Subgroups — C₅×#21119 #11943839

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#2295	C₂	1	1	yes	maximal, characteristic
3	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#1928	C₂	1	2	yes	maximal
5	C₅×#1921	C₂	1	2	yes	maximal
6	C₅×#1878	C₂	1	2	yes	maximal
7	C₅×#1863	C₂	1	2	yes	maximal
8	C₄×C₅×#107	C₂	1	1	yes	maximal, characteristic
9	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
11	C₅×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₄×C₅×Q₁₆	C₄	1	8	yes	complemented
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×#107	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	1	yes	characteristic
22	C₂×C₅×#103	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#391	C₂²	1	2	yes	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#387	—	2	2	no	—
28	C₄×C₅×C₄⋊C₄	—	2	2	no	—
29	C₄×C₅×C₄⋊C₄	—	2	1	no	—
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₅×#376	—	2	1	no	—
35	C₄³×C₅	—	2	1	no	—
36	C₄³×C₅	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#21119	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂×C₅×Q₁₆	—	2	4	no	—
46	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₄×C₅×Q₈	—	2	4	no	—
51	C₄×C₅×Q₈	—	2	4	no	—
52	C₄×C₅×Q₈	—	2	2	no	—
53	C₄×C₅×Q₈	—	2	2	no	—
54	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
55	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₄²×C₅	—	2	2	no	—
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	1	no	—
67	C₂×C₄²×C₅	—	2	2	no	—
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	D₄	1	2	yes	—
72	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	2	yes	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	4	no	—
76	C₅×#107	C₂×C₄	1	4	yes	—
77	C₅×#103	—	2	4	no	—
78	C₅×#103	—	2	4	no	—
79	C₅×#103	C₂×C₄	1	4	yes	—
80	C₅×#103	C₂×C₄	1	4	yes	—
81	C₄×C₅×C₈	—	2	2	no	—
82	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	1	no	—
89	C₂×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic
90	#2295	C₂×C₅	1	1	yes	characteristic
91	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic
92	#1928	C₂×C₅	1	2	yes	—
93	#1921	C₂×C₅	1	2	yes	—
94	#1878	C₂×C₅	1	2	yes	—
95	#1863	C₂×C₅	1	2	yes	—
96	C₄×#107	C₂×C₅	1	1	yes	characteristic
97	C₄×#103	C₂×C₅	1	1	yes	characteristic
98	C₄×#103	C₂×C₅	1	1	yes	characteristic
99	#1744	C₂×C₅	1	1	yes	characteristic
100	C₂×C₅×Q₈	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	2	2	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
106	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
107	C₂×C₅×Q₈	#41	1	4	yes	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₅×Q₁₆	—	2	8	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
127	C₅×C₄⋊C₄	—	2	8	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	2	4	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	4	4	no	—
136	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₅×C₄⋊C₄	#41	1	4	yes	—
139	C₄²×C₅	—	2	8	no	—
140	C₄²×C₅	—	2	4	no	—
141	C₄²×C₅	—	2	4	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	4	2	no	—
146	C₄²×C₅	—	4	4	no	—
147	C₄²×C₅	—	4	2	no	—
148	C₄²×C₅	—	4	2	no	—
149	C₄²×C₅	Q₁₆	1	4	yes	complemented
150	C₄²×C₅	C₂²×C₄	1	2	yes	—
151	C₄²×C₅	#41	1	2	yes	—
152	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
154	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₄×Q₁₆	C₄×C₅	1	8	yes	complemented
157	C₂×#107	C₂²×C₅	1	2	yes	—
158	C₂×#107	C₂²×C₅	1	1	yes	characteristic
159	C₂×#103	C₂²×C₅	1	2	yes	—
160	C₂×#103	C₂²×C₅	1	2	yes	—
161	C₂×#103	C₂²×C₅	1	1	yes	characteristic
162	C₂×#103	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
165	#391	C₂²×C₅	1	2	yes	—
166	#389	C₂²×C₅	1	2	yes	—
167	#387	—	2	2	no	—
168	C₄×C₄⋊C₄	—	2	1	no	—
169	C₄×C₄⋊C₄	—	2	2	no	—
170	C₄×C₄⋊C₄	—	2	1	no	—
171	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	#376	—	2	1	no	—
175	C₄³	—	2	1	no	—
176	C₄³	C₂²×C₅	1	1	yes	characteristic
177	#340	C₂²×C₅	1	2	yes	—
178	#340	C₂²×C₅	1	2	yes	—
179	#340	C₂²×C₅	1	2	yes	—
180	#336	C₂²×C₅	1	2	yes	—
181	#336	C₂²×C₅	1	2	yes	—
182	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₅×Q₈	—	2	2	no	—
184	C₅×Q₈	—	2	4	no	—
185	C₅×Q₈	—	2	2	no	—
186	C₅×Q₈	—	2	2	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₅×Q₈	#117	1	4	yes	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
212	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
213	C₂×C₄×C₅	#135	1	2	yes	—
214	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×#41	1	2	yes	—
216	C₂×C₄×C₅	C₂×#41	1	2	yes	—
217	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	—	4	2	no	—
221	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
222	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
223	C₂×Q₁₆	—	2	4	no	—
224	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	—
225	C₂²×C₈	C₂³×C₅	1	2	yes	—
226	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
228	C₄×Q₈	—	2	4	no	—
229	C₄×Q₈	—	2	4	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×Q₈	—	2	2	no	—
232	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
233	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	—	2	1	no	—
248	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
249	C₂×C₄²	C₅×D₄	1	2	yes	—
250	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₅	1	2	yes	—
252	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
253	#107	—	2	4	no	—
254	#107	C₂×C₄×C₅	1	4	yes	—
255	#103	—	2	4	no	—
256	#103	—	2	4	no	—
257	#103	C₂×C₄×C₅	1	4	yes	—
258	#103	C₂×C₄×C₅	1	4	yes	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	1	no	—
265	#95	—	2	2	no	—
266	#95	—	2	1	no	—
267	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂²×C₅	#525	1	2	yes	—
269	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
270	C₂²×C₅	C₂×#135	1	1	yes	characteristic
271	C₂²×C₅	#575	1	2	yes	—
272	C₄×C₅	—	2	4	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	2	4	no	—
275	C₄×C₅	—	4	2	no	—
276	C₄×C₅	—	4	4	no	—
277	C₄×C₅	—	4	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	8	2	no	—
281	C₄×C₅	C₄×Q₁₆	1	4	yes	—
282	C₄×C₅	C₂×#117	1	1	yes	characteristic
283	C₄×C₅	C₄×#41	1	1	yes	characteristic
284	C₄×C₅	#529	1	2	yes	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
291	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
292	C₂×Q₈	C₅×#41	1	4	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
302	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
304	Q₁₆	—	2	8	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
322	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
323	C₄⋊C₄	C₅×#41	1	4	yes	—
324	C₄²	—	2	8	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	2	no	—
331	C₄²	—	4	4	no	—
332	C₄²	—	4	2	no	—
333	C₄²	—	4	2	no	—
334	C₄²	C₅×Q₁₆	1	4	yes	complemented
335	C₄²	C₂²×C₄×C₅	1	2	yes	—
336	C₄²	C₅×#41	1	2	yes	—
337	C₂×C₅	#2290	1	1	yes	characteristic
338	C₂×C₅	C₂×C₄×Q₁₆	1	1	yes	characteristic
339	C₂×C₅	#2943	1	1	yes	characteristic
340	C₂×C₅	#3102	1	2	yes	—
341	C₂×C₅	#3104	1	2	yes	—
342	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	2	4	no	—
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	C₅×#117	1	4	yes	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
370	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
371	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
372	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
373	C₂×C₄	C₅×#135	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×#41	1	2	yes	—
376	C₂×C₄	C₂×C₅×#41	1	2	yes	—
377	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	2	no	—
381	C₅	#21119	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
383	C₂²	C₅×#525	1	2	yes	—
384	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
385	C₂²	C₂×C₅×#135	1	1	yes	characteristic
386	C₂²	C₅×#575	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₄×C₅×Q₁₆	1	4	yes	—
397	C₄	C₂×C₅×#117	1	1	yes	characteristic
398	C₄	C₄×C₅×#41	1	1	yes	characteristic
399	C₄	C₅×#529	1	2	yes	—
400	C₂	C₅×#2290	1	1	yes	characteristic
401	C₂	C₂×C₄×C₅×Q₁₆	1	1	yes	characteristic
402	C₂	C₅×#2943	1	1	yes	characteristic
403	C₂	C₅×#3102	1	2	yes	—
404	C₂	C₅×#3104	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂³×C₅	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₄×C₅×Q₁₆	C₄	semidirect
42. #21119	C₅	direct (N × H)
149. C₄²×C₅	Q₁₆	semidirect
156. C₄×Q₁₆	C₄×C₅	semidirect
334. C₄²	C₅×Q₁₆	semidirect
381. C₅	#21119	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Q₁₆	2
C₅×#2295	2
C₄²×C₅×Q₈	2
C₅×#1928	2
C₅×#1921	2
C₅×#1878	2
C₅×#1863	2
C₄×C₅×#107	2
C₄×C₅×#103	2
C₅×#1744	2
#21119	5

Subgroups — C5×#21119 #11943839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21119 #11943839