Subgroups — C₅×#18003 #11940723

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3104	C₂	1	1	yes	maximal, characteristic
2	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×#2962	C₂	1	1	yes	maximal, characteristic
4	C₅×#1593	C₂	1	2	yes	maximal, complemented
5	C₅×#1587	C₂	1	2	yes	maximal, complemented
6	C₅×#1587	C₂	1	2	yes	maximal, complemented
7	C₅×#1579	C₂	1	2	yes	maximal, complemented
8	C₅×#1570	C₂	1	1	yes	maximal, characteristic
9	C₅×#1493	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₅×#1451	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₅×#484	C₄	1	2	yes	—
15	C₅×#477	C₄	1	1	yes	characteristic
16	C₅×#477	C₄	1	1	yes	characteristic
17	C₅×#462	C₄	1	1	yes	characteristic
18	C₅×#462	C₄	1	1	yes	characteristic
19	C₅×#451	C₄	1	2	yes	—
20	C₅×#446	—	2	2	no	—
21	C₅×#446	—	2	2	no	—
22	C₅×#446	C₂²	1	2	yes	—
23	C₅×#446	C₂²	1	2	yes	—
24	C₅×C₈×Q₈	C₂²	1	2	yes	—
25	C₅×C₈×Q₈	C₂²	1	2	yes	—
26	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#424	—	2	1	no	—
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×#405	—	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×#334	C₂²	1	2	yes	—
38	C₅×#334	C₂²	1	2	yes	—
39	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
41	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#322	C₂²	1	2	yes	—
46	C₅×#322	C₂²	1	2	yes	—
47	#18003	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
53	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	—	2	1	no	—
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₅×#125	—	2	1	no	—
59	C₅×C₂²⋊Q₈	—	2	1	no	—
60	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
61	C₄×C₅×Q₈	—	2	1	no	—
62	C₄×C₅×Q₈	—	2	1	no	—
63	C₄×C₅×Q₈	—	2	1	no	—
64	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₄×C₅×Q₈	C₂³	1	2	yes	—
68	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₅×#117	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#107	C₂×C₄	1	2	yes	—
75	C₅×#107	C₂×C₄	1	2	yes	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	2	no	—
78	C₅×C₄⋊C₈	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	2	yes	—
87	C₅×#103	C₂×C₄	1	2	yes	—
88	C₅×#103	C₂×C₄	1	2	yes	—
89	C₅×#103	C₂×C₄	1	2	yes	—
90	C₅×#103	C₂×C₄	1	2	yes	—
91	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₅×#97	—	2	2	no	—
93	C₅×#97	—	2	2	no	—
94	C₅×#97	D₄	1	2	yes	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₄×C₅×C₈	—	2	2	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	2	yes	—
101	C₄×C₅×C₈	C₂³	1	2	yes	—
102	#3104	C₂×C₅	1	1	yes	characteristic
103	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic
104	#2962	C₂×C₅	1	1	yes	characteristic
105	#1593	C₂×C₅	1	2	yes	complemented
106	#1587	C₂×C₅	1	2	yes	complemented
107	#1587	C₂×C₅	1	2	yes	complemented
108	#1579	C₂×C₅	1	2	yes	complemented
109	#1570	C₂×C₅	1	1	yes	characteristic
110	#1493	C₂×C₅	1	1	yes	characteristic
111	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic
112	#1451	C₂×C₅	1	1	yes	characteristic
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	—	4	1	no	—
117	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
119	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	#41	1	1	yes	characteristic
125	C₅×Q₁₆	—	2	4	no	—
126	C₅×Q₁₆	—	4	2	no	—
127	C₅×M₁₆	—	2	2	no	—
128	C₅×M₁₆	—	2	2	no	—
129	C₅×M₁₆	—	4	2	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	4	2	no	—
136	C₂×C₅×C₈	—	4	2	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₅×C₂²⋊C₄	—	2	2	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅	#41	1	1	yes	characteristic
163	C₄²×C₅	C₂⁴	1	1	yes	characteristic
164	#533	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
166	#484	C₄×C₅	1	2	yes	—
167	#477	C₄×C₅	1	1	yes	characteristic
168	#477	C₄×C₅	1	1	yes	characteristic
169	#462	C₄×C₅	1	1	yes	characteristic
170	#462	C₄×C₅	1	1	yes	characteristic
171	#451	C₄×C₅	1	2	yes	—
172	#446	—	2	2	no	—
173	#446	—	2	2	no	—
174	#446	C₂²×C₅	1	2	yes	—
175	#446	C₂²×C₅	1	2	yes	—
176	C₈×Q₈	C₂²×C₅	1	2	yes	—
177	C₈×Q₈	C₂²×C₅	1	2	yes	—
178	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
179	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
180	#431	C₂²×C₅	1	1	yes	characteristic
181	#424	—	2	1	no	—
182	#423	—	2	1	no	—
183	#423	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
185	#405	—	2	1	no	—
186	C₄×M₁₆	—	2	1	no	—
187	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
189	#334	C₂²×C₅	1	2	yes	—
190	#334	C₂²×C₅	1	2	yes	—
191	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
192	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
193	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
196	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
197	#322	C₂²×C₅	1	2	yes	—
198	#322	C₂²×C₅	1	2	yes	—
199	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
200	C₅×Q₈	—	2	1	no	—
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	2	1	no	—
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	—	2	2	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₅×Q₈	—	8	1	no	—
207	C₅×Q₈	#131	1	2	yes	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	8	1	no	—
219	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	#137	1	2	yes	—
223	C₂×C₄×C₅	#137	1	2	yes	—
224	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
227	C₅×C₈	—	2	2	no	—
228	C₅×C₈	—	2	2	no	—
229	C₅×C₈	—	2	2	no	—
230	C₅×C₈	—	2	2	no	—
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	4	1	no	—
233	C₅×C₈	—	4	1	no	—
234	C₅×C₈	—	4	1	no	—
235	C₅×C₈	—	4	2	no	—
236	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
238	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
241	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
245	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
246	#125	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
253	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
254	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
255	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
256	C₄×Q₈	C₂³×C₅	1	2	yes	—
257	#117	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	#107	C₂×C₄×C₅	1	2	yes	—
263	#107	C₂×C₄×C₅	1	2	yes	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
271	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₅	1	2	yes	—
275	#103	C₂×C₄×C₅	1	2	yes	—
276	#103	C₂×C₄×C₅	1	2	yes	—
277	#103	C₂×C₄×C₅	1	2	yes	—
278	#103	C₂×C₄×C₅	1	2	yes	—
279	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
280	#97	—	2	2	no	—
281	#97	—	2	2	no	—
282	#97	C₅×D₄	1	2	yes	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₅	1	2	yes	—
289	C₄×C₈	C₂³×C₅	1	2	yes	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	#441	1	2	yes	—
293	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	4	1	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	4	1	no	—
302	C₄×C₅	—	4	2	no	—
303	C₄×C₅	#441	1	2	yes	—
304	C₄×C₅	C₂×#131	1	1	yes	characteristic
305	C₄×C₅	#568	1	1	yes	characteristic
306	C₄×C₅	C₂×#137	1	1	yes	characteristic
307	C₄×C₅	C₂×#137	1	1	yes	characteristic
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
313	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
314	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₅×#41	1	1	yes	characteristic
320	Q₁₆	—	2	4	no	—
321	Q₁₆	—	4	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	4	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	—	4	2	no	—
332	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
334	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
335	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
356	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
357	C₄²	C₅×#41	1	1	yes	characteristic
358	C₄²	C₂⁴×C₅	1	1	yes	characteristic
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	#2933	1	1	yes	characteristic
361	C₂×C₅	C₂×#441	1	1	yes	characteristic
362	C₂×C₅	#2956	1	1	yes	characteristic
363	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	C₅×#131	1	2	yes	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
384	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
386	C₂×C₄	C₅×#137	1	2	yes	—
387	C₂×C₄	C₅×#137	1	2	yes	—
388	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
390	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₅	#18003	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	C₅×#441	1	2	yes	—
404	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	C₅×#441	1	2	yes	—
415	C₄	C₂×C₅×#131	1	1	yes	characteristic
416	C₄	C₅×#568	1	1	yes	characteristic
417	C₄	C₂×C₅×#137	1	1	yes	characteristic
418	C₄	C₂×C₅×#137	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	C₅×#2933	1	1	yes	characteristic
421	C₂	C₂×C₅×#441	1	1	yes	characteristic
422	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	C₂³×C₅	C₄×D₄
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
4. C₅×#1593	C₂	semidirect
5. C₅×#1587	C₂	semidirect
6. C₅×#1587	C₂	semidirect
7. C₅×#1579	C₂	semidirect
47. #18003	C₅	direct (N × H)
105. #1593	C₂×C₅	semidirect
106. #1587	C₂×C₅	semidirect
107. #1587	C₂×C₅	semidirect
108. #1579	C₂×C₅	semidirect
400. C₅	#18003	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×#3104	2
C₅×Q₈×M₁₆	2
C₅×#2962	2
C₅×#1593	2
C₅×#1587	2
C₅×#1579	2
C₅×#1570	2
C₅×#1493	2
C₂×C₅×Q₈⋊C₈	2
C₅×#1451	2
#18003	5

Subgroups — C5×#18003 #11940723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18003 #11940723