×C₄	1	1	yes	characteristic
59	C₂×#676	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₅	—	2	4	no	—
61	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
65	#4018	C₈	1	1	yes	characteristic
66	#4018	C₈	1	1	yes	characteristic
67	#4018	C₈	1	1	yes	characteristic
68	#4018	C₈	1	1	yes	characteristic
69	#4018	C₂×C₄	1	1	yes	characteristic
70	#4018	C₂×C₄	1	1	yes	characteristic
71	#4018	C₂×C₄	1	1	yes	characteristic
72	#4018	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₁₆	C₂³	1	2	yes	—
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	#3947	C₂×C₄	1	1	yes	characteristic
80	#3947	C₂×C₄	1	1	yes	characteristic
81	#3947	C₂×C₄	1	1	yes	characteristic
82	#3947	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₅	C₂³	1	1	yes	characteristic
86	C₈×Dic₅	C₂³	1	1	yes	characteristic
87	C₂×#672	C₂³	1	2	yes	—
88	C₂×#672	C₂³	1	2	yes	—
89	#3935	C₂×C₄	1	1	yes	characteristic
90	#3935	C₂×C₄	1	1	yes	characteristic
91	#3935	C₂×C₄	1	1	yes	characteristic
92	#3935	C₂×C₄	1	1	yes	characteristic
93	#3930	—	2	4	no	—
94	D₅×C₁₆	—	2	4	no	—
95	C₂×#405	—	5	1	no	—
96	#2164	—	5	2	no	—
97	#2164	—	5	2	no	—
98	#2163	—	5	1	no	—
99	#2163	D₅	1	1	yes	characteristic, complemented
100	#2162	—	5	1	no	—
101	#2162	—	5	1	no	—
102	#2151	—	5	2	no	—
103	#2112	—	5	1	no	—
104	C₂×C₂²⋊C₁₆	—	5	1	no	—
105	#2108	—	5	2	no	—
106	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
111	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₅	—	2	2	no	—
114	C₂×C₄×D₅	—	2	2	no	—
115	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
125	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
126	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
127	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
129	#685	C₂×C₈	1	1	yes	characteristic
130	#685	C₂×C₈	1	1	yes	characteristic
131	#685	C₂×C₈	1	1	yes	characteristic
132	#685	C₂×C₈	1	1	yes	characteristic
133	#685	C₂×C₈	1	1	yes	characteristic
134	#685	C₂×C₈	1	1	yes	characteristic
135	#685	C₂×C₈	1	1	yes	characteristic
136	#685	C₂×C₈	1	1	yes	characteristic
137	#683	C₂×C₈	1	1	yes	characteristic
138	#683	C₂×C₈	1	1	yes	characteristic
139	#683	C₂×C₈	1	1	yes	characteristic
140	#683	C₂×C₈	1	1	yes	characteristic
141	#683	C₂×C₈	1	1	yes	characteristic
142	#683	C₂×C₈	1	1	yes	characteristic
143	#683	C₂×C₈	1	1	yes	characteristic
144	#683	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
149	C₂×#168	—	2	2	no	—
150	C₂×#168	—	2	2	no	—
151	C₂×#168	C₂²×C₄	1	1	yes	characteristic
152	C₂×#168	C₂²×C₄	1	1	yes	characteristic
153	C₂×#168	C₂²×C₄	1	1	yes	characteristic
154	C₂×#168	C₂²×C₄	1	1	yes	characteristic
155	#676	—	2	2	no	—
156	#676	—	2	2	no	—
157	#676	—	2	2	no	—
158	#676	M₁₆	1	4	yes	—
159	C₈×D₅	—	2	2	no	—
160	C₈×D₅	—	2	2	no	—
161	C₈×D₅	—	2	2	no	—
162	C₈×D₅	#41	1	4	yes	—
163	C₅×C₁₆	—	2	2	no	—
164	C₅×C₁₆	—	2	2	no	—
165	#672	—	2	2	no	—
166	#672	—	2	2	no	—
167	C₂²×M₁₆	—	5	1	no	—
168	C₂³×C₈	—	5	1	no	—
169	C₂×#117	—	5	1	no	—
170	C₂×M₃₂	—	5	2	no	—
171	C₂²×C₁₆	—	5	2	no	—
172	#405	—	5	1	no	—
173	#405	—	5	1	no	—
174	#405	—	5	1	no	—
175	#405	—	5	1	no	—
176	#405	—	5	1	no	—
177	#405	—	5	1	no	—
178	#405	—	5	1	no	—
179	#405	—	5	1	no	—
180	C₂×#97	—	5	1	no	—
181	C₂×#97	—	5	1	no	—
182	C₂×C₄×C₈	—	5	1	no	—
183	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
184	C₄⋊C₁₆	—	5	2	no	—
185	C₄⋊C₁₆	—	5	2	no	—
186	C₄⋊C₁₆	—	5	2	no	—
187	C₄⋊C₁₆	C₂×D₅	1	2	yes	complemented
188	C₂²⋊C₁₆	—	5	1	no	—
189	C₂²⋊C₁₆	—	5	1	no	—
190	C₂²⋊C₁₆	—	5	2	no	—
191	C₂²⋊C₁₆	—	5	2	no	—
192	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic
193	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic
194	#346	—	5	2	no	—
195	#346	C₂×D₅	1	2	yes	complemented
196	C₄×C₁₆	—	5	2	no	—
197	C₄×C₁₆	—	5	2	no	—
198	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
199	C₂²×D₅	—	2	2	no	—
200	C₂²×D₅	—	2	2	no	—
201	C₂²×D₅	—	4	1	no	—
202	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	4	1	no	—
217	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
219	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
220	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
221	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
222	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
223	C₄×D₅	—	2	2	no	—
224	C₄×D₅	—	2	1	no	—
225	C₄×D₅	—	2	1	no	—
226	C₄×D₅	—	2	2	no	—
227	C₄×D₅	#117	1	2	yes	—
228	C₄×D₅	C₂×M₁₆	1	2	yes	—
229	C₅×C₈	—	2	1	no	—
230	C₅×C₈	—	2	1	no	—
231	C₅×C₈	C₂×M₁₆	1	2	yes	—
232	C₅×C₈	C₂×#41	1	2	yes	—
233	#168	—	2	1	no	—
234	#168	—	2	1	no	—
235	#168	#117	1	2	yes	—
236	#168	C₂×M₁₆	1	2	yes	—
237	C₂³×C₄	—	5	1	no	—
238	C₂×M₁₆	—	5	1	no	—
239	C₂×M₁₆	—	5	1	no	—
240	C₂×M₁₆	—	5	1	no	—
241	C₂×M₁₆	—	5	1	no	—
242	C₂×M₁₆	—	10	4	no	—
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	—	5	1	no	—
246	C₂²×C₈	—	5	1	no	—
247	C₂²×C₈	—	5	1	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	10	4	no	—
250	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
252	#117	—	5	1	no	—
253	#117	—	5	1	no	—
254	#117	—	5	1	no	—
255	#117	—	5	1	no	—
256	#117	—	5	1	no	—
257	#117	—	5	1	no	—
258	#117	—	5	1	no	—
259	#117	—	5	1	no	—
260	C₂×C₄⋊C₄	—	5	1	no	—
261	C₂×C₄⋊C₄	—	5	1	no	—
262	C₂×C₂²⋊C₄	—	5	1	no	—
263	C₂×C₂²⋊C₄	—	5	1	no	—
264	C₂×C₄²	—	5	1	no	—
265	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
266	M₃₂	—	10	4	no	—
267	C₂×C₁₆	—	5	2	no	—
268	C₂×C₁₆	—	5	2	no	—
269	C₂×C₁₆	—	10	4	no	—
270	C₂×C₁₆	C₂²×D₅	1	2	yes	—
271	C₂×C₁₆	C₂²×D₅	1	2	yes	—
272	#97	—	5	1	no	—
273	#97	—	5	1	no	—
274	#97	—	5	1	no	—
275	#97	—	5	1	no	—
276	#97	—	5	1	no	—
277	#97	—	5	1	no	—
278	#97	—	5	1	no	—
279	#97	—	5	1	no	—
280	C₄×C₈	—	5	1	no	—
281	C₄×C₈	—	5	1	no	—
282	C₄×C₈	—	5	1	no	—
283	C₄×C₈	—	5	1	no	—
284	C₄×C₈	C₄×D₅	1	1	yes	characteristic
285	C₄×C₈	C₄×D₅	1	1	yes	characteristic
286	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
287	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	#504	1	2	yes	—
291	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
292	C₂×D₅	—	2	1	no	—
293	C₂×D₅	—	2	1	no	—
294	C₂×D₅	—	2	1	no	—
295	C₂×D₅	—	2	1	no	—
296	C₂×D₅	—	2	1	no	—
297	C₂×D₅	—	4	4	no	—
298	C₂×D₅	#431	1	2	yes	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	C₂×#117	1	1	yes	characteristic
305	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
306	Dic₅	—	2	1	no	—
307	Dic₅	—	2	1	no	—
308	Dic₅	—	2	1	no	—
309	Dic₅	—	2	1	no	—
310	Dic₅	—	2	1	no	—
311	Dic₅	#431	1	2	yes	—
312	C₂⁴	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	10	2	no	—
321	C₂²×C₄	—	10	2	no	—
322	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
323	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
325	M₁₆	—	5	4	no	—
326	M₁₆	—	10	2	no	—
327	M₁₆	—	10	2	no	—
328	M₁₆	—	10	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	5	1	no	—
332	C₂×C₈	—	5	1	no	—
333	C₂×C₈	—	5	4	no	—
334	C₂×C₈	—	5	1	no	—
335	C₂×C₈	—	5	1	no	—
336	C₂×C₈	—	10	2	no	—
337	C₂×C₈	—	10	2	no	—
338	C₂×C₈	—	10	2	no	—
339	C₂×C₈	—	10	2	no	—
340	C₂×C₈	—	10	2	no	—
341	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
342	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
345	C₄⋊C₄	—	5	1	no	—
346	C₄⋊C₄	—	5	1	no	—
347	C₄⋊C₄	—	5	1	no	—
348	C₄⋊C₄	—	5	1	no	—
349	C₄⋊C₄	—	5	1	no	—
350	C₄⋊C₄	—	5	1	no	—
351	C₄⋊C₄	—	5	1	no	—
352	C₄⋊C₄	—	5	1	no	—
353	C₂²⋊C₄	—	5	1	no	—
354	C₂²⋊C₄	—	5	1	no	—
355	C₂²⋊C₄	—	5	1	no	—
356	C₂²⋊C₄	—	5	1	no	—
357	C₂²⋊C₄	—	5	1	no	—
358	C₂²⋊C₄	—	5	1	no	—
359	C₂²⋊C₄	—	5	1	no	—
360	C₂²⋊C₄	—	5	1	no	—
361	C₄²	—	5	1	no	—
362	C₄²	—	5	1	no	—
363	C₄²	—	5	1	no	—
364	C₄²	—	5	1	no	—
365	C₄²	C₈×D₅	1	1	yes	characteristic
366	C₄²	C₈×D₅	1	1	yes	characteristic
367	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
368	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	2	no	—
371	C₁₆	—	10	2	no	—
372	C₁₆	—	10	2	no	—
373	C₂×C₅	—	2	2	no	—
374	C₂×C₅	C₂×#431	1	1	yes	characteristic
375	C₂×C₅	C₂×#504	1	1	yes	characteristic
376	C₂×C₅	#3407	1	1	yes	characteristic
377	D₅	—	2	2	no	—
378	D₅	—	4	1	no	—
379	C₂³	—	5	1	no	—
380	C₂³	—	5	1	no	—
381	C₂³	—	10	2	no	—
382	C₂³	—	10	2	no	—
383	C₂³	—	20	1	no	—
384	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	2	no	—
391	C₂×C₄	—	5	2	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	—	10	2	no	—
399	C₂×C₄	—	10	2	no	—
400	C₂×C₄	—	10	2	no	—
401	C₂×C₄	—	10	1	no	—
402	C₂×C₄	—	10	1	no	—
403	C₂×C₄	—	20	1	no	—
404	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
405	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	5	2	no	—
413	C₈	—	5	2	no	—
414	C₈	—	10	1	no	—
415	C₈	—	10	1	no	—
416	C₈	D₅×M₁₆	1	2	yes	—
417	C₈	D₅×#41	1	2	yes	—
418	C₅	#33422	1	1	yes	characteristic, complemented, Sylow
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	5	2	no	—
422	C₂²	—	10	1	no	—
423	C₂²	—	10	1	no	—
424	C₂²	—	10	1	no	—
425	C₂²	—	10	1	no	—
426	C₂²	—	10	1	no	—
427	C₂²	—	20	4	no	—
428	C₂²	#65196	1	2	yes	—
429	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	5	2	no	—
436	C₄	—	10	1	no	—
437	C₄	—	10	1	no	—
438	C₄	—	10	1	no	—
439	C₄	—	10	1	no	—
440	C₄	—	10	1	no	—
441	C₄	D₅×#117	1	1	yes	characteristic
442	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	10	2	no	—
445	C₂	—	20	1	no	—
446	C₂	D₅×#431	1	1	yes	characteristic
447	C₂	C₂×#65196	1	1	yes	characteristic
448	C₂	#10613738	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2163	C₂
prime radical	C₂³×D₅	C₂×C₈
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2163	D₅
hypocenter	C₅	#33422
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. C₅×#2163	C₂	semidirect
3. #10600537	C₂	semidirect
4. #10600078	C₂	semidirect
5. #10600069	C₂	semidirect
8. #10599886	C₂	semidirect
9. #10599885	C₂	semidirect
10. #10599867	C₂	semidirect
11. #10599865	C₂	semidirect
29. C₅×C₄⋊C₁₆	C₂²	semidirect
32. C₅×#346	C₂²	semidirect
37. #64722	C₂²	semidirect
38. #64721	C₂²	semidirect
39. #64721	C₂²	semidirect
40. C₁₆×Dic₅	C₂²	semidirect
41. C₄⋊#672	C₂²	semidirect
42. C₄×#672	C₂²	semidirect
99. #2163	D₅	semidirect
187. C₄⋊C₁₆	C₂×D₅	semidirect
195. #346	C₂×D₅	semidirect
418. C₅	#33422	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64978	2
C₅×#2163	2
#10600537	2
#10600078	2
#10600069	2
#10599899	2
D₅×C₂²⋊C₁₆	2
#10599886	2
#10599885	2
#10599867	2
#10599865	2
#33422	5