Subgroups — #12068741

Order 1280.

754 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	C₄×#4095	C₂	1	1	yes	maximal, characteristic
2	#10614251	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611017	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601539	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64679	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#681	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599007	C₂	1	2	yes	maximal, complemented
9	#10599005	C₂	1	2	yes	maximal, complemented
10	#10598944	C₂	1	2	yes	maximal, complemented
11	#10598941	C₂	1	2	yes	maximal, 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×#431	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
17	#65521	C₄	1	1	yes	characteristic
18	#65315	C₄	1	2	yes	—
19	C₄×#688	C₂²	1	2	yes	—
20	Q₈×#168	C₂²	1	2	yes	complemented
21	#65303	C₄	1	2	yes	—
22	C₄×#686	C₂²	1	2	yes	—
23	D₄×#168	—	2	2	no	—
24	D₄×#168	C₂²	1	2	yes	complemented
25	#65290	C₄	1	1	yes	characteristic
26	#65284	C₄	1	1	yes	characteristic
27	#65214	—	2	1	no	—
28	#65214	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#168	—	2	1	no	—
30	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
31	C₄×#681	C₂²	1	1	yes	characteristic
32	#65123	C₂²	1	2	yes	—
33	#65123	C₂²	1	2	yes	—
34	D₅×C₂²⋊C₈	—	2	2	no	—
35	C₈×D₂₀	—	2	1	no	—
36	C₈×D₂₀	—	2	1	no	—
37	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	#64700	C₂²	1	2	yes	complemented
42	#64699	C₂²	1	2	yes	complemented
43	#64679	C₂²	1	2	yes	—
44	#64679	C₂²	1	2	yes	—
45	#64674	C₂²	1	2	yes	complemented
46	C₈×#168	C₂²	1	2	yes	complemented
47	#17852	—	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	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
54	C₄×C₅×D₄	—	2	1	no	—
55	C₄×C₅×D₄	—	2	1	no	—
56	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₅×#117	—	2	1	no	—
59	C₅×#117	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	—	2	1	no	—
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	#4095	C₈	1	8	yes	complemented
63	C₂×#688	C₂×C₄	1	2	yes	—
64	C₂×#686	C₂×C₄	1	2	yes	—
65	C₂×#685	—	2	1	no	—
66	C₂×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
67	C₂×#681	C₂×C₄	1	1	yes	characteristic
68	C₂×#681	C₂×C₄	1	1	yes	characteristic
69	C₂²×#168	—	2	1	no	—
70	C₂²×#168	—	2	2	no	—
71	C₂×C₈×D₅	—	2	2	no	—
72	C₂×C₈×D₅	—	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	C₂³	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₅×C₂²⋊C₈	—	2	1	no	—
80	C₄×C₅×C₈	—	2	1	no	—
81	C₄×C₅×C₈	—	2	1	no	—
82	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
84	#3967	C₂×C₄	1	2	yes	—
85	#3964	C₂×C₄	1	2	yes	—
86	C₂²⋊#168	—	2	2	no	—
87	C₂²⋊#168	D₄	1	2	yes	—
88	#3952	—	2	2	no	—
89	#3952	—	2	2	no	—
90	#3941	C₂×C₄	1	2	yes	—
91	#3941	C₂×C₄	1	2	yes	—
92	#3940	C₂×C₄	1	2	yes	—
93	#3939	C₂×C₄	1	2	yes	—
94	C₄⋊#168	—	2	1	no	—
95	C₄⋊#168	—	2	2	no	—
96	C₄⋊#168	D₄	1	1	yes	characteristic
97	C₄⋊#168	D₄	1	1	yes	characteristic
98	C₄⋊#168	C₂³	1	2	yes	—
99	#3935	C₂×C₄	1	2	yes	—
100	C₄×#168	—	2	2	no	—
101	C₄×#168	C₂³	1	2	yes	—
102	C₄×#168	C₂³	1	2	yes	—
103	#2988	—	5	1	no	—
104	#2972	—	5	1	no	—
105	C₄×AGL(1,ℤ/8)	—	5	1	no	—
106	#1580	—	5	2	no	—
107	SD₁₆⋊C₈	—	5	2	no	—
108	C₈×SD₁₆	—	5	2	no	—
109	C₈×D₈	—	5	2	no	—
110	#1565	—	5	1	no	—
111	#1476	D₅	1	1	yes	characteristic, complemented
112	C₂×D₄⋊C₈	—	5	1	no	—
113	C₈×M₁₆	—	5	1	no	—
114	C₂³×D₅	—	2	1	no	—
115	C₅×#41	—	2	2	no	—
116	C₅×#41	C₂×C₈	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	1	no	—
128	C₂×D₂₀	—	2	2	no	—
129	C₂×D₂₀	C₂×C₈	1	4	yes	complemented
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	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	4	2	no	—
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	C₂×C₈	1	8	yes	complemented
155	#686	C₂×C₈	1	8	yes	complemented
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	C₂×C₈	1	4	yes	complemented
162	C₂×#168	—	2	2	no	—
163	C₂×#168	—	8	2	no	—
164	C₂×#168	—	8	1	no	—
165	C₂×#168	C₂²×C₄	1	2	yes	—
166	C₂×#168	C₂²×C₄	1	2	yes	—
167	C₂×#168	C₂×D₄	1	2	yes	—
168	C₂×#168	C₂×D₄	1	2	yes	—
169	C₈×D₅	—	8	2	no	—
170	C₈×D₅	—	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	—	5	2	no	—
175	#442	—	5	2	no	—
176	#440	—	5	2	no	—
177	C₄×SD₁₆	—	5	2	no	—
178	C₄×D₈	—	5	2	no	—
179	C₈×D₄	—	5	2	no	—
180	C₈×D₄	—	5	2	no	—
181	C₈×D₄	—	5	2	no	—
182	C₈×D₄	—	10	1	no	—
183	C₈×D₄	—	10	1	no	—
184	C₈×D₄	—	10	2	no	—
185	#431	—	5	1	no	—
186	#431	—	10	1	no	—
187	#431	C₂×D₅	1	1	yes	characteristic
188	#428	—	5	1	no	—
189	C₂×C₄⋊C₈	—	5	1	no	—
190	C₂×C₄⋊C₈	—	10	1	no	—
191	#418	—	5	1	no	—
192	#417	—	5	1	no	—
193	C₂×C₂²⋊C₈	—	10	2	no	—
194	C₄×M₁₆	—	5	1	no	—
195	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
196	#335	—	5	2	no	—
197	#334	—	5	2	no	—
198	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
199	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
200	D₄⋊C₈	—	5	2	no	—
201	D₄⋊C₈	—	5	2	no	—
202	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
203	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
204	#322	—	5	2	no	—
205	C₈²	—	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	—	2	4	no	—
210	C₂²×D₅	—	8	1	no	—
211	C₂²×D₅	—	8	1	no	—
212	C₅×Q₈	—	2	1	no	—
213	C₅×Q₈	C₂²×C₈	1	2	yes	—
214	C₅×D₄	—	2	4	no	—
215	C₅×D₄	—	2	1	no	—
216	C₅×D₄	C₂²×C₈	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	C₂²×C₈	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	4	no	—
239	D₂₀	C₂²×C₈	1	4	yes	—
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	—	4	1	no	—
245	C₅×C₈	—	4	1	no	—
246	C₅×C₈	—	4	1	no	—
247	#168	—	2	2	no	—
248	#168	—	2	2	no	—
249	#168	—	2	2	no	—
250	#168	—	4	2	no	—
251	#168	C₂²×C₈	1	4	yes	—
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)	—	5	8	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	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	10	2	no	—
262	C₂²×C₈	—	10	2	no	—
263	C₂²×C₈	—	10	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	—	5	1	no	—
284	C₄⋊C₈	—	5	1	no	—
285	C₄⋊C₈	—	5	2	no	—
286	C₄⋊C₈	—	10	2	no	—
287	C₄⋊C₈	—	10	1	no	—
288	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
290	#103	—	5	2	no	—
291	#102	—	5	2	no	—
292	#102	—	5	2	no	—
293	#102	—	5	2	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	5	2	no	—
296	C₂²⋊C₈	—	10	2	no	—
297	C₂²⋊C₈	—	10	2	no	—
298	C₂²⋊C₈	—	10	2	no	—
299	#97	—	5	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	5	2	no	—
303	C₄×C₈	—	5	2	no	—
304	C₄×C₈	—	10	2	no	—
305	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
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	C₈×D₄	1	2	yes	—
313	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×D₅	—	2	4	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	C₈×D₄	1	2	yes	—
325	C₄×C₅	C₂³×C₈	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	C₈×D₅	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	—	5	4	no	—
337	C₂×D₄	—	10	1	no	—
338	C₂×D₄	—	10	2	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	D₄×D₅	1	1	yes	characteristic
350	C₂²×C₄	#711	1	1	yes	characteristic
351	SD₁₆	—	5	8	no	—
352	D₈	—	5	8	no	—
353	M₁₆	—	5	4	no	—
354	M₁₆	—	10	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	5	2	no	—
361	C₂×C₈	—	5	2	no	—
362	C₂×C₈	—	5	2	no	—
363	C₂×C₈	—	5	2	no	—
364	C₂×C₈	—	10	2	no	—
365	C₂×C₈	—	40	2	no	—
366	C₂×C₈	—	40	2	no	—
367	C₂×C₈	—	40	2	no	—
368	C₂×C₈	—	40	1	no	—
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	D₄×D₅	1	1	yes	characteristic
385	C₄²	#711	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×C₈×D₄	1	1	yes	characteristic
390	C₂×C₅	#2946	1	1	yes	characteristic
391	C₂×C₅	#2956	1	1	yes	characteristic
392	D₅	—	4	4	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	10	2	no	—
395	C₂³	—	10	4	no	—
396	C₂³	—	40	1	no	—
397	C₂³	—	40	1	no	—
398	C₂³	#4027	1	1	yes	characteristic
399	Q₈	—	2	1	no	—
400	Q₈	C₂×C₈×D₅	1	2	yes	—
401	D₄	—	2	4	no	—
402	D₄	—	2	1	no	—
403	D₄	—	5	4	no	—
404	D₄	—	10	2	no	—
405	D₄	—	10	4	no	—
406	D₄	C₂×C₈×D₅	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	4	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	#4027	1	1	yes	characteristic
423	C₂×C₄	#4027	1	1	yes	characteristic
424	C₂×C₄	#4027	1	1	yes	characteristic
425	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
426	C₂×C₄	#4053	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
429	C₂×C₄	C₂×#711	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	5	4	no	—
435	C₈	—	10	2	no	—
436	C₈	—	10	2	no	—
437	C₈	—	10	2	no	—
438	C₈	—	20	2	no	—
439	C₅	#17852	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	—	10	4	no	—
446	C₂²	—	20	2	no	—
447	C₂²	—	20	2	no	—
448	C₂²	—	40	4	no	—
449	C₂²	#65014	1	2	yes	—
450	C₂²	C₂×#4027	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	20	2	no	—
458	C₄	#65014	1	2	yes	—
459	C₄	C₂²×C₈×D₅	1	1	yes	characteristic
460	C₄	C₂×#4053	1	1	yes	characteristic
461	C₄	#66103	1	1	yes	characteristic
462	C₄	#66104	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	20	4	no	—
466	C₂	C₂×#65014	1	1	yes	characteristic
467	C₂	#10610551	1	1	yes	characteristic
468	C₂	#10610711	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₈
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1476	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#4095	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1476	D₅
hypocenter	C₅	#17852
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #10614251	C₂	semidirect
3. #10611017	C₂	semidirect
4. C₅×#1476	C₂	semidirect
5. #10601539	C₂	semidirect
6. C₂×#64679	C₂	semidirect
7. C₈×#681	C₂	semidirect
8. #10599007	C₂	semidirect
9. #10599005	C₂	semidirect
10. #10598944	C₂	semidirect
11. #10598941	C₂	semidirect
20. Q₈×#168	C₂²	semidirect
24. D₄×#168	C₂²	semidirect
37. C₅×Q₈⋊C₈	C₂²	semidirect
38. C₅×Q₈⋊C₈	C₂²	semidirect
39. C₅×D₄⋊C₈	C₂²	semidirect
40. C₅×D₄⋊C₈	C₂²	semidirect
41. #64700	C₂²	semidirect
42. #64699	C₂²	semidirect
45. #64674	C₂²	semidirect
46. C₈×#168	C₂²	semidirect
62. #4095	C₈	semidirect
111. #1476	D₅	semidirect
116. C₅×#41	C₂×C₈	semidirect
129. C₂×D₂₀	C₂×C₈	semidirect
154. #688	C₂×C₈	semidirect
155. #686	C₂×C₈	semidirect
161. #681	C₂×C₈	semidirect
198. Q₈⋊C₈	C₂×D₅	semidirect
199. Q₈⋊C₈	C₂×D₅	semidirect
202. D₄⋊C₈	C₂×D₅	semidirect
203. D₄⋊C₈	C₂×D₅	semidirect
332. #41	C₈×D₅	semidirect
439. C₅	#17852	semidirect

Maximal subgroups

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

subgroup	index
C₄×#4095	2
#10614251	2
#10611017	2
C₅×#1476	2
#10601539	2
C₂×#64679	2
C₈×#681	2
#10599007	2
#10599005	2
#10598944	2
#10598941	2
#17852	5