Subgroups — C₂×C₅×#1929 #11943789

Order 1280.

1082 conjugacy classes of subgroups.

The subgroup lattice has 534 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, complemented
2	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1929	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	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	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×#108	—	2	4	no	—
17	C₂×C₅×#108	C₂²	1	4	yes	complemented
18	C₂×C₅×#104	—	2	4	no	—
19	C₂×C₅×#104	C₂²	1	4	yes	—
20	C₅×#416	C₄	1	4	yes	complemented
21	C₅×#416	C₂²	1	4	yes	—
22	C₂×C₅×#103	C₄	1	1	yes	characteristic, complemented
23	C₂×C₅×#103	C₄	1	1	yes	characteristic, complemented
24	C₂×C₅×#102	C₄	1	1	yes	characteristic, complemented
25	C₂×C₅×#102	C₄	1	1	yes	characteristic, complemented
26	C₅×#408	—	2	2	no	—
27	C₅×#408	C₂²	1	4	yes	—
28	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
30	C₅×#405	—	2	2	no	—
31	C₅×#405	C₂²	1	4	yes	complemented
32	C₂×C₅×#97	—	2	1	no	—
33	C₂×C₄×C₅×C₈	—	2	1	no	—
34	C₅×#339	C₂²	1	4	yes	complemented
35	C₅×#336	C₂²	1	4	yes	complemented
36	C₂×#1929	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₅×#41	—	2	1	no	—
38	C₂×C₅×#41	—	2	1	no	—
39	C₂×C₅×#41	—	2	2	no	—
40	C₂×C₅×#41	—	2	2	no	—
41	C₂×C₅×#41	—	2	2	no	—
42	C₂×C₅×#41	—	2	2	no	—
43	C₂×C₅×#41	C₂×C₄	1	2	yes	—
44	C₂×C₅×#41	C₂³	1	2	yes	—
45	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	D₄	1	4	yes	—
57	C₂×C₅×M₁₆	C₂³	1	2	yes	—
58	C₂×C₅×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	2	no	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
68	C₂²×C₅×C₈	D₄	1	2	yes	—
69	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
70	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	2	yes	—
72	C₂²×C₅×C₈	C₂³	1	2	yes	—
73	C₅×#117	—	2	1	no	—
74	C₅×#117	—	2	1	no	—
75	C₅×#117	C₂×C₄	1	2	yes	—
76	C₅×#117	C₂³	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	—	2	2	no	—
82	C₂×C₄²×C₅	—	2	2	no	—
83	C₂×C₄²×C₅	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	2	yes	—
85	C₅×#108	—	2	8	no	—
86	C₅×#104	—	2	8	no	—
87	C₅×#103	C₂×C₄	1	4	yes	complemented
88	C₅×#103	C₂×C₄	1	4	yes	complemented
89	C₅×#102	C₂×C₄	1	4	yes	complemented
90	C₅×#102	C₂×C₄	1	4	yes	complemented
91	C₅×C₂²⋊C₈	—	2	4	no	—
92	C₅×C₂²⋊C₈	—	2	4	no	—
93	C₅×#97	—	2	4	no	—
94	C₄×C₅×C₈	—	2	4	no	—
95	C₂²×#108	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×#104	C₂×C₅	1	1	yes	characteristic
97	C₂×#416	C₂×C₅	1	1	yes	characteristic
98	C₂×#408	C₂×C₅	1	1	yes	characteristic
99	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
100	#1929	C₂×C₅	1	8	yes	direct product factor
101	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#336	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂⁴×C₅	—	2	1	no	—
104	C₂⁴×C₅	#41	1	1	yes	characteristic
105	C₅×#41	—	2	4	no	—
106	C₅×#41	—	2	4	no	—
107	C₅×#41	—	2	2	no	—
108	C₅×#41	—	2	2	no	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	4	2	no	—
112	C₅×#41	—	4	2	no	—
113	C₅×#41	—	4	2	no	—
114	C₅×#41	—	4	2	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	4	2	no	—
125	C₂×C₅×D₄	—	4	2	no	—
126	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	2	2	no	—
134	C₂²×C₄×C₅	—	4	2	no	—
135	C₂²×C₄×C₅	—	4	2	no	—
136	C₂²×C₄×C₅	—	4	2	no	—
137	C₂²×C₄×C₅	—	4	2	no	—
138	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	#41	1	2	yes	—
144	C₂²×C₄×C₅	#41	1	2	yes	—
145	C₂²×C₄×C₅	#41	1	2	yes	—
146	C₂²×C₄×C₅	#41	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×M₁₆	—	2	4	no	—
149	C₅×M₁₆	—	2	2	no	—
150	C₅×M₁₆	—	2	2	no	—
151	C₅×M₁₆	—	2	2	no	—
152	C₅×M₁₆	—	4	2	no	—
153	C₅×M₁₆	C₂×D₄	1	4	yes	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	4	no	—
157	C₂×C₅×C₈	—	2	4	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	—	2	2	no	—
160	C₂×C₅×C₈	—	2	4	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	2	2	no	—
163	C₂×C₅×C₈	—	2	2	no	—
164	C₂×C₅×C₈	—	2	2	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	4	2	no	—
168	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
171	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
175	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	2	2	no	—
178	C₄²×C₅	—	2	2	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	—	4	2	no	—
183	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
184	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
185	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×#117	C₂²×C₅	1	1	yes	characteristic
189	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
190	C₂×#108	—	2	4	no	—
191	C₂×#108	C₂²×C₅	1	4	yes	complemented
192	C₂×#104	—	2	4	no	—
193	C₂×#104	C₂²×C₅	1	4	yes	—
194	#416	C₄×C₅	1	4	yes	complemented
195	#416	C₂²×C₅	1	4	yes	—
196	C₂×#103	C₄×C₅	1	1	yes	characteristic, complemented
197	C₂×#103	C₄×C₅	1	1	yes	characteristic, complemented
198	C₂×#102	C₄×C₅	1	1	yes	characteristic, complemented
199	C₂×#102	C₄×C₅	1	1	yes	characteristic, complemented
200	#408	—	2	2	no	—
201	#408	C₂²×C₅	1	4	yes	—
202	C₂×C₂²⋊C₈	—	2	1	no	—
203	C₂×C₂²⋊C₈	—	2	1	no	—
204	#405	—	2	2	no	—
205	#405	C₂²×C₅	1	4	yes	complemented
206	C₂×#97	—	2	1	no	—
207	C₂×C₄×C₈	—	2	1	no	—
208	#339	C₂²×C₅	1	4	yes	complemented
209	#336	C₂²×C₅	1	4	yes	complemented
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	2	2	no	—
212	C₂³×C₅	—	2	2	no	—
213	C₂³×C₅	—	4	2	no	—
214	C₂³×C₅	—	4	2	no	—
215	C₂³×C₅	—	4	2	no	—
216	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
217	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₅	#124	1	2	yes	—
219	C₂³×C₅	#126	1	2	yes	—
220	C₂³×C₅	C₂×#41	1	1	yes	characteristic
221	C₅×Q₈	—	2	2	no	—
222	C₅×Q₈	—	2	2	no	—
223	C₅×Q₈	—	4	2	no	—
224	C₅×D₄	—	2	2	no	—
225	C₅×D₄	—	2	2	no	—
226	C₅×D₄	—	4	2	no	—
227	C₅×D₄	—	4	2	no	—
228	C₅×D₄	—	4	4	no	—
229	C₅×D₄	—	4	2	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	4	8	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	4	no	—
243	C₂×C₄×C₅	#117	1	2	yes	—
244	C₂×C₄×C₅	#117	1	2	yes	—
245	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	#121	1	2	yes	—
250	C₂×C₄×C₅	#121	1	2	yes	—
251	C₂×C₄×C₅	#123	1	2	yes	—
252	C₂×C₄×C₅	#123	1	2	yes	—
253	C₂×C₄×C₅	#124	1	2	yes	—
254	C₂×C₄×C₅	#126	1	2	yes	—
255	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	2	2	no	—
263	C₅×C₈	—	2	4	no	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	2	2	no	—
266	C₅×C₈	—	4	2	no	—
267	C₂×#41	—	2	1	no	—
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	C₂×C₄×C₅	1	2	yes	—
274	C₂×#41	C₂³×C₅	1	2	yes	—
275	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	C₅×D₄	1	4	yes	—
287	C₂×M₁₆	C₂³×C₅	1	2	yes	—
288	C₂×M₁₆	C₂³×C₅	1	2	yes	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
296	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
297	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
298	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
299	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
300	C₂²×C₈	C₅×D₄	1	2	yes	—
301	C₂²×C₈	C₂³×C₅	1	2	yes	—
302	C₂²×C₈	C₂³×C₅	1	2	yes	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	C₂×C₄×C₅	1	2	yes	—
306	#117	C₂³×C₅	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₅	1	2	yes	—
315	#108	—	2	8	no	—
316	#104	—	2	8	no	—
317	#103	C₂×C₄×C₅	1	4	yes	complemented
318	#103	C₂×C₄×C₅	1	4	yes	complemented
319	#102	C₂×C₄×C₅	1	4	yes	complemented
320	#102	C₂×C₄×C₅	1	4	yes	complemented
321	C₂²⋊C₈	—	2	4	no	—
322	C₂²⋊C₈	—	2	4	no	—
323	#97	—	2	4	no	—
324	C₄×C₈	—	2	4	no	—
325	C₂²×C₅	—	2	4	no	—
326	C₂²×C₅	—	2	4	no	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	4	2	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	8	4	no	—
335	C₂²×C₅	#388	1	2	yes	—
336	C₂²×C₅	#388	1	2	yes	—
337	C₂²×C₅	#443	1	2	yes	—
338	C₂²×C₅	#444	1	2	yes	—
339	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
340	C₂²×C₅	C₂×#124	1	1	yes	characteristic
341	C₂²×C₅	C₂×#126	1	1	yes	characteristic
342	C₄×C₅	—	4	4	no	—
343	C₄×C₅	—	4	2	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	#388	1	2	yes	—
347	C₄×C₅	#388	1	2	yes	—
348	C₄×C₅	C₂×#117	1	1	yes	characteristic
349	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
350	C₄×C₅	C₂×#121	1	1	yes	characteristic
351	C₄×C₅	C₂×#123	1	1	yes	characteristic
352	C₂⁴	—	2	1	no	—
353	C₂⁴	C₅×#41	1	1	yes	characteristic
354	#41	—	2	4	no	—
355	#41	—	2	4	no	—
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
390	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₅×#41	1	2	yes	—
393	C₂²×C₄	C₅×#41	1	2	yes	—
394	C₂²×C₄	C₅×#41	1	2	yes	—
395	C₂²×C₄	C₅×#41	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
397	M₁₆	—	2	4	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	4	2	no	—
402	M₁₆	C₂×C₅×D₄	1	4	yes	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	4	2	no	—
417	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
418	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
419	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
424	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	2	no	—
432	C₂×C₅	—	2	1	no	—
433	C₂×C₅	—	2	1	no	—
434	C₂×C₅	—	2	2	no	—
435	C₂×C₅	—	8	2	no	—
436	C₂×C₅	#1929	1	4	yes	direct product factor
437	C₂×C₅	C₂×#388	1	1	yes	characteristic
438	C₂×C₅	C₂×#443	1	1	yes	characteristic
439	C₂×C₅	C₂×#444	1	1	yes	characteristic
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
447	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
448	C₂³	C₅×#124	1	2	yes	—
449	C₂³	C₅×#126	1	2	yes	—
450	C₂³	C₂×C₅×#41	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	4	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	4	4	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	C₅×#117	1	2	yes	—
474	C₂×C₄	C₅×#117	1	2	yes	—
475	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
476	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
477	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
478	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
479	C₂×C₄	C₅×#121	1	2	yes	—
480	C₂×C₄	C₅×#121	1	2	yes	—
481	C₂×C₄	C₅×#123	1	2	yes	—
482	C₂×C₄	C₅×#123	1	2	yes	—
483	C₂×C₄	C₅×#124	1	2	yes	—
484	C₂×C₄	C₅×#126	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
489	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
490	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	2	4	no	—
494	C₈	—	2	2	no	—
495	C₈	—	2	2	no	—
496	C₈	—	4	2	no	—
497	C₅	C₂×#1929	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	C₅×#388	1	2	yes	—
509	C₂²	C₅×#388	1	2	yes	—
510	C₂²	C₅×#443	1	2	yes	—
511	C₂²	C₅×#444	1	2	yes	—
512	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
513	C₂²	C₂×C₅×#124	1	1	yes	characteristic
514	C₂²	C₂×C₅×#126	1	1	yes	characteristic
515	C₄	—	4	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	C₅×#388	1	2	yes	—
520	C₄	C₅×#388	1	2	yes	—
521	C₄	C₂×C₅×#117	1	1	yes	characteristic
522	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
523	C₄	C₂×C₅×#121	1	1	yes	characteristic
524	C₄	C₂×C₅×#123	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	8	2	no	—
529	C₂	C₅×#1929	1	4	yes	direct product factor
530	C₂	C₂×C₅×#388	1	1	yes	characteristic
531	C₂	C₂×C₅×#443	1	1	yes	characteristic
532	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	C₂²×C₅×#41	C₂²
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
1. C₂²×C₅×#108	C₂	semidirect
5. C₂×C₅×#405	C₂	semidirect
6. C₅×#1929	C₂	direct (N × H)
7. C₂×C₅×#339	C₂	semidirect
8. C₂×C₅×#336	C₂	semidirect
17. C₂×C₅×#108	C₂²	semidirect
20. C₅×#416	C₄	semidirect
22. C₂×C₅×#103	C₄	semidirect
23. C₂×C₅×#103	C₄	semidirect
24. C₂×C₅×#102	C₄	semidirect
25. C₂×C₅×#102	C₄	semidirect
31. C₅×#405	C₂²	semidirect
34. C₅×#339	C₂²	semidirect
35. C₅×#336	C₂²	semidirect
36. C₂×#1929	C₅	direct (N × H)
87. C₅×#103	C₂×C₄	semidirect
88. C₅×#103	C₂×C₄	semidirect
89. C₅×#102	C₂×C₄	semidirect
90. C₅×#102	C₂×C₄	semidirect
95. C₂²×#108	C₂×C₅	semidirect
99. C₂×#405	C₂×C₅	semidirect
100. #1929	C₂×C₅	direct (N × H)
101. C₂×#339	C₂×C₅	semidirect
102. C₂×#336	C₂×C₅	semidirect
191. C₂×#108	C₂²×C₅	semidirect
194. #416	C₄×C₅	semidirect
196. C₂×#103	C₄×C₅	semidirect
197. C₂×#103	C₄×C₅	semidirect
198. C₂×#102	C₄×C₅	semidirect
199. C₂×#102	C₄×C₅	semidirect
205. #405	C₂²×C₅	semidirect
208. #339	C₂²×C₅	semidirect
209. #336	C₂²×C₅	semidirect
317. #103	C₂×C₄×C₅	semidirect
318. #103	C₂×C₄×C₅	semidirect
319. #102	C₂×C₄×C₅	semidirect
320. #102	C₂×C₄×C₅	semidirect
436. C₂×C₅	#1929	direct (N × H)
497. C₅	C₂×#1929	direct (N × H)
529. C₂	C₅×#1929	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
C₂²×C₅×#104	2
C₂×C₅×#416	2
C₂×C₅×#408	2
C₂×C₅×#405	2
C₅×#1929	2
C₂×C₅×#339	2
C₂×C₅×#336	2
C₂×#1929	5

Subgroups — C2×C5×#1929 #11943789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1929 #11943789