Subgroups — C₅×#10911 #11933631

Order 1280.

734 conjugacy classes of subgroups.

The subgroup lattice has 478 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×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic
6	C₅×#1728	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#108	—	2	2	no	—
16	C₂×C₅×#108	—	2	2	no	—
17	C₂×C₅×#108	C₄	1	4	yes	complemented
18	C₄×C₅×M₁₆	—	2	2	no	—
19	C₄×C₅×M₁₆	—	2	2	no	—
20	C₂×C₅×#97	—	2	1	no	—
21	C₂×C₄×C₅×C₈	—	2	1	no	—
22	C₅×#341	—	2	2	no	—
23	C₅×#341	—	2	2	no	—
24	C₅×#341	C₄	1	4	yes	complemented
25	C₅×#336	—	2	1	no	—
26	C₅×#336	—	2	1	no	—
27	C₅×#336	C₄	1	4	yes	—
28	#10911	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂³×C₄×C₅	Q₈	1	2	yes	—
30	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	1	no	—
32	C₂×C₅×M₁₆	—	2	1	no	—
33	C₂×C₅×M₁₆	—	2	1	no	—
34	C₂×C₅×M₁₆	—	2	1	no	—
35	C₂×C₅×M₁₆	—	2	1	no	—
36	C₂×C₅×M₁₆	—	2	1	no	—
37	C₂×C₅×M₁₆	—	2	1	no	—
38	C₂×C₅×M₁₆	—	2	1	no	—
39	C₂×C₅×M₁₆	—	2	1	no	—
40	C₂×C₅×M₁₆	—	2	1	no	—
41	C₂×C₅×M₁₆	—	2	1	no	—
42	C₂×C₅×M₁₆	—	2	1	no	—
43	C₂×C₅×M₁₆	—	2	1	no	—
44	C₂×C₅×M₁₆	—	2	1	no	—
45	C₂×C₅×M₁₆	—	2	1	no	—
46	C₂×C₅×M₁₆	—	2	1	no	—
47	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₅×M₁₆	D₄	1	2	yes	—
52	C₂×C₅×M₁₆	D₄	1	2	yes	—
53	C₂×C₅×M₁₆	D₄	1	2	yes	—
54	C₂×C₅×M₁₆	Q₈	1	2	yes	—
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	—	2	1	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	—	2	1	no	—
66	C₂²×C₅×C₈	—	2	1	no	—
67	C₂²×C₅×C₈	—	2	1	no	—
68	C₂²×C₅×C₈	—	2	1	no	—
69	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
70	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
71	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
72	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₅×#108	—	2	8	no	—
81	C₅×#97	—	2	4	no	—
82	C₄×C₅×C₈	—	2	4	no	—
83	C₂²×#108	C₂×C₅	1	1	yes	characteristic
84	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
85	C₂×#341	C₂×C₅	1	1	yes	characteristic
86	C₂×#341	C₂×C₅	1	1	yes	characteristic
87	C₂×#341	C₂×C₅	1	1	yes	characteristic
88	#1728	C₂×C₅	1	1	yes	characteristic
89	C₂×#336	C₂×C₅	1	1	yes	characteristic
90	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	4	no	—
94	C₂²×C₄×C₅	—	4	2	no	—
95	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₅	#41	1	1	yes	characteristic
106	C₂²×C₄×C₅	#41	1	1	yes	characteristic
107	C₂²×C₄×C₅	#41	1	1	yes	characteristic
108	C₂²×C₄×C₅	#41	1	1	yes	characteristic
109	C₂²×C₄×C₅	#41	1	1	yes	characteristic
110	C₂²×C₄×C₅	#41	1	1	yes	characteristic
111	C₅×M₁₆	—	2	2	no	—
112	C₅×M₁₆	—	2	2	no	—
113	C₅×M₁₆	—	2	2	no	—
114	C₅×M₁₆	—	2	2	no	—
115	C₅×M₁₆	—	2	2	no	—
116	C₅×M₁₆	—	2	2	no	—
117	C₅×M₁₆	—	2	2	no	—
118	C₅×M₁₆	—	2	2	no	—
119	C₅×M₁₆	—	2	2	no	—
120	C₅×M₁₆	—	2	2	no	—
121	C₅×M₁₆	—	4	1	no	—
122	C₅×M₁₆	—	4	1	no	—
123	C₅×M₁₆	—	4	1	no	—
124	C₅×M₁₆	—	4	1	no	—
125	C₅×M₁₆	C₂²⋊C₄	1	4	yes	—
126	C₅×M₁₆	C₄⋊C₄	1	4	yes	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	2	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	2	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	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	4	1	no	—
145	C₂×C₅×C₈	—	4	1	no	—
146	C₂×C₅×C₈	—	4	1	no	—
147	C₂×C₅×C₈	—	4	1	no	—
148	C₂×C₅×C₈	—	4	1	no	—
149	C₂×C₅×C₈	—	4	1	no	—
150	C₂×C₅×C₈	—	4	1	no	—
151	C₂×C₅×C₈	—	4	1	no	—
152	C₂×C₅×C₈	C₄²	1	4	yes	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
160	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
162	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
166	C₂×#108	—	2	2	no	—
167	C₂×#108	—	2	2	no	—
168	C₂×#108	C₄×C₅	1	4	yes	complemented
169	C₄×M₁₆	—	2	2	no	—
170	C₄×M₁₆	—	2	2	no	—
171	C₂×#97	—	2	1	no	—
172	C₂×C₄×C₈	—	2	1	no	—
173	#341	—	2	2	no	—
174	#341	—	2	2	no	—
175	#341	C₄×C₅	1	4	yes	complemented
176	#336	—	2	1	no	—
177	#336	—	2	1	no	—
178	#336	C₄×C₅	1	4	yes	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
183	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
184	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂³×C₅	#125	1	1	yes	characteristic
187	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	4	4	no	—
194	C₂×C₄×C₅	—	4	4	no	—
195	C₂×C₄×C₅	#108	1	4	yes	complemented
196	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	#117	1	1	yes	characteristic
200	C₂×C₄×C₅	#117	1	1	yes	characteristic
201	C₂×C₄×C₅	#117	1	1	yes	characteristic
202	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₅	#120	1	1	yes	characteristic
213	C₂×C₄×C₅	#121	1	1	yes	characteristic
214	C₂×C₄×C₅	#121	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
217	C₂×C₄×C₅	#123	1	1	yes	characteristic
218	C₂×C₄×C₅	#123	1	1	yes	characteristic
219	C₂×C₄×C₅	#123	1	1	yes	characteristic
220	C₂×C₄×C₅	#124	1	1	yes	characteristic
221	C₂×C₄×C₅	#125	1	1	yes	characteristic
222	C₂×C₄×C₅	#126	1	1	yes	characteristic
223	C₂×C₄×C₅	#126	1	1	yes	characteristic
224	C₅×C₈	—	2	4	no	—
225	C₅×C₈	—	2	4	no	—
226	C₅×C₈	—	2	4	no	—
227	C₅×C₈	—	4	2	no	—
228	C₅×C₈	—	4	2	no	—
229	C₅×C₈	—	4	2	no	—
230	C₂³×C₄	C₅×Q₈	1	2	yes	—
231	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
249	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
250	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
251	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
252	C₂×M₁₆	C₅×D₄	1	2	yes	—
253	C₂×M₁₆	C₅×D₄	1	2	yes	—
254	C₂×M₁₆	C₅×D₄	1	2	yes	—
255	C₂×M₁₆	C₅×Q₈	1	2	yes	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
271	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
272	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
273	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
279	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
280	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
281	#108	—	2	8	no	—
282	#97	—	2	4	no	—
283	C₄×C₈	—	2	4	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	2	2	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
293	C₂²×C₅	#385	1	1	yes	characteristic
294	C₂²×C₅	#387	1	1	yes	characteristic
295	C₂²×C₅	#387	1	1	yes	characteristic
296	C₂²×C₅	#389	1	1	yes	characteristic
297	C₂²×C₅	#389	1	1	yes	characteristic
298	C₂²×C₅	#391	1	1	yes	characteristic
299	C₂²×C₅	C₂×#108	1	2	yes	—
300	C₂²×C₅	#430	1	2	yes	—
301	C₄×C₅	—	2	4	no	—
302	C₄×C₅	—	4	2	no	—
303	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
305	C₄×C₅	#385	1	1	yes	characteristic
306	C₄×C₅	#386	1	1	yes	characteristic
307	C₄×C₅	#387	1	1	yes	characteristic
308	C₄×C₅	#387	1	1	yes	characteristic
309	C₄×C₅	#388	1	1	yes	characteristic
310	C₄×C₅	#388	1	1	yes	characteristic
311	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
317	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
318	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
326	C₂²×C₄	C₅×#41	1	1	yes	characteristic
327	C₂²×C₄	C₅×#41	1	1	yes	characteristic
328	C₂²×C₄	C₅×#41	1	1	yes	characteristic
329	C₂²×C₄	C₅×#41	1	1	yes	characteristic
330	C₂²×C₄	C₅×#41	1	1	yes	characteristic
331	C₂²×C₄	C₅×#41	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	4	1	no	—
346	M₁₆	C₅×C₂²⋊C₄	1	4	yes	—
347	M₁₆	C₅×C₄⋊C₄	1	4	yes	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	C₄²×C₅	1	4	yes	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₂×C₅	—	2	1	no	—
381	C₂×C₅	—	2	1	no	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	#1436	1	1	yes	characteristic
385	C₂×C₅	C₄×#108	1	1	yes	characteristic
386	C₂×C₅	#1778	1	1	yes	characteristic
387	C₂×C₅	#1855	1	2	yes	—
388	C₂×C₅	#1950	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
392	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
393	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
394	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
395	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
396	C₂³	C₅×#125	1	1	yes	characteristic
397	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₅×#108	1	4	yes	complemented
406	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
407	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
408	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
409	C₂×C₄	C₅×#117	1	1	yes	characteristic
410	C₂×C₄	C₅×#117	1	1	yes	characteristic
411	C₂×C₄	C₅×#117	1	1	yes	characteristic
412	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
413	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
414	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
415	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
418	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
419	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
420	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
421	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
422	C₂×C₄	C₅×#120	1	1	yes	characteristic
423	C₂×C₄	C₅×#121	1	1	yes	characteristic
424	C₂×C₄	C₅×#121	1	1	yes	characteristic
425	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
426	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
427	C₂×C₄	C₅×#123	1	1	yes	characteristic
428	C₂×C₄	C₅×#123	1	1	yes	characteristic
429	C₂×C₄	C₅×#123	1	1	yes	characteristic
430	C₂×C₄	C₅×#124	1	1	yes	characteristic
431	C₂×C₄	C₅×#125	1	1	yes	characteristic
432	C₂×C₄	C₅×#126	1	1	yes	characteristic
433	C₂×C₄	C₅×#126	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	2	4	no	—
436	C₈	—	2	4	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₅	#10911	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
450	C₂²	C₅×#385	1	1	yes	characteristic
451	C₂²	C₅×#387	1	1	yes	characteristic
452	C₂²	C₅×#387	1	1	yes	characteristic
453	C₂²	C₅×#389	1	1	yes	characteristic
454	C₂²	C₅×#389	1	1	yes	characteristic
455	C₂²	C₅×#391	1	1	yes	characteristic
456	C₂²	C₂×C₅×#108	1	2	yes	—
457	C₂²	C₅×#430	1	2	yes	—
458	C₄	—	2	4	no	—
459	C₄	—	4	2	no	—
460	C₄	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
461	C₄	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
462	C₄	C₅×#385	1	1	yes	characteristic
463	C₄	C₅×#386	1	1	yes	characteristic
464	C₄	C₅×#387	1	1	yes	characteristic
465	C₄	C₅×#387	1	1	yes	characteristic
466	C₄	C₅×#388	1	1	yes	characteristic
467	C₄	C₅×#388	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	1	no	—
472	C₂	C₅×#1436	1	1	yes	characteristic
473	C₂	C₄×C₅×#108	1	1	yes	characteristic
474	C₂	C₅×#1778	1	1	yes	characteristic
475	C₂	C₅×#1855	1	2	yes	—
476	C₂	C₅×#1950	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂³×C₅	C₂×C₄⋊C₄
prime radical	C₂⁴×C₅	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₂×C₅×#108	C₄	semidirect
24. C₅×#341	C₄	semidirect
28. #10911	C₅	direct (N × H)
168. C₂×#108	C₄×C₅	semidirect
175. #341	C₄×C₅	semidirect
195. C₂×C₄×C₅	#108	semidirect
405. C₂×C₄	C₅×#108	semidirect
440. C₅	#10911	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×C₄×C₅×M₁₆	2
C₂×C₅×#341	2
C₅×#1728	2
C₂×C₅×#336	2
#10911	5

Subgroups — C5×#10911 #11933631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10911 #11933631