Subgroups — C₅×#22805 #11945525

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×#2355	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×#1927	C₂	1	2	yes	maximal, complemented
6	C₅×#1926	C₂	1	2	yes	maximal
7	C₅×#1844	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1802	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#106	C₂	1	2	yes	maximal, complemented
11	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	—	2	1	no	—
16	C₄×C₅×SD₁₆	C₄	1	8	yes	complemented
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×#106	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	1	yes	characteristic
23	C₂×C₅×#102	C₂²	1	2	yes	—
24	C₂×C₅×#102	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₅×#391	C₂²	1	2	yes	—
28	C₅×#390	C₂²	1	2	yes	—
29	C₅×#388	—	2	2	no	—
30	C₅×#387	—	2	2	no	—
31	C₅×#384	C₂²	1	1	yes	characteristic
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#382	—	2	1	no	—
34	C₅×#380	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#22805	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂×C₅×SD₁₆	—	2	2	no	—
47	C₂×C₅×SD₁₆	—	2	2	no	—
48	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	—
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₄×C₅×Q₈	—	2	2	no	—
53	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
54	C₄×C₅×D₄	—	2	2	no	—
55	C₄×C₅×D₄	C₂×C₄	1	4	yes	—
56	C₅×#117	—	4	4	no	—
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	1	no	—
62	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	1	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	C₂³	1	2	yes	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#106	—	2	4	no	—
77	C₅×#106	—	4	2	no	—
78	C₅×#106	C₂×C₄	1	4	yes	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×#103	—	4	2	no	—
81	C₅×#103	C₂×C₄	1	4	yes	—
82	C₅×#102	—	4	2	no	—
83	C₅×#102	C₂×C₄	1	4	yes	—
84	C₄×C₅×C₈	—	2	4	no	—
85	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
86	C₅×#95	—	2	2	no	—
87	C₅×#95	—	2	2	no	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	2	no	—
90	C₅×#95	D₄	1	2	yes	—
91	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic
92	#2355	C₂×C₅	1	1	yes	characteristic, complemented
93	#2354	C₂×C₅	1	1	yes	characteristic
94	#1968	C₂×C₅	1	2	yes	—
95	#1927	C₂×C₅	1	2	yes	complemented
96	#1926	C₂×C₅	1	2	yes	—
97	#1844	C₂×C₅	1	1	yes	characteristic, complemented
98	#1803	C₂×C₅	1	1	yes	characteristic, complemented
99	#1802	C₂×C₅	1	1	yes	characteristic
100	C₄×#106	C₂×C₅	1	2	yes	complemented
101	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂⁴×C₅	—	2	1	no	—
103	C₂×C₅×Q₈	—	2	1	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
109	C₂×C₅×D₄	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₅	—	2	1	no	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	4	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	4	2	no	—
122	C₂²×C₄×C₅	—	4	2	no	—
123	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₅×SD₁₆	—	2	8	no	—
129	C₂×C₅×C₈	—	2	1	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	2	no	—
134	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₅×C₈	#41	1	2	yes	—
137	C₂×C₅×C₈	#41	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	2	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	4	2	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	—	8	1	no	—
149	C₅×C₄⋊C₄	—	8	1	no	—
150	C₅×C₄⋊C₄	SD₁₆	1	4	yes	complemented
151	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₅×C₂²⋊C₄	—	2	4	no	—
154	C₅×C₂²⋊C₄	—	4	4	no	—
155	C₅×C₂²⋊C₄	—	8	2	no	—
156	C₄²×C₅	—	2	4	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	4	4	no	—
160	C₄²×C₅	—	8	2	no	—
161	C₄²×C₅	C₂²×C₄	1	2	yes	—
162	C₄²×C₅	#41	1	2	yes	—
163	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×#117	—	2	1	no	—
167	C₄×SD₁₆	C₄×C₅	1	8	yes	complemented
168	C₂×#106	C₂²×C₅	1	2	yes	—
169	C₂×#106	C₂²×C₅	1	2	yes	—
170	C₂×#106	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
172	C₂×#103	C₂²×C₅	1	2	yes	—
173	C₂×#103	C₂²×C₅	1	1	yes	characteristic
174	C₂×#102	C₂²×C₅	1	2	yes	—
175	C₂×#102	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
178	#391	C₂²×C₅	1	2	yes	—
179	#390	C₂²×C₅	1	2	yes	—
180	#388	—	2	2	no	—
181	#387	—	2	2	no	—
182	#384	C₂²×C₅	1	1	yes	characteristic
183	#384	C₂²×C₅	1	1	yes	characteristic
184	#382	—	2	1	no	—
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	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	#340	C₂²×C₅	1	2	yes	—
191	#340	C₂²×C₅	1	2	yes	—
192	#336	C₂²×C₅	1	2	yes	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	2	2	no	—
203	C₅×Q₈	—	4	1	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	2	2	no	—
207	C₅×D₄	—	4	1	no	—
208	C₅×D₄	—	4	1	no	—
209	C₂×C₄×C₅	—	2	2	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	2	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	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	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	8	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
233	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
235	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
236	C₂×C₄×C₅	#135	1	2	yes	—
237	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	4	2	no	—
245	C₅×C₈	#117	1	4	yes	complemented
246	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
248	C₂³×C₄	—	2	1	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	—
252	C₂²×C₈	C₂³×C₅	1	2	yes	—
253	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	C₂×C₄×C₅	1	4	yes	—
259	#117	—	4	4	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂³×C₅	1	2	yes	—
278	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
279	#106	—	2	4	no	—
280	#106	—	4	2	no	—
281	#106	C₂×C₄×C₅	1	4	yes	—
282	C₄⋊C₈	—	2	2	no	—
283	#103	—	4	2	no	—
284	#103	C₂×C₄×C₅	1	4	yes	—
285	#102	—	4	2	no	—
286	#102	C₂×C₄×C₅	1	4	yes	—
287	C₄×C₈	—	2	4	no	—
288	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	C₅×D₄	1	2	yes	—
294	C₂²×C₅	—	4	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	8	1	no	—
298	C₂²×C₅	—	8	1	no	—
299	C₂²×C₅	—	8	1	no	—
300	C₂²×C₅	—	8	1	no	—
301	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₅	#547	1	1	yes	characteristic
303	C₂²×C₅	#550	1	1	yes	characteristic
304	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
305	C₂²×C₅	C₂×#135	1	1	yes	characteristic
306	C₂²×C₅	#577	1	1	yes	characteristic
307	C₂²×C₅	#577	1	1	yes	characteristic
308	C₄×C₅	—	2	4	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	4	2	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	4	2	no	—
314	C₄×C₅	—	8	2	no	—
315	C₄×C₅	—	8	2	no	—
316	C₄×C₅	C₄×SD₁₆	1	4	yes	—
317	C₄×C₅	C₂×#117	1	1	yes	characteristic
318	C₄×C₅	#520	1	1	yes	characteristic
319	C₄×C₅	#555	1	1	yes	characteristic
320	C₄×C₅	#556	1	1	yes	characteristic
321	C₂⁴	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
345	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
347	SD₁₆	—	2	8	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
355	C₂×C₈	C₅×#41	1	2	yes	—
356	C₂×C₈	C₅×#41	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	8	1	no	—
368	C₄⋊C₄	—	8	1	no	—
369	C₄⋊C₄	C₅×SD₁₆	1	4	yes	complemented
370	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
371	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	4	no	—
379	C₄²	—	8	2	no	—
380	C₄²	C₂²×C₄×C₅	1	2	yes	—
381	C₄²	C₅×#41	1	2	yes	—
382	C₂×C₅	—	8	2	no	—
383	C₂×C₅	#2354	1	1	yes	characteristic
384	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
385	C₂×C₅	#2952	1	1	yes	characteristic
386	C₂×C₅	#3335	1	1	yes	characteristic
387	C₂×C₅	#3340	1	1	yes	characteristic
388	C₂×C₅	#3392	1	1	yes	characteristic
389	C₂×C₅	#3394	1	1	yes	characteristic
390	C₂³	—	2	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	4	1	no	—
401	Q₈	—	4	1	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
430	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
431	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
432	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
433	C₂×C₄	C₅×#135	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
435	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
437	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
438	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	4	2	no	—
442	C₈	C₅×#117	1	4	yes	complemented
443	C₅	#22805	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
452	C₂²	C₅×#547	1	1	yes	characteristic
453	C₂²	C₅×#550	1	1	yes	characteristic
454	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
455	C₂²	C₂×C₅×#135	1	1	yes	characteristic
456	C₂²	C₅×#577	1	1	yes	characteristic
457	C₂²	C₅×#577	1	1	yes	characteristic
458	C₄	—	2	4	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₄×C₅×SD₁₆	1	4	yes	—
467	C₄	C₂×C₅×#117	1	1	yes	characteristic
468	C₄	C₅×#520	1	1	yes	characteristic
469	C₄	C₅×#555	1	1	yes	characteristic
470	C₄	C₅×#556	1	1	yes	characteristic
471	C₂	—	8	2	no	—
472	C₂	C₅×#2354	1	1	yes	characteristic
473	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
474	C₂	C₅×#2952	1	1	yes	characteristic
475	C₂	C₅×#3335	1	1	yes	characteristic
476	C₂	C₅×#3340	1	1	yes	characteristic
477	C₂	C₅×#3392	1	1	yes	characteristic
478	C₂	C₅×#3394	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×#2355	C₂	semidirect
5. C₅×#1927	C₂	semidirect
7. C₅×#1844	C₂	semidirect
8. C₅×#1803	C₂	semidirect
10. C₄×C₅×#106	C₂	semidirect
11. C₅×C₈×C₄⋊C₄	C₂	semidirect
16. C₄×C₅×SD₁₆	C₄	semidirect
42. #22805	C₅	direct (N × H)
92. #2355	C₂×C₅	semidirect
95. #1927	C₂×C₅	semidirect
97. #1844	C₂×C₅	semidirect
98. #1803	C₂×C₅	semidirect
100. C₄×#106	C₂×C₅	semidirect
101. C₈×C₄⋊C₄	C₂×C₅	semidirect
150. C₅×C₄⋊C₄	SD₁₆	semidirect
167. C₄×SD₁₆	C₄×C₅	semidirect
245. C₅×C₈	#117	semidirect
369. C₄⋊C₄	C₅×SD₁₆	semidirect
442. C₈	C₅×#117	semidirect
443. C₅	#22805	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×SD₁₆	2
C₅×#2355	2
C₅×#2354	2
C₅×#1968	2
C₅×#1927	2
C₅×#1926	2
C₅×#1844	2
C₅×#1803	2
C₅×#1802	2
C₄×C₅×#106	2
C₅×C₈×C₄⋊C₄	2
#22805	5

Subgroups — C5×#22805 #11945525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22805 #11945525