Subgroups — C₅×#17944 #11940664

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3107	C₂	1	1	yes	maximal, characteristic
2	C₅×#2965	C₂	1	1	yes	maximal, characteristic
3	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1591	C₂	1	2	yes	maximal, complemented
5	C₅×#1590	C₂	1	2	yes	maximal, complemented
6	C₅×#1588	C₂	1	2	yes	maximal, complemented
7	C₅×#1587	C₂	1	2	yes	maximal, complemented
8	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1489	C₂	1	1	yes	maximal, characteristic
10	C₅×#1485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#485	C₄	1	2	yes	—
15	C₅×#475	C₄	1	1	yes	characteristic
16	C₅×#474	C₄	1	1	yes	characteristic
17	C₅×#462	C₄	1	1	yes	characteristic
18	C₅×#461	C₄	1	1	yes	characteristic
19	C₅×#452	C₄	1	2	yes	—
20	C₅×#446	—	2	1	no	—
21	C₅×#446	C₂²	1	1	yes	characteristic
22	C₅×#446	C₂²	1	2	yes	—
23	C₅×#446	C₂²	1	1	yes	characteristic
24	C₅×C₈×Q₈	—	2	1	no	—
25	C₅×C₈×Q₈	C₂²	1	2	yes	—
26	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
28	C₅×#436	C₂²	1	1	yes	characteristic
29	C₅×#436	C₂²	1	1	yes	characteristic
30	C₅×#435	—	2	1	no	—
31	C₅×#435	—	2	1	no	—
32	C₅×#431	—	2	1	no	—
33	C₅×#431	C₂²	1	1	yes	characteristic
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₅×#424	—	2	1	no	—
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₅×#405	—	2	1	no	—
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	2	yes	—
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₅×D₄⋊C₈	C₂²	1	2	yes	—
47	C₅×#322	C₂²	1	2	yes	—
48	C₅×C₈²	C₂²	1	2	yes	—
49	#17944	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₅×#125	—	2	1	no	—
62	C₅×C₂²⋊Q₈	—	2	1	no	—
63	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
64	C₄×C₅×Q₈	—	2	1	no	—
65	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂³	1	2	yes	—
67	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
71	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₅×#117	—	2	1	no	—
73	C₅×#117	—	2	1	no	—
74	C₅×#117	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	C₂×C₄	1	2	yes	—
78	C₅×#106	C₂×C₄	1	2	yes	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	2	yes	—
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×#103	C₂×C₄	1	2	yes	—
90	C₅×#103	C₂×C₄	1	2	yes	—
91	C₅×#103	C₂×C₄	1	2	yes	—
92	C₅×#102	C₂×C₄	1	2	yes	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
97	C₅×#97	—	2	1	no	—
98	C₅×#97	—	2	1	no	—
99	C₅×#97	—	2	2	no	—
100	C₅×#97	—	2	1	no	—
101	C₄×C₅×C₈	—	2	2	no	—
102	C₄×C₅×C₈	—	2	1	no	—
103	C₄×C₅×C₈	D₄	1	1	yes	characteristic
104	C₄×C₅×C₈	D₄	1	1	yes	characteristic
105	C₄×C₅×C₈	C₂³	1	2	yes	—
106	C₄×C₅×C₈	C₂³	1	2	yes	—
107	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	#3107	C₂×C₅	1	1	yes	characteristic
110	#2965	C₂×C₅	1	1	yes	characteristic
111	#2960	C₂×C₅	1	1	yes	characteristic, complemented
112	#1591	C₂×C₅	1	2	yes	complemented
113	#1590	C₂×C₅	1	2	yes	complemented
114	#1588	C₂×C₅	1	2	yes	complemented
115	#1587	C₂×C₅	1	2	yes	complemented
116	#1574	C₂×C₅	1	1	yes	characteristic, complemented
117	#1489	C₂×C₅	1	1	yes	characteristic
118	#1485	C₂×C₅	1	1	yes	characteristic, complemented
119	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
120	C₅×#41	—	4	1	no	—
121	C₅×#41	—	4	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	#41	1	1	yes	characteristic
133	C₅×Q₁₆	—	4	2	no	—
134	C₅×SD₁₆	—	4	2	no	—
135	C₅×M₁₆	—	2	4	no	—
136	C₅×M₁₆	—	4	2	no	—
137	C₅×M₁₆	—	4	2	no	—
138	C₅×M₁₆	—	4	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	4	1	no	—
145	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
160	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
161	C₅×C₂²⋊C₄	—	2	2	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅	#41	1	1	yes	characteristic
172	C₄²×C₅	C₂⁴	1	1	yes	characteristic
173	#533	C₂²×C₅	1	1	yes	characteristic
174	C₄×#41	C₂²×C₅	1	1	yes	characteristic
175	#485	C₄×C₅	1	2	yes	—
176	#475	C₄×C₅	1	1	yes	characteristic
177	#474	C₄×C₅	1	1	yes	characteristic
178	#462	C₄×C₅	1	1	yes	characteristic
179	#461	C₄×C₅	1	1	yes	characteristic
180	#452	C₄×C₅	1	2	yes	—
181	#446	—	2	1	no	—
182	#446	C₂²×C₅	1	1	yes	characteristic
183	#446	C₂²×C₅	1	2	yes	—
184	#446	C₂²×C₅	1	1	yes	characteristic
185	C₈×Q₈	—	2	1	no	—
186	C₈×Q₈	C₂²×C₅	1	2	yes	—
187	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
188	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
189	#436	C₂²×C₅	1	1	yes	characteristic
190	#436	C₂²×C₅	1	1	yes	characteristic
191	#435	—	2	1	no	—
192	#435	—	2	1	no	—
193	#431	—	2	1	no	—
194	#431	C₂²×C₅	1	1	yes	characteristic
195	#431	C₂²×C₅	1	1	yes	characteristic
196	#424	—	2	1	no	—
197	#423	C₂²×C₅	1	1	yes	characteristic
198	#405	—	2	1	no	—
199	C₄×M₁₆	—	2	1	no	—
200	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
202	#335	C₂²×C₅	1	2	yes	—
203	#334	C₂²×C₅	1	2	yes	—
204	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
205	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
206	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
207	D₄⋊C₈	C₂²×C₅	1	2	yes	—
208	#322	C₂²×C₅	1	2	yes	—
209	C₈²	C₂²×C₅	1	2	yes	—
210	C₂³×C₅	—	2	1	no	—
211	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
212	C₅×Q₈	—	2	2	no	—
213	C₅×Q₈	—	2	1	no	—
214	C₅×Q₈	—	2	2	no	—
215	C₅×Q₈	—	2	1	no	—
216	C₅×Q₈	—	4	2	no	—
217	C₅×D₄	—	2	1	no	—
218	C₅×D₄	—	2	1	no	—
219	C₅×D₄	—	4	2	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₅×C₈	—	2	4	no	—
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	2	2	no	—
243	C₅×C₈	—	2	1	no	—
244	C₅×C₈	—	2	1	no	—
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	—	4	1	no	—
247	C₅×C₈	—	4	1	no	—
248	C₅×C₈	—	4	2	no	—
249	C₅×C₈	#137	1	2	yes	—
250	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
252	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
258	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
259	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
260	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
261	#125	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
266	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
267	C₄×Q₈	C₂³×C₅	1	2	yes	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
271	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
272	#117	—	2	1	no	—
273	#117	—	2	1	no	—
274	#117	C₂×C₄×C₅	1	1	yes	characteristic
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	#107	C₂×C₄×C₅	1	2	yes	—
278	#106	C₂×C₄×C₅	1	2	yes	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
285	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
286	C₄⋊C₈	C₂³×C₅	1	2	yes	—
287	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
289	#103	C₂×C₄×C₅	1	2	yes	—
290	#103	C₂×C₄×C₅	1	2	yes	—
291	#103	C₂×C₄×C₅	1	2	yes	—
292	#102	C₂×C₄×C₅	1	2	yes	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
297	#97	—	2	1	no	—
298	#97	—	2	1	no	—
299	#97	—	2	2	no	—
300	#97	—	2	1	no	—
301	C₄×C₈	—	2	2	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	C₅×D₄	1	1	yes	characteristic
304	C₄×C₈	C₅×D₄	1	1	yes	characteristic
305	C₄×C₈	C₂³×C₅	1	2	yes	—
306	C₄×C₈	C₂³×C₅	1	2	yes	—
307	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
308	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
309	C₂²×C₅	—	2	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	4	1	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	4	1	no	—
322	C₄×C₅	—	4	1	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	#443	1	2	yes	—
325	C₄×C₅	#568	1	1	yes	characteristic
326	C₄×C₅	#568	1	1	yes	characteristic
327	C₄×C₅	C₂×#137	1	1	yes	characteristic
328	C₄×C₅	#575	1	1	yes	characteristic
329	#41	—	4	1	no	—
330	#41	—	4	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
333	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₅×#41	1	1	yes	characteristic
342	Q₁₆	—	4	2	no	—
343	SD₁₆	—	4	2	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	—	4	2	no	—
347	M₁₆	—	4	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
355	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
356	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
368	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
379	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
380	C₄²	C₅×#41	1	1	yes	characteristic
381	C₄²	C₂⁴×C₅	1	1	yes	characteristic
382	C₂×C₅	—	4	1	no	—
383	C₂×C₅	—	8	1	no	—
384	C₂×C₅	#2930	1	1	yes	characteristic
385	C₂×C₅	C₄×#137	1	1	yes	characteristic
386	C₂×C₅	C₂×#443	1	1	yes	characteristic
387	C₂³	—	2	1	no	—
388	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	1	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	4	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
413	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	C₅×#137	1	2	yes	—
427	C₅	#17944	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	C₅×#443	1	2	yes	—
444	C₄	C₅×#568	1	1	yes	characteristic
445	C₄	C₅×#568	1	1	yes	characteristic
446	C₄	C₂×C₅×#137	1	1	yes	characteristic
447	C₄	C₅×#575	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	8	1	no	—
450	C₂	C₅×#2930	1	1	yes	characteristic
451	C₂	C₄×C₅×#137	1	1	yes	characteristic
452	C₂	C₂×C₅×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2960	C₂	semidirect
4. C₅×#1591	C₂	semidirect
5. C₅×#1590	C₂	semidirect
6. C₅×#1588	C₂	semidirect
7. C₅×#1587	C₂	semidirect
8. C₅×#1574	C₂	semidirect
10. C₅×#1485	C₂	semidirect
11. C₅×C₈×M₁₆	C₂	semidirect
49. #17944	C₅	direct (N × H)
111. #2960	C₂×C₅	semidirect
112. #1591	C₂×C₅	semidirect
113. #1590	C₂×C₅	semidirect
114. #1588	C₂×C₅	semidirect
115. #1587	C₂×C₅	semidirect
116. #1574	C₂×C₅	semidirect
118. #1485	C₂×C₅	semidirect
119. C₈×M₁₆	C₂×C₅	semidirect
427. C₅	#17944	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3107	2
C₅×#2965	2
C₅×#2960	2
C₅×#1591	2
C₅×#1590	2
C₅×#1588	2
C₅×#1587	2
C₅×#1574	2
C₅×#1489	2
C₅×#1485	2
C₅×C₈×M₁₆	2
#17944	5

Subgroups — C5×#17944 #11940664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17944 #11940664