Subgroups — C₅×#23094 #11945814

Order 1280.

902 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic
2	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2354	C₂	1	1	yes	maximal, characteristic
4	C₅×#1968	C₂	1	2	yes	maximal
5	C₅×#1956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1927	C₂	1	2	yes	maximal, complemented
8	C₅×#1880	C₂	1	2	yes	maximal
9	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#103	C₂	1	2	yes	maximal, complemented
11	C₄×C₅×#102	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₅×SD₁₆	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×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	—	2	1	no	—
17	C₅×#461	C₄	1	8	yes	complemented
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₅×#102	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₅×#391	C₂²	1	2	yes	—
28	C₅×#390	C₂²	1	2	yes	—
29	C₅×#389	—	2	1	no	—
30	C₅×#388	—	2	2	no	—
31	C₅×#387	—	2	2	no	—
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#380	—	2	1	no	—
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#23094	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂×C₅×SD₁₆	—	4	2	no	—
47	C₂×C₅×SD₁₆	—	4	2	no	—
48	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	—
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
54	C₄×C₅×Q₈	—	2	4	no	—
55	C₄×C₅×Q₈	—	4	2	no	—
56	C₄×C₅×D₄	—	2	2	no	—
57	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
58	C₅×#117	—	4	4	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	2	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	C₂³	1	2	yes	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₅×#106	—	4	2	no	—
79	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
80	C₅×#103	—	2	4	no	—
81	C₅×#103	—	4	2	no	—
82	C₅×#103	C₂×C₄	1	8	yes	—
83	C₅×#102	—	2	2	no	—
84	C₅×#102	—	2	2	no	—
85	C₄×C₅×C₈	—	2	2	no	—
86	C₄×C₅×C₈	—	4	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	D₄	1	2	yes	—
92	C₂×#461	C₂×C₅	1	1	yes	characteristic
93	#2365	C₂×C₅	1	1	yes	characteristic, complemented
94	#2354	C₂×C₅	1	1	yes	characteristic
95	#1968	C₂×C₅	1	2	yes	—
96	#1956	C₂×C₅	1	1	yes	characteristic, complemented
97	#1948	C₂×C₅	1	1	yes	characteristic, complemented
98	#1927	C₂×C₅	1	2	yes	complemented
99	#1880	C₂×C₅	1	2	yes	—
100	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
101	C₄×#103	C₂×C₅	1	2	yes	complemented
102	C₄×#102	C₂×C₅	1	1	yes	characteristic
103	C₂⁴×C₅	—	2	1	no	—
104	C₂×C₅×Q₈	—	2	2	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	1	no	—
115	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	4	2	no	—
123	C₂²×C₄×C₅	—	4	2	no	—
124	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×SD₁₆	—	4	8	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₅×C₈	#41	1	2	yes	—
139	C₅×C₄⋊C₄	—	2	4	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	2	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	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	4	4	no	—
149	C₅×C₄⋊C₄	—	4	2	no	—
150	C₅×C₄⋊C₄	—	8	1	no	—
151	C₅×C₄⋊C₄	SD₁₆	1	4	yes	complemented
152	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₅×C₄⋊C₄	#41	1	2	yes	—
154	C₅×C₂²⋊C₄	—	2	4	no	—
155	C₅×C₂²⋊C₄	—	4	4	no	—
156	C₅×C₂²⋊C₄	—	8	2	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	4	4	no	—
160	C₄²×C₅	—	4	4	no	—
161	C₄²×C₅	—	4	2	no	—
162	C₄²×C₅	C₂²×C₄	1	2	yes	—
163	C₄²×C₅	#41	1	2	yes	—
164	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
165	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
167	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×#117	—	2	1	no	—
169	#461	C₄×C₅	1	8	yes	complemented
170	C₂×#106	C₂²×C₅	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
172	C₂×#103	C₂²×C₅	1	2	yes	—
173	C₂×#103	C₂²×C₅	1	2	yes	—
174	C₂×#103	C₂²×C₅	1	2	yes	—
175	C₂×#102	C₂²×C₅	1	1	yes	characteristic
176	C₂×#102	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
179	#391	C₂²×C₅	1	2	yes	—
180	#390	C₂²×C₅	1	2	yes	—
181	#389	—	2	1	no	—
182	#388	—	2	2	no	—
183	#387	—	2	2	no	—
184	#384	C₂²×C₅	1	1	yes	characteristic
185	#380	—	2	1	no	—
186	C₄×C₄⋊C₄	—	2	1	no	—
187	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
188	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	#340	C₂²×C₅	1	2	yes	—
191	#340	C₂²×C₅	1	1	yes	characteristic
192	#340	C₂²×C₅	1	1	yes	characteristic
193	#336	C₂²×C₅	1	2	yes	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	—	4	1	no	—
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	—	4	1	no	—
201	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₅×Q₈	—	2	4	no	—
203	C₅×Q₈	—	2	4	no	—
204	C₅×Q₈	—	4	2	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₅×D₄	—	2	2	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	1	no	—
209	C₅×D₄	—	4	1	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	4	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	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	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	8	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
235	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
236	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
237	C₂×C₄×C₅	#135	1	2	yes	—
238	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
243	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
244	C₅×C₈	—	2	4	no	—
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	4	1	no	—
247	C₂²×Q₈	C₂³×C₅	1	2	yes	—
248	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
249	C₂³×C₄	—	2	1	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂×SD₁₆	—	4	2	no	—
252	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	—
253	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₅	1	2	yes	—
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	—	4	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
262	#117	—	4	4	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₅	1	2	yes	—
281	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
282	#106	—	4	2	no	—
283	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
284	#103	—	2	4	no	—
285	#103	—	4	2	no	—
286	#103	C₂×C₄×C₅	1	8	yes	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	—	4	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	1	no	—
294	#95	—	2	2	no	—
295	#95	C₅×D₄	1	2	yes	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	4	2	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	8	1	no	—
300	C₂²×C₅	—	8	1	no	—
301	C₂²×C₅	—	8	1	no	—
302	C₂²×C₅	—	8	1	no	—
303	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₅	#546	1	1	yes	characteristic
305	C₂²×C₅	#550	1	1	yes	characteristic
306	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
307	C₂²×C₅	C₂×#135	1	1	yes	characteristic
308	C₂²×C₅	#577	1	1	yes	characteristic
309	C₂²×C₅	#578	1	1	yes	characteristic
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	2	4	no	—
312	C₄×C₅	—	4	4	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	8	2	no	—
317	C₄×C₅	—	8	1	no	—
318	C₄×C₅	C₄×SD₁₆	1	4	yes	—
319	C₄×C₅	C₄×#41	1	1	yes	characteristic
320	C₄×C₅	#518	1	1	yes	characteristic
321	C₄×C₅	#553	1	1	yes	characteristic
322	C₄×C₅	#555	1	1	yes	characteristic
323	C₂⁴	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
345	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
347	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
349	SD₁₆	—	4	8	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
358	C₂×C₈	C₅×#41	1	2	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	8	1	no	—
371	C₄⋊C₄	C₅×SD₁₆	1	4	yes	complemented
372	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
373	C₄⋊C₄	C₅×#41	1	2	yes	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	8	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	4	no	—
380	C₄²	—	4	4	no	—
381	C₄²	—	4	2	no	—
382	C₄²	C₂²×C₄×C₅	1	2	yes	—
383	C₄²	C₅×#41	1	2	yes	—
384	C₂×C₅	—	8	2	no	—
385	C₂×C₅	#2363	1	1	yes	characteristic
386	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
387	C₂×C₅	#2947	1	1	yes	characteristic
388	C₂×C₅	#3298	1	1	yes	characteristic
389	C₂×C₅	#3303	1	1	yes	characteristic
390	C₂×C₅	#3392	1	1	yes	characteristic
391	C₂×C₅	#3393	1	1	yes	characteristic
392	C₂³	—	2	2	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	2	4	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
432	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
433	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
434	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
435	C₂×C₄	C₅×#135	1	2	yes	—
436	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
437	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
438	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
439	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
440	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
442	C₈	—	2	4	no	—
443	C₈	—	2	2	no	—
444	C₈	—	4	1	no	—
445	C₅	#23094	1	1	yes	characteristic, direct product factor, Sylow
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
454	C₂²	C₅×#546	1	1	yes	characteristic
455	C₂²	C₅×#550	1	1	yes	characteristic
456	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
457	C₂²	C₂×C₅×#135	1	1	yes	characteristic
458	C₂²	C₅×#577	1	1	yes	characteristic
459	C₂²	C₅×#578	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	1	no	—
468	C₄	C₄×C₅×SD₁₆	1	4	yes	—
469	C₄	C₄×C₅×#41	1	1	yes	characteristic
470	C₄	C₅×#518	1	1	yes	characteristic
471	C₄	C₅×#553	1	1	yes	characteristic
472	C₄	C₅×#555	1	1	yes	characteristic
473	C₂	—	8	2	no	—
474	C₂	C₅×#2363	1	1	yes	characteristic
475	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
476	C₂	C₅×#2947	1	1	yes	characteristic
477	C₂	C₅×#3298	1	1	yes	characteristic
478	C₂	C₅×#3303	1	1	yes	characteristic
479	C₂	C₅×#3392	1	1	yes	characteristic
480	C₂	C₅×#3393	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
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
2. C₅×#2365	C₂	semidirect
5. C₅×#1956	C₂	semidirect
6. C₅×#1948	C₂	semidirect
7. C₅×#1927	C₂	semidirect
9. C₅×C₈×C₄⋊C₄	C₂	semidirect
10. C₄×C₅×#103	C₂	semidirect
17. C₅×#461	C₄	semidirect
42. #23094	C₅	direct (N × H)
93. #2365	C₂×C₅	semidirect
96. #1956	C₂×C₅	semidirect
97. #1948	C₂×C₅	semidirect
98. #1927	C₂×C₅	semidirect
100. C₈×C₄⋊C₄	C₂×C₅	semidirect
101. C₄×#103	C₂×C₅	semidirect
151. C₅×C₄⋊C₄	SD₁₆	semidirect
169. #461	C₄×C₅	semidirect
371. C₄⋊C₄	C₅×SD₁₆	semidirect
445. C₅	#23094	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×#461	2
C₅×#2365	2
C₅×#2354	2
C₅×#1968	2
C₅×#1956	2
C₅×#1948	2
C₅×#1927	2
C₅×#1880	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#103	2
C₄×C₅×#102	2
#23094	5

Subgroups — C5×#23094 #11945814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23094 #11945814