Subgroups — #12070413

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3106	C₂	1	1	yes	maximal, characteristic
2	#10615008	C₂	1	1	yes	maximal, characteristic, complemented
3	#10614250	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602596	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602432	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601691	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601689	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601675	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601674	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601673	C₂	1	1	yes	maximal, characteristic, complemented
13	#10601672	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601545	C₂	1	1	yes	maximal, characteristic, complemented
15	#10601536	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#532	C₂²	1	1	yes	characteristic
17	C₄×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×#4094	—	2	1	no	—
19	C₅×#482	C₄	1	1	yes	characteristic
20	C₅×#482	C₄	1	1	yes	characteristic
21	C₅×#477	C₄	1	1	yes	characteristic
22	C₅×#476	C₄	1	1	yes	characteristic
23	C₅×#460	C₄	1	1	yes	characteristic
24	C₅×#459	C₄	1	1	yes	characteristic
25	C₅×#449	C₄	1	1	yes	characteristic
26	C₅×#449	C₄	1	1	yes	characteristic
27	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
28	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
30	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
31	C₅×#431	C₂²	1	1	yes	characteristic
32	#65523	—	2	1	no	—
33	Q₈×#168	C₂²	1	1	yes	characteristic
34	Q₈×#168	C₂²	1	1	yes	characteristic
35	#65301	—	2	1	no	—
36	#65301	—	2	1	no	—
37	#65301	C₂²	1	1	yes	characteristic
38	#65301	C₂²	1	1	yes	characteristic
39	#65301	C₂²	1	1	yes	characteristic
40	#65301	C₂²	1	1	yes	characteristic
41	#65300	—	2	1	no	—
42	#65300	—	2	1	no	—
43	D₄×#168	C₂²	1	1	yes	characteristic
44	D₄×#168	C₂²	1	1	yes	characteristic
45	#65215	—	2	1	no	—
46	#65215	C₂²	1	1	yes	characteristic
47	#65214	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
49	C₄×#681	—	2	1	no	—
50	C₄×#681	C₂²	1	1	yes	characteristic
51	Q₈⋊#168	C₂²	1	1	yes	characteristic
52	Q₈⋊#168	C₂²	1	1	yes	characteristic
53	D₄⋊#168	C₂²	1	1	yes	characteristic
54	D₄⋊#168	C₂²	1	1	yes	characteristic
55	D₄⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	D₄⋊#168	C₂²	1	1	yes	characteristic
58	D₄⋊#168	C₂²	1	1	yes	characteristic
59	#64678	C₂²	1	1	yes	characteristic
60	#64678	C₂²	1	1	yes	characteristic
61	#64677	C₂²	1	1	yes	characteristic
62	#64677	C₂²	1	1	yes	characteristic
63	#64675	C₂²	1	1	yes	characteristic
64	#64674	C₂²	1	1	yes	characteristic
65	#64674	C₂²	1	1	yes	characteristic
66	C₈×#168	C₂²	1	1	yes	characteristic
67	#18011	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
74	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
75	C₅×#127	C₂×C₄	1	1	yes	characteristic
76	C₅×#124	—	2	1	no	—
77	C₅×#121	—	2	1	no	—
78	C₅×#121	C₂×C₄	1	1	yes	characteristic
79	C₅×#121	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₄×C₅×D₄	—	2	1	no	—
83	C₄×C₅×D₄	—	2	1	no	—
84	C₄×C₅×D₄	—	2	1	no	—
85	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₅×#117	—	2	1	no	—
90	C₅×#117	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	#4094	—	4	4	no	—
94	C₂×#681	—	2	1	no	—
95	C₂×#681	—	2	1	no	—
96	C₂×#681	—	2	1	no	—
97	C₂×#681	—	2	1	no	—
98	C₂×#681	D₄	1	1	yes	characteristic
99	C₂×#681	D₄	1	1	yes	characteristic
100	C₂²×#168	—	2	1	no	—
101	C₂²×#168	—	2	1	no	—
102	C₂²×#168	—	2	1	no	—
103	C₅×#107	C₂×C₄	1	1	yes	characteristic
104	C₅×#107	C₂×C₄	1	1	yes	characteristic
105	C₅×#106	C₂×C₄	1	1	yes	characteristic
106	C₅×#106	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
109	C₅×#103	C₂×C₄	1	1	yes	characteristic
110	C₅×#103	C₂×C₄	1	1	yes	characteristic
111	C₅×#102	C₂×C₄	1	1	yes	characteristic
112	C₅×#102	C₂×C₄	1	1	yes	characteristic
113	C₅×#102	C₂×C₄	1	1	yes	characteristic
114	C₅×#102	C₂×C₄	1	1	yes	characteristic
115	C₅×#102	C₂×C₄	1	1	yes	characteristic
116	C₅×#102	C₂×C₄	1	1	yes	characteristic
117	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
118	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
119	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
120	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
121	C₂²⋊#168	—	2	1	no	—
122	C₂²⋊#168	—	2	1	no	—
123	C₂²⋊#168	—	2	1	no	—
124	C₂²⋊#168	—	2	1	no	—
125	C₂²⋊#168	—	2	1	no	—
126	C₂²⋊#168	—	2	1	no	—
127	C₂²⋊#168	—	2	1	no	—
128	C₂²⋊#168	—	2	1	no	—
129	C₄⋊#168	—	2	1	no	—
130	C₄⋊#168	—	2	1	no	—
131	C₄⋊#168	—	2	1	no	—
132	C₄⋊#168	—	2	1	no	—
133	C₄⋊#168	C₂³	1	1	yes	characteristic
134	C₄⋊#168	C₂³	1	1	yes	characteristic
135	C₄⋊#168	C₂³	1	1	yes	characteristic
136	C₄⋊#168	C₂³	1	1	yes	characteristic
137	#3935	—	2	1	no	—
138	#3935	D₄	1	1	yes	characteristic
139	#3935	D₄	1	1	yes	characteristic
140	C₄×#168	—	2	1	no	—
141	C₄×#168	—	2	1	no	—
142	C₄×#168	C₂³	1	1	yes	characteristic
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	C₄×#168	C₂³	1	1	yes	characteristic
146	#3106	D₅	1	1	yes	characteristic
147	#2971	—	5	1	no	—
148	#2935	—	5	1	no	—
149	#1594	—	5	1	no	—
150	#1589	—	5	1	no	—
151	#1588	—	5	1	no	—
152	#1586	—	5	1	no	—
153	#1583	—	5	1	no	—
154	#1581	—	5	1	no	—
155	SD₁₆⋊C₈	—	5	1	no	—
156	C₈×SD₁₆	—	5	1	no	—
157	#1573	—	5	1	no	—
158	#1496	—	5	1	no	—
159	#1477	—	5	1	no	—
160	#1453	—	5	1	no	—
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	4	1	no	—
163	C₅×#41	—	4	2	no	—
164	C₅×#41	—	4	2	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	#41	1	1	yes	characteristic
183	C₅×SD₁₆	—	2	2	no	—
184	C₅×SD₁₆	—	2	2	no	—
185	C₅×D₈	—	4	1	no	—
186	C₅×D₈	—	4	1	no	—
187	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₅×C₂²⋊C₄	—	2	1	no	—
200	C₅×C₂²⋊C₄	—	2	1	no	—
201	C₅×C₂²⋊C₄	—	2	1	no	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₅×C₂²⋊C₄	—	2	1	no	—
204	C₅×C₂²⋊C₄	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₅	#41	1	1	yes	characteristic
211	C₄²×C₅	C₂⁴	1	1	yes	characteristic
212	#681	—	2	2	no	—
213	#681	—	4	1	no	—
214	#681	—	4	2	no	—
215	#681	—	4	2	no	—
216	#681	—	4	2	no	—
217	#681	—	4	2	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	2	1	no	—
222	C₂×#168	—	2	1	no	—
223	C₂×#168	—	2	1	no	—
224	C₂×#168	—	4	2	no	—
225	C₂×#168	—	4	2	no	—
226	C₂×#168	—	4	2	no	—
227	C₂×#168	C₂×D₄	1	1	yes	characteristic
228	C₂×#168	C₂×D₄	1	1	yes	characteristic
229	C₂×#168	C₂×D₄	1	1	yes	characteristic
230	C₂×#168	C₂×D₄	1	1	yes	characteristic
231	C₂×#131	—	10	1	no	—
232	#532	C₂×D₅	1	1	yes	characteristic
233	C₄×#41	C₂×D₅	1	1	yes	characteristic
234	#482	Dic₅	1	1	yes	characteristic
235	#482	Dic₅	1	1	yes	characteristic
236	#477	Dic₅	1	1	yes	characteristic
237	#476	Dic₅	1	1	yes	characteristic
238	#460	Dic₅	1	1	yes	characteristic
239	#459	Dic₅	1	1	yes	characteristic
240	#449	Dic₅	1	1	yes	characteristic
241	#449	Dic₅	1	1	yes	characteristic
242	C₈×Q₈	—	5	1	no	—
243	C₈×Q₈	—	5	1	no	—
244	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
245	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
246	C₄×D₈	C₂×D₅	1	1	yes	characteristic
247	C₄×D₈	C₂×D₅	1	1	yes	characteristic
248	#436	—	5	1	no	—
249	#436	—	5	1	no	—
250	#436	—	5	1	no	—
251	#436	—	5	1	no	—
252	#436	—	10	1	no	—
253	#436	—	10	1	no	—
254	#435	—	10	1	no	—
255	#435	—	10	1	no	—
256	C₈×D₄	—	5	1	no	—
257	C₈×D₄	—	5	1	no	—
258	#432	—	5	1	no	—
259	#432	—	10	1	no	—
260	#431	—	5	1	no	—
261	#431	C₂×D₅	1	1	yes	characteristic
262	C₂×C₄⋊C₈	—	5	1	no	—
263	#408	—	10	1	no	—
264	C₄×M₁₆	—	5	1	no	—
265	C₄×M₁₆	—	10	1	no	—
266	#335	—	5	1	no	—
267	#335	—	5	1	no	—
268	#334	—	5	1	no	—
269	#334	—	5	1	no	—
270	Q₈⋊C₈	—	5	1	no	—
271	Q₈⋊C₈	—	5	1	no	—
272	D₄⋊C₈	—	5	1	no	—
273	D₄⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	—	5	1	no	—
278	#322	—	5	1	no	—
279	#322	—	5	1	no	—
280	#322	—	5	1	no	—
281	C₈²	—	5	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	4	2	no	—
288	C₅×Q₈	#131	1	2	yes	complemented
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	4	2	no	—
296	C₅×D₄	—	4	2	no	—
297	C₅×D₄	—	4	2	no	—
298	C₅×D₄	—	4	2	no	—
299	C₅×D₄	—	8	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	8	1	no	—
318	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	#168	—	2	1	no	—
329	#168	—	2	1	no	—
330	#168	—	2	1	no	—
331	#168	—	4	1	no	—
332	#168	—	4	1	no	—
333	#168	—	4	1	no	—
334	#168	—	4	1	no	—
335	#168	—	4	1	no	—
336	#168	—	4	1	no	—
337	#168	AGL(1,ℤ/8)	1	2	yes	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	C₂×Dic₅	1	1	yes	characteristic
340	C₂×SD₁₆	C₂×Dic₅	1	1	yes	characteristic
341	C₂×SD₁₆	C₂×Dic₅	1	1	yes	characteristic
342	C₂×D₈	C₂×Dic₅	1	1	yes	characteristic
343	C₂×D₈	C₂×Dic₅	1	1	yes	characteristic
344	#131	—	20	4	no	—
345	C₂×M₁₆	—	5	1	no	—
346	C₂×M₁₆	—	5	1	no	—
347	C₂×M₁₆	—	10	1	no	—
348	C₂×M₁₆	—	10	1	no	—
349	C₂×M₁₆	—	10	1	no	—
350	C₂×M₁₆	—	10	1	no	—
351	C₂²×C₈	—	10	1	no	—
352	C₂²×C₈	—	10	1	no	—
353	C₂²×C₈	—	10	1	no	—
354	C₄⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
355	#127	C₂×Dic₅	1	1	yes	characteristic
356	#124	—	2	1	no	—
357	#121	—	2	1	no	—
358	#121	C₂×Dic₅	1	1	yes	characteristic
359	#121	C₂×Dic₅	1	1	yes	characteristic
360	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
361	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
366	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
367	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
368	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	C₂×Dic₅	1	1	yes	characteristic
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
373	#107	C₂×Dic₅	1	1	yes	characteristic
374	#107	C₂×Dic₅	1	1	yes	characteristic
375	#106	C₂×Dic₅	1	1	yes	characteristic
376	#106	C₂×Dic₅	1	1	yes	characteristic
377	C₄⋊C₈	—	5	1	no	—
378	C₄⋊C₈	—	5	1	no	—
379	C₄⋊C₈	—	5	1	no	—
380	C₄⋊C₈	—	5	1	no	—
381	C₄⋊C₈	—	10	1	no	—
382	C₄⋊C₈	—	10	1	no	—
383	C₄⋊C₈	—	10	1	no	—
384	C₄⋊C₈	—	10	1	no	—
385	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
386	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
387	#103	C₂×Dic₅	1	1	yes	characteristic
388	#103	C₂×Dic₅	1	1	yes	characteristic
389	#102	C₂×Dic₅	1	1	yes	characteristic
390	#102	C₂×Dic₅	1	1	yes	characteristic
391	#102	C₂×Dic₅	1	1	yes	characteristic
392	#102	C₂×Dic₅	1	1	yes	characteristic
393	#102	C₂×Dic₅	1	1	yes	characteristic
394	#102	C₂×Dic₅	1	1	yes	characteristic
395	C₂²⋊C₈	—	10	1	no	—
396	C₂²⋊C₈	—	10	1	no	—
397	C₂²⋊C₈	—	10	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	C₂²⋊C₈	—	10	1	no	—
402	C₂²⋊C₈	—	10	1	no	—
403	C₂²⋊C₈	C₂×Dic₅	1	1	yes	characteristic
404	C₂²⋊C₈	C₂×Dic₅	1	1	yes	characteristic
405	#97	—	5	1	no	—
406	#97	—	5	1	no	—
407	#97	—	10	1	no	—
408	C₄×C₈	—	5	1	no	—
409	C₄×C₈	—	5	1	no	—
410	C₄×C₈	—	5	1	no	—
411	C₄×C₈	—	5	1	no	—
412	C₄×C₈	—	10	1	no	—
413	C₄×C₈	—	10	1	no	—
414	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	C₂×#131	1	1	yes	characteristic
439	C₄×C₅	#568	1	1	yes	characteristic
440	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₄×C₅	#575	1	1	yes	characteristic
442	#41	—	2	2	no	—
443	#41	—	4	1	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
454	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
455	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
462	C₂²×C₄	#711	1	1	yes	characteristic
463	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
464	SD₁₆	—	2	2	no	—
465	SD₁₆	—	2	2	no	—
466	D₈	—	4	1	no	—
467	D₈	—	4	1	no	—
468	M₁₆	—	10	2	no	—
469	M₁₆	—	20	2	no	—
470	M₁₆	—	20	2	no	—
471	M₁₆	—	20	1	no	—
472	M₁₆	—	20	2	no	—
473	M₁₆	—	20	2	no	—
474	C₂×C₈	—	5	1	no	—
475	C₂×C₈	—	5	1	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	10	1	no	—
479	C₂×C₈	—	10	1	no	—
480	C₂×C₈	—	10	1	no	—
481	C₂×C₈	—	10	1	no	—
482	C₂×C₈	—	10	1	no	—
483	C₂×C₈	—	10	1	no	—
484	C₂×C₈	—	20	2	no	—
485	C₂×C₈	—	20	2	no	—
486	C₂×C₈	—	20	2	no	—
487	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
488	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
489	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
490	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	D₄×D₅	1	1	yes	characteristic
509	C₄²	#711	1	1	yes	characteristic
510	C₄²	C₂²×Dic₅	1	1	yes	characteristic
511	C₄²	C₂³×D₅	1	1	yes	characteristic
512	C₂×C₅	—	4	1	no	—
513	C₂×C₅	—	8	1	no	—
514	C₂×C₅	—	8	1	no	—
515	C₂×C₅	—	8	1	no	—
516	C₂×C₅	#2933	1	1	yes	characteristic
517	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂×C₅	#2957	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	D₄×Dic₅	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	4	2	no	—
525	Q₈	#4094	1	2	yes	complemented
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	8	1	no	—
555	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
556	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
557	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
558	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
559	C₂×C₄	C₂×#711	1	1	yes	characteristic
560	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	5	2	no	—
566	C₈	—	10	1	no	—
567	C₈	—	10	1	no	—
568	C₈	—	10	1	no	—
569	C₈	—	20	1	no	—
570	C₈	—	20	1	no	—
571	C₈	—	20	1	no	—
572	C₈	—	20	1	no	—
573	C₈	—	20	1	no	—
574	C₈	—	20	1	no	—
575	C₅	#18011	1	1	yes	characteristic, complemented, Sylow
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
599	C₄	#66107	1	1	yes	characteristic
600	C₄	C₂×#4094	1	1	yes	characteristic
601	C₄	#66153	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	8	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	1	no	—
606	C₂	#10614649	1	1	yes	characteristic
607	C₂	#10615641	1	1	yes	characteristic
608	C₂	Dic₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting, prime radical	C₅×#3106	C₂
socle	C₂²×C₅	C₂×C₄×D₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#3106	D₅
hypocenter	C₅	#18011
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3106

Complements

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

N	H ≅ G/N	type
2. #10615008	C₂	semidirect
3. #10614250	C₂	semidirect
4. #10602596	C₂	semidirect
5. #10602432	C₂	semidirect
6. #10601691	C₂	semidirect
7. #10601689	C₂	semidirect
8. SD₁₆⋊#168	C₂	semidirect
9. SD₁₆×#168	C₂	semidirect
10. #10601675	C₂	semidirect
11. #10601674	C₂	semidirect
12. #10601673	C₂	semidirect
13. #10601672	C₂	semidirect
14. #10601545	C₂	semidirect
15. #10601536	C₂	semidirect
288. C₅×Q₈	#131	semidirect
525. Q₈	#4094	semidirect
575. C₅	#18011	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3106	2
#10615008	2
#10614250	2
#10602596	2
#10602432	2
#10601691	2
#10601689	2
SD₁₆⋊#168	2
SD₁₆×#168	2
#10601675	2
#10601674	2
#10601673	2
#10601672	2
#10601545	2
#10601536	2
#18011	5