Subgroups — C₂×C₅×#3302 #11983840

Order 1280.

2146 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
3	C₅×#3302	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#467	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#416	C₂	1	2	yes	maximal, complemented
13	C₂²×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₅×C₈	C₂²	1	2	yes	—
17	C₅×#556	—	2	4	no	—
18	C₅×#556	C₂²	1	8	yes	complemented
19	C₅×#547	—	2	4	no	—
20	C₅×#547	C₂²	1	8	yes	—
21	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×#126	—	2	2	no	—
24	C₂×C₅×#124	—	2	1	no	—
25	C₂×C₅×#123	—	2	2	no	—
26	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₅×#121	—	2	1	no	—
29	C₂×C₄×C₅×Q₈	—	2	1	no	—
30	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×#117	C₂²	1	2	yes	—
34	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
35	C₅×#487	C₂²	1	8	yes	complemented
36	C₅×#485	C₂²	1	16	yes	complemented
37	C₅×#474	C₂²	1	8	yes	complemented
38	C₅×#467	C₂²	1	16	yes	complemented
39	C₅×#462	C₂²	1	8	yes	complemented
40	C₅×#452	C₂²	1	16	yes	complemented
41	C₄×C₅×SD₁₆	C₂²	1	8	yes	complemented
42	C₅×C₈×D₄	C₂²	1	8	yes	complemented
43	C₂×C₅×#107	C₂²	1	2	yes	—
44	C₂×C₅×#106	C₂²	1	1	yes	characteristic
45	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×#416	C₂²	1	16	yes	complemented
47	C₂×C₅×#103	C₂²	1	2	yes	—
48	C₂×C₅×#103	C₂²	1	2	yes	—
49	C₂×C₅×#103	C₂²	1	1	yes	characteristic
50	C₂×C₅×#103	C₂²	1	2	yes	—
51	C₂×C₅×#102	C₂²	1	2	yes	—
52	C₂×C₅×#102	C₂²	1	1	yes	characteristic
53	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3302	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₅×#41	—	2	4	no	—
57	C₂×C₅×#41	—	2	8	no	—
58	C₂×C₅×#41	—	4	4	no	—
59	C₂×C₅×#41	C₂³	1	8	yes	—
60	C₂²×C₅×Q₈	—	2	1	no	—
61	C₂²×C₅×Q₈	C₂³	1	2	yes	—
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	—	2	2	no	—
64	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂³×C₄×C₅	—	2	2	no	—
68	C₂³×C₄×C₅	C₂³	1	2	yes	—
69	C₂×C₅×Q₁₆	—	4	4	no	—
70	C₂×C₅×Q₁₆	C₂³	1	8	yes	—
71	C₂×C₅×SD₁₆	—	2	4	no	—
72	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
73	C₂²×C₅×C₈	—	4	4	no	—
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	2	yes	—
77	C₂²×C₅×C₈	C₂³	1	8	yes	—
78	C₅×C₄⋊Q₈	—	2	2	no	—
79	C₅×C₄⋊Q₈	—	2	2	no	—
80	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
81	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₅×#126	—	2	16	no	—
83	C₅×#124	—	2	8	no	—
84	C₅×#123	—	2	16	no	—
85	C₅×C₂²⋊Q₈	—	2	4	no	—
86	C₅×C₂²⋊Q₈	—	2	4	no	—
87	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₅×#121	—	2	8	no	—
90	C₄×C₅×Q₈	—	2	8	no	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×Q₈	C₂³	1	4	yes	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	D₄	1	4	yes	—
95	C₄×C₅×D₄	C₂³	1	4	yes	—
96	C₄×C₅×D₄	C₂³	1	4	yes	—
97	C₅×#117	—	2	4	no	—
98	C₅×#117	C₂³	1	8	yes	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	2	no	—
101	C₂×C₅×C₄⋊C₄	—	2	2	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	2	1	no	—
105	C₂×C₅×C₄⋊C₄	—	2	8	no	—
106	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₅	—	2	2	no	—
116	C₂×C₄²×C₅	—	2	1	no	—
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#107	C₂³	1	8	yes	—
119	C₅×#106	C₂³	1	4	yes	—
120	C₅×C₄⋊C₈	C₂³	1	4	yes	—
121	C₅×#103	C₂³	1	8	yes	—
122	C₅×#103	C₂³	1	8	yes	—
123	C₅×#103	C₂³	1	4	yes	—
124	C₅×#103	C₂³	1	8	yes	—
125	C₅×#102	C₂³	1	4	yes	—
126	C₅×#102	C₂³	1	8	yes	—
127	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₅×C₈	C₂³	1	4	yes	—
129	C₂×#556	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂×#547	C₂×C₅	1	1	yes	characteristic
131	#3302	C₂×C₅	1	16	yes	direct product factor
132	C₂×#487	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂×#485	C₂×C₅	1	2	yes	complemented
134	C₂×#474	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#467	C₂×C₅	1	2	yes	complemented
136	C₂×#462	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×#452	C₂×C₅	1	2	yes	complemented
138	C₂×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#416	C₂×C₅	1	2	yes	complemented
141	C₂⁴×C₅	—	2	1	no	—
142	C₂⁴×C₅	C₂×D₄	1	2	yes	—
143	C₅×#41	—	2	16	no	—
144	C₅×#41	—	4	8	no	—
145	C₅×#41	—	4	16	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	—	2	4	no	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	2	no	—
150	C₂×C₅×Q₈	—	2	4	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	—	4	4	no	—
154	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
155	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
156	C₂×C₅×D₄	—	2	8	no	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	2	no	—
160	C₂×C₅×D₄	—	4	8	no	—
161	C₂×C₅×D₄	C₂×D₄	1	4	yes	—
162	C₂×C₅×D₄	#41	1	4	yes	—
163	C₂×C₅×D₄	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₅	—	2	4	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	—	2	8	no	—
173	C₂²×C₄×C₅	—	4	8	no	—
174	C₂²×C₄×C₅	—	4	4	no	—
175	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₅×Q₁₆	—	4	8	no	—
182	C₅×SD₁₆	—	2	8	no	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₂×C₅×C₈	—	2	2	no	—
185	C₂×C₅×C₈	—	2	4	no	—
186	C₂×C₅×C₈	—	4	8	no	—
187	C₂×C₅×C₈	C₂⁴	1	2	yes	—
188	C₂×C₅×C₈	C₂⁴	1	4	yes	—
189	C₂×C₅×C₈	C₂⁴	1	2	yes	—
190	C₅×C₄⋊C₄	—	2	4	no	—
191	C₅×C₄⋊C₄	—	2	8	no	—
192	C₅×C₄⋊C₄	—	2	8	no	—
193	C₅×C₄⋊C₄	—	2	4	no	—
194	C₅×C₄⋊C₄	—	2	4	no	—
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
200	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₅×C₂²⋊C₄	—	2	8	no	—
204	C₅×C₂²⋊C₄	—	2	8	no	—
205	C₅×C₂²⋊C₄	—	2	8	no	—
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
208	C₄²×C₅	—	2	8	no	—
209	C₄²×C₅	—	2	4	no	—
210	C₄²×C₅	C₂×D₄	1	2	yes	—
211	C₄²×C₅	C₂⁴	1	2	yes	—
212	C₂²×#41	C₂²×C₅	1	2	yes	—
213	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
214	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
215	C₂³×C₈	C₂²×C₅	1	2	yes	—
216	#556	—	2	4	no	—
217	#556	C₂²×C₅	1	8	yes	complemented
218	#547	—	2	4	no	—
219	#547	C₂²×C₅	1	8	yes	—
220	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×#126	—	2	2	no	—
223	C₂×#124	—	2	1	no	—
224	C₂×#123	—	2	2	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
227	C₂×#121	—	2	1	no	—
228	C₂×C₄×Q₈	—	2	1	no	—
229	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×#117	C₂²×C₅	1	2	yes	—
233	C₂²×C₄⋊C₄	—	2	1	no	—
234	#487	C₂²×C₅	1	8	yes	complemented
235	#485	C₂²×C₅	1	16	yes	complemented
236	#474	C₂²×C₅	1	8	yes	complemented
237	#467	C₂²×C₅	1	16	yes	complemented
238	#462	C₂²×C₅	1	8	yes	complemented
239	#452	C₂²×C₅	1	16	yes	complemented
240	C₄×SD₁₆	C₂²×C₅	1	8	yes	complemented
241	C₈×D₄	C₂²×C₅	1	8	yes	complemented
242	C₂×#107	C₂²×C₅	1	2	yes	—
243	C₂×#106	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
245	#416	C₂²×C₅	1	16	yes	complemented
246	C₂×#103	C₂²×C₅	1	2	yes	—
247	C₂×#103	C₂²×C₅	1	2	yes	—
248	C₂×#103	C₂²×C₅	1	2	yes	—
249	C₂×#103	C₂²×C₅	1	1	yes	characteristic
250	C₂×#102	C₂²×C₅	1	1	yes	characteristic
251	C₂×#102	C₂²×C₅	1	2	yes	—
252	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
254	C₂³×C₅	—	2	4	no	—
255	C₂³×C₅	—	2	4	no	—
256	C₂³×C₅	—	2	4	no	—
257	C₂³×C₅	—	2	4	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂²×D₄	1	4	yes	—
262	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₅×Q₈	—	2	2	no	—
264	C₅×Q₈	—	2	4	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×Q₈	—	2	4	no	—
267	C₅×Q₈	—	4	2	no	—
268	C₅×Q₈	—	4	4	no	—
269	C₅×Q₈	—	4	8	no	—
270	C₅×D₄	—	2	4	no	—
271	C₅×D₄	—	2	8	no	—
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	4	16	no	—
274	C₅×D₄	C₂×#41	1	4	yes	—
275	C₂×C₄×C₅	—	2	4	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	8	no	—
278	C₂×C₄×C₅	—	2	4	no	—
279	C₂×C₄×C₅	—	2	4	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	4	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	4	16	no	—
286	C₂×C₄×C₅	—	4	4	no	—
287	C₂×C₄×C₅	—	4	2	no	—
288	C₂×C₄×C₅	—	4	2	no	—
289	C₂×C₄×C₅	—	4	4	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	4	8	no	—
292	C₂×C₄×C₅	#135	1	4	yes	—
293	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₅	C₂×#41	1	2	yes	—
298	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
299	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
300	C₅×C₈	—	2	2	no	—
301	C₅×C₈	—	2	2	no	—
302	C₅×C₈	—	2	4	no	—
303	C₂×#41	—	2	4	no	—
304	C₂×#41	—	2	8	no	—
305	C₂×#41	—	4	4	no	—
306	C₂×#41	C₂³×C₅	1	8	yes	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
309	C₂²×Q₈	C₂³×C₅	1	2	yes	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	2	no	—
315	C₂³×C₄	C₂³×C₅	1	2	yes	—
316	C₂×Q₁₆	—	4	4	no	—
317	C₂×Q₁₆	C₂³×C₅	1	8	yes	—
318	C₂×SD₁₆	—	2	4	no	—
319	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
320	C₂²×C₈	—	4	4	no	—
321	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₅	1	2	yes	—
323	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₅	1	8	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
328	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
329	#126	—	2	16	no	—
330	#124	—	2	8	no	—
331	#123	—	2	16	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
335	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
336	#121	—	2	8	no	—
337	C₄×Q₈	—	2	8	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	C₂³×C₅	1	4	yes	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	C₅×D₄	1	4	yes	—
342	C₄×D₄	C₂³×C₅	1	4	yes	—
343	C₄×D₄	C₂³×C₅	1	4	yes	—
344	#117	—	2	4	no	—
345	#117	C₂³×C₅	1	8	yes	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	8	no	—
353	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
365	#107	C₂³×C₅	1	8	yes	—
366	#106	C₂³×C₅	1	4	yes	—
367	C₄⋊C₈	C₂³×C₅	1	4	yes	—
368	#103	C₂³×C₅	1	8	yes	—
369	#103	C₂³×C₅	1	8	yes	—
370	#103	C₂³×C₅	1	4	yes	—
371	#103	C₂³×C₅	1	8	yes	—
372	#102	C₂³×C₅	1	4	yes	—
373	#102	C₂³×C₅	1	8	yes	—
374	C₂²⋊C₈	C₂³×C₅	1	8	yes	—
375	C₄×C₈	C₂³×C₅	1	4	yes	—
376	C₂²×C₅	—	2	4	no	—
377	C₂²×C₅	—	2	4	no	—
378	C₂²×C₅	—	2	4	no	—
379	C₂²×C₅	—	2	4	no	—
380	C₂²×C₅	—	4	8	no	—
381	C₂²×C₅	—	4	8	no	—
382	C₂²×C₅	—	4	2	no	—
383	C₂²×C₅	—	4	2	no	—
384	C₂²×C₅	#546	1	2	yes	—
385	C₂²×C₅	C₂×#135	1	2	yes	—
386	C₂²×C₅	#578	1	2	yes	—
387	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₅	—	2	4	no	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	4	4	no	—
391	C₄×C₅	—	4	2	no	—
392	C₄×C₅	—	4	2	no	—
393	C₄×C₅	—	4	4	no	—
394	C₄×C₅	—	4	2	no	—
395	C₄×C₅	#546	1	2	yes	—
396	C₄×C₅	C₂×#135	1	4	yes	—
397	C₄×C₅	C₂²×#41	1	1	yes	characteristic
398	C₄×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂⁴	—	2	1	no	—
400	C₂⁴	C₂×C₅×D₄	1	2	yes	—
401	#41	—	2	16	no	—
402	#41	—	4	8	no	—
403	#41	—	4	16	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
413	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	C₂×C₅×D₄	1	4	yes	—
420	C₂×D₄	C₅×#41	1	4	yes	—
421	C₂×D₄	C₂⁴×C₅	1	2	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	4	8	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
434	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
436	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
439	Q₁₆	—	4	8	no	—
440	SD₁₆	—	2	8	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	4	no	—
444	C₂×C₈	—	4	8	no	—
445	C₂×C₈	C₂⁴×C₅	1	2	yes	—
446	C₂×C₈	C₂⁴×C₅	1	2	yes	—
447	C₂×C₈	C₂⁴×C₅	1	4	yes	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
458	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
459	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
460	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
466	C₄²	—	2	8	no	—
467	C₄²	—	2	4	no	—
468	C₄²	C₂×C₅×D₄	1	2	yes	—
469	C₄²	C₂⁴×C₅	1	2	yes	—
470	C₂×C₅	—	4	4	no	—
471	C₂×C₅	—	4	4	no	—
472	C₂×C₅	#3302	1	4	yes	direct product factor
473	C₂×C₅	C₂×#546	1	1	yes	characteristic
474	C₂×C₅	C₂²×#135	1	1	yes	characteristic
475	C₂×C₅	C₂×#578	1	1	yes	characteristic
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	C₂²×C₅×D₄	1	4	yes	—
484	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
485	Q₈	—	2	2	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	2	4	no	—
489	Q₈	—	4	4	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	8	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	8	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	16	no	—
496	D₄	C₂×C₅×#41	1	4	yes	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	16	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	C₅×#135	1	4	yes	—
515	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
516	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
517	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
519	C₂×C₄	C₂×C₅×#41	1	2	yes	—
520	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
521	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	4	no	—
525	C₅	C₂×#3302	1	1	yes	characteristic, direct product factor, Sylow
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	4	8	no	—
531	C₂²	—	4	8	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	C₅×#546	1	2	yes	—
535	C₂²	C₂×C₅×#135	1	2	yes	—
536	C₂²	C₅×#578	1	2	yes	—
537	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
538	C₄	—	2	4	no	—
539	C₄	—	2	2	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	C₅×#546	1	2	yes	—
546	C₄	C₂×C₅×#135	1	4	yes	—
547	C₄	C₂²×C₅×#41	1	1	yes	characteristic
548	C₄	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂	—	4	4	no	—
550	C₂	—	4	4	no	—
551	C₂	C₅×#3302	1	4	yes	direct product factor
552	C₂	C₂×C₅×#546	1	1	yes	characteristic
553	C₂	C₂²×C₅×#135	1	1	yes	characteristic
554	C₂	C₂×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#547	C₂
LCS	G ▷ C₂×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. C₂×C₅×#556	C₂	semidirect
3. C₅×#3302	C₂	direct (N × H)
4. C₂×C₅×#487	C₂	semidirect
5. C₂×C₅×#485	C₂	semidirect
6. C₂×C₅×#474	C₂	semidirect
7. C₂×C₅×#467	C₂	semidirect
8. C₂×C₅×#462	C₂	semidirect
9. C₂×C₅×#452	C₂	semidirect
10. C₂×C₄×C₅×SD₁₆	C₂	semidirect
11. C₂×C₅×C₈×D₄	C₂	semidirect
12. C₂×C₅×#416	C₂	semidirect
18. C₅×#556	C₂²	semidirect
35. C₅×#487	C₂²	semidirect
36. C₅×#485	C₂²	semidirect
37. C₅×#474	C₂²	semidirect
38. C₅×#467	C₂²	semidirect
39. C₅×#462	C₂²	semidirect
40. C₅×#452	C₂²	semidirect
41. C₄×C₅×SD₁₆	C₂²	semidirect
42. C₅×C₈×D₄	C₂²	semidirect
46. C₅×#416	C₂²	semidirect
55. C₂×#3302	C₅	direct (N × H)
129. C₂×#556	C₂×C₅	semidirect
131. #3302	C₂×C₅	direct (N × H)
132. C₂×#487	C₂×C₅	semidirect
133. C₂×#485	C₂×C₅	semidirect
134. C₂×#474	C₂×C₅	semidirect
135. C₂×#467	C₂×C₅	semidirect
136. C₂×#462	C₂×C₅	semidirect
137. C₂×#452	C₂×C₅	semidirect
138. C₂×C₄×SD₁₆	C₂×C₅	semidirect
139. C₂×C₈×D₄	C₂×C₅	semidirect
140. C₂×#416	C₂×C₅	semidirect
217. #556	C₂²×C₅	semidirect
234. #487	C₂²×C₅	semidirect
235. #485	C₂²×C₅	semidirect
236. #474	C₂²×C₅	semidirect
237. #467	C₂²×C₅	semidirect
238. #462	C₂²×C₅	semidirect
239. #452	C₂²×C₅	semidirect
240. C₄×SD₁₆	C₂²×C₅	semidirect
241. C₈×D₄	C₂²×C₅	semidirect
245. #416	C₂²×C₅	semidirect
472. C₂×C₅	#3302	direct (N × H)
525. C₅	C₂×#3302	direct (N × H)
551. C₂	C₅×#3302	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×#556	2
C₂×C₅×#547	2
C₅×#3302	2
C₂×C₅×#487	2
C₂×C₅×#485	2
C₂×C₅×#474	2
C₂×C₅×#467	2
C₂×C₅×#462	2
C₂×C₅×#452	2
C₂×C₄×C₅×SD₁₆	2
C₂×C₅×C₈×D₄	2
C₂×C₅×#416	2
C₂×#3302	5

Subgroups — C2×C5×#3302 #11983840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3302 #11983840