Subgroups — D₅×#3498 #13007615

Order 1280.

12982 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	C₅×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	#10619183	C₂	1	2	yes	maximal, complemented
4	D₅×#550	C₂	1	4	yes	maximal, complemented
5	#10618671	C₂	1	4	yes	maximal, complemented
6	D₄²×D₅	C₂	1	12	yes	maximal, complemented
7	#10618509	C₂	1	12	yes	maximal, complemented
8	D₅×#535	C₂	1	6	yes	maximal, complemented
9	#10618217	C₂	1	6	yes	maximal, complemented
10	#10618143	C₂	1	3	yes	maximal, complemented
11	D₅×#532	C₂	1	3	yes	maximal, complemented
12	#10618096	C₂	1	3	yes	maximal, complemented
13	C₂×D₅×#127	C₂	1	3	yes	maximal, complemented
14	#10617747	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	D₅×H(5,𝔽₂)	—	2	32	no	—
18	C₂×#4149	C₂²	1	6	yes	complemented
19	C₂×#4149	C₂²	1	4	yes	complemented
20	C₂×#4149	C₂²	1	2	yes	complemented
21	C₂×D₅×#41	C₂²	1	1	yes	characteristic
22	C₂×D₅×#41	C₂²	1	6	yes	complemented
23	C₂×D₅×#41	C₂²	1	4	yes	complemented
24	C₂×#4144	C₂²	1	6	yes	complemented
25	C₂×#4144	C₂²	1	12	yes	complemented
26	C₂²×D₄×D₅	C₂²	1	6	yes	complemented
27	C₂²×D₄×D₅	C₂²	1	12	yes	complemented
28	C₂²×D₄×D₅	C₂²	1	12	yes	complemented
29	C₅×#550	C₂²	1	4	yes	complemented
30	C₅×D₄²	C₂²	1	12	yes	complemented
31	C₅×#535	C₂²	1	6	yes	complemented
32	C₅×#532	C₂²	1	3	yes	complemented
33	C₂×C₅×#127	C₂²	1	3	yes	complemented
34	C₄×C₅×#41	C₂²	1	1	yes	characteristic, complemented
35	#66168	C₂²	1	8	yes	complemented
36	#66166	C₂²	1	6	yes	complemented
37	#66164	C₂²	1	6	yes	complemented
38	#41×Dic₅	C₂²	1	1	yes	characteristic, complemented
39	#66139	C₂²	1	6	yes	complemented
40	C₂×#4086	C₂²	1	6	yes	complemented
41	C₂×#4086	C₂²	1	12	yes	complemented
42	D₄×C₂²⋊D₅	C₂²	1	24	yes	complemented
43	D₄×C₂²⋊D₅	C₂²	1	24	yes	complemented
44	#66059	C₂²	1	3	yes	complemented
45	D₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	#66052	C₂²	1	12	yes	complemented
47	#66051	C₂²	1	12	yes	complemented
48	#66050	C₂²	1	3	yes	complemented
49	#66049	C₂²	1	12	yes	complemented
50	D₅×#127	C₂²	1	3	yes	complemented
51	D₅×#127	C₂²	1	12	yes	complemented
52	D₅×#127	C₂²	1	6	yes	complemented
53	D₅×#127	C₂²	1	6	yes	complemented
54	D₅×#127	C₂²	1	12	yes	complemented
55	D₅×#127	C₂²	1	6	yes	complemented
56	#66008	C₂²	1	12	yes	complemented
57	D₅×#124	C₂²	1	6	yes	complemented
58	#66002	C₂²	1	6	yes	complemented
59	#65943	C₂²	1	24	yes	complemented
60	#65943	C₂²	1	24	yes	complemented
61	#65941	C₂²	1	24	yes	complemented
62	D₅×#121	C₂²	1	12	yes	complemented
63	D₅×#121	C₂²	1	24	yes	complemented
64	#65933	C₂²	1	24	yes	complemented
65	#65930	C₂²	1	12	yes	complemented
66	#65926	C₂²	1	24	yes	complemented
67	#65924	C₂²	1	48	yes	complemented
68	D₅×#120	C₂²	1	24	yes	complemented
69	#65911	C₂²	1	4	yes	complemented
70	C₄×#713	C₂²	1	2	yes	complemented
71	C₄×Q₈×D₅	C₂²	1	2	yes	complemented
72	#65887	C₂²	1	12	yes	complemented
73	D₄×D₂₀	C₂²	1	12	yes	complemented
74	D₄×D₂₀	C₂²	1	12	yes	complemented
75	#65882	C₂²	1	12	yes	complemented
76	C₄×D₄×D₅	C₂²	1	12	yes	complemented
77	C₄×D₄×D₅	C₂²	1	6	yes	complemented
78	C₄×#711	C₂²	1	6	yes	complemented
79	#65859	C₂²	1	6	yes	complemented
80	#65856	C₂²	1	3	yes	complemented
81	D₅×#117	C₂²	1	3	yes	complemented
82	#65811	C₂²	1	3	yes	complemented
83	C₂×#4020	C₂²	1	3	yes	complemented
84	C₄×#709	C₂²	1	3	yes	complemented
85	C₂×C₄²×D₅	C₂²	1	3	yes	complemented
86	C₂×#3498	—	5	1	no	maximal, Sylow
87	C₂⁴×D₅	C₂³	1	12	yes	—
88	C₅×H(5,𝔽₂)	—	2	16	no	—
89	C₂×C₅×#41	C₂³	1	1	yes	characteristic
90	C₂×C₅×#41	C₂³	1	6	yes	complemented
91	C₂×C₅×#41	C₂³	1	4	yes	complemented
92	C₂²×C₅×D₄	C₂³	1	12	yes	complemented
93	C₂²×C₅×D₄	C₂³	1	6	yes	complemented
94	C₂²×C₅×D₄	C₂³	1	12	yes	complemented
95	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
96	C₂²×C₂²⋊D₅	C₂³	1	12	yes	complemented
97	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
98	#4149	—	2	16	no	—
99	#4149	—	2	32	no	—
100	#4149	—	2	48	no	—
101	D₅×#41	—	2	32	no	—
102	D₅×#41	—	2	48	no	—
103	D₅×#41	D₄	1	16	yes	complemented
104	C₂×#713	C₂³	1	1	yes	characteristic
105	C₂×#713	C₂³	1	6	yes	complemented
106	C₂×#713	C₂³	1	4	yes	complemented
107	C₂×Q₈×D₅	C₂³	1	2	yes	—
108	C₂×Q₈×D₅	C₂³	1	1	yes	characteristic
109	#4144	—	2	96	no	—
110	#4144	—	2	48	no	—
111	C₂×#711	C₂³	1	3	yes	—
112	C₂×#711	C₂³	1	6	yes	complemented
113	C₂×#711	C₂³	1	12	yes	complemented
114	C₂×#711	C₂³	1	12	yes	complemented
115	C₂×D₄×D₅	—	2	96	no	—
116	C₂×D₄×D₅	—	2	48	no	—
117	C₂×D₄×D₅	—	4	48	no	—
118	C₂×D₄×D₅	C₂³	1	12	yes	—
119	C₂×D₄×D₅	C₂³	1	6	yes	—
120	C₂×D₄×D₅	C₂³	1	12	yes	—
121	C₂×D₄×D₅	C₂³	1	12	yes	—
122	C₂×D₄×D₅	C₂³	1	24	yes	—
123	C₂×D₄×D₅	C₂³	1	3	yes	—
124	C₂×D₄×D₅	C₂³	1	12	yes	complemented
125	C₂×D₄×D₅	C₂³	1	12	yes	complemented
126	C₂×D₄×D₅	C₂³	1	12	yes	complemented
127	C₂×D₄×D₅	C₂³	1	12	yes	complemented
128	C₂×D₄×D₅	C₂³	1	24	yes	complemented
129	C₂×D₄×D₅	C₂³	1	24	yes	complemented
130	C₂×D₄×D₅	C₂³	1	24	yes	complemented
131	C₂×#709	C₂³	1	3	yes	—
132	C₂×#709	C₂³	1	6	yes	complemented
133	C₂×#709	C₂³	1	12	yes	complemented
134	C₂×#709	C₂³	1	12	yes	complemented
135	C₂²×D₂₀	C₂³	1	6	yes	complemented
136	C₂²×D₂₀	C₂³	1	12	yes	complemented
137	C₂²×D₂₀	C₂³	1	12	yes	complemented
138	C₂²×C₄×D₅	C₂³	1	6	yes	—
139	C₂²×C₄×D₅	C₂³	1	12	yes	—
140	C₂²×C₄×D₅	C₂³	1	3	yes	—
141	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
142	C₅×#127	C₂³	1	3	yes	complemented
143	C₅×#127	C₂³	1	6	yes	complemented
144	C₅×#127	C₂³	1	12	yes	complemented
145	C₅×#124	C₂³	1	6	yes	complemented
146	C₅×#121	C₂³	1	12	yes	complemented
147	C₅×#121	C₂³	1	24	yes	complemented
148	C₅×#120	C₂³	1	24	yes	complemented
149	C₄×C₅×Q₈	C₂³	1	2	yes	complemented
150	C₄×C₅×D₄	C₂³	1	6	yes	complemented
151	C₄×C₅×D₄	C₂³	1	12	yes	complemented
152	C₅×#117	C₂³	1	3	yes	complemented
153	C₂×C₄²×C₅	C₂³	1	3	yes	complemented
154	#4099	C₂³	1	24	yes	complemented
155	#4093	C₂³	1	6	yes	complemented
156	Q₈×Dic₅	C₂³	1	2	yes	complemented
157	#4090	C₂³	1	2	yes	complemented
158	#4086	C₂³	1	12	yes	complemented
159	#4086	C₂³	1	6	yes	complemented
160	#4086	C₂³	1	12	yes	complemented
161	#4086	C₂³	1	24	yes	complemented
162	#4086	C₂³	1	24	yes	complemented
163	#4086	C₂³	1	24	yes	complemented
164	#4086	C₂³	1	24	yes	complemented
165	#4085	C₂³	1	48	yes	complemented
166	#4085	C₂³	1	24	yes	complemented
167	#4084	C₂³	1	12	yes	complemented
168	#4084	C₂³	1	24	yes	complemented
169	#4083	C₂³	1	48	yes	complemented
170	#4083	C₂³	1	24	yes	complemented
171	#4082	C₂³	1	6	yes	complemented
172	D₄×Dic₅	C₂³	1	12	yes	complemented
173	D₄×Dic₅	C₂³	1	6	yes	complemented
174	#4076	C₂³	1	12	yes	complemented
175	#4076	C₂³	1	24	yes	complemented
176	C₄×C₂²⋊D₅	C₂³	1	12	yes	complemented
177	C₄×C₂²⋊D₅	C₂³	1	24	yes	complemented
178	#4072	C₂³	1	3	yes	complemented
179	C₂×C₄×Dic₅	C₂³	1	3	yes	complemented
180	C₂×C₄×Dic₅	C₂³	1	6	yes	complemented
181	#4041	C₂³	1	12	yes	complemented
182	#4041	C₂³	1	24	yes	complemented
183	#4039	C₂³	1	12	yes	complemented
184	#4039	C₂³	1	6	yes	complemented
185	#4038	C₂³	1	6	yes	complemented
186	D₅×C₄⋊C₄	C₂³	1	4	yes	—
187	D₅×C₄⋊C₄	C₂³	1	6	yes	—
188	#4034	C₂³	1	4	yes	complemented
189	#4033	C₂³	1	6	yes	complemented
190	#4031	C₂³	1	24	yes	complemented
191	#4030	C₂³	1	24	yes	complemented
192	#4030	C₂³	1	48	yes	complemented
193	#4028	C₂³	1	24	yes	complemented
194	#4028	C₂³	1	48	yes	complemented
195	#4027	C₂³	1	12	yes	complemented
196	#4027	C₂³	1	24	yes	complemented
197	D₅×C₂²⋊C₄	C₂³	1	6	yes	—
198	D₅×C₂²⋊C₄	C₂³	1	24	yes	—
199	#4023	C₂³	1	6	yes	complemented
200	#4021	C₂³	1	6	yes	complemented
201	#4020	C₂³	1	3	yes	complemented
202	#4020	C₂³	1	6	yes	complemented
203	#4020	C₂³	1	12	yes	complemented
204	C₄×D₂₀	C₂³	1	6	yes	complemented
205	C₄×D₂₀	C₂³	1	12	yes	complemented
206	#4018	C₂³	1	6	yes	complemented
207	C₄²×D₅	C₂³	1	1	yes	characteristic
208	C₄²×D₅	C₂³	1	3	yes	—
209	C₄²×D₅	C₂³	1	6	yes	—
210	C₄²×D₅	C₂³	1	3	yes	complemented
211	C₄²×D₅	C₂³	1	3	yes	complemented
212	C₄²×D₅	C₂³	1	6	yes	complemented
213	#4015	C₂³	1	1	yes	characteristic, complemented
214	C₄×Dic₁₀	C₂³	1	6	yes	complemented
215	C₂²×H(5,𝔽₂)	—	5	2	no	—
216	#3498	—	5	2	no	—
217	#3498	—	5	4	no	—
218	#3498	—	5	12	no	—
219	#3498	—	5	6	no	—
220	#3498	—	5	3	no	—
221	#3498	—	5	3	no	—
222	#3498	—	5	1	no	—
223	#3498	D₅	1	1	yes	characteristic, direct product factor
224	C₂×#550	—	5	4	no	—
225	C₂×D₄²	—	5	12	no	—
226	C₂×#535	—	5	6	no	—
227	C₂×#532	—	5	3	no	—
228	C₂²×#127	—	5	3	no	—
229	C₂×C₄×#41	—	5	1	no	—
230	C₂⁴×C₅	C₂⁴	1	12	yes	—
231	C₂³×D₅	—	2	48	no	—
232	C₂³×D₅	—	4	48	no	—
233	C₂³×D₅	C₂⁴	1	12	yes	—
234	C₂³×D₅	C₂⁴	1	3	yes	—
235	C₂³×D₅	C₂⁴	1	12	yes	—
236	C₂³×D₅	C₂⁴	1	24	yes	—
237	C₅×#41	—	2	16	no	—
238	C₅×#41	—	2	24	no	—
239	C₅×#41	C₂×D₄	1	8	yes	complemented
240	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
241	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
242	C₂×C₅×D₄	—	2	48	no	—
243	C₂×C₅×D₄	—	2	24	no	—
244	C₂×C₅×D₄	—	4	24	no	—
245	C₂×C₅×D₄	C₂⁴	1	12	yes	—
246	C₂×C₅×D₄	C₂⁴	1	12	yes	—
247	C₂×C₅×D₄	C₂⁴	1	12	yes	—
248	C₂×C₅×D₄	C₂⁴	1	6	yes	—
249	C₂×C₅×D₄	C₂⁴	1	24	yes	—
250	C₂×C₅×D₄	C₂⁴	1	3	yes	—
251	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
252	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
253	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
254	C₂×C₂²⋊D₅	—	2	96	no	—
255	C₂×C₂²⋊D₅	—	2	48	no	—
256	C₂×C₂²⋊D₅	—	4	48	no	—
257	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
258	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
259	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
260	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
261	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
262	C₂×C₂²⋊D₅	C₂⁴	1	48	yes	—
263	C₂×C₂²⋊D₅	C₂⁴	1	6	yes	—
264	C₂²×Dic₅	C₂⁴	1	12	yes	—
265	C₂²×Dic₅	C₂⁴	1	6	yes	—
266	C₂²×Dic₅	C₂⁴	1	3	yes	—
267	#713	—	2	16	no	—
268	#713	—	2	24	no	—
269	#713	C₂×D₄	1	8	yes	complemented
270	Q₈×D₅	—	2	8	no	—
271	Q₈×D₅	C₂×D₄	1	8	yes	complemented
272	#711	—	2	48	no	—
273	#711	—	2	24	no	—
274	#711	—	2	48	no	—
275	#711	C₂×D₄	1	24	yes	complemented
276	D₄×D₅	—	2	48	no	—
277	D₄×D₅	—	2	48	no	—
278	D₄×D₅	—	2	96	no	—
279	D₄×D₅	—	2	48	no	—
280	D₄×D₅	—	2	48	no	—
281	D₄×D₅	—	2	24	no	—
282	D₄×D₅	—	2	48	no	—
283	D₄×D₅	—	2	48	no	—
284	D₄×D₅	—	2	48	no	—
285	D₄×D₅	—	4	48	no	—
286	D₄×D₅	—	4	48	no	—
287	D₄×D₅	—	4	48	no	—
288	D₄×D₅	C₂×D₄	1	24	yes	complemented
289	#709	—	2	24	no	—
290	#709	—	2	48	no	—
291	#709	—	2	48	no	—
292	#709	C₂×D₄	1	24	yes	complemented
293	C₂×D₂₀	—	2	24	no	—
294	C₂×D₂₀	—	2	48	no	—
295	C₂×D₂₀	—	4	24	no	—
296	C₂×D₂₀	C₂⁴	1	6	yes	—
297	C₂×D₂₀	C₂⁴	1	12	yes	—
298	C₂×D₂₀	C₂⁴	1	12	yes	—
299	C₂×D₂₀	C₂⁴	1	12	yes	—
300	C₂×D₂₀	C₂⁴	1	24	yes	—
301	C₂×D₂₀	C₂⁴	1	3	yes	—
302	C₂×C₄×D₅	—	2	48	no	—
303	C₂×C₄×D₅	—	2	24	no	—
304	C₂×C₄×D₅	C₂×D₄	1	24	yes	complemented
305	C₂×C₄×D₅	C₂⁴	1	4	yes	—
306	C₂×C₄×D₅	C₂⁴	1	12	yes	—
307	C₂×C₄×D₅	C₂⁴	1	12	yes	—
308	C₂×C₄×D₅	C₂⁴	1	6	yes	—
309	C₂×C₄×D₅	C₂⁴	1	6	yes	—
310	C₂×C₄×D₅	C₂⁴	1	6	yes	—
311	C₂×C₄×D₅	C₂⁴	1	3	yes	—
312	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
313	C₂×C₄×D₅	C₂⁴	1	3	yes	—
314	C₂×C₄×D₅	C₂⁴	1	3	yes	—
315	C₂×C₄×D₅	C₂⁴	1	2	yes	—
316	C₂×Dic₁₀	C₂⁴	1	2	yes	—
317	C₂×Dic₁₀	C₂⁴	1	4	yes	—
318	C₂×Dic₁₀	C₂⁴	1	3	yes	—
319	C₅×C₄⋊C₄	C₂⁴	1	6	yes	—
320	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
321	C₅×C₂²⋊C₄	C₂⁴	1	6	yes	—
322	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
323	C₄²×C₅	C₂⁴	1	1	yes	characteristic
324	C₄²×C₅	C₂⁴	1	3	yes	—
325	C₄²×C₅	C₂⁴	1	6	yes	—
326	C₂²⋊Dic₅	C₂⁴	1	6	yes	—
327	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
328	#685	C₂⁴	1	12	yes	—
329	#685	C₂⁴	1	24	yes	—
330	#685	C₂⁴	1	24	yes	—
331	C₄⋊Dic₅	C₂⁴	1	6	yes	—
332	C₄⋊Dic₅	C₂⁴	1	4	yes	—
333	#683	C₂⁴	1	12	yes	—
334	#683	C₂⁴	1	8	yes	—
335	C₄×Dic₅	C₂⁴	1	6	yes	—
336	C₄×Dic₅	C₂⁴	1	2	yes	—
337	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
338	C₄×Dic₅	C₂⁴	1	3	yes	—
339	C₄×Dic₅	C₂⁴	1	6	yes	—
340	C₄×Dic₅	C₂⁴	1	6	yes	—
341	C₄×Dic₅	C₂⁴	1	6	yes	—
342	C₂×H(5,𝔽₂)	—	5	2	no	—
343	C₂×H(5,𝔽₂)	—	5	4	no	—
344	C₂×H(5,𝔽₂)	—	5	6	no	—
345	C₂×H(5,𝔽₂)	—	5	12	no	—
346	C₂×H(5,𝔽₂)	—	5	6	no	—
347	C₂×H(5,𝔽₂)	—	10	32	no	—
348	C₂×H(5,𝔽₂)	C₂×D₅	1	2	yes	complemented
349	C₂²×#41	—	5	1	no	—
350	C₂²×#41	—	5	6	no	—
351	C₂²×#41	—	5	4	no	—
352	C₂³×D₄	—	5	6	no	—
353	C₂³×D₄	—	5	12	no	—
354	C₂³×D₄	—	5	12	no	—
355	#550	—	5	8	no	—
356	#550	—	5	12	no	—
357	#550	—	5	24	no	—
358	#550	—	5	4	no	—
359	#550	—	5	12	no	—
360	#550	C₂×D₅	1	4	yes	complemented
361	D₄²	—	5	24	no	—
362	D₄²	—	5	24	no	—
363	D₄²	—	5	12	no	—
364	D₄²	—	5	24	no	—
365	D₄²	—	5	24	no	—
366	D₄²	—	5	48	no	—
367	D₄²	—	5	12	no	—
368	D₄²	—	5	12	no	—
369	D₄²	C₂×D₅	1	12	yes	complemented
370	#535	—	5	6	no	—
371	#535	—	5	6	no	—
372	#535	—	5	12	no	—
373	#535	—	5	12	no	—
374	#535	—	5	24	no	—
375	#535	—	5	24	no	—
376	#535	—	5	6	no	—
377	#535	C₂×D₅	1	6	yes	complemented
378	#532	—	5	6	no	—
379	#532	—	5	3	no	—
380	#532	—	5	3	no	—
381	#532	—	5	6	no	—
382	#532	—	5	12	no	—
383	#532	—	5	12	no	—
384	#532	—	5	3	no	—
385	#532	C₂×D₅	1	3	yes	complemented
386	C₂×C₄⋊Q₈	—	5	1	no	—
387	C₂×#127	—	5	12	no	—
388	C₂×#127	—	5	6	no	—
389	C₂×#127	—	5	3	no	—
390	C₂×#127	—	5	6	no	—
391	C₂×#127	—	5	12	no	—
392	C₂×#127	—	5	12	no	—
393	C₂×#127	—	5	6	no	—
394	C₂×#127	—	5	6	no	—
395	C₂×#127	—	5	3	no	—
396	C₂×#127	C₂×D₅	1	3	yes	complemented
397	C₂×#124	—	5	6	no	—
398	C₂×#121	—	5	12	no	—
399	C₂×#121	—	5	24	no	—
400	C₂×#120	—	5	24	no	—
401	C₄×#41	—	5	1	no	—
402	C₄×#41	—	5	2	no	—
403	C₄×#41	—	5	6	no	—
404	C₄×#41	—	5	3	no	—
405	C₄×#41	—	5	3	no	—
406	C₄×#41	C₂×D₅	1	1	yes	characteristic, complemented
407	C₂×C₄×Q₈	—	5	2	no	—
408	C₂×C₄×D₄	—	5	6	no	—
409	C₂×C₄×D₄	—	5	12	no	—
410	C₂×#117	—	5	3	no	—
411	C₂²×C₄²	—	5	3	no	—
412	C₂³×C₅	—	2	24	no	—
413	C₂³×C₅	—	4	24	no	—
414	C₂³×C₅	C₂⁵	1	12	yes	—
415	C₂³×C₅	C₂⁵	1	3	yes	—
416	C₂²×D₅	—	2	12	no	—
417	C₂²×D₅	—	2	24	no	—
418	C₂²×D₅	—	2	24	no	—
419	C₂²×D₅	—	2	48	no	—
420	C₂²×D₅	—	2	48	no	—
421	C₂²×D₅	—	4	24	no	—
422	C₂²×D₅	—	4	48	no	—
423	C₂²×D₅	—	8	96	no	—
424	C₂²×D₅	C₂²×D₄	1	12	yes	—
425	C₂²×D₅	C₂⁵	1	12	yes	—
426	C₂²×D₅	C₂⁵	1	3	yes	—
427	C₂²×D₅	C₂⁵	1	1	yes	characteristic
428	C₅×Q₈	—	2	4	no	—
429	C₅×Q₈	C₂²×D₄	1	4	yes	complemented
430	C₅×D₄	—	2	24	no	—
431	C₅×D₄	—	2	12	no	—
432	C₅×D₄	—	2	24	no	—
433	C₅×D₄	—	2	24	no	—
434	C₅×D₄	—	4	24	no	—
435	C₅×D₄	C₂²×D₄	1	12	yes	complemented
436	C₂×C₄×C₅	—	2	24	no	—
437	C₂×C₄×C₅	—	2	12	no	—
438	C₂×C₄×C₅	C₂²×D₄	1	12	yes	complemented
439	C₂×C₄×C₅	C₂⁵	1	6	yes	—
440	C₂×C₄×C₅	C₂⁵	1	4	yes	—
441	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
442	C₂×C₄×C₅	C₂⁵	1	3	yes	—
443	C₂×C₄×C₅	C₂⁵	1	2	yes	—
444	C₂²⋊D₅	—	2	24	no	—
445	C₂²⋊D₅	—	2	24	no	—
446	C₂²⋊D₅	—	2	24	no	—
447	C₂²⋊D₅	—	2	48	no	—
448	C₂²⋊D₅	—	2	48	no	—
449	C₂²⋊D₅	—	4	48	no	—
450	C₂²⋊D₅	C₂²×D₄	1	24	yes	complemented
451	C₂×Dic₅	—	2	24	no	—
452	C₂×Dic₅	—	2	12	no	—
453	C₂×Dic₅	C₂²×D₄	1	12	yes	complemented
454	C₂×Dic₅	C₂⁵	1	6	yes	—
455	C₂×Dic₅	C₂⁵	1	4	yes	—
456	C₂×Dic₅	C₂⁵	1	1	yes	characteristic
457	C₂×Dic₅	C₂⁵	1	3	yes	—
458	C₂×Dic₅	C₂⁵	1	2	yes	—
459	D₂₀	—	2	24	no	—
460	D₂₀	—	2	12	no	—
461	D₂₀	—	2	24	no	—
462	D₂₀	—	2	24	no	—
463	D₂₀	—	4	24	no	—
464	D₂₀	C₂²×D₄	1	12	yes	complemented
465	C₄×D₅	—	2	8	no	—
466	C₄×D₅	—	2	12	no	—
467	C₄×D₅	—	2	24	no	—
468	C₄×D₅	—	2	12	no	—
469	C₄×D₅	—	2	24	no	—
470	C₄×D₅	—	2	12	no	—
471	C₄×D₅	C₂²×D₄	1	12	yes	—
472	C₄×D₅	C₂²×D₄	1	4	yes	—
473	C₄×D₅	C₂²×D₄	1	12	yes	complemented
474	C₄×D₅	C₂²×D₄	1	12	yes	complemented
475	C₄×D₅	H(5,𝔽₂)	1	8	yes	complemented
476	Dic₁₀	—	2	4	no	—
477	Dic₁₀	—	2	8	no	—
478	Dic₁₀	C₂²×D₄	1	12	yes	complemented
479	C₂⁵	—	5	12	no	—
480	H(5,𝔽₂)	—	2	16	no	—
481	H(5,𝔽₂)	—	10	96	no	—
482	H(5,𝔽₂)	—	10	48	no	—
483	H(5,𝔽₂)	—	10	32	no	—
484	H(5,𝔽₂)	—	10	48	no	—
485	H(5,𝔽₂)	—	10	16	no	—
486	C₂×#41	—	5	16	no	—
487	C₂×#41	—	5	1	no	—
488	C₂×#41	—	5	6	no	—
489	C₂×#41	—	5	4	no	—
490	C₂×#41	—	5	3	no	—
491	C₂×#41	—	5	12	no	—
492	C₂×#41	—	5	6	no	—
493	C₂×#41	—	5	12	no	—
494	C₂×#41	—	5	3	no	—
495	C₂×#41	—	5	12	no	—
496	C₂×#41	—	5	6	no	—
497	C₂×#41	—	5	12	no	—
498	C₂×#41	—	10	48	no	—
499	C₂×#41	—	10	32	no	—
500	C₂×#41	C₂²×D₅	1	1	yes	characteristic
501	C₂×#41	C₂²×D₅	1	6	yes	complemented
502	C₂×#41	C₂²×D₅	1	4	yes	complemented
503	C₂²×Q₈	—	5	1	no	—
504	C₂²×Q₈	—	5	2	no	—
505	C₂²×D₄	—	5	3	no	—
506	C₂²×D₄	—	5	12	no	—
507	C₂²×D₄	—	5	24	no	—
508	C₂²×D₄	—	5	24	no	—
509	C₂²×D₄	—	5	12	no	—
510	C₂²×D₄	—	5	12	no	—
511	C₂²×D₄	—	5	12	no	—
512	C₂²×D₄	—	5	6	no	—
513	C₂²×D₄	—	5	12	no	—
514	C₂²×D₄	—	5	12	no	—
515	C₂²×D₄	—	5	24	no	—
516	C₂²×D₄	—	5	12	no	—
517	C₂²×D₄	—	5	12	no	—
518	C₂²×D₄	—	5	24	no	—
519	C₂²×D₄	—	5	24	no	—
520	C₂²×D₄	—	5	24	no	—
521	C₂²×D₄	—	5	6	no	—
522	C₂²×D₄	—	5	12	no	—
523	C₂²×D₄	—	5	12	no	—
524	C₂²×D₄	—	10	48	no	—
525	C₂²×D₄	—	10	96	no	—
526	C₂²×D₄	—	20	48	no	—
527	C₂²×D₄	C₂²×D₅	1	6	yes	complemented
528	C₂²×D₄	C₂²×D₅	1	12	yes	complemented
529	C₂²×D₄	C₂²×D₅	1	12	yes	complemented
530	C₂³×C₄	—	5	3	no	—
531	C₂³×C₄	—	5	6	no	—
532	C₂³×C₄	—	5	12	no	—
533	C₄⋊Q₈	—	5	2	no	—
534	C₄⋊Q₈	—	5	4	no	—
535	C₄⋊Q₈	—	5	1	no	—
536	C₄⋊Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
537	#127	—	5	6	no	—
538	#127	—	5	12	no	—
539	#127	—	5	24	no	—
540	#127	—	5	12	no	—
541	#127	—	5	24	no	—
542	#127	—	5	24	no	—
543	#127	—	5	24	no	—
544	#127	—	5	3	no	—
545	#127	—	5	6	no	—
546	#127	—	5	12	no	—
547	#127	C₂²×D₅	1	3	yes	complemented
548	#127	C₂²×D₅	1	6	yes	complemented
549	#127	C₂²×D₅	1	12	yes	complemented
550	#124	—	5	6	no	—
551	#124	—	5	6	no	—
552	#124	—	5	24	no	—
553	#124	—	5	6	no	—
554	#124	C₂²×D₅	1	6	yes	complemented
555	#121	—	5	12	no	—
556	#121	—	5	24	no	—
557	#121	—	5	24	no	—
558	#121	—	5	48	no	—
559	#121	—	5	12	no	—
560	#121	—	5	24	no	—
561	#121	—	5	12	no	—
562	#121	—	5	24	no	—
563	#121	—	5	24	no	—
564	#121	—	5	48	no	—
565	#121	C₂²×D₅	1	12	yes	complemented
566	#121	C₂²×D₅	1	24	yes	complemented
567	#120	—	5	24	no	—
568	#120	—	5	24	no	—
569	#120	—	5	48	no	—
570	#120	—	5	48	no	—
571	#120	—	5	24	no	—
572	#120	C₂²×D₅	1	24	yes	complemented
573	C₄×Q₈	—	5	2	no	—
574	C₄×Q₈	—	5	6	no	—
575	C₄×Q₈	—	5	6	no	—
576	C₄×Q₈	C₂²×D₅	1	2	yes	complemented
577	C₄×D₄	—	5	6	no	—
578	C₄×D₄	—	5	12	no	—
579	C₄×D₄	—	5	12	no	—
580	C₄×D₄	—	5	24	no	—
581	C₄×D₄	—	5	6	no	—
582	C₄×D₄	—	5	12	no	—
583	C₄×D₄	—	5	12	no	—
584	C₄×D₄	—	5	24	no	—
585	C₄×D₄	—	5	6	no	—
586	C₄×D₄	—	5	12	no	—
587	C₄×D₄	C₂²×D₅	1	6	yes	complemented
588	C₄×D₄	C₂²×D₅	1	12	yes	complemented
589	#117	—	5	3	no	—
590	#117	—	5	6	no	—
591	#117	—	5	6	no	—
592	#117	—	5	6	no	—
593	#117	C₂²×D₅	1	3	yes	complemented
594	C₂×C₄⋊C₄	—	5	6	no	—
595	C₂×C₄⋊C₄	—	5	4	no	—
596	C₂×C₂²⋊C₄	—	5	6	no	—
597	C₂×C₂²⋊C₄	—	5	24	no	—
598	C₂×C₄²	—	5	6	no	—
599	C₂×C₄²	—	5	3	no	—
600	C₂×C₄²	—	5	3	no	—
601	C₂×C₄²	—	5	6	no	—
602	C₂×C₄²	—	5	6	no	—
603	C₂×C₄²	—	5	3	no	—
604	C₂×C₄²	—	5	3	no	—
605	C₂×C₄²	—	5	1	no	—
606	C₂×C₄²	C₂²×D₅	1	3	yes	complemented
607	C₂²×C₅	—	2	6	no	—
608	C₂²×C₅	—	2	12	no	—
609	C₂²×C₅	—	2	24	no	—
610	C₂²×C₅	—	8	24	no	—
611	C₂²×C₅	C₂³×D₄	1	6	yes	—
612	C₂²×C₅	C₂⁶	1	1	yes	characteristic
613	C₂×D₅	—	2	6	no	—
614	C₂×D₅	—	2	24	no	—
615	C₂×D₅	—	2	12	no	—
616	C₂×D₅	—	2	24	no	—
617	C₂×D₅	—	4	48	no	—
618	C₂×D₅	—	8	48	no	—
619	C₂×D₅	—	8	24	no	—
620	C₂×D₅	C₂³×D₄	1	6	yes	—
621	C₂×D₅	C₂³×D₄	1	2	yes	—
622	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
623	C₄×C₅	—	2	4	no	—
624	C₄×C₅	—	2	6	no	—
625	C₄×C₅	C₂³×D₄	1	2	yes	—
626	C₄×C₅	C₂³×D₄	1	6	yes	—
627	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	complemented
628	Dic₅	—	2	4	no	—
629	Dic₅	—	2	6	no	—
630	Dic₅	C₂³×D₄	1	2	yes	—
631	Dic₅	C₂³×D₄	1	6	yes	—
632	Dic₅	C₂×H(5,𝔽₂)	1	4	yes	complemented
633	C₂⁴	—	5	3	no	—
634	C₂⁴	—	5	12	no	—
635	C₂⁴	—	5	24	no	—
636	C₂⁴	—	5	12	no	—
637	C₂⁴	—	10	48	no	—
638	C₂⁴	—	20	48	no	—
639	C₂⁴	C₂³×D₅	1	12	yes	—
640	#41	—	2	16	no	—
641	#41	—	2	24	no	—
642	#41	—	5	8	no	—
643	#41	—	5	24	no	—
644	#41	—	5	24	no	—
645	#41	—	10	48	no	—
646	#41	—	10	48	no	—
647	#41	—	10	48	no	—
648	#41	—	10	24	no	—
649	#41	—	10	24	no	—
650	#41	—	10	48	no	—
651	#41	—	10	16	no	—
652	#41	—	10	24	no	—
653	#41	D₄×D₅	1	8	yes	complemented
654	C₂×Q₈	—	5	8	no	—
655	C₂×Q₈	—	5	3	no	—
656	C₂×Q₈	—	5	4	no	—
657	C₂×Q₈	—	5	2	no	—
658	C₂×Q₈	—	10	8	no	—
659	C₂×Q₈	C₂³×D₅	1	2	yes	—
660	C₂×Q₈	C₂³×D₅	1	1	yes	characteristic
661	C₂×D₄	—	2	48	no	—
662	C₂×D₄	—	2	24	no	—
663	C₂×D₄	—	4	24	no	—
664	C₂×D₄	—	5	6	no	—
665	C₂×D₄	—	5	24	no	—
666	C₂×D₄	—	5	24	no	—
667	C₂×D₄	—	5	12	no	—
668	C₂×D₄	—	5	12	no	—
669	C₂×D₄	—	5	24	no	—
670	C₂×D₄	—	5	12	no	—
671	C₂×D₄	—	5	48	no	—
672	C₂×D₄	—	5	3	no	—
673	C₂×D₄	—	5	12	no	—
674	C₂×D₄	—	5	12	no	—
675	C₂×D₄	—	5	12	no	—
676	C₂×D₄	—	5	6	no	—
677	C₂×D₄	—	5	24	no	—
678	C₂×D₄	—	10	48	no	—
679	C₂×D₄	—	10	24	no	—
680	C₂×D₄	—	10	48	no	—
681	C₂×D₄	—	10	48	no	—
682	C₂×D₄	—	10	48	no	—
683	C₂×D₄	—	10	48	no	—
684	C₂×D₄	—	10	48	no	—
685	C₂×D₄	—	10	96	no	—
686	C₂×D₄	—	10	48	no	—
687	C₂×D₄	—	10	48	no	—
688	C₂×D₄	—	10	96	no	—
689	C₂×D₄	—	10	48	no	—
690	C₂×D₄	—	10	24	no	—
691	C₂×D₄	—	20	24	no	—
692	C₂×D₄	—	20	48	no	—
693	C₂×D₄	—	20	48	no	—
694	C₂×D₄	—	20	48	no	—
695	C₂×D₄	—	20	48	no	—
696	C₂×D₄	C₂³×D₅	1	12	yes	—
697	C₂×D₄	C₂³×D₅	1	12	yes	—
698	C₂×D₄	C₂³×D₅	1	12	yes	—
699	C₂×D₄	C₂³×D₅	1	6	yes	—
700	C₂×D₄	C₂³×D₅	1	24	yes	—
701	C₂×D₄	C₂³×D₅	1	3	yes	—
702	C₂²×C₄	—	5	3	no	—
703	C₂²×C₄	—	5	24	no	—
704	C₂²×C₄	—	5	2	no	—
705	C₂²×C₄	—	5	1	no	—
706	C₂²×C₄	—	5	3	no	—
707	C₂²×C₄	—	5	3	no	—
708	C₂²×C₄	—	5	3	no	—
709	C₂²×C₄	—	5	6	no	—
710	C₂²×C₄	—	5	12	no	—
711	C₂²×C₄	—	5	6	no	—
712	C₂²×C₄	—	5	6	no	—
713	C₂²×C₄	—	5	6	no	—
714	C₂²×C₄	—	5	4	no	—
715	C₂²×C₄	—	5	12	no	—
716	C₂²×C₄	—	5	12	no	—
717	C₂²×C₄	—	10	48	no	—
718	C₂²×C₄	—	10	24	no	—
719	C₂²×C₄	C₂³×D₅	1	6	yes	—
720	C₂²×C₄	C₂³×D₅	1	12	yes	—
721	C₂²×C₄	C₂³×D₅	1	3	yes	—
722	C₄⋊C₄	—	5	12	no	—
723	C₄⋊C₄	—	5	6	no	—
724	C₄⋊C₄	—	5	8	no	—
725	C₄⋊C₄	—	5	4	no	—
726	C₄⋊C₄	C₂³×D₅	1	6	yes	—
727	C₄⋊C₄	C₂³×D₅	1	4	yes	—
728	C₂²⋊C₄	—	5	6	no	—
729	C₂²⋊C₄	—	5	24	no	—
730	C₂²⋊C₄	—	5	12	no	—
731	C₂²⋊C₄	—	5	24	no	—
732	C₂²⋊C₄	—	5	24	no	—
733	C₂²⋊C₄	C₂³×D₅	1	6	yes	—
734	C₂²⋊C₄	C₂³×D₅	1	24	yes	—
735	C₄²	—	5	1	no	—
736	C₄²	—	5	2	no	—
737	C₄²	—	5	6	no	—
738	C₄²	—	5	3	no	—
739	C₄²	—	5	6	no	—
740	C₄²	—	5	6	no	—
741	C₄²	—	5	6	no	—
742	C₄²	C₂³×D₅	1	1	yes	characteristic
743	C₄²	C₂³×D₅	1	3	yes	—
744	C₄²	C₂³×D₅	1	6	yes	—
745	C₂×C₅	—	2	6	no	—
746	C₂×C₅	—	4	12	no	—
747	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
748	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
749	D₅	—	2	6	no	—
750	D₅	—	4	12	no	—
751	D₅	#3498	1	4	yes	direct product factor
752	C₂³	—	2	24	no	—
753	C₂³	—	4	24	no	—
754	C₂³	—	5	1	no	—
755	C₂³	—	5	12	no	—
756	C₂³	—	5	3	no	—
757	C₂³	—	5	12	no	—
758	C₂³	—	10	12	no	—
759	C₂³	—	10	24	no	—
760	C₂³	—	10	48	no	—
761	C₂³	—	10	48	no	—
762	C₂³	—	10	24	no	—
763	C₂³	—	20	24	no	—
764	C₂³	—	20	48	no	—
765	C₂³	—	40	96	no	—
766	C₂³	C₂⁴×D₅	1	12	yes	—
767	C₂³	C₂⁴×D₅	1	3	yes	—
768	Q₈	—	2	4	no	—
769	Q₈	—	5	12	no	—
770	Q₈	—	10	8	no	—
771	Q₈	—	10	4	no	—
772	Q₈	C₂×D₄×D₅	1	4	yes	complemented
773	D₄	—	2	24	no	—
774	D₄	—	2	24	no	—
775	D₄	—	2	12	no	—
776	D₄	—	2	24	no	—
777	D₄	—	4	24	no	—
778	D₄	—	5	24	no	—
779	D₄	—	5	12	no	—
780	D₄	—	10	24	no	—
781	D₄	—	10	24	no	—
782	D₄	—	10	48	no	—
783	D₄	—	10	48	no	—
784	D₄	—	10	24	no	—
785	D₄	—	10	24	no	—
786	D₄	—	10	24	no	—
787	D₄	—	10	12	no	—
788	D₄	—	10	24	no	—
789	D₄	—	20	24	no	—
790	D₄	—	20	48	no	—
791	D₄	C₂×D₄×D₅	1	12	yes	complemented
792	C₂×C₄	—	2	24	no	—
793	C₂×C₄	—	2	12	no	—
794	C₂×C₄	—	5	12	no	—
795	C₂×C₄	—	5	2	no	—
796	C₂×C₄	—	5	1	no	—
797	C₂×C₄	—	5	3	no	—
798	C₂×C₄	—	5	4	no	—
799	C₂×C₄	—	5	12	no	—
800	C₂×C₄	—	5	12	no	—
801	C₂×C₄	—	5	12	no	—
802	C₂×C₄	—	5	8	no	—
803	C₂×C₄	—	5	6	no	—
804	C₂×C₄	—	5	4	no	—
805	C₂×C₄	—	10	24	no	—
806	C₂×C₄	—	10	12	no	—
807	C₂×C₄	—	10	8	no	—
808	C₂×C₄	—	10	12	no	—
809	C₂×C₄	—	10	24	no	—
810	C₂×C₄	—	10	12	no	—
811	C₂×C₄	—	10	24	no	—
812	C₂×C₄	—	10	12	no	—
813	C₂×C₄	C₂×D₄×D₅	1	12	yes	complemented
814	C₂×C₄	C₂⁴×D₅	1	6	yes	—
815	C₂×C₄	C₂⁴×D₅	1	4	yes	—
816	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
817	C₂×C₄	C₂⁴×D₅	1	3	yes	—
818	C₂×C₄	C₂⁴×D₅	1	2	yes	—
819	C₅	C₂×#3498	1	1	yes	characteristic, complemented, Sylow
820	C₂²	—	2	6	no	—
821	C₂²	—	2	12	no	—
822	C₂²	—	2	24	no	—
823	C₂²	—	5	2	no	—
824	C₂²	—	5	4	no	—
825	C₂²	—	5	6	no	—
826	C₂²	—	8	24	no	—
827	C₂²	—	10	24	no	—
828	C₂²	—	10	6	no	—
829	C₂²	—	10	12	no	—
830	C₂²	—	10	24	no	—
831	C₂²	—	20	48	no	—
832	C₂²	—	40	24	no	—
833	C₂²	—	40	48	no	—
834	C₂²	C₂²×D₄×D₅	1	6	yes	—
835	C₂²	C₂⁵×D₅	1	1	yes	characteristic
836	C₄	—	2	4	no	—
837	C₄	—	2	6	no	—
838	C₄	—	5	2	no	—
839	C₄	—	5	6	no	—
840	C₄	—	5	4	no	—
841	C₄	—	10	4	no	—
842	C₄	—	10	6	no	—
843	C₄	C₂²×D₄×D₅	1	6	yes	—
844	C₄	C₂²×D₄×D₅	1	2	yes	—
845	C₄	D₅×H(5,𝔽₂)	1	4	yes	complemented
846	C₂	—	2	6	no	—
847	C₂	—	4	12	no	—
848	C₂	—	5	4	no	—
849	C₂	—	10	6	no	—
850	C₂	—	20	12	no	—
851	C₂	C₂³×D₄×D₅	1	1	yes	characteristic
852	C₂	C₂×D₅×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁶
Fitting	C₅×#3498	C₂
hypercenter	#3498	D₅
hypocenter	C₅	C₂×#3498
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #3498

Complements

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

N	H ≅ G/N	type
1. C₂×D₅×H(5,𝔽₂)	C₂	semidirect
2. C₅×#3498	C₂	semidirect
3. #10619183	C₂	semidirect
4. D₅×#550	C₂	semidirect
5. #10618671	C₂	semidirect
6. D₄²×D₅	C₂	semidirect
7. #10618509	C₂	semidirect
8. D₅×#535	C₂	semidirect
9. #10618217	C₂	semidirect
10. #10618143	C₂	semidirect
11. D₅×#532	C₂	semidirect
12. #10618096	C₂	semidirect
13. C₂×D₅×#127	C₂	semidirect
14. #10617747	C₂	semidirect
15. C₄×D₅×#41	C₂	semidirect
16. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
18. C₂×#4149	C₂²	semidirect
19. C₂×#4149	C₂²	semidirect
20. C₂×#4149	C₂²	semidirect
22. C₂×D₅×#41	C₂²	semidirect
23. C₂×D₅×#41	C₂²	semidirect
24. C₂×#4144	C₂²	semidirect
25. C₂×#4144	C₂²	semidirect
26. C₂²×D₄×D₅	C₂²	semidirect
27. C₂²×D₄×D₅	C₂²	semidirect
28. C₂²×D₄×D₅	C₂²	semidirect
29. C₅×#550	C₂²	semidirect
30. C₅×D₄²	C₂²	semidirect
31. C₅×#535	C₂²	semidirect
32. C₅×#532	C₂²	semidirect
33. C₂×C₅×#127	C₂²	semidirect
34. C₄×C₅×#41	C₂²	semidirect
35. #66168	C₂²	semidirect
36. #66166	C₂²	semidirect
37. #66164	C₂²	semidirect
38. #41×Dic₅	C₂²	semidirect
39. #66139	C₂²	semidirect
40. C₂×#4086	C₂²	semidirect
41. C₂×#4086	C₂²	semidirect
42. D₄×C₂²⋊D₅	C₂²	semidirect
43. D₄×C₂²⋊D₅	C₂²	semidirect
44. #66059	C₂²	semidirect
45. D₅×C₄⋊Q₈	C₂²	semidirect
46. #66052	C₂²	semidirect
47. #66051	C₂²	semidirect
48. #66050	C₂²	semidirect
49. #66049	C₂²	semidirect
50. D₅×#127	C₂²	semidirect
51. D₅×#127	C₂²	semidirect
52. D₅×#127	C₂²	semidirect
53. D₅×#127	C₂²	semidirect
54. D₅×#127	C₂²	semidirect
55. D₅×#127	C₂²	semidirect
56. #66008	C₂²	semidirect
57. D₅×#124	C₂²	semidirect
58. #66002	C₂²	semidirect
59. #65943	C₂²	semidirect
60. #65943	C₂²	semidirect
61. #65941	C₂²	semidirect
62. D₅×#121	C₂²	semidirect
63. D₅×#121	C₂²	semidirect
64. #65933	C₂²	semidirect
65. #65930	C₂²	semidirect
66. #65926	C₂²	semidirect
67. #65924	C₂²	semidirect
68. D₅×#120	C₂²	semidirect
69. #65911	C₂²	semidirect
70. C₄×#713	C₂²	semidirect
71. C₄×Q₈×D₅	C₂²	semidirect
72. #65887	C₂²	semidirect
73. D₄×D₂₀	C₂²	semidirect
74. D₄×D₂₀	C₂²	semidirect
75. #65882	C₂²	semidirect
76. C₄×D₄×D₅	C₂²	semidirect
77. C₄×D₄×D₅	C₂²	semidirect
78. C₄×#711	C₂²	semidirect
79. #65859	C₂²	semidirect
80. #65856	C₂²	semidirect
81. D₅×#117	C₂²	semidirect
82. #65811	C₂²	semidirect
83. C₂×#4020	C₂²	semidirect
84. C₄×#709	C₂²	semidirect
85. C₂×C₄²×D₅	C₂²	semidirect
90. C₂×C₅×#41	C₂³	semidirect
91. C₂×C₅×#41	C₂³	semidirect
92. C₂²×C₅×D₄	C₂³	semidirect
93. C₂²×C₅×D₄	C₂³	semidirect
94. C₂²×C₅×D₄	C₂³	semidirect
95. C₂²×C₂²⋊D₅	C₂³	semidirect
96. C₂²×C₂²⋊D₅	C₂³	semidirect
97. C₂²×C₂²⋊D₅	C₂³	semidirect
103. D₅×#41	D₄	semidirect
105. C₂×#713	C₂³	semidirect
106. C₂×#713	C₂³	semidirect
112. C₂×#711	C₂³	semidirect
113. C₂×#711	C₂³	semidirect
114. C₂×#711	C₂³	semidirect
124. C₂×D₄×D₅	C₂³	semidirect
125. C₂×D₄×D₅	C₂³	semidirect
126. C₂×D₄×D₅	C₂³	semidirect
127. C₂×D₄×D₅	C₂³	semidirect
128. C₂×D₄×D₅	C₂³	semidirect
129. C₂×D₄×D₅	C₂³	semidirect
130. C₂×D₄×D₅	C₂³	semidirect
132. C₂×#709	C₂³	semidirect
133. C₂×#709	C₂³	semidirect
134. C₂×#709	C₂³	semidirect
135. C₂²×D₂₀	C₂³	semidirect
136. C₂²×D₂₀	C₂³	semidirect
137. C₂²×D₂₀	C₂³	semidirect
141. C₅×C₄⋊Q₈	C₂³	semidirect
142. C₅×#127	C₂³	semidirect
143. C₅×#127	C₂³	semidirect
144. C₅×#127	C₂³	semidirect
145. C₅×#124	C₂³	semidirect
146. C₅×#121	C₂³	semidirect
147. C₅×#121	C₂³	semidirect
148. C₅×#120	C₂³	semidirect
149. C₄×C₅×Q₈	C₂³	semidirect
150. C₄×C₅×D₄	C₂³	semidirect
151. C₄×C₅×D₄	C₂³	semidirect
152. C₅×#117	C₂³	semidirect
153. C₂×C₄²×C₅	C₂³	semidirect
154. #4099	C₂³	semidirect
155. #4093	C₂³	semidirect
156. Q₈×Dic₅	C₂³	semidirect
157. #4090	C₂³	semidirect
158. #4086	C₂³	semidirect
159. #4086	C₂³	semidirect
160. #4086	C₂³	semidirect
161. #4086	C₂³	semidirect
162. #4086	C₂³	semidirect
163. #4086	C₂³	semidirect
164. #4086	C₂³	semidirect
165. #4085	C₂³	semidirect
166. #4085	C₂³	semidirect
167. #4084	C₂³	semidirect
168. #4084	C₂³	semidirect
169. #4083	C₂³	semidirect
170. #4083	C₂³	semidirect
171. #4082	C₂³	semidirect
172. D₄×Dic₅	C₂³	semidirect
173. D₄×Dic₅	C₂³	semidirect
174. #4076	C₂³	semidirect
175. #4076	C₂³	semidirect
176. C₄×C₂²⋊D₅	C₂³	semidirect
177. C₄×C₂²⋊D₅	C₂³	semidirect
178. #4072	C₂³	semidirect
179. C₂×C₄×Dic₅	C₂³	semidirect
180. C₂×C₄×Dic₅	C₂³	semidirect
181. #4041	C₂³	semidirect
182. #4041	C₂³	semidirect
183. #4039	C₂³	semidirect
184. #4039	C₂³	semidirect
185. #4038	C₂³	semidirect
188. #4034	C₂³	semidirect
189. #4033	C₂³	semidirect
190. #4031	C₂³	semidirect
191. #4030	C₂³	semidirect
192. #4030	C₂³	semidirect
193. #4028	C₂³	semidirect
194. #4028	C₂³	semidirect
195. #4027	C₂³	semidirect
196. #4027	C₂³	semidirect
199. #4023	C₂³	semidirect
200. #4021	C₂³	semidirect
201. #4020	C₂³	semidirect
202. #4020	C₂³	semidirect
203. #4020	C₂³	semidirect
204. C₄×D₂₀	C₂³	semidirect
205. C₄×D₂₀	C₂³	semidirect
206. #4018	C₂³	semidirect
210. C₄²×D₅	C₂³	semidirect
211. C₄²×D₅	C₂³	semidirect
212. C₄²×D₅	C₂³	semidirect
213. #4015	C₂³	semidirect
214. C₄×Dic₁₀	C₂³	semidirect
223. #3498	D₅	direct (N × H)
239. C₅×#41	C₂×D₄	semidirect
269. #713	C₂×D₄	semidirect
271. Q₈×D₅	C₂×D₄	semidirect
275. #711	C₂×D₄	semidirect
288. D₄×D₅	C₂×D₄	semidirect
292. #709	C₂×D₄	semidirect
304. C₂×C₄×D₅	C₂×D₄	semidirect
348. C₂×H(5,𝔽₂)	C₂×D₅	semidirect
360. #550	C₂×D₅	semidirect
369. D₄²	C₂×D₅	semidirect
377. #535	C₂×D₅	semidirect
385. #532	C₂×D₅	semidirect
396. C₂×#127	C₂×D₅	semidirect
406. C₄×#41	C₂×D₅	semidirect
429. C₅×Q₈	C₂²×D₄	semidirect
435. C₅×D₄	C₂²×D₄	semidirect
438. C₂×C₄×C₅	C₂²×D₄	semidirect
450. C₂²⋊D₅	C₂²×D₄	semidirect
453. C₂×Dic₅	C₂²×D₄	semidirect
464. D₂₀	C₂²×D₄	semidirect
473. C₄×D₅	C₂²×D₄	semidirect
474. C₄×D₅	C₂²×D₄	semidirect
475. C₄×D₅	H(5,𝔽₂)	semidirect
478. Dic₁₀	C₂²×D₄	semidirect
501. C₂×#41	C₂²×D₅	semidirect
502. C₂×#41	C₂²×D₅	semidirect
527. C₂²×D₄	C₂²×D₅	semidirect
528. C₂²×D₄	C₂²×D₅	semidirect
529. C₂²×D₄	C₂²×D₅	semidirect
536. C₄⋊Q₈	C₂²×D₅	semidirect
547. #127	C₂²×D₅	semidirect
548. #127	C₂²×D₅	semidirect
549. #127	C₂²×D₅	semidirect
554. #124	C₂²×D₅	semidirect
565. #121	C₂²×D₅	semidirect
566. #121	C₂²×D₅	semidirect
572. #120	C₂²×D₅	semidirect
576. C₄×Q₈	C₂²×D₅	semidirect
587. C₄×D₄	C₂²×D₅	semidirect
588. C₄×D₄	C₂²×D₅	semidirect
593. #117	C₂²×D₅	semidirect
606. C₂×C₄²	C₂²×D₅	semidirect
627. C₄×C₅	C₂×H(5,𝔽₂)	semidirect
632. Dic₅	C₂×H(5,𝔽₂)	semidirect
653. #41	D₄×D₅	semidirect
751. D₅	#3498	direct (N × H)
772. Q₈	C₂×D₄×D₅	semidirect
791. D₄	C₂×D₄×D₅	semidirect
813. C₂×C₄	C₂×D₄×D₅	semidirect
819. C₅	C₂×#3498	semidirect
845. C₄	D₅×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×H(5,𝔽₂)	2
C₅×#3498	2
#10619183	2
D₅×#550	2
#10618671	2
D₄²×D₅	2
#10618509	2
D₅×#535	2
#10618217	2
#10618143	2
D₅×#532	2
#10618096	2
C₂×D₅×#127	2
#10617747	2
C₄×D₅×#41	2
C₂×#3498	5

Subgroups — D5×#3498 #13007615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#3498 #13007615