Subgroups — C₂×C₅×#1922 #11943760

Order 1280.

854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#1922	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#427	C₄	1	4	yes	complemented
17	C₅×#427	C₂²	1	4	yes	—
18	C₂×C₅×#107	C₄	1	1	yes	characteristic, complemented
19	C₂×C₅×#107	C₄	1	1	yes	characteristic, complemented
20	C₂×C₅×#106	C₄	1	1	yes	characteristic, complemented
21	C₂×C₅×#106	C₄	1	1	yes	characteristic, complemented
22	C₅×#424	—	2	2	no	—
23	C₅×#424	C₂²	1	4	yes	—
24	C₂×C₅×C₄⋊C₈	—	2	1	no	—
25	C₂×C₅×C₄⋊C₈	—	2	1	no	—
26	C₅×#405	—	2	2	no	—
27	C₅×#405	C₂²	1	4	yes	—
28	C₂×C₅×#97	—	2	1	no	—
29	C₂×C₄×C₅×C₈	—	2	1	no	—
30	C₅×#341	C₂²	1	4	yes	—
31	C₅×#339	C₂²	1	4	yes	—
32	C₅×#339	C₂²	1	4	yes	—
33	C₅×#336	C₂²	1	4	yes	—
34	C₂×#1922	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂³×C₄×C₅	—	2	1	no	—
36	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×M₁₆	—	2	1	no	—
38	C₂×C₅×M₁₆	—	2	2	no	—
39	C₂×C₅×M₁₆	—	2	1	no	—
40	C₂×C₅×M₁₆	—	2	2	no	—
41	C₂×C₅×M₁₆	—	2	2	no	—
42	C₂×C₅×M₁₆	Q₈	1	4	yes	—
43	C₂×C₅×M₁₆	C₂³	1	2	yes	—
44	C₂×C₅×M₁₆	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	—	2	1	no	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	—	2	2	no	—
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	—	2	1	no	—
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
54	C₂²×C₅×C₈	D₄	1	2	yes	—
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₂²×C₅×C₈	C₂³	1	2	yes	—
59	C₅×#117	—	2	1	no	—
60	C₅×#117	—	2	1	no	—
61	C₅×#117	—	2	1	no	—
62	C₅×#117	—	2	1	no	—
63	C₅×#117	C₂×C₄	1	2	yes	—
64	C₅×#117	C₂×C₄	1	2	yes	—
65	C₅×#117	C₂³	1	2	yes	—
66	C₅×#117	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	—	2	2	no	—
77	C₂×C₄²×C₅	—	2	1	no	—
78	C₂×C₄²×C₅	C₂³	1	2	yes	—
79	C₅×#107	C₂×C₄	1	4	yes	complemented
80	C₅×#107	C₂×C₄	1	4	yes	complemented
81	C₅×#106	C₂×C₄	1	4	yes	complemented
82	C₅×#106	C₂×C₄	1	4	yes	complemented
83	C₅×C₄⋊C₈	—	2	4	no	—
84	C₅×C₄⋊C₈	—	2	4	no	—
85	C₅×#97	—	2	4	no	—
86	C₄×C₅×C₈	—	2	4	no	—
87	C₂×#427	C₂×C₅	1	1	yes	characteristic
88	C₂×#424	C₂×C₅	1	1	yes	characteristic
89	C₂×#405	C₂×C₅	1	1	yes	characteristic
90	#1922	C₂×C₅	1	8	yes	direct product factor
91	C₂×#341	C₂×C₅	1	1	yes	characteristic
92	C₂×#339	C₂×C₅	1	1	yes	characteristic
93	C₂×#339	C₂×C₅	1	1	yes	characteristic
94	C₂×#336	C₂×C₅	1	1	yes	characteristic
95	C₂⁴×C₅	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅	—	2	4	no	—
97	C₂²×C₄×C₅	—	2	1	no	—
98	C₂²×C₄×C₅	—	2	1	no	—
99	C₂²×C₄×C₅	—	2	1	no	—
100	C₂²×C₄×C₅	—	2	1	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	4	2	no	—
103	C₂²×C₄×C₅	—	4	2	no	—
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₅	#41	1	2	yes	—
110	C₂²×C₄×C₅	#41	1	2	yes	—
111	C₂²×C₄×C₅	#41	1	1	yes	characteristic
112	C₂²×C₄×C₅	#41	1	2	yes	—
113	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₅×M₁₆	—	2	4	no	—
115	C₅×M₁₆	—	2	2	no	—
116	C₅×M₁₆	—	2	2	no	—
117	C₅×M₁₆	—	2	2	no	—
118	C₅×M₁₆	—	4	2	no	—
119	C₅×M₁₆	C₂×Q₈	1	4	yes	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	4	no	—
123	C₂×C₅×C₈	—	2	4	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	4	no	—
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	—	4	2	no	—
134	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
144	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₅×C₂²⋊C₄	—	2	2	no	—
147	C₅×C₂²⋊C₄	—	2	2	no	—
148	C₅×C₂²⋊C₄	—	2	2	no	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₄²×C₅	—	2	2	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	2	2	no	—
156	C₄²×C₅	—	4	2	no	—
157	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
158	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
159	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×#117	C₂²×C₅	1	1	yes	characteristic
162	C₂×#117	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
164	#427	C₄×C₅	1	4	yes	complemented
165	#427	C₂²×C₅	1	4	yes	—
166	C₂×#107	C₄×C₅	1	1	yes	characteristic, complemented
167	C₂×#107	C₄×C₅	1	1	yes	characteristic, complemented
168	C₂×#106	C₄×C₅	1	1	yes	characteristic, complemented
169	C₂×#106	C₄×C₅	1	1	yes	characteristic, complemented
170	#424	—	2	2	no	—
171	#424	C₂²×C₅	1	4	yes	—
172	C₂×C₄⋊C₈	—	2	1	no	—
173	C₂×C₄⋊C₈	—	2	1	no	—
174	#405	—	2	2	no	—
175	#405	C₂²×C₅	1	4	yes	—
176	C₂×#97	—	2	1	no	—
177	C₂×C₄×C₈	—	2	1	no	—
178	#341	C₂²×C₅	1	4	yes	—
179	#339	C₂²×C₅	1	4	yes	—
180	#339	C₂²×C₅	1	4	yes	—
181	#336	C₂²×C₅	1	4	yes	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₅	#125	1	2	yes	—
187	C₂³×C₅	#126	1	2	yes	—
188	C₂³×C₅	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₅	—	2	4	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	—	2	2	no	—
194	C₂×C₄×C₅	—	4	8	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	#117	1	2	yes	—
202	C₂×C₄×C₅	#117	1	2	yes	—
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×Q₈	1	2	yes	—
206	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
207	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₅	#123	1	2	yes	—
210	C₂×C₄×C₅	#123	1	2	yes	—
211	C₂×C₄×C₅	#125	1	2	yes	—
212	C₂×C₄×C₅	#126	1	2	yes	—
213	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	—	2	2	no	—
221	C₅×C₈	—	2	4	no	—
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	4	2	no	—
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂×M₁₆	—	2	1	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	1	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	C₅×Q₈	1	4	yes	—
233	C₂×M₁₆	C₂³×C₅	1	2	yes	—
234	C₂×M₁₆	C₂³×C₅	1	2	yes	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
244	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
245	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
246	C₂²×C₈	C₅×D₄	1	2	yes	—
247	C₂²×C₈	C₂³×C₅	1	2	yes	—
248	C₂²×C₈	C₂³×C₅	1	2	yes	—
249	#117	—	2	1	no	—
250	#117	—	2	1	no	—
251	#117	—	2	1	no	—
252	#117	—	2	1	no	—
253	#117	C₂×C₄×C₅	1	2	yes	—
254	#117	C₂×C₄×C₅	1	2	yes	—
255	#117	C₂³×C₅	1	2	yes	—
256	#117	C₂³×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂³×C₅	1	2	yes	—
269	#107	C₂×C₄×C₅	1	4	yes	complemented
270	#107	C₂×C₄×C₅	1	4	yes	complemented
271	#106	C₂×C₄×C₅	1	4	yes	complemented
272	#106	C₂×C₄×C₅	1	4	yes	complemented
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	4	no	—
275	#97	—	2	4	no	—
276	C₄×C₈	—	2	4	no	—
277	C₂²×C₅	—	2	4	no	—
278	C₂²×C₅	—	2	4	no	—
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	#387	1	2	yes	—
284	C₂²×C₅	#387	1	2	yes	—
285	C₂²×C₅	#443	1	2	yes	—
286	C₂²×C₅	#444	1	2	yes	—
287	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₅	C₂×#125	1	1	yes	characteristic
289	C₂²×C₅	C₂×#126	1	1	yes	characteristic
290	C₄×C₅	—	4	4	no	—
291	C₄×C₅	—	4	2	no	—
292	C₄×C₅	—	4	2	no	—
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	#387	1	2	yes	—
296	C₄×C₅	#387	1	2	yes	—
297	C₄×C₅	C₂×#117	1	1	yes	characteristic
298	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
299	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
300	C₄×C₅	C₂×#123	1	1	yes	characteristic
301	C₂⁴	C₅×#41	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
315	C₂²×C₄	C₅×#41	1	2	yes	—
316	C₂²×C₄	C₅×#41	1	2	yes	—
317	C₂²×C₄	C₅×#41	1	1	yes	characteristic
318	C₂²×C₄	C₅×#41	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	4	2	no	—
325	M₁₆	C₂×C₅×Q₈	1	4	yes	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
341	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
342	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
343	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
349	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
350	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
351	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	4	2	no	—
363	C₂×C₅	—	2	1	no	—
364	C₂×C₅	—	2	1	no	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	#1922	1	4	yes	direct product factor
367	C₂×C₅	C₂×#387	1	1	yes	characteristic
368	C₂×C₅	C₂×#443	1	1	yes	characteristic
369	C₂×C₅	C₂×#444	1	1	yes	characteristic
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
373	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
374	C₂³	C₅×#125	1	2	yes	—
375	C₂³	C₅×#126	1	2	yes	—
376	C₂³	C₂×C₅×#41	1	1	yes	characteristic
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	C₅×#117	1	2	yes	—
390	C₂×C₄	C₅×#117	1	2	yes	—
391	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
394	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
395	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
396	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
397	C₂×C₄	C₅×#123	1	2	yes	—
398	C₂×C₄	C₅×#123	1	2	yes	—
399	C₂×C₄	C₅×#125	1	2	yes	—
400	C₂×C₄	C₅×#126	1	2	yes	—
401	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
404	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
405	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
406	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	—	2	4	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	4	2	no	—
413	C₅	C₂×#1922	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	C₅×#387	1	2	yes	—
421	C₂²	C₅×#387	1	2	yes	—
422	C₂²	C₅×#443	1	2	yes	—
423	C₂²	C₅×#444	1	2	yes	—
424	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
425	C₂²	C₂×C₅×#125	1	1	yes	characteristic
426	C₂²	C₂×C₅×#126	1	1	yes	characteristic
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	C₅×#387	1	2	yes	—
433	C₄	C₅×#387	1	2	yes	—
434	C₄	C₂×C₅×#117	1	1	yes	characteristic
435	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
436	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
437	C₄	C₂×C₅×#123	1	1	yes	characteristic
438	C₂	—	2	1	no	—
439	C₂	—	2	2	no	—
440	C₂	—	2	1	no	—
441	C₂	C₅×#1922	1	4	yes	direct product factor
442	C₂	C₂×C₅×#387	1	1	yes	characteristic
443	C₂	C₂×C₅×#443	1	1	yes	characteristic
444	C₂	C₂×C₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₄×D₄
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1922	C₂	direct (N × H)
16. C₅×#427	C₄	semidirect
18. C₂×C₅×#107	C₄	semidirect
19. C₂×C₅×#107	C₄	semidirect
20. C₂×C₅×#106	C₄	semidirect
21. C₂×C₅×#106	C₄	semidirect
34. C₂×#1922	C₅	direct (N × H)
79. C₅×#107	C₂×C₄	semidirect
80. C₅×#107	C₂×C₄	semidirect
81. C₅×#106	C₂×C₄	semidirect
82. C₅×#106	C₂×C₄	semidirect
90. #1922	C₂×C₅	direct (N × H)
164. #427	C₄×C₅	semidirect
166. C₂×#107	C₄×C₅	semidirect
167. C₂×#107	C₄×C₅	semidirect
168. C₂×#106	C₄×C₅	semidirect
169. C₂×#106	C₄×C₅	semidirect
269. #107	C₂×C₄×C₅	semidirect
270. #107	C₂×C₄×C₅	semidirect
271. #106	C₂×C₄×C₅	semidirect
272. #106	C₂×C₄×C₅	semidirect
366. C₂×C₅	#1922	direct (N × H)
413. C₅	C₂×#1922	direct (N × H)
441. C₂	C₅×#1922	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×#427	2
C₂×C₅×#424	2
C₂×C₅×#405	2
C₅×#1922	2
C₂×C₅×#341	2
C₂×C₅×#339	2
C₂×C₅×#336	2
C₂×#1922	5

Subgroups — C2×C5×#1922 #11943760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1922 #11943760