Subgroups — C₅×#10868 #11933588

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#344	C₂	1	2	yes	maximal
5	C₂×C₅×H(3,ℤ/4)	C₂	1	2	yes	maximal
6	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
8	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×#117	C₂²	1	2	yes	—
10	C₂×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×C₅×#108	—	2	2	no	—
12	C₂×C₅×#108	—	2	1	no	—
13	C₂×C₅×#108	—	2	1	no	—
14	C₂×C₅×#108	C₄	1	4	yes	complemented
15	C₅×#427	—	2	2	no	—
16	C₅×#427	C₄	1	4	yes	complemented
17	C₂×C₅×#107	—	2	1	no	—
18	C₂×C₅×#106	—	2	1	no	—
19	C₅×#405	—	2	2	no	—
20	C₅×#405	—	2	2	no	—
21	C₂×C₅×#97	C₄	1	2	yes	complemented
22	C₂×C₄×C₅×C₈	C₄	1	2	yes	complemented
23	C₅×#344	—	2	4	no	—
24	C₅×H(3,ℤ/4)	—	2	4	no	—
25	#10868	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₂×C₅×M₁₆	—	2	1	no	—
28	C₂×C₅×M₁₆	—	2	1	no	—
29	C₂×C₅×M₁₆	—	2	1	no	—
30	C₂×C₅×M₁₆	—	2	1	no	—
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	2	2	no	—
34	C₂×C₅×M₁₆	—	2	2	no	—
35	C₂×C₅×M₁₆	—	2	2	no	—
36	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
37	C₂×C₅×M₁₆	D₄	1	2	yes	—
38	C₂×C₅×M₁₆	Q₈	1	2	yes	—
39	C₂²×C₅×C₈	—	2	2	no	—
40	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₅×C₈	D₄	1	2	yes	—
46	C₂²×C₅×C₈	D₄	1	2	yes	—
47	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
50	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
51	C₅×#117	—	2	1	no	—
52	C₅×#117	—	2	1	no	—
53	C₅×#117	—	2	2	no	—
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	2	2	no	—
56	C₅×#117	C₂×C₄	1	4	yes	—
57	C₅×#117	D₄	1	2	yes	—
58	C₅×#117	Q₈	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₄²×C₅	—	2	2	no	—
64	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
65	C₅×#108	—	2	4	no	—
66	C₅×#108	—	2	4	no	—
67	C₅×#107	—	2	4	no	—
68	C₅×#106	—	2	4	no	—
69	C₅×#97	—	2	4	no	—
70	C₄×C₅×C₈	—	2	4	no	—
71	C₂²×#108	C₂×C₅	1	1	yes	characteristic
72	C₂×#427	C₂×C₅	1	1	yes	characteristic
73	C₂×#405	C₂×C₅	1	1	yes	characteristic
74	C₂×#344	C₂×C₅	1	2	yes	—
75	C₂×H(3,ℤ/4)	C₂×C₅	1	2	yes	—
76	C₂⁴×C₅	#41	1	1	yes	characteristic
77	C₂²×C₄×C₅	—	2	2	no	—
78	C₂²×C₄×C₅	—	4	2	no	—
79	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₅	#41	1	1	yes	characteristic
91	C₂²×C₄×C₅	#41	1	1	yes	characteristic
92	C₂²×C₄×C₅	#41	1	1	yes	characteristic
93	C₅×M₁₆	—	2	2	no	—
94	C₅×M₁₆	—	2	2	no	—
95	C₅×M₁₆	—	2	2	no	—
96	C₅×M₁₆	—	2	2	no	—
97	C₅×M₁₆	—	2	4	no	—
98	C₅×M₁₆	—	2	4	no	—
99	C₅×M₁₆	—	4	2	no	—
100	C₅×M₁₆	—	4	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	4	no	—
104	C₂×C₅×C₈	—	4	2	no	—
105	C₂×C₅×C₈	—	4	2	no	—
106	C₂×C₅×C₈	C₄²	1	2	yes	—
107	C₂×C₅×C₈	C₄²	1	2	yes	—
108	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
109	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
110	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
111	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
112	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
113	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
114	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
115	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
120	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
121	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
122	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	2	2	no	—
128	C₅×C₂²⋊C₄	—	2	2	no	—
129	C₅×C₂²⋊C₄	—	2	4	no	—
130	C₅×C₂²⋊C₄	—	4	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	4	no	—
133	C₄²×C₅	—	4	2	no	—
134	C₄²×C₅	C₄⋊C₄	1	4	yes	—
135	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
136	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
137	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
138	C₂×#117	C₂²×C₅	1	2	yes	—
139	C₂×#117	C₂²×C₅	1	1	yes	characteristic
140	C₂×#108	—	2	2	no	—
141	C₂×#108	—	2	1	no	—
142	C₂×#108	—	2	1	no	—
143	C₂×#108	C₄×C₅	1	4	yes	complemented
144	#427	—	2	2	no	—
145	#427	C₄×C₅	1	4	yes	complemented
146	C₂×#107	—	2	1	no	—
147	C₂×#106	—	2	1	no	—
148	#405	—	2	2	no	—
149	#405	—	2	2	no	—
150	C₂×#97	C₄×C₅	1	2	yes	complemented
151	C₂×C₄×C₈	C₄×C₅	1	2	yes	complemented
152	#344	—	2	4	no	—
153	H(3,ℤ/4)	—	2	4	no	—
154	C₂³×C₅	—	4	2	no	—
155	C₂³×C₅	#117	1	1	yes	characteristic
156	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
157	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
158	C₂³×C₅	#121	1	1	yes	characteristic
159	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂³×C₅	#124	1	1	yes	characteristic
161	C₂³×C₅	#125	1	1	yes	characteristic
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	4	4	no	—
164	C₂×C₄×C₅	—	4	4	no	—
165	C₂×C₄×C₅	—	8	4	no	—
166	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅	#117	1	1	yes	characteristic
176	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	#121	1	1	yes	characteristic
183	C₂×C₄×C₅	#121	1	1	yes	characteristic
184	C₂×C₄×C₅	#121	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₅	#124	1	1	yes	characteristic
189	C₂×C₄×C₅	#125	1	1	yes	characteristic
190	C₂×C₄×C₅	#127	1	1	yes	characteristic
191	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
194	C₅×C₈	—	2	4	no	—
195	C₅×C₈	—	4	4	no	—
196	C₅×C₈	#95	1	2	yes	—
197	C₅×C₈	#95	1	2	yes	—
198	C₅×C₈	#95	1	2	yes	—
199	C₅×C₈	#95	1	2	yes	—
200	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂×M₁₆	—	2	1	no	—
202	C₂×M₁₆	—	2	1	no	—
203	C₂×M₁₆	—	2	1	no	—
204	C₂×M₁₆	—	2	1	no	—
205	C₂×M₁₆	—	2	2	no	—
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
211	C₂×M₁₆	C₅×D₄	1	2	yes	—
212	C₂×M₁₆	C₅×Q₈	1	2	yes	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
215	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
218	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
219	C₂²×C₈	C₅×D₄	1	2	yes	—
220	C₂²×C₈	C₅×D₄	1	2	yes	—
221	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
222	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
223	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
224	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
225	#117	—	2	1	no	—
226	#117	—	2	1	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	C₂×C₄×C₅	1	4	yes	—
231	#117	C₅×D₄	1	2	yes	—
232	#117	C₅×Q₈	1	2	yes	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
239	#108	—	2	4	no	—
240	#108	—	2	4	no	—
241	#107	—	2	4	no	—
242	#106	—	2	4	no	—
243	#97	—	2	4	no	—
244	C₄×C₈	—	2	4	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	2	2	no	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	4	1	no	—
249	C₂²×C₅	—	4	1	no	—
250	C₂²×C₅	—	4	1	no	—
251	C₂²×C₅	—	4	1	no	—
252	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
253	C₂²×C₅	#380	1	1	yes	characteristic
254	C₂²×C₅	#382	1	1	yes	characteristic
255	C₂²×C₅	#389	1	1	yes	characteristic
256	C₂²×C₅	#389	1	1	yes	characteristic
257	C₂²×C₅	#390	1	1	yes	characteristic
258	C₂²×C₅	#391	1	1	yes	characteristic
259	C₄×C₅	—	4	4	no	—
260	C₄×C₅	—	8	4	no	—
261	C₄×C₅	C₂×#95	1	1	yes	characteristic
262	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
263	C₄×C₅	#380	1	1	yes	characteristic
264	C₄×C₅	#384	1	1	yes	characteristic
265	C₄×C₅	#389	1	1	yes	characteristic
266	C₄×C₅	#389	1	1	yes	characteristic
267	C₄×C₅	#390	1	1	yes	characteristic
268	C₄×C₅	#391	1	1	yes	characteristic
269	C₂⁴	C₅×#41	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
283	C₂²×C₄	C₅×#41	1	1	yes	characteristic
284	C₂²×C₄	C₅×#41	1	1	yes	characteristic
285	C₂²×C₄	C₅×#41	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	2	4	no	—
291	M₁₆	—	2	4	no	—
292	M₁₆	—	4	2	no	—
293	M₁₆	—	4	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	C₄²×C₅	1	2	yes	—
300	C₂×C₈	C₄²×C₅	1	2	yes	—
301	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
302	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
303	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
304	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
305	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
306	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
307	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
308	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
309	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
310	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
311	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
312	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
313	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
314	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
315	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	4	2	no	—
327	C₄²	C₅×C₄⋊C₄	1	4	yes	—
328	C₂×C₅	—	2	1	no	—
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	2	1	no	—
331	C₂×C₅	—	2	1	no	—
332	C₂×C₅	—	2	1	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
335	C₂×C₅	#1833	1	2	yes	—
336	C₂³	—	4	2	no	—
337	C₂³	C₅×#117	1	1	yes	characteristic
338	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
339	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
340	C₂³	C₅×#121	1	1	yes	characteristic
341	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
342	C₂³	C₅×#124	1	1	yes	characteristic
343	C₂³	C₅×#125	1	1	yes	characteristic
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
349	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₅×#117	1	1	yes	characteristic
358	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
359	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
360	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
362	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
363	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
364	C₂×C₄	C₅×#121	1	1	yes	characteristic
365	C₂×C₄	C₅×#121	1	1	yes	characteristic
366	C₂×C₄	C₅×#121	1	1	yes	characteristic
367	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
370	C₂×C₄	C₅×#124	1	1	yes	characteristic
371	C₂×C₄	C₅×#125	1	1	yes	characteristic
372	C₂×C₄	C₅×#127	1	1	yes	characteristic
373	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
374	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
375	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
376	C₈	—	2	4	no	—
377	C₈	—	4	4	no	—
378	C₈	C₅×#95	1	2	yes	—
379	C₈	C₅×#95	1	2	yes	—
380	C₈	C₅×#95	1	2	yes	—
381	C₈	C₅×#95	1	2	yes	—
382	C₅	#10868	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
391	C₂²	C₅×#380	1	1	yes	characteristic
392	C₂²	C₅×#382	1	1	yes	characteristic
393	C₂²	C₅×#389	1	1	yes	characteristic
394	C₂²	C₅×#389	1	1	yes	characteristic
395	C₂²	C₅×#390	1	1	yes	characteristic
396	C₂²	C₅×#391	1	1	yes	characteristic
397	C₄	—	4	4	no	—
398	C₄	—	8	4	no	—
399	C₄	C₂×C₅×#95	1	1	yes	characteristic
400	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
401	C₄	C₅×#380	1	1	yes	characteristic
402	C₄	C₅×#384	1	1	yes	characteristic
403	C₄	C₅×#389	1	1	yes	characteristic
404	C₄	C₅×#389	1	1	yes	characteristic
405	C₄	C₅×#390	1	1	yes	characteristic
406	C₄	C₅×#391	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	C₅×C₄⋊#95	1	1	yes	characteristic
414	C₂	C₅×#1833	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	#117
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	#382
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂×C₅×#108	C₄	semidirect
16. C₅×#427	C₄	semidirect
21. C₂×C₅×#97	C₄	semidirect
22. C₂×C₄×C₅×C₈	C₄	semidirect
25. #10868	C₅	direct (N × H)
143. C₂×#108	C₄×C₅	semidirect
145. #427	C₄×C₅	semidirect
150. C₂×#97	C₄×C₅	semidirect
151. C₂×C₄×C₈	C₄×C₅	semidirect
382. C₅	#10868	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#108	2
C₂×C₅×#427	2
C₂×C₅×#405	2
C₂×C₅×#344	2
C₂×C₅×H(3,ℤ/4)	2
#10868	5

Subgroups — C5×#10868 #11933588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10868 #11933588