Subgroups — C₅×#23096 #11945816

Order 1280.

826 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#462	C₂	1	1	yes	maximal, characteristic
2	C₅×#2365	C₂	1	1	yes	maximal, characteristic
3	C₅×#2355	C₂	1	1	yes	maximal, characteristic
4	C₅×#1969	C₂	1	2	yes	maximal
5	C₅×#1956	C₂	1	1	yes	maximal, characteristic
6	C₅×#1947	C₂	1	1	yes	maximal, characteristic
7	C₅×#1928	C₂	1	2	yes	maximal
8	C₅×#1878	C₂	1	2	yes	maximal
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#103	C₂	1	2	yes	maximal
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₅×#462	C₄	1	8	yes	complemented
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	1	yes	characteristic
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₅×#391	C₂²	1	2	yes	—
27	C₅×#391	C₂²	1	2	yes	—
28	C₅×#389	—	2	1	no	—
29	C₅×#387	—	2	2	no	—
30	C₅×#387	—	2	2	no	—
31	C₅×#384	C₂²	1	1	yes	characteristic
32	C₅×#382	—	2	1	no	—
33	C₄×C₅×C₄⋊C₄	—	2	1	no	—
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#336	C₂²	1	2	yes	—
42	#23096	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	2	yes	—
45	C₂×C₅×Q₁₆	—	4	2	no	—
46	C₂×C₅×Q₁₆	—	4	2	no	—
47	C₂×C₅×Q₁₆	C₂×C₄	1	8	yes	—
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₅×C₄⋊Q₈	—	2	2	no	—
52	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
53	C₄×C₅×Q₈	—	2	2	no	—
54	C₄×C₅×Q₈	—	2	4	no	—
55	C₄×C₅×Q₈	—	4	2	no	—
56	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	C₂³	1	2	yes	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	4	2	no	—
76	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
77	C₅×#103	—	2	4	no	—
78	C₅×#103	—	2	2	no	—
79	C₅×#103	—	2	2	no	—
80	C₅×#103	—	4	2	no	—
81	C₅×#103	C₂×C₄	1	8	yes	—
82	C₄×C₅×C₈	—	2	2	no	—
83	C₄×C₅×C₈	—	4	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	—	2	2	no	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	2	no	—
90	C₅×#95	D₄	1	2	yes	—
91	C₂×#462	C₂×C₅	1	1	yes	characteristic
92	#2365	C₂×C₅	1	1	yes	characteristic
93	#2355	C₂×C₅	1	1	yes	characteristic
94	#1969	C₂×C₅	1	2	yes	—
95	#1956	C₂×C₅	1	1	yes	characteristic
96	#1947	C₂×C₅	1	1	yes	characteristic
97	#1928	C₂×C₅	1	2	yes	—
98	#1878	C₂×C₅	1	2	yes	—
99	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
100	C₄×#103	C₂×C₅	1	2	yes	—
101	C₄×#103	C₂×C₅	1	1	yes	characteristic
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	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	1	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
113	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₅×Q₁₆	—	4	8	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	1	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	C₂²×C₄	1	4	yes	—
134	C₂×C₅×C₈	#41	1	2	yes	—
135	C₅×C₄⋊C₄	—	2	4	no	—
136	C₅×C₄⋊C₄	—	2	4	no	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	4	4	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₄⋊C₄	—	8	1	no	—
148	C₅×C₄⋊C₄	Q₁₆	1	4	yes	complemented
149	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
150	C₅×C₄⋊C₄	#41	1	2	yes	—
151	C₄²×C₅	—	2	4	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	4	4	no	—
155	C₄²×C₅	—	4	2	no	—
156	C₄²×C₅	—	8	2	no	—
157	C₄²×C₅	C₂²×C₄	1	2	yes	—
158	C₄²×C₅	#41	1	2	yes	—
159	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
160	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
162	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
163	#462	C₄×C₅	1	8	yes	complemented
164	C₂×#107	C₂²×C₅	1	2	yes	—
165	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×#103	C₂²×C₅	1	1	yes	characteristic
167	C₂×#103	C₂²×C₅	1	2	yes	—
168	C₂×#103	C₂²×C₅	1	1	yes	characteristic
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×#103	C₂²×C₅	1	2	yes	—
171	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
173	#391	C₂²×C₅	1	2	yes	—
174	#391	C₂²×C₅	1	2	yes	—
175	#389	—	2	1	no	—
176	#387	—	2	2	no	—
177	#387	—	2	2	no	—
178	#384	C₂²×C₅	1	1	yes	characteristic
179	#382	—	2	1	no	—
180	C₄×C₄⋊C₄	—	2	1	no	—
181	C₄×C₄⋊C₄	—	2	1	no	—
182	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
183	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	#340	C₂²×C₅	1	2	yes	—
186	#340	C₂²×C₅	1	1	yes	characteristic
187	#340	C₂²×C₅	1	1	yes	characteristic
188	#336	C₂²×C₅	1	2	yes	—
189	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₅×Q₈	—	2	4	no	—
191	C₅×Q₈	—	2	2	no	—
192	C₅×Q₈	—	2	2	no	—
193	C₅×Q₈	—	2	4	no	—
194	C₅×Q₈	—	4	1	no	—
195	C₅×Q₈	—	4	2	no	—
196	C₅×Q₈	—	4	1	no	—
197	C₅×Q₈	—	4	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	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	—	4	2	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
226	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
227	C₂×C₄×C₅	#135	1	2	yes	—
228	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
234	C₅×C₈	—	2	4	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	4	1	no	—
237	C₂²×Q₈	C₂³×C₅	1	2	yes	—
238	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
239	C₂×Q₁₆	—	4	2	no	—
240	C₂×Q₁₆	—	4	2	no	—
241	C₂×Q₁₆	C₂×C₄×C₅	1	8	yes	—
242	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₅	1	2	yes	—
244	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	4	2	no	—
250	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₅	1	2	yes	—
268	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
269	#107	—	4	2	no	—
270	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
271	#103	—	2	4	no	—
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	—	4	2	no	—
275	#103	C₂×C₄×C₅	1	8	yes	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	—	4	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	C₅×D₄	1	2	yes	—
285	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₅	#546	1	1	yes	characteristic
287	C₂²×C₅	#550	1	1	yes	characteristic
288	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
289	C₂²×C₅	C₂×#135	1	1	yes	characteristic
290	C₂²×C₅	#577	1	1	yes	characteristic
291	C₂²×C₅	#578	1	1	yes	characteristic
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	4	no	—
296	C₄×C₅	—	4	2	no	—
297	C₄×C₅	—	4	2	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	8	1	no	—
300	C₄×C₅	—	8	2	no	—
301	C₄×C₅	C₄×Q₁₆	1	4	yes	—
302	C₄×C₅	C₄×#41	1	1	yes	characteristic
303	C₄×C₅	#518	1	1	yes	characteristic
304	C₄×C₅	#553	1	1	yes	characteristic
305	C₄×C₅	#555	1	1	yes	characteristic
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
317	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
327	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
329	Q₁₆	—	4	8	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
338	C₂×C₈	C₅×#41	1	2	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	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	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	8	1	no	—
352	C₄⋊C₄	C₅×Q₁₆	1	4	yes	complemented
353	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
354	C₄⋊C₄	C₅×#41	1	2	yes	—
355	C₄²	—	2	4	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	4	4	no	—
359	C₄²	—	4	2	no	—
360	C₄²	—	8	2	no	—
361	C₄²	C₂²×C₄×C₅	1	2	yes	—
362	C₄²	C₅×#41	1	2	yes	—
363	C₂×C₅	#2363	1	1	yes	characteristic
364	C₂×C₅	C₂×C₄×Q₁₆	1	1	yes	characteristic
365	C₂×C₅	#2947	1	1	yes	characteristic
366	C₂×C₅	#3299	1	1	yes	characteristic
367	C₂×C₅	#3302	1	1	yes	characteristic
368	C₂×C₅	#3394	1	1	yes	characteristic
369	C₂×C₅	#3395	1	1	yes	characteristic
370	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	4	1	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
405	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
406	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
407	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
408	C₂×C₄	C₅×#135	1	2	yes	—
409	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
410	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
413	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
415	C₈	—	2	4	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₅	#23096	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
420	C₂²	C₅×#546	1	1	yes	characteristic
421	C₂²	C₅×#550	1	1	yes	characteristic
422	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
423	C₂²	C₂×C₅×#135	1	1	yes	characteristic
424	C₂²	C₅×#577	1	1	yes	characteristic
425	C₂²	C₅×#578	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₄×C₅×Q₁₆	1	4	yes	—
436	C₄	C₄×C₅×#41	1	1	yes	characteristic
437	C₄	C₅×#518	1	1	yes	characteristic
438	C₄	C₅×#553	1	1	yes	characteristic
439	C₄	C₅×#555	1	1	yes	characteristic
440	C₂	C₅×#2363	1	1	yes	characteristic
441	C₂	C₂×C₄×C₅×Q₁₆	1	1	yes	characteristic
442	C₂	C₅×#2947	1	1	yes	characteristic
443	C₂	C₅×#3299	1	1	yes	characteristic
444	C₂	C₅×#3302	1	1	yes	characteristic
445	C₂	C₅×#3394	1	1	yes	characteristic
446	C₂	C₅×#3395	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
16. C₅×#462	C₄	semidirect
42. #23096	C₅	direct (N × H)
148. C₅×C₄⋊C₄	Q₁₆	semidirect
163. #462	C₄×C₅	semidirect
352. C₄⋊C₄	C₅×Q₁₆	semidirect
418. C₅	#23096	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×C₅×#462	2
C₅×#2365	2
C₅×#2355	2
C₅×#1969	2
C₅×#1956	2
C₅×#1947	2
C₅×#1928	2
C₅×#1878	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#103	2
#23096	5

Subgroups — C5×#23096 #11945816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23096 #11945816