Subgroups — C₅×#24268 #11946988

Order 1280.

1410 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	C₂³×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#467	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#2409	C₂	1	2	yes	maximal
5	C₅×#2056	C₂	1	2	yes	maximal, complemented
6	C₅×#2001	C₂	1	2	yes	maximal, complemented
7	C₅×#1969	C₂	1	2	yes	maximal, complemented
8	C₅×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1787	C₂	1	2	yes	maximal, complemented
10	C₂³×C₅×Q₈	C₂²	1	2	yes	—
11	C₂²×C₅×Q₁₆	—	2	8	no	—
12	C₂²×C₅×Q₁₆	—	2	4	no	—
13	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₅×#467	—	2	8	no	—
20	C₅×C₈×D₄	—	2	4	no	—
21	C₂×C₅×#107	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#103	C₂²	1	4	yes	—
24	C₂×C₅×#103	C₂²	1	4	yes	—
25	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₅×#395	—	2	2	no	—
29	C₅×#393	—	2	2	no	—
30	C₅×#391	C₂²	1	4	yes	—
31	C₅×#386	—	2	2	no	—
32	C₅×#385	—	2	2	no	—
33	C₅×#380	C₂²	1	2	yes	—
34	C₅×#340	C₂²	1	2	yes	—
35	#24268	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₅×Q₈	—	2	2	no	—
37	C₂²×C₅×Q₈	—	2	8	no	—
38	C₂²×C₅×Q₈	—	2	4	no	—
39	C₂²×C₅×Q₈	—	2	4	no	—
40	C₂²×C₅×Q₈	—	4	4	no	—
41	C₂²×C₅×Q₈	C₂³	1	4	yes	—
42	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₅	—	2	2	no	—
44	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×Q₁₆	—	2	32	no	—
47	C₂×C₅×Q₁₆	—	2	8	no	—
48	C₂×C₅×Q₁₆	—	2	4	no	—
49	C₂×C₅×Q₁₆	—	2	4	no	—
50	C₂×C₅×Q₁₆	—	2	4	no	—
51	C₂×C₅×Q₁₆	D₄	1	8	yes	complemented
52	C₂²×C₅×C₈	—	2	4	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	—	2	4	no	—
55	C₂²×C₅×C₈	D₄	1	4	yes	—
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×C₂²⋊Q₈	—	2	8	no	—
61	C₅×C₂²⋊Q₈	—	4	4	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	4	no	—
65	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#107	—	2	4	no	—
73	C₅×C₄⋊C₈	—	2	2	no	—
74	C₅×#103	—	2	8	no	—
75	C₅×#103	—	4	4	no	—
76	C₅×C₂²⋊C₈	—	2	2	no	—
77	C₅×C₂²⋊C₈	—	2	2	no	—
78	C₄×C₅×C₈	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	4	no	—
81	C₅×#95	—	2	4	no	—
82	C₂³×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×#467	C₂×C₅	1	2	yes	complemented
84	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
85	#2409	C₂×C₅	1	2	yes	—
86	#2056	C₂×C₅	1	2	yes	complemented
87	#2001	C₂×C₅	1	2	yes	complemented
88	#1969	C₂×C₅	1	2	yes	complemented
89	#1808	C₂×C₅	1	1	yes	characteristic, complemented
90	#1787	C₂×C₅	1	2	yes	complemented
91	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₅×Q₈	—	2	4	no	—
94	C₂×C₅×Q₈	—	2	16	no	—
95	C₂×C₅×Q₈	—	2	4	no	—
96	C₂×C₅×Q₈	—	2	4	no	—
97	C₂×C₅×Q₈	—	2	4	no	—
98	C₂×C₅×Q₈	—	2	4	no	—
99	C₂×C₅×Q₈	—	4	8	no	—
100	C₂×C₅×Q₈	—	4	16	no	—
101	C₂×C₅×Q₈	—	4	8	no	—
102	C₂×C₅×Q₈	—	4	4	no	—
103	C₂×C₅×Q₈	C₂×D₄	1	8	yes	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	Q₁₆	1	4	yes	complemented
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	4	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	4	8	no	—
116	C₂²×C₄×C₅	—	4	4	no	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	#41	1	2	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×Q₁₆	—	2	16	no	—
125	C₅×Q₁₆	—	2	16	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	2	8	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	4	4	no	—
133	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
135	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	4	8	no	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	4	8	no	—
143	C₅×C₂²⋊C₄	—	4	4	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₂³×Q₈	C₂²×C₅	1	2	yes	—
147	C₂²×Q₁₆	—	2	8	no	—
148	C₂²×Q₁₆	—	2	4	no	—
149	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
150	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
151	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
152	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
154	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
155	#467	—	2	8	no	—
156	C₈×D₄	—	2	4	no	—
157	C₂×#107	C₂²×C₅	1	2	yes	—
158	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×#103	C₂²×C₅	1	4	yes	—
160	C₂×#103	C₂²×C₅	1	4	yes	—
161	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
164	#395	—	2	2	no	—
165	#393	—	2	2	no	—
166	#391	C₂²×C₅	1	4	yes	—
167	#386	—	2	2	no	—
168	#385	—	2	2	no	—
169	#380	C₂²×C₅	1	2	yes	—
170	#340	C₂²×C₅	1	2	yes	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	1	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	1	no	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	#121	1	2	yes	—
178	C₂³×C₅	C₂×Q₁₆	1	2	yes	—
179	C₂³×C₅	C₂×Q₁₆	1	2	yes	complemented
180	C₂³×C₅	#135	1	2	yes	—
181	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₅×Q₈	—	2	8	no	—
183	C₅×Q₈	—	2	8	no	—
184	C₅×Q₈	—	4	16	no	—
185	C₅×Q₈	—	4	4	no	—
186	C₅×Q₈	—	4	4	no	—
187	C₅×D₄	—	2	8	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	8	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	4	16	no	—
200	C₂×C₄×C₅	—	4	4	no	—
201	C₂×C₄×C₅	—	4	4	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	4	no	—
206	C₂×C₄×C₅	—	4	4	no	—
207	C₂×C₄×C₅	—	4	4	no	—
208	C₂×C₄×C₅	#121	1	2	yes	—
209	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	complemented
210	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	—	4	1	no	—
216	C₅×C₈	—	4	1	no	—
217	C₅×C₈	#120	1	4	yes	—
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	—	2	8	no	—
220	C₂²×Q₈	—	2	4	no	—
221	C₂²×Q₈	—	2	4	no	—
222	C₂²×Q₈	—	4	4	no	—
223	C₂²×Q₈	C₂³×C₅	1	4	yes	—
224	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂×Q₁₆	—	2	32	no	—
229	C₂×Q₁₆	—	2	8	no	—
230	C₂×Q₁₆	—	2	4	no	—
231	C₂×Q₁₆	—	2	4	no	—
232	C₂×Q₁₆	—	2	4	no	—
233	C₂×Q₁₆	C₅×D₄	1	8	yes	complemented
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	C₅×D₄	1	4	yes	—
238	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
242	C₂²⋊Q₈	—	2	8	no	—
243	C₂²⋊Q₈	—	4	4	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
249	C₂×C₂²⋊C₄	—	2	4	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	#107	—	2	4	no	—
255	C₄⋊C₈	—	2	2	no	—
256	#103	—	2	8	no	—
257	#103	—	4	4	no	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	4	no	—
263	#95	—	2	4	no	—
264	C₂²×C₅	—	2	2	no	—
265	C₂²×C₅	—	2	4	no	—
266	C₂²×C₅	—	2	4	no	—
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	2	4	no	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	4	1	no	—
271	C₂²×C₅	—	4	2	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	#467	1	4	yes	complemented
274	C₂²×C₅	C₂×#121	1	1	yes	characteristic
275	C₂²×C₅	D₄²	1	2	yes	—
276	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
277	C₂²×C₅	C₂×#135	1	1	yes	characteristic
278	C₂²×C₅	#578	1	2	yes	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	—	4	8	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	8	4	no	—
285	C₄×C₅	C₂×#120	1	1	yes	characteristic
286	C₄×C₅	#535	1	1	yes	characteristic
287	C₄×C₅	#546	1	2	yes	—
288	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	16	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	4	8	no	—
297	C₂×Q₈	—	4	16	no	—
298	C₂×Q₈	—	4	8	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	C₂×C₅×D₄	1	8	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	C₅×Q₁₆	1	4	yes	complemented
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	8	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₅×#41	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
321	Q₁₆	—	2	16	no	—
322	Q₁₆	—	2	16	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	4	no	—
330	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
331	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
332	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	8	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	4	8	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₂×C₅	—	2	4	no	—
344	C₂×C₅	—	4	2	no	—
345	C₂×C₅	#2408	1	1	yes	characteristic
346	C₂×C₅	C₂×#467	1	1	yes	characteristic
347	C₂×C₅	#3059	1	1	yes	characteristic
348	C₂×C₅	#3285	1	2	yes	—
349	C₂×C₅	D₄×Q₁₆	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	C₅×#121	1	2	yes	—
357	C₂³	C₂×C₅×Q₁₆	1	2	yes	—
358	C₂³	C₂×C₅×Q₁₆	1	2	yes	complemented
359	C₂³	C₅×#135	1	2	yes	—
360	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	Q₈	—	2	8	no	—
363	Q₈	—	4	16	no	—
364	Q₈	—	4	4	no	—
365	Q₈	—	4	4	no	—
366	D₄	—	2	8	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	16	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	C₅×#121	1	2	yes	—
388	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	complemented
389	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
391	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
392	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	C₅×#120	1	4	yes	—
397	C₅	#24268	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₅×#467	1	4	yes	complemented
408	C₂²	C₂×C₅×#121	1	1	yes	characteristic
409	C₂²	C₅×D₄²	1	2	yes	—
410	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
411	C₂²	C₂×C₅×#135	1	1	yes	characteristic
412	C₂²	C₅×#578	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	8	no	—
418	C₄	—	8	4	no	—
419	C₄	C₂×C₅×#120	1	1	yes	characteristic
420	C₄	C₅×#535	1	1	yes	characteristic
421	C₄	C₅×#546	1	2	yes	—
422	C₂	—	2	4	no	—
423	C₂	—	4	2	no	—
424	C₂	C₅×#2408	1	1	yes	characteristic
425	C₂	C₂×C₅×#467	1	1	yes	characteristic
426	C₂	C₅×#3059	1	1	yes	characteristic
427	C₂	C₅×#3285	1	2	yes	—
428	C₂	C₅×D₄×Q₁₆	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×Q₁₆	C₂	semidirect
2. C₂×C₅×#467	C₂	semidirect
5. C₅×#2056	C₂	semidirect
6. C₅×#2001	C₂	semidirect
7. C₅×#1969	C₂	semidirect
8. C₅×#1808	C₂	semidirect
9. C₅×#1787	C₂	semidirect
35. #24268	C₅	direct (N × H)
51. C₂×C₅×Q₁₆	D₄	semidirect
82. C₂³×Q₁₆	C₂×C₅	semidirect
83. C₂×#467	C₂×C₅	semidirect
86. #2056	C₂×C₅	semidirect
87. #2001	C₂×C₅	semidirect
88. #1969	C₂×C₅	semidirect
89. #1808	C₂×C₅	semidirect
90. #1787	C₂×C₅	semidirect
106. C₂×C₅×D₄	Q₁₆	semidirect
179. C₂³×C₅	C₂×Q₁₆	semidirect
209. C₂×C₄×C₅	C₂×Q₁₆	semidirect
233. C₂×Q₁₆	C₅×D₄	semidirect
273. C₂²×C₅	#467	semidirect
303. C₂×D₄	C₅×Q₁₆	semidirect
358. C₂³	C₂×C₅×Q₁₆	semidirect
388. C₂×C₄	C₂×C₅×Q₁₆	semidirect
397. C₅	#24268	direct (N × H)
407. C₂²	C₅×#467	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×Q₁₆	2
C₂×C₅×#467	2
C₂×C₅×C₈×D₄	2
C₅×#2409	2
C₅×#2056	2
C₅×#2001	2
C₅×#1969	2
C₅×#1808	2
C₅×#1787	2
#24268	5

Subgroups — C5×#24268 #11946988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24268 #11946988