Subgroups — #12068950

Order 1280.

698 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#4057	C₂	1	1	yes	maximal, characteristic
2	#10611274	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611136	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1586	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601672	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601657	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601634	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599321	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599313	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598958	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598952	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598950	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598881	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598862	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4057	C₄	1	1	yes	characteristic
17	C₄×D₄×D₅	C₂²	1	1	yes	characteristic
18	C₄×#711	C₂²	1	1	yes	characteristic
19	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₅×#436	C₂²	1	1	yes	characteristic
21	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
22	#65441	C₄	1	1	yes	characteristic
23	#65417	—	2	1	no	—
24	#65415	—	2	1	no	—
25	C₈×C₂²⋊D₅	—	2	1	no	—
26	C₂×#3946	—	2	1	no	—
27	C₄×#687	C₂²	1	1	yes	characteristic
28	C₄×#686	C₂²	1	1	yes	characteristic
29	#65301	C₂²	1	1	yes	characteristic
30	D₄×#168	C₂²	1	1	yes	characteristic, complemented
31	#65178	C₄	1	1	yes	characteristic
32	#65170	C₄	1	1	yes	characteristic
33	#65127	C₂²	1	1	yes	characteristic
34	#65122	C₂²	1	1	yes	characteristic
35	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	#65119	C₂²	1	1	yes	characteristic, complemented
37	#65074	C₄	1	1	yes	characteristic
38	#65060	C₄	1	1	yes	characteristic
39	#65059	C₄	1	1	yes	characteristic
40	#65046	C₄	1	1	yes	characteristic
41	#65018	—	2	1	no	—
42	#65015	—	2	1	no	—
43	#65014	—	2	1	no	—
44	#65007	—	2	1	no	—
45	C₄×#677	C₂²	1	1	yes	characteristic
46	#64977	C₂²	1	1	yes	characteristic
47	C₄×#676	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
51	C₅×#334	C₂²	1	1	yes	characteristic, complemented
52	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×#322	C₂²	1	1	yes	characteristic, complemented
55	D₄⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
57	#64704	C₂²	1	1	yes	characteristic, complemented
58	#64703	C₂²	1	1	yes	characteristic
59	#64700	C₂²	1	1	yes	characteristic, complemented
60	#64699	C₂²	1	1	yes	characteristic, complemented
61	#64679	C₂²	1	1	yes	characteristic
62	#64678	C₂²	1	1	yes	characteristic, complemented
63	#64676	C₂²	1	1	yes	characteristic, complemented
64	#64675	C₂²	1	1	yes	characteristic, complemented
65	#64675	C₂²	1	1	yes	characteristic, complemented
66	#64674	C₂²	1	1	yes	characteristic, complemented
67	#17875	—	5	1	no	maximal, Sylow
68	C₂×#711	C₂×C₄	1	1	yes	characteristic
69	C₂×D₄×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₄×D₅	—	2	1	no	—
71	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂²×C₅×C₈	—	2	1	no	—
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₂×#687	C₂×C₄	1	1	yes	characteristic
79	C₂×#686	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₅	—	2	1	no	—
81	C₄×C₂²⋊D₅	—	2	1	no	—
82	C₂×C₄×Dic₅	—	2	1	no	—
83	C₂×#681	—	2	1	no	—
84	C₂²×#168	—	2	1	no	—
85	#4057	—	2	4	no	—
86	C₂×#677	C₂×C₄	1	1	yes	characteristic
87	C₂×#676	—	2	1	no	—
88	C₂×#676	—	2	1	no	—
89	C₂×#676	C₂×C₄	1	1	yes	characteristic
90	C₂×#676	C₂×C₄	1	1	yes	characteristic
91	C₂×C₈×D₅	—	2	1	no	—
92	C₂×C₈×D₅	—	2	1	no	—
93	#4039	C₂×C₄	1	1	yes	characteristic
94	#4038	C₂×C₄	1	1	yes	characteristic
95	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	#4033	C₂×C₄	1	1	yes	characteristic
97	#4027	—	2	1	no	—
98	#4027	—	2	1	no	—
99	D₅×C₂²⋊C₄	—	2	1	no	—
100	#4023	—	2	1	no	—
101	C₄×D₂₀	C₂³	1	1	yes	characteristic
102	C₄²×D₅	C₂³	1	1	yes	characteristic
103	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
104	C₅×#107	C₂×C₄	1	1	yes	characteristic
105	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₅×#102	C₂×C₄	1	1	yes	characteristic
108	C₅×#102	C₂×C₄	1	1	yes	characteristic
109	C₅×C₂²⋊C₈	—	2	1	no	—
110	C₅×C₂²⋊C₈	—	2	1	no	—
111	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	#3964	C₂×C₄	1	1	yes	characteristic
115	#3964	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#168	—	2	1	no	—
117	C₂²⋊#168	—	2	1	no	—
118	#3953	C₂×C₄	1	1	yes	characteristic
119	#3952	—	2	1	no	—
120	#3952	—	2	1	no	—
121	#3952	—	2	1	no	—
122	#3952	D₄	1	1	yes	characteristic
123	#3952	D₄	1	1	yes	characteristic
124	#3949	C₂×C₄	1	1	yes	characteristic
125	#3948	C₂×C₄	1	1	yes	characteristic
126	#3947	C₂×C₄	1	1	yes	characteristic
127	#3947	C₂×C₄	1	1	yes	characteristic
128	#3946	—	2	1	no	—
129	#3946	—	2	1	no	—
130	#3946	—	2	1	no	—
131	#3946	D₄	1	1	yes	characteristic
132	#3946	D₄	1	1	yes	characteristic
133	C₈×Dic₅	—	2	1	no	—
134	C₈×Dic₅	—	2	1	no	—
135	C₈×Dic₅	—	2	1	no	—
136	C₈×Dic₅	—	2	1	no	—
137	#3942	C₂×C₄	1	1	yes	characteristic
138	#3941	C₂×C₄	1	1	yes	characteristic
139	#3940	C₂×C₄	1	1	yes	characteristic
140	#3939	C₂×C₄	1	1	yes	characteristic
141	C₄⋊#168	C₂³	1	1	yes	characteristic
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	#2988	—	5	1	no	—
147	#2975	—	5	1	no	—
148	C₄×AGL(1,ℤ/8)	—	5	1	no	—
149	#1588	—	5	1	no	—
150	#1588	—	5	1	no	—
151	#1586	—	5	1	no	—
152	#1586	D₅	1	1	yes	characteristic, complemented
153	#1583	—	5	1	no	—
154	#1583	—	5	1	no	—
155	#1581	—	5	1	no	—
156	#1581	—	5	1	no	—
157	#1565	—	5	1	no	—
158	#1476	—	5	1	no	—
159	C₂×D₄⋊C₈	—	5	1	no	—
160	#1451	—	5	1	no	—
161	C₂³×D₅	—	2	1	no	—
162	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	C₂×C₂²⋊D₅	—	2	1	no	—
168	C₂²×Dic₅	—	2	1	no	—
169	C₂²×Dic₅	—	2	1	no	—
170	C₂²×Dic₅	—	2	1	no	—
171	#711	—	2	2	no	—
172	#711	M₁₆	1	4	yes	complemented
173	D₄×D₅	—	2	2	no	—
174	D₄×D₅	—	2	2	no	—
175	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	2	1	no	—
178	C₂×C₄×D₅	—	2	1	no	—
179	C₂×C₄×D₅	—	8	1	no	—
180	C₂×C₄×D₅	—	8	1	no	—
181	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
183	C₂×C₄×D₅	#41	1	1	yes	characteristic
184	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
185	C₅×D₈	—	2	2	no	—
186	C₅×M₁₆	—	8	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	8	1	no	—
191	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂×D₄	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×C₂²⋊C₄	—	2	1	no	—
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₄²×C₅	C₂⁴	1	1	yes	characteristic
200	C₂²⋊Dic₅	—	2	1	no	—
201	C₂²⋊Dic₅	—	2	1	no	—
202	#687	—	2	2	no	—
203	#686	—	2	2	no	—
204	#685	—	2	1	no	—
205	#685	—	2	1	no	—
206	#685	—	2	1	no	—
207	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
209	#683	—	2	1	no	—
210	#683	—	2	1	no	—
211	#683	—	2	1	no	—
212	C₄×Dic₅	—	2	1	no	—
213	C₄×Dic₅	—	2	1	no	—
214	C₄×Dic₅	—	2	1	no	—
215	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
217	C₄×Dic₅	#41	1	1	yes	characteristic
218	#681	—	8	1	no	—
219	C₂×#168	—	2	1	no	—
220	C₂×#168	—	2	1	no	—
221	C₂×#168	—	2	1	no	—
222	C₂×#168	—	8	1	no	—
223	C₂×#168	C₂²×C₄	1	1	yes	characteristic
224	C₂×#168	C₂²×C₄	1	1	yes	characteristic
225	C₂×#168	C₂×D₄	1	1	yes	characteristic
226	C₂×#168	C₂×D₄	1	1	yes	characteristic
227	#677	—	2	2	no	—
228	#676	—	2	2	no	—
229	#676	—	2	2	no	—
230	#676	—	8	1	no	—
231	#676	—	8	1	no	—
232	C₈×D₅	—	4	2	no	—
233	C₈×D₅	—	8	1	no	—
234	C₂×AGL(1,ℤ/8)	—	5	1	no	—
235	C₄×#41	—	5	1	no	—
236	C₂×C₄×D₄	—	5	1	no	—
237	C₈×Q₈	—	5	1	no	—
238	C₈×Q₈	—	5	1	no	—
239	#442	—	5	1	no	—
240	#442	—	5	1	no	—
241	#440	—	5	1	no	—
242	#440	—	5	1	no	—
243	C₄×SD₁₆	—	5	1	no	—
244	C₄×SD₁₆	—	5	1	no	—
245	C₄×D₈	—	5	1	no	—
246	C₄×D₈	C₂×D₅	1	1	yes	characteristic
247	#436	—	5	1	no	—
248	#436	—	5	1	no	—
249	#436	—	5	1	no	—
250	#436	—	10	1	no	—
251	#436	—	10	1	no	—
252	#436	C₂×D₅	1	1	yes	characteristic
253	C₈×D₄	—	5	1	no	—
254	C₈×D₄	—	10	1	no	—
255	C₈×D₄	—	10	1	no	—
256	C₈×D₄	C₂×D₅	1	1	yes	characteristic, complemented
257	#431	—	5	1	no	—
258	#431	—	5	1	no	—
259	#431	—	10	1	no	—
260	#428	—	5	1	no	—
261	C₂×C₄⋊C₈	—	5	1	no	—
262	C₂×C₄⋊C₈	—	10	1	no	—
263	#418	—	5	1	no	—
264	#417	—	5	1	no	—
265	#407	—	10	1	no	—
266	#407	—	10	1	no	—
267	C₄×M₁₆	—	5	1	no	—
268	C₂×C₄×C₈	—	5	1	no	—
269	#335	—	5	1	no	—
270	#335	—	5	1	no	—
271	#334	—	5	1	no	—
272	#334	C₂×D₅	1	1	yes	characteristic, complemented
273	Q₈⋊C₈	—	5	1	no	—
274	Q₈⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	—	5	1	no	—
278	D₄⋊C₈	—	5	1	no	—
279	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
280	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
281	#322	—	5	1	no	—
282	#322	—	5	1	no	—
283	#322	—	5	1	no	—
284	#322	C₂×D₅	1	1	yes	characteristic, complemented
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	2	1	no	—
287	C₂²×D₅	—	2	1	no	—
288	C₂²×D₅	—	4	2	no	—
289	C₂²×D₅	—	8	1	no	—
290	C₂²×D₅	—	8	1	no	—
291	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	C₂×M₁₆	1	2	yes	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
305	C₂²⋊D₅	—	2	4	no	—
306	C₂²⋊D₅	—	4	2	no	—
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	2	4	no	—
309	C₂×Dic₅	—	2	1	no	—
310	C₂×Dic₅	—	2	1	no	—
311	C₂×Dic₅	—	8	1	no	—
312	C₂×Dic₅	—	8	1	no	—
313	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
314	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
315	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
316	D₂₀	—	2	1	no	—
317	D₂₀	—	2	1	no	—
318	C₄×D₅	—	2	1	no	—
319	C₄×D₅	—	2	1	no	—
320	C₄×D₅	—	4	1	no	—
321	C₄×D₅	—	4	1	no	—
322	C₄×D₅	—	4	1	no	—
323	C₄×D₅	—	8	1	no	—
324	C₄×D₅	—	8	1	no	—
325	C₄×D₅	C₂×M₁₆	1	2	yes	—
326	C₄×D₅	#131	1	2	yes	—
327	Dic₁₀	—	2	1	no	—
328	Dic₁₀	C₂×M₁₆	1	2	yes	—
329	C₅×C₈	—	2	2	no	—
330	C₅×C₈	—	2	1	no	—
331	C₅×C₈	—	2	1	no	—
332	C₅×C₈	—	2	1	no	—
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	—	4	1	no	—
336	#168	—	2	1	no	—
337	#168	—	2	1	no	—
338	#168	—	2	1	no	—
339	#168	—	2	1	no	—
340	#168	—	4	1	no	—
341	#168	—	4	1	no	—
342	#168	—	4	1	no	—
343	C₂×#41	—	5	1	no	—
344	C₂²×D₄	—	5	1	no	—
345	C₂³×C₄	—	10	1	no	—
346	AGL(1,ℤ/8)	—	10	4	no	—
347	C₂×SD₁₆	—	5	1	no	—
348	C₂×SD₁₆	—	5	1	no	—
349	C₂×D₈	—	5	1	no	—
350	C₂×D₈	C₄×D₅	1	1	yes	characteristic
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	5	1	no	—
353	C₂×M₁₆	—	5	1	no	—
354	C₂×M₁₆	—	10	1	no	—
355	C₂×M₁₆	—	10	1	no	—
356	C₂×M₁₆	—	10	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	10	1	no	—
359	C₂²×C₈	—	10	1	no	—
360	C₂²×C₈	—	10	1	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×D₄	—	5	1	no	—
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	5	1	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	10	1	no	—
368	C₄×D₄	—	10	1	no	—
369	C₄×D₄	—	10	1	no	—
370	C₄×D₄	—	10	1	no	—
371	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
372	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
373	#117	—	5	1	no	—
374	#117	—	10	1	no	—
375	C₂×C₄⋊C₄	—	5	1	no	—
376	C₂×C₂²⋊C₄	—	10	1	no	—
377	C₂×C₄²	—	5	1	no	—
378	C₂×C₄²	—	10	1	no	—
379	#107	—	5	1	no	—
380	#107	C₄×D₅	1	1	yes	characteristic
381	#106	—	5	1	no	—
382	#106	—	5	1	no	—
383	C₄⋊C₈	—	5	1	no	—
384	C₄⋊C₈	—	5	1	no	—
385	C₄⋊C₈	—	5	1	no	—
386	C₄⋊C₈	—	5	1	no	—
387	C₄⋊C₈	—	10	1	no	—
388	C₄⋊C₈	—	10	1	no	—
389	C₄⋊C₈	—	10	1	no	—
390	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
391	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
392	#103	—	5	1	no	—
393	#103	—	5	1	no	—
394	#102	—	5	1	no	—
395	#102	—	5	1	no	—
396	#102	—	5	1	no	—
397	#102	—	5	1	no	—
398	#102	C₄×D₅	1	1	yes	characteristic
399	#102	C₄×D₅	1	1	yes	characteristic
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	5	1	no	—
403	C₂²⋊C₈	—	5	1	no	—
404	C₂²⋊C₈	—	10	1	no	—
405	C₂²⋊C₈	—	10	1	no	—
406	C₂²⋊C₈	—	10	1	no	—
407	C₂²⋊C₈	—	10	1	no	—
408	C₂²⋊C₈	—	10	1	no	—
409	#97	—	5	1	no	—
410	#97	—	5	1	no	—
411	C₄×C₈	—	5	1	no	—
412	C₄×C₈	—	5	1	no	—
413	C₄×C₈	—	5	1	no	—
414	C₄×C₈	—	10	1	no	—
415	C₄×C₈	—	10	1	no	—
416	C₄×C₈	—	10	1	no	—
417	C₄×C₈	—	10	1	no	—
418	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
421	C₂²×C₅	—	2	2	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	C₂×C₄×D₄	1	1	yes	characteristic
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	4	1	no	—
431	C₂×D₅	—	4	1	no	—
432	C₂×D₅	—	4	1	no	—
433	C₂×D₅	—	8	4	no	—
434	C₂×D₅	#435	1	2	yes	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
439	C₄×C₅	C₂×#131	1	1	yes	characteristic
440	C₄×C₅	#576	1	1	yes	characteristic
441	C₄×C₅	#577	1	1	yes	characteristic
442	Dic₅	—	2	2	no	—
443	Dic₅	—	2	1	no	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	4	1	no	—
446	Dic₅	—	4	1	no	—
447	Dic₅	#435	1	2	yes	—
448	C₂⁴	—	10	1	no	—
449	#41	—	5	4	no	—
450	#41	—	10	2	no	—
451	C₂×Q₈	—	5	1	no	—
452	C₂×D₄	—	5	1	no	—
453	C₂×D₄	—	10	2	no	—
454	C₂×D₄	—	10	2	no	—
455	C₂×D₄	—	10	1	no	—
456	C₂×D₄	—	10	1	no	—
457	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
458	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	5	1	no	—
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	1	no	—
464	C₂²×C₄	—	10	1	no	—
465	C₂²×C₄	—	10	1	no	—
466	C₂²×C₄	—	10	1	no	—
467	C₂²×C₄	—	10	1	no	—
468	C₂²×C₄	—	10	1	no	—
469	C₂²×C₄	—	10	1	no	—
470	C₂²×C₄	—	40	1	no	—
471	C₂²×C₄	—	40	1	no	—
472	SD₁₆	—	10	2	no	—
473	SD₁₆	—	10	2	no	—
474	D₈	—	2	2	no	—
475	D₈	—	10	2	no	—
476	M₁₆	—	8	1	no	—
477	M₁₆	—	10	2	no	—
478	M₁₆	—	10	2	no	—
479	M₁₆	—	40	1	no	—
480	M₁₆	—	40	1	no	—
481	M₁₆	—	40	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	5	1	no	—
486	C₂×C₈	—	5	1	no	—
487	C₂×C₈	—	5	1	no	—
488	C₂×C₈	—	5	1	no	—
489	C₂×C₈	—	8	1	no	—
490	C₂×C₈	—	10	1	no	—
491	C₂×C₈	—	10	1	no	—
492	C₂×C₈	—	10	1	no	—
493	C₂×C₈	—	20	2	no	—
494	C₂×C₈	—	40	1	no	—
495	C₂×C₈	—	40	1	no	—
496	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
497	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
498	C₂×C₈	D₄×D₅	1	1	yes	characteristic
499	C₂×C₈	D₄×D₅	1	1	yes	characteristic
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	10	1	no	—
503	C₄⋊C₄	—	10	1	no	—
504	C₄⋊C₄	—	10	1	no	—
505	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
506	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	10	1	no	—
510	C₂²⋊C₄	—	10	1	no	—
511	C₂²⋊C₄	—	10	1	no	—
512	C₂²⋊C₄	—	10	1	no	—
513	C₂²⋊C₄	—	10	1	no	—
514	C₄²	—	5	1	no	—
515	C₄²	—	5	1	no	—
516	C₄²	—	5	1	no	—
517	C₄²	—	10	1	no	—
518	C₄²	—	10	1	no	—
519	C₄²	—	10	1	no	—
520	C₄²	C₂³×D₅	1	1	yes	characteristic
521	C₂×C₅	—	4	2	no	—
522	C₂×C₅	—	8	1	no	—
523	C₂×C₅	C₂×#435	1	1	yes	characteristic
524	C₂×C₅	#2946	1	1	yes	characteristic
525	C₂×C₅	#2956	1	1	yes	characteristic
526	D₅	—	2	2	no	—
527	D₅	—	8	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	5	1	no	—
531	C₂³	—	10	1	no	—
532	C₂³	—	20	2	no	—
533	C₂³	—	40	1	no	—
534	C₂³	—	40	1	no	—
535	Q₈	—	5	2	no	—
536	Q₈	—	10	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	10	4	no	—
541	D₄	—	10	1	no	—
542	D₄	—	10	1	no	—
543	D₄	—	20	2	no	—
544	D₄	D₅×M₁₆	1	2	yes	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	5	1	no	—
552	C₂×C₄	—	5	2	no	—
553	C₂×C₄	—	5	2	no	—
554	C₂×C₄	—	5	1	no	—
555	C₂×C₄	—	5	1	no	—
556	C₂×C₄	—	10	4	no	—
557	C₂×C₄	—	10	1	no	—
558	C₂×C₄	—	10	1	no	—
559	C₂×C₄	—	10	1	no	—
560	C₂×C₄	—	10	1	no	—
561	C₂×C₄	—	10	1	no	—
562	C₂×C₄	—	20	1	no	—
563	C₂×C₄	—	20	1	no	—
564	C₂×C₄	—	20	1	no	—
565	C₂×C₄	—	40	1	no	—
566	C₂×C₄	—	40	1	no	—
567	C₂×C₄	—	40	1	no	—
568	C₂×C₄	—	40	1	no	—
569	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
570	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
571	C₂×C₄	D₅×#41	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	2	1	no	—
574	C₈	—	2	1	no	—
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	4	1	no	—
578	C₈	—	4	1	no	—
579	C₈	—	10	1	no	—
580	C₈	—	10	1	no	—
581	C₈	—	10	1	no	—
582	C₈	—	10	1	no	—
583	C₈	—	20	1	no	—
584	C₈	—	20	1	no	—
585	C₈	—	20	1	no	—
586	C₅	#17875	1	1	yes	characteristic, complemented, Sylow
587	C₂²	—	2	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	5	2	no	—
594	C₂²	—	10	1	no	—
595	C₂²	—	10	1	no	—
596	C₂²	—	20	1	no	—
597	C₂²	—	20	1	no	—
598	C₂²	—	20	1	no	—
599	C₂²	—	40	4	no	—
600	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	5	2	no	—
605	C₄	—	10	2	no	—
606	C₄	—	10	1	no	—
607	C₄	—	10	1	no	—
608	C₄	—	20	1	no	—
609	C₄	—	20	1	no	—
610	C₄	C₂×D₅×M₁₆	1	1	yes	characteristic
611	C₄	D₅×#131	1	1	yes	characteristic
612	C₄	#66108	1	1	yes	characteristic
613	C₄	#66109	1	1	yes	characteristic
614	C₂	—	4	2	no	—
615	C₂	—	8	1	no	—
616	C₂	—	10	2	no	—
617	C₂	—	40	1	no	—
618	C₂	D₅×#435	1	1	yes	characteristic
619	C₂	#10611597	1	1	yes	characteristic
620	C₂	#10611620	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1586	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4057	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1586	D₅
hypocenter	C₅	#17875
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1586

Complements

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

N	H ≅ G/N	type
2. #10611274	C₂	semidirect
3. #10611136	C₂	semidirect
4. C₅×#1586	C₂	semidirect
5. #10601672	C₂	semidirect
6. #10601657	C₂	semidirect
7. #10601634	C₂	semidirect
8. #10599321	C₂	semidirect
9. #10599313	C₂	semidirect
10. #10598958	C₂	semidirect
11. D₅×D₄⋊C₈	C₂	semidirect
12. #10598952	C₂	semidirect
13. #10598950	C₂	semidirect
14. #10598881	C₂	semidirect
15. #10598862	C₂	semidirect
21. C₅×C₈×D₄	C₂²	semidirect
30. D₄×#168	C₂²	semidirect
36. #65119	C₂²	semidirect
50. C₈×Dic₁₀	C₂²	semidirect
51. C₅×#334	C₂²	semidirect
53. C₅×D₄⋊C₈	C₂²	semidirect
54. C₅×#322	C₂²	semidirect
56. D₄⋊#168	C₂²	semidirect
57. #64704	C₂²	semidirect
59. #64700	C₂²	semidirect
60. #64699	C₂²	semidirect
62. #64678	C₂²	semidirect
63. #64676	C₂²	semidirect
64. #64675	C₂²	semidirect
65. #64675	C₂²	semidirect
66. #64674	C₂²	semidirect
152. #1586	D₅	semidirect
172. #711	M₁₆	semidirect
256. C₈×D₄	C₂×D₅	semidirect
272. #334	C₂×D₅	semidirect
280. D₄⋊C₈	C₂×D₅	semidirect
284. #322	C₂×D₅	semidirect
586. C₅	#17875	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4057	2
#10611274	2
#10611136	2
C₅×#1586	2
#10601672	2
#10601657	2
#10601634	2
#10599321	2
#10599313	2
#10598958	2
D₅×D₄⋊C₈	2
#10598952	2
#10598950	2
#10598881	2
#10598862	2
#17875	5