Subgroups — #12068949

Order 1280.

698 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2988	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#4095	C₂	1	1	yes	maximal, characteristic
3	#10611019	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602431	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601729	C₂	1	2	yes	maximal, complemented
6	#10601726	C₂	1	2	yes	maximal, complemented
7	#10601637	C₂	1	2	yes	maximal, complemented
8	#10601634	C₂	1	2	yes	maximal, complemented
9	#10601534	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#64703	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×#4095	C₄	1	1	yes	characteristic
14	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic
15	C₅×C₈×Q₈	C₂²	1	2	yes	complemented
16	C₅×C₈×D₄	—	2	2	no	—
17	C₅×C₈×D₄	C₂²	1	2	yes	complemented
18	C₅×#431	—	2	1	no	—
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	—	2	1	no	—
21	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	#65521	C₄	1	1	yes	characteristic
23	#65315	C₄	1	2	yes	—
24	C₄×#688	C₂²	1	2	yes	—
25	#65303	C₄	1	2	yes	—
26	C₄×#686	C₂²	1	2	yes	—
27	#65290	C₄	1	1	yes	characteristic
28	#65284	C₄	1	1	yes	characteristic
29	#65214	C₂²	1	1	yes	characteristic
30	C₄×#681	C₂²	1	1	yes	characteristic
31	C₂×C₄×#168	C₂²	1	1	yes	characteristic
32	#65127	—	2	1	no	—
33	#65127	—	2	1	no	—
34	#65015	—	2	2	no	—
35	#64977	C₂²	1	2	yes	—
36	#64977	C₂²	1	2	yes	—
37	Q₈⋊#168	C₂²	1	1	yes	characteristic, complemented
38	Q₈⋊#168	C₂²	1	1	yes	characteristic, complemented
39	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
40	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
41	#64703	C₂²	1	2	yes	—
42	#64703	C₂²	1	2	yes	—
43	#64700	C₂²	1	2	yes	complemented
44	#64699	C₂²	1	2	yes	complemented
45	#64675	C₂²	1	2	yes	complemented
46	#64674	C₂²	1	2	yes	complemented
47	#17875	—	5	1	no	maximal, Sylow
48	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₂₀	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₅	—	2	1	no	—
51	C₂²×C₅×C₈	—	2	1	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₄×C₅×D₄	—	2	1	no	—
56	C₄×C₅×D₄	—	2	1	no	—
57	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
59	C₅×#117	—	2	1	no	—
60	C₅×#117	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	—	2	1	no	—
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	#4095	—	2	4	no	—
64	C₂×#688	C₂×C₄	1	2	yes	—
65	C₂×#686	C₂×C₄	1	2	yes	—
66	C₂×#685	—	2	1	no	—
67	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
68	C₂×#681	C₂×C₄	1	1	yes	characteristic
69	C₂×#681	C₂×C₄	1	1	yes	characteristic
70	C₂²×#168	—	2	1	no	—
71	C₂×#676	—	2	2	no	—
72	C₂×#676	—	2	2	no	—
73	C₄×D₂₀	—	2	1	no	—
74	C₄×D₂₀	—	2	1	no	—
75	C₄×D₂₀	C₂×C₄	1	2	yes	—
76	C₄×D₂₀	C₂³	1	2	yes	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	2	1	no	—
79	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
80	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	C₅×C₂²⋊C₈	D₄	1	2	yes	—
84	C₄×C₅×C₈	—	2	2	no	—
85	C₄×C₅×C₈	C₂³	1	2	yes	—
86	#3967	C₂×C₄	1	2	yes	—
87	#3964	C₂×C₄	1	2	yes	—
88	C₂²⋊#168	—	2	1	no	—
89	#3952	—	2	2	no	—
90	#3952	—	2	2	no	—
91	#3941	C₂×C₄	1	2	yes	—
92	#3941	C₂×C₄	1	2	yes	—
93	#3940	C₂×C₄	1	2	yes	—
94	#3939	C₂×C₄	1	2	yes	—
95	C₄⋊#168	C₂³	1	1	yes	characteristic
96	C₄⋊#168	C₂³	1	1	yes	characteristic
97	#3935	C₂×C₄	1	2	yes	—
98	C₄×#168	—	2	1	no	—
99	C₄×#168	—	2	1	no	—
100	C₄×#168	C₂³	1	1	yes	characteristic
101	C₄×#168	C₂³	1	1	yes	characteristic
102	C₄×#168	C₂³	1	2	yes	—
103	#2988	D₅	1	1	yes	characteristic, complemented
104	#2975	—	5	1	no	—
105	C₄×AGL(1,ℤ/8)	—	5	1	no	—
106	#1588	—	5	2	no	—
107	#1586	—	5	2	no	—
108	#1583	—	5	2	no	—
109	#1581	—	5	2	no	—
110	#1565	—	5	1	no	—
111	#1476	—	5	1	no	—
112	C₂×D₄⋊C₈	—	5	1	no	—
113	#1451	—	5	1	no	—
114	C₂³×D₅	—	2	1	no	—
115	C₅×#41	—	2	2	no	—
116	C₅×#41	M₁₆	1	4	yes	complemented
117	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	#41	1	1	yes	characteristic
126	C₂²×Dic₅	—	2	1	no	—
127	C₂×D₂₀	—	2	2	no	—
128	C₂×D₂₀	—	2	2	no	—
129	C₂×D₂₀	—	2	1	no	—
130	C₂×D₂₀	C₂²×C₄	1	2	yes	—
131	C₂×C₄×D₅	—	2	2	no	—
132	C₂×C₄×D₅	—	2	2	no	—
133	C₂×C₄×D₅	—	8	1	no	—
134	C₂×C₄×D₅	—	8	1	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	8	2	no	—
137	C₂×C₅×C₈	—	8	1	no	—
138	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
139	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
143	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
144	C₅×C₂²⋊C₄	—	2	1	no	—
145	C₅×C₂²⋊C₄	—	2	1	no	—
146	C₅×C₂²⋊C₄	—	2	1	no	—
147	C₄²×C₅	—	2	1	no	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₅	#41	1	1	yes	characteristic
153	C₄²×C₅	C₂⁴	1	1	yes	characteristic
154	#688	—	2	4	no	—
155	#686	—	2	4	no	—
156	#685	—	2	2	no	—
157	#685	—	2	2	no	—
158	C₄⋊Dic₅	—	2	1	no	—
159	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
160	#681	—	2	2	no	—
161	#681	—	2	2	no	—
162	C₂×#168	—	2	1	no	—
163	C₂×#168	—	2	1	no	—
164	C₂×#168	—	2	1	no	—
165	C₂×#168	—	2	1	no	—
166	C₂×#168	—	4	2	no	—
167	C₂×#168	C₂²×C₄	1	2	yes	—
168	C₂×#168	C₂²×C₄	1	2	yes	—
169	#676	—	8	2	no	—
170	#676	—	8	2	no	—
171	C₂×AGL(1,ℤ/8)	—	5	1	no	—
172	C₄×#41	C₂×D₅	1	1	yes	characteristic
173	C₂×C₄×D₄	—	5	1	no	—
174	C₈×Q₈	C₂×D₅	1	2	yes	complemented
175	#442	—	5	2	no	—
176	#440	—	5	2	no	—
177	C₄×SD₁₆	—	5	2	no	—
178	C₄×D₈	—	5	2	no	—
179	#436	—	5	2	no	—
180	#436	—	5	2	no	—
181	#436	—	10	1	no	—
182	#436	—	10	1	no	—
183	C₈×D₄	—	2	2	no	—
184	C₈×D₄	C₂×D₅	1	2	yes	complemented
185	#431	—	2	1	no	—
186	#431	—	5	1	no	—
187	#431	C₂×D₅	1	1	yes	characteristic
188	#428	—	5	1	no	—
189	C₂×C₄⋊C₈	—	2	1	no	—
190	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
191	#418	—	5	1	no	—
192	#417	—	5	1	no	—
193	#407	—	10	2	no	—
194	C₄×M₁₆	—	5	1	no	—
195	C₂×C₄×C₈	—	5	1	no	—
196	#335	—	5	2	no	—
197	#334	—	5	2	no	—
198	Q₈⋊C₈	—	5	1	no	—
199	Q₈⋊C₈	—	5	1	no	—
200	D₄⋊C₈	—	5	1	no	—
201	D₄⋊C₈	—	5	1	no	—
202	D₄⋊C₈	—	5	2	no	—
203	D₄⋊C₈	—	5	2	no	—
204	#322	—	5	2	no	—
205	#322	—	5	2	no	—
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
208	C₂²×D₅	—	2	2	no	—
209	C₂²×D₅	—	4	2	no	—
210	C₂²×D₅	—	8	1	no	—
211	C₂²×D₅	—	8	1	no	—
212	C₅×Q₈	—	2	1	no	—
213	C₅×Q₈	C₂×M₁₆	1	2	yes	—
214	C₅×D₄	—	2	4	no	—
215	C₅×D₄	—	2	1	no	—
216	C₅×D₄	C₂×M₁₆	1	2	yes	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	8	1	no	—
227	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
231	C₂×C₄×C₅	#131	1	2	yes	—
232	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
235	C₂×Dic₅	—	2	2	no	—
236	C₂×Dic₅	—	8	1	no	—
237	D₂₀	—	2	2	no	—
238	D₂₀	—	2	2	no	—
239	D₂₀	—	4	2	no	—
240	C₄×D₅	—	4	2	no	—
241	C₄×D₅	—	4	2	no	—
242	C₄×D₅	—	8	2	no	—
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	4	2	no	—
246	#168	—	2	2	no	—
247	#168	—	2	2	no	—
248	#168	—	2	2	no	—
249	#168	—	4	1	no	—
250	#168	—	4	1	no	—
251	#168	—	4	1	no	—
252	C₂×#41	C₄×D₅	1	1	yes	characteristic
253	C₂²×D₄	—	5	1	no	—
254	C₂³×C₄	—	10	1	no	—
255	AGL(1,ℤ/8)	—	10	4	no	—
256	C₂×SD₁₆	—	5	2	no	—
257	C₂×D₈	—	5	2	no	—
258	C₂×M₁₆	—	5	1	no	—
259	C₂×M₁₆	—	5	1	no	—
260	C₂×M₁₆	—	10	2	no	—
261	C₂×M₁₆	—	10	2	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	10	1	no	—
265	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
266	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	5	2	no	—
270	C₄×D₄	—	5	2	no	—
271	C₄×D₄	—	10	1	no	—
272	C₄×D₄	—	10	1	no	—
273	C₄×D₄	C₄×D₅	1	1	yes	characteristic
274	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
275	#117	—	2	1	no	—
276	#117	C₄×D₅	1	1	yes	characteristic
277	C₂×C₄⋊C₄	—	5	1	no	—
278	C₂×C₂²⋊C₄	—	10	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
281	#107	—	5	2	no	—
282	#106	—	5	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	5	1	no	—
286	C₄⋊C₈	—	5	1	no	—
287	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
288	C₄⋊C₈	C₂²⋊D₅	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₅	1	2	yes	—
290	#103	—	5	2	no	—
291	#102	—	5	2	no	—
292	#102	—	5	2	no	—
293	#102	—	5	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	10	1	no	—
296	C₂²⋊C₈	—	10	2	no	—
297	C₂²⋊C₈	—	10	2	no	—
298	C₂²⋊C₈	C₂²⋊D₅	1	2	yes	—
299	#97	—	5	2	no	—
300	C₄×C₈	—	2	2	no	—
301	C₄×C₈	—	5	2	no	—
302	C₄×C₈	—	5	1	no	—
303	C₄×C₈	—	5	1	no	—
304	C₄×C₈	—	10	1	no	—
305	C₄×C₈	—	10	1	no	—
306	C₄×C₈	C₂²×D₅	1	2	yes	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	—	2	1	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	4	1	no	—
312	C₂²×C₅	#435	1	2	yes	—
313	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×D₅	—	4	2	no	—
315	C₂×D₅	—	4	2	no	—
316	C₂×D₅	—	4	2	no	—
317	C₂×D₅	—	8	4	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	4	1	no	—
323	C₄×C₅	—	4	1	no	—
324	C₄×C₅	#435	1	2	yes	—
325	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
326	C₄×C₅	C₂×#131	1	1	yes	characteristic
327	C₄×C₅	#576	1	1	yes	characteristic
328	C₄×C₅	#577	1	1	yes	characteristic
329	Dic₅	—	4	2	no	—
330	C₂⁴	—	10	1	no	—
331	#41	—	2	2	no	—
332	#41	#676	1	4	yes	complemented
333	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	5	2	no	—
336	C₂×D₄	—	10	2	no	—
337	C₂×D₄	—	10	2	no	—
338	C₂×D₄	—	10	1	no	—
339	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	10	1	no	—
344	C₂²×C₄	—	10	2	no	—
345	C₂²×C₄	—	10	2	no	—
346	C₂²×C₄	—	40	1	no	—
347	C₂²×C₄	—	40	1	no	—
348	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
349	C₂²×C₄	#709	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
351	SD₁₆	—	10	4	no	—
352	D₈	—	10	4	no	—
353	M₁₆	—	10	2	no	—
354	M₁₆	—	10	2	no	—
355	M₁₆	—	40	2	no	—
356	M₁₆	—	40	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	5	2	no	—
359	C₂×C₈	—	5	2	no	—
360	C₂×C₈	—	8	2	no	—
361	C₂×C₈	—	8	1	no	—
362	C₂×C₈	—	10	1	no	—
363	C₂×C₈	—	10	1	no	—
364	C₂×C₈	—	10	1	no	—
365	C₂×C₈	—	10	1	no	—
366	C₂×C₈	—	20	2	no	—
367	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
368	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	5	2	no	—
372	C₄⋊C₄	—	10	1	no	—
373	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
374	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	10	2	no	—
379	C₂²⋊C₄	—	10	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
384	C₄²	#709	1	1	yes	characteristic
385	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
386	C₄²	C₂³×D₅	1	1	yes	characteristic
387	C₂×C₅	—	2	2	no	—
388	C₂×C₅	—	4	2	no	—
389	C₂×C₅	C₂×#435	1	1	yes	characteristic
390	C₂×C₅	#2946	1	1	yes	characteristic
391	C₂×C₅	#2956	1	1	yes	characteristic
392	D₅	—	8	2	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	10	2	no	—
395	C₂³	—	20	2	no	—
396	C₂³	—	40	1	no	—
397	C₂³	—	40	1	no	—
398	C₂³	C₄×C₂²⋊D₅	1	1	yes	characteristic
399	Q₈	—	2	1	no	—
400	Q₈	C₂×#676	1	2	yes	—
401	D₄	—	2	4	no	—
402	D₄	—	2	1	no	—
403	D₄	—	10	2	no	—
404	D₄	—	10	2	no	—
405	D₄	—	20	2	no	—
406	D₄	C₂×#676	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	8	1	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	20	2	no	—
419	C₂×C₄	—	20	2	no	—
420	C₂×C₄	—	40	2	no	—
421	C₂×C₄	—	40	1	no	—
422	C₂×C₄	C₂×#676	1	2	yes	—
423	C₂×C₄	#4047	1	2	yes	—
424	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
426	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
428	C₂×C₄	C₂×#709	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	10	2	no	—
434	C₈	—	10	2	no	—
435	C₈	—	10	2	no	—
436	C₈	—	20	1	no	—
437	C₈	—	20	1	no	—
438	C₈	—	20	1	no	—
439	C₅	#17875	1	1	yes	characteristic, complemented, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	20	2	no	—
446	C₂²	—	20	2	no	—
447	C₂²	—	20	2	no	—
448	C₂²	—	40	4	no	—
449	C₂²	#65400	1	2	yes	—
450	C₂²	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	20	2	no	—
458	C₄	#65400	1	2	yes	—
459	C₄	C₂²×#676	1	1	yes	characteristic
460	C₄	C₂×#4047	1	1	yes	characteristic
461	C₄	#66169	1	1	yes	characteristic
462	C₄	#66171	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	40	2	no	—
466	C₂	#10614295	1	1	yes	characteristic
467	C₂	C₂×#65400	1	1	yes	characteristic
468	C₂	#10615542	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2988	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4095	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2988	D₅
hypocenter	C₅	#17875
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2988

Complements

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

N	H ≅ G/N	type
1. C₅×#2988	C₂	semidirect
3. #10611019	C₂	semidirect
4. #10602431	C₂	semidirect
5. #10601729	C₂	semidirect
6. #10601726	C₂	semidirect
7. #10601637	C₂	semidirect
8. #10601634	C₂	semidirect
9. #10601534	C₂	semidirect
10. C₂×#64703	C₂	semidirect
11. #10601213	C₂	semidirect
15. C₅×C₈×Q₈	C₂²	semidirect
17. C₅×C₈×D₄	C₂²	semidirect
37. Q₈⋊#168	C₂²	semidirect
38. Q₈⋊#168	C₂²	semidirect
39. D₄⋊#168	C₂²	semidirect
40. D₄⋊#168	C₂²	semidirect
43. #64700	C₂²	semidirect
44. #64699	C₂²	semidirect
45. #64675	C₂²	semidirect
46. #64674	C₂²	semidirect
103. #2988	D₅	semidirect
116. C₅×#41	M₁₆	semidirect
174. C₈×Q₈	C₂×D₅	semidirect
184. C₈×D₄	C₂×D₅	semidirect
332. #41	#676	semidirect
439. C₅	#17875	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2988	2
C₄×#4095	2
#10611019	2
#10602431	2
#10601729	2
#10601726	2
#10601637	2
#10601634	2
#10601534	2
C₂×#64703	2
#10601213	2
#17875	5