Subgroups — #12252503

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#65196	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#3930	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611152	C₂	1	1	yes	maximal, characteristic
4	C₅×#2168	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602223	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×#672	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600078	C₂	1	1	yes	maximal, characteristic, complemented
9	#10600072	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599900	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599895	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599895	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599868	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599865	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4047	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
18	#65881	C₄	1	1	yes	characteristic
19	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
21	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂²×#672	C₂²	1	1	yes	characteristic
25	C₂²×#672	C₂²	1	1	yes	characteristic, complemented
26	#65300	C₄	1	1	yes	characteristic
27	#65196	—	2	4	no	—
28	C₂×#3930	—	2	4	no	—
29	C₂×#3930	C₂²	1	1	yes	characteristic
30	C₂×#3930	C₂²	1	1	yes	characteristic
31	C₂×#3930	C₂²	1	1	yes	characteristic
32	C₂×#3930	C₂²	1	1	yes	characteristic
33	C₂×#3930	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
35	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic
36	C₂×D₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
37	#65128	C₄	1	1	yes	characteristic
38	#65125	C₄	1	1	yes	characteristic
39	#65019	C₄	1	1	yes	characteristic
40	#65017	C₄	1	1	yes	characteristic
41	#65016	C₄	1	1	yes	characteristic
42	#65015	C₄	1	1	yes	characteristic
43	#64978	C₂²	1	1	yes	characteristic
44	C₈×D₂₀	C₂²	1	1	yes	characteristic
45	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
47	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₅×#346	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#672	C₂²	1	1	yes	characteristic
50	C₂²⋊#672	C₂²	1	1	yes	characteristic, complemented
51	#64727	C₂²	1	1	yes	characteristic
52	#64727	C₂²	1	1	yes	characteristic
53	#64727	C₂²	1	1	yes	characteristic, complemented
54	#64727	C₂²	1	1	yes	characteristic, complemented
55	#64722	C₂²	1	1	yes	characteristic, complemented
56	#64721	C₂²	1	1	yes	characteristic, complemented
57	#64721	C₂²	1	1	yes	characteristic, complemented
58	C₁₆×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#672	C₂²	1	1	yes	characteristic, complemented
60	C₄×#672	C₂²	1	1	yes	characteristic, complemented
61	#33436	—	5	1	no	maximal, Sylow
62	C₂×#709	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
67	#4085	C₈	1	1	yes	characteristic
68	#4083	C₈	1	1	yes	characteristic
69	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	C₂×#681	C₂×C₄	1	1	yes	characteristic
72	C₂²×#168	C₂×C₄	1	1	yes	characteristic
73	#4047	—	2	2	no	—
74	#4047	—	2	2	no	—
75	C₂×#676	C₂×C₄	1	1	yes	characteristic
76	C₂×#676	C₂×C₄	1	1	yes	characteristic
77	C₂×#676	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₅	—	2	2	no	—
79	C₂×C₈×D₅	—	2	2	no	—
80	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
85	#4042	C₈	1	1	yes	characteristic
86	#4040	C₈	1	1	yes	characteristic
87	#4030	C₈	1	1	yes	characteristic
88	#4029	C₈	1	1	yes	characteristic
89	#4028	C₈	1	1	yes	characteristic
90	#4024	C₈	1	1	yes	characteristic
91	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
92	#4018	C₂×C₄	1	1	yes	characteristic
93	C₅×M₃₂	—	2	2	no	—
94	C₂×C₅×C₁₆	—	2	2	no	—
95	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
105	#3952	C₂×C₄	1	1	yes	characteristic
106	#3952	C₂×C₄	1	1	yes	characteristic
107	#3952	C₂×C₄	1	1	yes	characteristic
108	#3952	C₂×C₄	1	1	yes	characteristic
109	#3947	C₂×C₄	1	1	yes	characteristic
110	#3946	C₂×C₄	1	1	yes	characteristic
111	#3946	C₂×C₄	1	1	yes	characteristic
112	C₈×Dic₅	C₂³	1	1	yes	characteristic
113	C₂×#672	—	2	2	no	—
114	C₂×#672	—	2	2	no	—
115	C₂×#672	C₂³	1	1	yes	characteristic
116	C₂×#672	C₂³	1	1	yes	characteristic
117	C₂×#672	C₂³	1	1	yes	characteristic
118	C₂×#672	C₂³	1	1	yes	characteristic
119	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
120	#3935	C₂×C₄	1	1	yes	characteristic
121	#3930	—	2	2	no	—
122	#3930	—	2	2	no	—
123	#3930	—	2	2	no	—
124	#3930	—	2	2	no	—
125	#3930	D₄	1	4	yes	complemented
126	D₅×C₁₆	—	2	2	no	—
127	D₅×C₁₆	—	2	2	no	—
128	D₅×C₁₆	—	2	2	no	—
129	C₂×#504	—	5	1	no	—
130	C₂²×M₃₂	—	5	1	no	—
131	#2929	—	5	1	no	—
132	#2169	—	5	1	no	—
133	#2169	—	5	1	no	—
134	#2168	—	5	1	no	—
135	#2168	—	5	1	no	—
136	#2168	—	5	1	no	—
137	#2168	D₅	1	1	yes	characteristic, complemented
138	D₄×C₁₆	—	5	1	no	—
139	D₄×C₁₆	—	5	1	no	—
140	#2151	—	5	1	no	—
141	#2113	—	5	1	no	—
142	C₂×C₂²⋊C₁₆	—	5	1	no	—
143	#2108	—	5	1	no	—
144	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
145	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
150	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
151	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
152	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
153	#709	—	2	2	no	—
154	#709	—	2	2	no	—
155	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
156	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
157	C₂×C₄×D₅	—	2	2	no	—
158	C₂×C₄×D₅	—	2	2	no	—
159	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
160	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×Dic₁₀	C₂×C₈	1	1	yes	characteristic
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	1	no	—
167	C₂×C₅×C₈	—	2	1	no	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
173	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
174	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
175	C₅×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
176	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
177	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
178	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
179	#685	C₂×C₈	1	1	yes	characteristic
180	#685	C₂×C₈	1	1	yes	characteristic
181	#685	C₂×C₈	1	1	yes	characteristic
182	#685	C₂×C₈	1	1	yes	characteristic
183	#685	C₂×C₈	1	1	yes	characteristic
184	#685	C₂×C₈	1	1	yes	characteristic
185	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
186	#683	C₂×C₈	1	1	yes	characteristic
187	#683	C₂×C₈	1	1	yes	characteristic
188	#683	C₂×C₈	1	1	yes	characteristic
189	#683	C₂×C₈	1	1	yes	characteristic
190	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
191	#681	—	2	2	no	—
192	C₂×#168	—	2	2	no	—
193	C₂×#168	C₂²×C₄	1	1	yes	characteristic
194	C₂×#168	C₂²×C₄	1	1	yes	characteristic
195	C₂×#168	C₂²×C₄	1	1	yes	characteristic
196	C₂×#168	C₂²×C₄	1	1	yes	characteristic
197	#676	—	2	2	no	—
198	#676	—	2	2	no	—
199	#676	—	2	2	no	—
200	C₈×D₅	—	2	2	no	—
201	C₈×D₅	—	2	1	no	—
202	C₈×D₅	—	2	1	no	—
203	C₈×D₅	—	2	1	no	—
204	C₈×D₅	—	2	1	no	—
205	C₈×D₅	—	2	2	no	—
206	C₈×D₅	C₂×D₄	1	2	yes	—
207	C₈×D₅	#41	1	2	yes	—
208	C₅×C₁₆	—	2	1	no	—
209	C₅×C₁₆	—	2	1	no	—
210	C₅×C₁₆	—	2	1	no	—
211	C₅×C₁₆	C₂×D₄	1	2	yes	—
212	#672	—	2	1	no	—
213	#672	—	2	1	no	—
214	#672	—	2	1	no	—
215	#672	C₂×D₄	1	2	yes	—
216	C₂×#131	—	5	1	no	—
217	C₂³×C₈	—	5	1	no	—
218	#525	—	5	1	no	—
219	#504	—	10	4	no	—
220	C₂×M₃₂	—	5	1	no	—
221	C₂×M₃₂	—	5	1	no	—
222	C₂×M₃₂	—	5	1	no	—
223	C₂×M₃₂	—	5	1	no	—
224	C₂×M₃₂	—	5	1	no	—
225	C₂×M₃₂	—	10	4	no	—
226	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
227	C₂²×C₁₆	—	5	1	no	—
228	C₂²×C₁₆	—	5	1	no	—
229	C₂²×C₁₆	—	5	1	no	—
230	C₂²×C₁₆	—	5	1	no	—
231	C₂²×C₁₆	—	5	1	no	—
232	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
233	#435	—	5	1	no	—
234	#435	—	5	1	no	—
235	#435	—	5	1	no	—
236	#435	—	5	1	no	—
237	C₈×D₄	—	5	1	no	—
238	C₈×D₄	—	5	1	no	—
239	C₈×D₄	—	5	1	no	—
240	C₈×D₄	C₂×D₅	1	1	yes	characteristic
241	#424	—	5	1	no	—
242	#408	—	5	1	no	—
243	#407	—	5	1	no	—
244	#405	—	5	1	no	—
245	C₄⋊C₁₆	—	5	1	no	—
246	C₄⋊C₁₆	—	5	1	no	—
247	C₄⋊C₁₆	—	5	1	no	—
248	C₄⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
249	C₂²⋊C₁₆	—	5	1	no	—
250	C₂²⋊C₁₆	—	5	1	no	—
251	C₂²⋊C₁₆	—	5	1	no	—
252	C₂²⋊C₁₆	—	5	1	no	—
253	C₂²⋊C₁₆	—	5	1	no	—
254	C₂²⋊C₁₆	—	5	1	no	—
255	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic
256	C₂²⋊C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
257	#346	—	5	1	no	—
258	#346	C₂×D₅	1	1	yes	characteristic, complemented
259	C₄×C₁₆	—	5	1	no	—
260	C₄×C₁₆	—	5	1	no	—
261	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
262	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
263	C₂²×D₅	—	2	2	no	—
264	C₂²×D₅	—	2	2	no	—
265	C₂²×D₅	—	4	1	no	—
266	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
267	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
268	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
269	C₅×D₄	—	2	2	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	1	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
279	C₂²⋊D₅	—	2	2	no	—
280	C₂²⋊D₅	—	2	2	no	—
281	C₂²⋊D₅	—	2	2	no	—
282	C₂²⋊D₅	—	4	1	no	—
283	C₂×Dic₅	—	2	2	no	—
284	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
285	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
286	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
287	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
288	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
289	D₂₀	—	2	2	no	—
290	D₂₀	—	4	1	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	2	1	no	—
293	C₄×D₅	—	2	1	no	—
294	C₄×D₅	—	2	1	no	—
295	C₄×D₅	—	2	1	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	C₄×D₄	1	2	yes	—
298	C₄×D₅	#131	1	2	yes	—
299	Dic₁₀	—	2	2	no	—
300	C₅×C₈	—	2	1	no	—
301	C₅×C₈	—	2	1	no	—
302	C₅×C₈	—	2	1	no	—
303	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
304	C₅×C₈	C₂×#41	1	1	yes	characteristic
305	#168	—	2	1	no	—
306	#168	—	2	1	no	—
307	#168	—	2	1	no	—
308	#168	C₄×D₄	1	2	yes	—
309	C₂×#41	—	5	1	no	—
310	C₂³×C₄	—	5	1	no	—
311	#131	—	10	2	no	—
312	#131	—	10	2	no	—
313	C₂×M₁₆	—	5	1	no	—
314	C₂×M₁₆	—	5	1	no	—
315	C₂×M₁₆	—	5	1	no	—
316	C₂×M₁₆	—	5	1	no	—
317	C₂²×C₈	—	5	1	no	—
318	C₂²×C₈	—	5	1	no	—
319	C₂²×C₈	—	5	1	no	—
320	C₂²×C₈	—	5	1	no	—
321	C₂²×C₈	—	5	1	no	—
322	C₂²×C₈	—	5	1	no	—
323	C₂²×C₈	—	10	2	no	—
324	C₂²×C₈	—	10	2	no	—
325	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
327	#123	—	5	1	no	—
328	#123	—	5	1	no	—
329	C₂²⋊Q₈	—	5	1	no	—
330	C₂²⋊Q₈	—	5	1	no	—
331	#121	—	5	1	no	—
332	#121	—	5	1	no	—
333	#120	—	5	1	no	—
334	#120	—	5	1	no	—
335	C₄×D₄	—	5	1	no	—
336	C₄×D₄	—	5	1	no	—
337	C₄×D₄	—	5	1	no	—
338	C₄×D₄	C₄×D₅	1	1	yes	characteristic
339	#117	—	5	1	no	—
340	M₃₂	—	2	2	no	—
341	M₃₂	—	5	4	no	—
342	M₃₂	—	10	2	no	—
343	M₃₂	—	10	2	no	—
344	M₃₂	—	10	2	no	—
345	M₃₂	—	10	2	no	—
346	C₂×C₁₆	—	2	2	no	—
347	C₂×C₁₆	—	5	1	no	—
348	C₂×C₁₆	—	5	1	no	—
349	C₂×C₁₆	—	5	1	no	—
350	C₂×C₁₆	—	5	1	no	—
351	C₂×C₁₆	—	10	2	no	—
352	C₂×C₁₆	—	10	2	no	—
353	C₂×C₁₆	—	10	2	no	—
354	C₂×C₁₆	—	10	2	no	—
355	C₂×C₁₆	—	10	2	no	—
356	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
357	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
358	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
359	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
360	C₄⋊C₈	—	5	1	no	—
361	C₄⋊C₈	—	5	1	no	—
362	C₄⋊C₈	—	5	1	no	—
363	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
364	C₂²⋊C₈	—	5	1	no	—
365	C₂²⋊C₈	—	5	1	no	—
366	C₂²⋊C₈	—	5	1	no	—
367	C₂²⋊C₈	—	5	1	no	—
368	C₂²⋊C₈	—	5	1	no	—
369	C₂²⋊C₈	—	5	1	no	—
370	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
371	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
372	#97	—	5	1	no	—
373	#97	—	5	1	no	—
374	C₄×C₈	—	5	1	no	—
375	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
376	C₂²×C₅	—	2	1	no	—
377	C₂²×C₅	—	2	1	no	—
378	C₂²×C₅	—	2	1	no	—
379	C₂²×C₅	—	2	1	no	—
380	C₂²×C₅	—	2	1	no	—
381	C₂²×C₅	#504	1	2	yes	complemented
382	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
383	C₂×D₅	—	2	1	no	—
384	C₂×D₅	—	2	1	no	—
385	C₂×D₅	—	2	1	no	—
386	C₂×D₅	—	2	1	no	—
387	C₂×D₅	—	2	1	no	—
388	C₂×D₅	—	2	1	no	—
389	C₂×D₅	—	2	1	no	—
390	C₂×D₅	—	2	1	no	—
391	C₂×D₅	—	4	4	no	—
392	C₂×D₅	C₈×D₄	1	2	yes	—
393	C₄×C₅	—	2	1	no	—
394	C₄×C₅	—	2	1	no	—
395	C₄×C₅	—	2	1	no	—
396	C₄×C₅	—	2	1	no	—
397	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
398	C₄×C₅	C₂×#131	1	1	yes	characteristic
399	Dic₅	—	2	1	no	—
400	Dic₅	—	2	1	no	—
401	Dic₅	—	2	1	no	—
402	Dic₅	—	2	1	no	—
403	Dic₅	C₈×D₄	1	2	yes	—
404	C₂⁴	—	5	1	no	—
405	#41	—	10	2	no	—
406	#41	—	10	2	no	—
407	C₂×Q₈	—	5	1	no	—
408	C₂×D₄	—	5	1	no	—
409	C₂×D₄	—	5	1	no	—
410	C₂×D₄	—	5	1	no	—
411	C₂×D₄	—	5	1	no	—
412	C₂×D₄	—	5	1	no	—
413	C₂×D₄	—	5	1	no	—
414	C₂×D₄	C₈×D₅	1	1	yes	characteristic
415	C₂²×C₄	—	5	1	no	—
416	C₂²×C₄	—	5	1	no	—
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	5	1	no	—
420	C₂²×C₄	—	5	1	no	—
421	C₂²×C₄	—	10	2	no	—
422	C₂²×C₄	—	10	2	no	—
423	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
425	M₁₆	—	10	2	no	—
426	M₁₆	—	10	2	no	—
427	M₁₆	—	10	2	no	—
428	M₁₆	—	10	2	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	5	1	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	—	5	2	no	—
436	C₂×C₈	—	5	1	no	—
437	C₂×C₈	—	5	1	no	—
438	C₂×C₈	—	5	1	no	—
439	C₂×C₈	—	10	2	no	—
440	C₂×C₈	—	10	2	no	—
441	C₂×C₈	—	10	2	no	—
442	C₂×C₈	—	10	1	no	—
443	C₂×C₈	—	10	1	no	—
444	C₂×C₈	—	10	1	no	—
445	C₂×C₈	—	10	1	no	—
446	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
447	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
448	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
449	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	—	5	1	no	—
452	C₄⋊C₄	—	5	1	no	—
453	C₄⋊C₄	—	5	1	no	—
454	C₄⋊C₄	—	5	1	no	—
455	C₄⋊C₄	C₈×D₅	1	1	yes	characteristic
456	C₂²⋊C₄	—	5	1	no	—
457	C₂²⋊C₄	—	5	1	no	—
458	C₂²⋊C₄	—	5	1	no	—
459	C₂²⋊C₄	—	5	1	no	—
460	C₂²⋊C₄	—	5	1	no	—
461	C₂²⋊C₄	—	5	1	no	—
462	C₂²⋊C₄	—	5	1	no	—
463	C₂²⋊C₄	—	5	1	no	—
464	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
465	C₂²⋊C₄	C₈×D₅	1	1	yes	characteristic
466	C₄²	—	5	1	no	—
467	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
468	C₁₆	—	2	1	no	—
469	C₁₆	—	2	1	no	—
470	C₁₆	—	2	1	no	—
471	C₁₆	—	5	2	no	—
472	C₁₆	—	10	1	no	—
473	C₁₆	—	10	1	no	—
474	C₁₆	—	10	1	no	—
475	C₁₆	D₄×D₅	1	2	yes	—
476	C₂×C₅	—	2	2	no	—
477	C₂×C₅	—	4	1	no	—
478	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
479	C₂×C₅	C₂×#504	1	1	yes	characteristic
480	C₂×C₅	#3407	1	1	yes	characteristic
481	D₅	—	2	2	no	—
482	D₅	—	4	1	no	—
483	D₅	—	4	1	no	—
484	C₂³	—	5	1	no	—
485	C₂³	—	5	1	no	—
486	C₂³	—	5	1	no	—
487	C₂³	—	10	2	no	—
488	C₂³	—	10	2	no	—
489	C₂³	—	20	1	no	—
490	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
491	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
492	Q₈	—	10	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	10	2	no	—
495	D₄	—	10	2	no	—
496	D₄	—	10	2	no	—
497	D₄	—	10	2	no	—
498	D₄	—	20	1	no	—
499	D₄	—	20	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	2	no	—
506	C₂×C₄	—	5	2	no	—
507	C₂×C₄	—	5	1	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	10	2	no	—
512	C₂×C₄	—	10	2	no	—
513	C₂×C₄	—	10	2	no	—
514	C₂×C₄	—	10	1	no	—
515	C₂×C₄	—	10	1	no	—
516	C₂×C₄	—	10	1	no	—
517	C₂×C₄	—	10	1	no	—
518	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
519	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
520	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
521	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
522	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	5	2	no	—
527	C₈	—	10	1	no	—
528	C₈	—	10	1	no	—
529	C₈	—	10	1	no	—
530	C₈	C₂×D₄×D₅	1	1	yes	characteristic
531	C₈	D₅×#41	1	1	yes	characteristic
532	C₅	#33436	1	1	yes	characteristic, complemented, Sylow
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	5	2	no	—
539	C₂²	—	10	1	no	—
540	C₂²	—	10	1	no	—
541	C₂²	—	10	1	no	—
542	C₂²	—	10	1	no	—
543	C₂²	—	10	1	no	—
544	C₂²	—	10	1	no	—
545	C₂²	—	10	1	no	—
546	C₂²	—	10	1	no	—
547	C₂²	—	20	4	no	—
548	C₂²	#65196	1	2	yes	complemented
549	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	5	2	no	—
555	C₄	—	10	1	no	—
556	C₄	—	10	1	no	—
557	C₄	—	10	1	no	—
558	C₄	—	10	1	no	—
559	C₄	C₄×D₄×D₅	1	1	yes	characteristic
560	C₄	D₅×#131	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	10	2	no	—
564	C₂	—	20	1	no	—
565	C₂	—	20	1	no	—
566	C₂	C₈×D₄×D₅	1	1	yes	characteristic
567	C₂	C₂×#65196	1	1	yes	characteristic
568	C₂	#10613743	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₅×#2168	C₂
prime radical	#65881	C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	#2168	D₅
hypocenter	C₅	#33436
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×#65196	C₂	semidirect
2. C₂²×#3930	C₂	semidirect
4. C₅×#2168	C₂	semidirect
5. #10602223	C₂	semidirect
6. C₁₆×C₂²⋊D₅	C₂	semidirect
7. D₄×#672	C₂	semidirect
8. #10600078	C₂	semidirect
9. #10600072	C₂	semidirect
10. #10599900	C₂	semidirect
11. D₅×C₂²⋊C₁₆	C₂	semidirect
12. #10599895	C₂	semidirect
13. #10599895	C₂	semidirect
14. #10599868	C₂	semidirect
15. #10599865	C₂	semidirect
19. C₂×C₅×M₃₂	C₂²	semidirect
25. C₂²×#672	C₂²	semidirect
33. C₂×#3930	C₂²	semidirect
36. C₂×D₅×C₁₆	C₂²	semidirect
45. C₅×C₄⋊C₁₆	C₂²	semidirect
47. C₅×C₂²⋊C₁₆	C₂²	semidirect
48. C₅×#346	C₂²	semidirect
50. C₂²⋊#672	C₂²	semidirect
53. #64727	C₂²	semidirect
54. #64727	C₂²	semidirect
55. #64722	C₂²	semidirect
56. #64721	C₂²	semidirect
57. #64721	C₂²	semidirect
58. C₁₆×Dic₅	C₂²	semidirect
59. C₄⋊#672	C₂²	semidirect
60. C₄×#672	C₂²	semidirect
125. #3930	D₄	semidirect
137. #2168	D₅	semidirect
226. C₂×M₃₂	C₂×D₅	semidirect
248. C₄⋊C₁₆	C₂×D₅	semidirect
256. C₂²⋊C₁₆	C₂×D₅	semidirect
258. #346	C₂×D₅	semidirect
381. C₂²×C₅	#504	semidirect
532. C₅	#33436	semidirect
548. C₂²	#65196	semidirect

Maximal subgroups

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

subgroup	index
C₂×#65196	2
C₂²×#3930	2
#10611152	2
C₅×#2168	2
#10602223	2
C₁₆×C₂²⋊D₅	2
D₄×#672	2
#10600078	2
#10600072	2
#10599900	2
D₅×C₂²⋊C₁₆	2
#10599895	2
#10599868	2
#10599865	2
#33436	5