Subgroups — C₅×#18024 #11940744

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 430 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×#2991	C₂	1	1	yes	maximal, characteristic
3	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1592	C₂	1	2	yes	maximal, complemented
5	C₅×#1584	C₂	1	2	yes	maximal, complemented
6	C₅×#1583	C₂	1	2	yes	maximal, complemented
7	C₅×#1579	C₂	1	2	yes	maximal, complemented
8	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1493	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1476	C₂	1	1	yes	maximal, characteristic
11	C₅×#1452	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	2	yes	—
22	C₅×C₈×Q₈	—	2	1	no	—
23	C₅×C₈×Q₈	C₂²	1	2	yes	—
24	C₅×C₈×Q₈	C₂²	1	2	yes	—
25	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
26	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
27	C₅×#436	—	2	2	no	—
28	C₅×#436	C₂²	1	2	yes	—
29	C₅×#433	—	2	2	no	—
30	C₅×#431	—	2	1	no	—
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#431	C₂²	1	1	yes	characteristic
33	C₅×#431	C₂²	1	1	yes	characteristic
34	C₅×#423	—	2	1	no	—
35	C₅×#423	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	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	2	yes	—
42	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×#322	C₂²	1	2	yes	—
46	C₅×#322	C₂²	1	2	yes	—
47	#18024	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
56	C₅×#125	—	2	1	no	—
57	C₅×C₂²⋊Q₈	—	2	1	no	—
58	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Q₈	C₂³	1	2	yes	—
62	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
66	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₅×#117	—	2	1	no	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#107	C₂×C₄	1	2	yes	—
73	C₅×#106	C₂×C₄	1	2	yes	—
74	C₅×C₄⋊C₈	—	2	2	no	—
75	C₅×C₄⋊C₈	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	2	no	—
77	C₅×C₄⋊C₈	—	2	1	no	—
78	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	2	yes	—
85	C₅×#103	C₂×C₄	1	2	yes	—
86	C₅×#103	C₂×C₄	1	2	yes	—
87	C₅×#103	C₂×C₄	1	2	yes	—
88	C₅×#102	C₂×C₄	1	2	yes	—
89	C₅×C₂²⋊C₈	—	2	1	no	—
90	C₅×C₂²⋊C₈	—	2	2	no	—
91	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₅×C₂²⋊C₈	D₄	1	2	yes	—
93	C₅×#97	—	2	2	no	—
94	C₄×C₅×C₈	—	2	2	no	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₄×C₅×C₈	—	2	1	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	#3107	C₂×C₅	1	1	yes	characteristic
103	#2991	C₂×C₅	1	1	yes	characteristic
104	#2986	C₂×C₅	1	1	yes	characteristic, complemented
105	#1592	C₂×C₅	1	2	yes	complemented
106	#1584	C₂×C₅	1	2	yes	complemented
107	#1583	C₂×C₅	1	2	yes	complemented
108	#1579	C₂×C₅	1	2	yes	complemented
109	#1574	C₂×C₅	1	1	yes	characteristic, complemented
110	#1493	C₂×C₅	1	1	yes	characteristic, complemented
111	#1476	C₂×C₅	1	1	yes	characteristic
112	#1452	C₂×C₅	1	1	yes	characteristic, complemented
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	4	1	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
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	C₅×Q₁₆	—	2	4	no	—
127	C₅×SD₁₆	—	4	2	no	—
128	C₅×M₁₆	—	8	2	no	—
129	C₅×M₁₆	—	8	1	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	4	2	no	—
136	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
150	C₅×C₂²⋊C₄	—	2	2	no	—
151	C₅×C₂²⋊C₄	—	2	1	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₄²×C₅	—	2	1	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	#41	1	1	yes	characteristic
161	C₄²×C₅	C₂⁴	1	1	yes	characteristic
162	#533	C₂²×C₅	1	1	yes	characteristic
163	C₄×#41	C₂²×C₅	1	1	yes	characteristic
164	#485	C₄×C₅	1	2	yes	—
165	#475	C₄×C₅	1	1	yes	characteristic
166	#474	C₄×C₅	1	1	yes	characteristic
167	#462	C₄×C₅	1	1	yes	characteristic
168	#461	C₄×C₅	1	1	yes	characteristic
169	#452	C₄×C₅	1	2	yes	—
170	#446	—	2	1	no	—
171	#446	C₂²×C₅	1	2	yes	—
172	C₈×Q₈	—	2	1	no	—
173	C₈×Q₈	C₂²×C₅	1	2	yes	—
174	C₈×Q₈	C₂²×C₅	1	2	yes	—
175	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
176	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
177	#436	—	2	2	no	—
178	#436	C₂²×C₅	1	2	yes	—
179	#433	—	2	2	no	—
180	#431	—	2	1	no	—
181	#431	C₂²×C₅	1	1	yes	characteristic
182	#431	C₂²×C₅	1	1	yes	characteristic
183	#431	C₂²×C₅	1	1	yes	characteristic
184	#423	—	2	1	no	—
185	#423	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
187	#335	C₂²×C₅	1	2	yes	—
188	#334	C₂²×C₅	1	2	yes	—
189	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
190	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
191	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
192	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
193	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	#322	C₂²×C₅	1	2	yes	—
196	#322	C₂²×C₅	1	2	yes	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
199	C₅×Q₈	—	2	1	no	—
200	C₅×Q₈	—	2	2	no	—
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	#131	1	2	yes	—
204	C₅×D₄	—	2	1	no	—
205	C₅×D₄	—	2	1	no	—
206	C₅×D₄	—	4	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
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	2	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
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	—	4	1	no	—
232	C₅×C₈	—	4	1	no	—
233	C₅×C₈	—	4	1	no	—
234	C₅×C₈	—	4	2	no	—
235	C₅×C₈	—	4	1	no	—
236	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
238	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
244	#125	—	2	1	no	—
245	C₂²⋊Q₈	—	2	1	no	—
246	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
249	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
250	C₄×Q₈	C₂³×C₅	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
254	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
260	#107	C₂×C₄×C₅	1	2	yes	—
261	#106	C₂×C₄×C₅	1	2	yes	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
267	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
268	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
269	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
271	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₅	1	2	yes	—
273	#103	C₂×C₄×C₅	1	2	yes	—
274	#103	C₂×C₄×C₅	1	2	yes	—
275	#103	C₂×C₄×C₅	1	2	yes	—
276	#102	C₂×C₄×C₅	1	2	yes	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
280	C₂²⋊C₈	C₅×D₄	1	2	yes	—
281	#97	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	1	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	—	2	1	no	—
293	C₂²×C₅	—	4	1	no	—
294	C₂²×C₅	—	4	1	no	—
295	C₂²×C₅	—	4	1	no	—
296	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	4	1	no	—
303	C₄×C₅	—	4	1	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	#444	1	2	yes	—
306	C₄×C₅	C₂×#131	1	1	yes	characteristic
307	C₄×C₅	#568	1	1	yes	characteristic
308	C₄×C₅	#577	1	1	yes	characteristic
309	C₄×C₅	#578	1	1	yes	characteristic
310	#41	—	2	2	no	—
311	#41	—	4	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
314	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×C₄	C₅×#41	1	1	yes	characteristic
323	Q₁₆	—	2	4	no	—
324	SD₁₆	—	4	2	no	—
325	M₁₆	—	8	2	no	—
326	M₁₆	—	8	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
334	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
335	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
336	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
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	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
345	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	2	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	—	4	1	no	—
360	C₂×C₅	—	8	1	no	—
361	C₂×C₅	#2933	1	1	yes	characteristic
362	C₂×C₅	#2947	1	1	yes	characteristic
363	C₂×C₅	C₂×#444	1	1	yes	characteristic
364	C₂³	—	2	1	no	—
365	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
366	Q₈	—	2	1	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	C₅×#131	1	2	yes	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
389	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
390	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₅	#18024	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	C₅×#444	1	2	yes	—
420	C₄	C₂×C₅×#131	1	1	yes	characteristic
421	C₄	C₅×#568	1	1	yes	characteristic
422	C₄	C₅×#577	1	1	yes	characteristic
423	C₄	C₅×#578	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	8	1	no	—
426	C₂	C₅×#2933	1	1	yes	characteristic
427	C₂	C₅×#2947	1	1	yes	characteristic
428	C₂	C₂×C₅×#444	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 ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#2986	C₂	semidirect
4. C₅×#1592	C₂	semidirect
5. C₅×#1584	C₂	semidirect
6. C₅×#1583	C₂	semidirect
7. C₅×#1579	C₂	semidirect
8. C₅×#1574	C₂	semidirect
9. C₅×#1493	C₂	semidirect
11. C₅×#1452	C₂	semidirect
47. #18024	C₅	direct (N × H)
104. #2986	C₂×C₅	semidirect
105. #1592	C₂×C₅	semidirect
106. #1584	C₂×C₅	semidirect
107. #1583	C₂×C₅	semidirect
108. #1579	C₂×C₅	semidirect
109. #1574	C₂×C₅	semidirect
110. #1493	C₂×C₅	semidirect
112. #1452	C₂×C₅	semidirect
403. C₅	#18024	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×#2991	2
C₅×#2986	2
C₅×#1592	2
C₅×#1584	2
C₅×#1583	2
C₅×#1579	2
C₅×#1574	2
C₅×#1493	2
C₅×#1476	2
C₅×#1452	2
#18024	5

Subgroups — C5×#18024 #11940744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18024 #11940744