Subgroups — C₅×#18004 #11940724

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3103	C₂	1	1	yes	maximal, characteristic
2	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2935	C₂	1	1	yes	maximal, characteristic
4	C₅×#1592	C₂	1	2	yes	maximal, complemented
5	C₅×#1588	C₂	1	2	yes	maximal, complemented
6	C₅×#1585	C₂	1	2	yes	maximal, complemented
7	C₅×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₅×#1571	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1492	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#481	C₄	1	2	yes	—
16	C₅×#475	C₄	1	1	yes	characteristic
17	C₅×#475	C₄	1	1	yes	characteristic
18	C₅×#460	C₄	1	1	yes	characteristic
19	C₅×#460	C₄	1	1	yes	characteristic
20	C₅×#448	C₄	1	2	yes	—
21	C₅×#446	—	2	2	no	—
22	C₅×#446	C₂²	1	2	yes	—
23	C₅×C₈×Q₈	C₂²	1	2	yes	—
24	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
25	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
26	C₅×#436	C₂²	1	2	yes	—
27	C₅×#435	—	2	2	no	—
28	C₅×C₈×D₄	C₂²	1	2	yes	—
29	C₅×#431	C₂²	1	1	yes	characteristic
30	C₅×#423	—	2	1	no	—
31	C₅×#423	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₅×#408	—	2	1	no	—
34	C₄×C₅×M₁₆	—	2	1	no	—
35	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	—
38	C₅×#335	C₂²	1	2	yes	—
39	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	2	yes	—
44	C₅×D₄⋊C₈	C₂²	1	2	yes	—
45	C₅×#322	C₂²	1	2	yes	—
46	C₅×#322	C₂²	1	2	yes	—
47	#18004	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
52	C₅×#131	—	4	4	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
56	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	—	2	1	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₅×#127	C₂×C₄	1	1	yes	characteristic
62	C₅×#124	—	2	1	no	—
63	C₅×#121	—	2	1	no	—
64	C₅×#121	C₂×C₄	1	2	yes	—
65	C₄×C₅×Q₈	—	2	1	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
70	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	C₂³	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#106	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	C₂×C₄	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	2	yes	—
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×#103	C₂×C₄	1	2	yes	—
89	C₅×#103	C₂×C₄	1	2	yes	—
90	C₅×#102	C₂×C₄	1	2	yes	—
91	C₅×#102	C₂×C₄	1	2	yes	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	2	no	—
94	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
95	C₅×#97	—	2	2	no	—
96	C₅×#97	D₄	1	2	yes	—
97	C₄×C₅×C₈	—	2	2	no	—
98	C₄×C₅×C₈	—	2	1	no	—
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₅×C₈	C₂³	1	2	yes	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#3103	C₂×C₅	1	1	yes	characteristic
104	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
105	#2935	C₂×C₅	1	1	yes	characteristic
106	#1592	C₂×C₅	1	2	yes	complemented
107	#1588	C₂×C₅	1	2	yes	complemented
108	#1585	C₂×C₅	1	2	yes	complemented
109	SD₁₆⋊C₈	C₂×C₅	1	2	yes	complemented
110	#1571	C₂×C₅	1	1	yes	characteristic, complemented
111	#1492	C₂×C₅	1	1	yes	characteristic
112	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
113	#1451	C₂×C₅	1	1	yes	characteristic, complemented
114	C₅×#41	—	4	2	no	—
115	C₅×#41	—	4	2	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	4	1	no	—
120	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₅×SD₁₆	—	2	4	no	—
133	C₅×SD₁₆	—	4	2	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	4	4	no	—
137	C₅×M₁₆	—	4	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	4	2	no	—
144	C₂×C₅×C₈	—	4	4	no	—
145	C₂×C₅×C₈	—	4	2	no	—
146	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	1	no	—
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	1	no	—
156	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₅×C₂²⋊C₄	—	2	2	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₅	#41	1	1	yes	characteristic
168	C₄²×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×#131	—	2	1	no	—
170	#532	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
172	#481	C₄×C₅	1	2	yes	—
173	#475	C₄×C₅	1	1	yes	characteristic
174	#475	C₄×C₅	1	1	yes	characteristic
175	#460	C₄×C₅	1	1	yes	characteristic
176	#460	C₄×C₅	1	1	yes	characteristic
177	#448	C₄×C₅	1	2	yes	—
178	#446	—	2	2	no	—
179	#446	C₂²×C₅	1	2	yes	—
180	C₈×Q₈	C₂²×C₅	1	2	yes	—
181	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
182	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
183	#436	C₂²×C₅	1	2	yes	—
184	#435	—	2	2	no	—
185	C₈×D₄	C₂²×C₅	1	2	yes	—
186	#431	C₂²×C₅	1	1	yes	characteristic
187	#423	—	2	1	no	—
188	#423	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
190	#408	—	2	1	no	—
191	C₄×M₁₆	—	2	1	no	—
192	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
194	#335	C₂²×C₅	1	2	yes	—
195	#335	C₂²×C₅	1	2	yes	—
196	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
197	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
198	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
199	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
200	D₄⋊C₈	C₂²×C₅	1	2	yes	—
201	D₄⋊C₈	C₂²×C₅	1	2	yes	—
202	#322	C₂²×C₅	1	2	yes	—
203	#322	C₂²×C₅	1	2	yes	—
204	C₂³×C₅	—	2	2	no	—
205	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	2	1	no	—
208	C₅×Q₈	—	2	1	no	—
209	C₅×Q₈	—	4	2	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₅×Q₈	#131	1	2	yes	complemented
212	C₅×D₄	—	2	2	no	—
213	C₅×D₄	—	2	2	no	—
214	C₅×D₄	—	4	4	no	—
215	C₅×D₄	—	4	2	no	—
216	C₅×D₄	—	8	1	no	—
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	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	8	1	no	—
229	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄×C₅	#137	1	2	yes	—
234	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	2	no	—
240	C₅×C₈	—	2	2	no	—
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	1	no	—
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	—	4	2	no	—
246	C₂×#41	—	2	1	no	—
247	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
249	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
250	#131	—	4	4	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
254	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
259	#127	C₂×C₄×C₅	1	1	yes	characteristic
260	#124	—	2	1	no	—
261	#121	—	2	1	no	—
262	#121	C₂×C₄×C₅	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
266	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
267	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
268	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	C₂³×C₅	1	2	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
275	#106	C₂×C₄×C₅	1	2	yes	—
276	#106	C₂×C₄×C₅	1	2	yes	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
282	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₅	1	2	yes	—
284	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
285	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
286	#103	C₂×C₄×C₅	1	2	yes	—
287	#103	C₂×C₄×C₅	1	2	yes	—
288	#102	C₂×C₄×C₅	1	2	yes	—
289	#102	C₂×C₄×C₅	1	2	yes	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
293	#97	—	2	2	no	—
294	#97	C₅×D₄	1	2	yes	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
299	C₄×C₈	C₂³×C₅	1	2	yes	—
300	C₄×C₈	C₂³×C₅	1	2	yes	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	4	2	no	—
306	C₂²×C₅	#440	1	2	yes	—
307	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	4	1	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	#440	1	2	yes	—
317	C₄×C₅	C₂×#131	1	1	yes	characteristic
318	C₄×C₅	#568	1	1	yes	characteristic
319	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₄×C₅	C₂×#137	1	1	yes	characteristic
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
328	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₅×#41	1	1	yes	characteristic
339	SD₁₆	—	2	4	no	—
340	SD₁₆	—	4	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	4	no	—
344	M₁₆	—	4	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	4	4	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
355	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
356	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
365	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
374	C₄²	C₅×#41	1	1	yes	characteristic
375	C₄²	C₂⁴×C₅	1	1	yes	characteristic
376	C₂×C₅	—	2	2	no	—
377	C₂×C₅	—	8	2	no	—
378	C₂×C₅	#2933	1	1	yes	characteristic
379	C₂×C₅	C₂×#440	1	1	yes	characteristic
380	C₂×C₅	#2956	1	1	yes	characteristic
381	C₂³	—	2	2	no	—
382	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	C₅×#131	1	2	yes	complemented
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	1	no	—
406	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
407	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
408	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
409	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
410	C₂×C₄	C₅×#137	1	2	yes	—
411	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₅	#18004	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₅×#440	1	2	yes	—
430	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	C₅×#440	1	2	yes	—
440	C₄	C₂×C₅×#131	1	1	yes	characteristic
441	C₄	C₅×#568	1	1	yes	characteristic
442	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₄	C₂×C₅×#137	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	8	2	no	—
446	C₂	C₅×#2933	1	1	yes	characteristic
447	C₂	C₂×C₅×#440	1	1	yes	characteristic
448	C₂	C₅×#2956	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	C₅×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×Q₈×M₁₆	C₂	semidirect
4. C₅×#1592	C₂	semidirect
5. C₅×#1588	C₂	semidirect
6. C₅×#1585	C₂	semidirect
7. C₅×SD₁₆⋊C₈	C₂	semidirect
8. C₅×#1571	C₂	semidirect
10. C₂×C₅×Q₈⋊C₈	C₂	semidirect
11. C₅×#1451	C₂	semidirect
47. #18004	C₅	direct (N × H)
104. Q₈×M₁₆	C₂×C₅	semidirect
106. #1592	C₂×C₅	semidirect
107. #1588	C₂×C₅	semidirect
108. #1585	C₂×C₅	semidirect
109. SD₁₆⋊C₈	C₂×C₅	semidirect
110. #1571	C₂×C₅	semidirect
112. C₂×Q₈⋊C₈	C₂×C₅	semidirect
113. #1451	C₂×C₅	semidirect
211. C₅×Q₈	#131	semidirect
388. Q₈	C₅×#131	semidirect
423. C₅	#18004	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×#3103	2
C₅×Q₈×M₁₆	2
C₅×#2935	2
C₅×#1592	2
C₅×#1588	2
C₅×#1585	2
C₅×SD₁₆⋊C₈	2
C₅×#1571	2
C₅×#1492	2
C₂×C₅×Q₈⋊C₈	2
C₅×#1451	2
#18004	5

Subgroups — C5×#18004 #11940724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18004 #11940724