Subgroups — D₅×#3529 #13006187

Order 1280.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3529	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×#563	C₂	1	3	yes	maximal, complemented
3	#10619016	C₂	1	3	yes	maximal, complemented
4	D₅×#562	C₂	1	6	yes	maximal, complemented
5	#10618994	C₂	1	6	yes	maximal, complemented
6	D₅×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
7	#10618986	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#560	C₂	1	6	yes	maximal, complemented
9	#10618971	C₂	1	6	yes	maximal, complemented
10	#10618149	C₂	1	3	yes	maximal, complemented
11	D₅×#532	C₂	1	3	yes	maximal, complemented
12	#10618072	C₂	1	6	yes	maximal, complemented
13	D₅×#529	C₂	1	6	yes	maximal, complemented
14	#10617949	C₂	1	6	yes	maximal, complemented
15	D₅×#525	C₂	1	6	yes	maximal, complemented
16	C₂×D₅×#41	C₂²	1	3	yes	—
17	C₂×D₅×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₄×D₅	C₂²	1	2	yes	complemented
19	C₅×#563	C₂²	1	3	yes	complemented
20	C₅×#562	C₂²	1	6	yes	complemented
21	C₅×H(3,𝔽₄)	C₂²	1	1	yes	characteristic, complemented
22	C₅×#560	C₂²	1	6	yes	complemented
23	C₅×#532	C₂²	1	3	yes	complemented
24	C₅×#529	C₂²	1	6	yes	complemented
25	C₅×#525	C₂²	1	6	yes	complemented
26	#66166	C₂²	1	3	yes	complemented
27	#66166	C₂²	1	3	yes	complemented
28	#66162	C₂²	1	6	yes	complemented
29	#66125	C₂²	1	6	yes	complemented
30	#66069	C₂²	1	6	yes	complemented
31	#66059	C₂²	1	3	yes	complemented
32	D₅×C₄⋊Q₈	C₂²	1	3	yes	complemented
33	#66054	C₂²	1	6	yes	complemented
34	#66050	C₂²	1	3	yes	complemented
35	D₅×#127	C₂²	1	3	yes	—
36	#66046	C₂²	1	12	yes	complemented
37	#66045	C₂²	1	12	yes	complemented
38	#66040	C₂²	1	12	yes	complemented
39	D₅×#126	C₂²	1	12	yes	complemented
40	#66034	C₂²	1	6	yes	complemented
41	#66033	C₂²	1	6	yes	complemented
42	#66025	C₂²	1	6	yes	complemented
43	D₅×#125	C₂²	1	6	yes	complemented
44	#66018	C₂²	1	6	yes	complemented
45	#66018	C₂²	1	6	yes	complemented
46	#66017	C₂²	1	3	yes	complemented
47	#66017	C₂²	1	6	yes	complemented
48	#66014	C₂²	1	6	yes	complemented
49	D₅×#124	C₂²	1	3	yes	—
50	D₅×#124	C₂²	1	6	yes	—
51	D₅×#124	C₂²	1	3	yes	complemented
52	#66006	C₂²	1	3	yes	complemented
53	#66002	C₂²	1	3	yes	complemented
54	#66002	C₂²	1	3	yes	complemented
55	#66001	C₂²	1	12	yes	complemented
56	#66001	C₂²	1	12	yes	complemented
57	#66000	C₂²	1	6	yes	complemented
58	#66000	C₂²	1	12	yes	complemented
59	#65990	C₂²	1	6	yes	complemented
60	#65990	C₂²	1	6	yes	complemented
61	D₅×#123	C₂²	1	6	yes	—
62	D₅×#123	C₂²	1	6	yes	complemented
63	D₅×#123	C₂²	1	12	yes	complemented
64	#65985	C₂²	1	6	yes	complemented
65	#65983	C₂²	1	12	yes	complemented
66	#65981	C₂²	1	12	yes	complemented
67	#65981	C₂²	1	12	yes	complemented
68	#65980	C₂²	1	12	yes	complemented
69	#65961	C₂²	1	12	yes	complemented
70	D₅×C₂²⋊Q₈	C₂²	1	12	yes	complemented
71	D₅×C₂²⋊Q₈	C₂²	1	6	yes	complemented
72	#65958	C₂²	1	6	yes	complemented
73	#65955	C₂²	1	12	yes	complemented
74	#65955	C₂²	1	12	yes	complemented
75	#65954	C₂²	1	12	yes	complemented
76	#65954	C₂²	1	12	yes	complemented
77	#65954	C₂²	1	12	yes	complemented
78	#65940	C₂²	1	12	yes	complemented
79	D₅×#121	C₂²	1	12	yes	—
80	D₅×#121	C₂²	1	6	yes	—
81	D₅×#121	C₂²	1	12	yes	complemented
82	#65934	C₂²	1	6	yes	complemented
83	#65930	C₂²	1	12	yes	complemented
84	#65929	C₂²	1	12	yes	complemented
85	#65929	C₂²	1	6	yes	complemented
86	#65928	C₂²	1	6	yes	complemented
87	D₅×#120	C₂²	1	6	yes	—
88	D₅×#120	C₂²	1	6	yes	complemented
89	#65920	C₂²	1	6	yes	complemented
90	#65920	C₂²	1	6	yes	complemented
91	#65914	C₂²	1	6	yes	complemented
92	C₄×Q₈×D₅	C₂²	1	2	yes	complemented
93	#65891	C₂²	1	6	yes	complemented
94	#65882	C₂²	1	12	yes	complemented
95	#65881	C₂²	1	12	yes	complemented
96	#65881	C₂²	1	12	yes	complemented
97	C₄×D₄×D₅	C₂²	1	6	yes	—
98	C₄×D₄×D₅	C₂²	1	12	yes	complemented
99	#65872	C₂²	1	12	yes	complemented
100	#65862	C₂²	1	12	yes	complemented
101	#65858	C₂²	1	6	yes	complemented
102	D₅×#117	C₂²	1	6	yes	complemented
103	#65813	C₂²	1	6	yes	complemented
104	#65811	C₂²	1	3	yes	complemented
105	C₂×C₄²×D₅	C₂²	1	3	yes	complemented
106	C₂×#3529	—	5	1	no	maximal, Sylow
107	C₂⁴×D₅	C₂³	1	2	yes	—
108	C₂×C₅×#41	C₂³	1	3	yes	—
109	C₂×C₅×#41	C₂³	1	1	yes	characteristic, complemented
110	C₂³×C₄×C₅	C₂³	1	2	yes	complemented
111	C₂³×Dic₅	C₂³	1	2	yes	complemented
112	D₅×#41	—	4	12	no	—
113	D₅×#41	—	4	4	no	—
114	C₂×#713	C₂³	1	3	yes	—
115	C₂×#713	C₂³	1	1	yes	characteristic, complemented
116	C₂×Q₈×D₅	C₂³	1	1	yes	characteristic
117	C₂×Q₈×D₅	C₂³	1	3	yes	—
118	C₂×Q₈×D₅	C₂³	1	2	yes	—
119	C₂×#711	C₂³	1	3	yes	—
120	C₂×#711	C₂³	1	6	yes	—
121	C₂×#711	C₂³	1	3	yes	complemented
122	C₂×D₄×D₅	C₂³	1	12	yes	—
123	C₂×D₄×D₅	C₂³	1	3	yes	—
124	C₂×D₄×D₅	C₂³	1	3	yes	—
125	C₂×D₄×D₅	C₂³	1	6	yes	—
126	C₂×D₄×D₅	C₂³	1	6	yes	—
127	C₂×#709	C₂³	1	3	yes	—
128	C₂×#709	C₂³	1	6	yes	—
129	C₂×#709	C₂³	1	3	yes	complemented
130	C₂²×C₄×D₅	—	4	8	no	—
131	C₂²×C₄×D₅	C₂³	1	3	yes	—
132	C₂²×C₄×D₅	C₂³	1	6	yes	—
133	C₂²×C₄×D₅	C₂³	1	6	yes	—
134	C₂²×C₄×D₅	C₂³	1	6	yes	—
135	C₂²×C₄×D₅	C₂³	1	6	yes	complemented
136	C₂²×C₄×D₅	C₂³	1	6	yes	complemented
137	C₅×C₄⋊Q₈	C₂³	1	3	yes	complemented
138	C₅×#127	C₂³	1	3	yes	—
139	C₅×#126	C₂³	1	12	yes	complemented
140	C₅×#125	C₂³	1	6	yes	complemented
141	C₅×#124	C₂³	1	6	yes	—
142	C₅×#124	C₂³	1	3	yes	—
143	C₅×#124	C₂³	1	3	yes	complemented
144	C₅×#123	C₂³	1	6	yes	—
145	C₅×#123	C₂³	1	6	yes	complemented
146	C₅×#123	C₂³	1	12	yes	complemented
147	C₅×C₂²⋊Q₈	C₂³	1	12	yes	complemented
148	C₅×C₂²⋊Q₈	C₂³	1	6	yes	complemented
149	C₅×#121	C₂³	1	12	yes	—
150	C₅×#121	C₂³	1	6	yes	—
151	C₅×#121	C₂³	1	12	yes	complemented
152	C₅×#120	C₂³	1	6	yes	—
153	C₅×#120	C₂³	1	6	yes	complemented
154	C₄×C₅×Q₈	C₂³	1	2	yes	complemented
155	C₄×C₅×D₄	C₂³	1	6	yes	—
156	C₄×C₅×D₄	C₂³	1	12	yes	complemented
157	C₅×#117	C₂³	1	6	yes	complemented
158	C₂×C₄²×C₅	C₂³	1	3	yes	complemented
159	#4099	C₂³	1	6	yes	—
160	#4099	C₂³	1	6	yes	complemented
161	#4093	C₂³	1	3	yes	—
162	#4093	C₂³	1	6	yes	—
163	#4093	C₂³	1	3	yes	complemented
164	#4092	C₂³	1	12	yes	complemented
165	#4092	C₂³	1	6	yes	complemented
166	Q₈×Dic₅	C₂³	1	2	yes	complemented
167	#4090	C₂³	1	3	yes	complemented
168	#4090	C₂³	1	3	yes	complemented
169	#4086	C₂³	1	12	yes	—
170	#4086	C₂³	1	3	yes	—
171	#4086	C₂³	1	3	yes	—
172	#4085	C₂³	1	12	yes	—
173	#4085	C₂³	1	12	yes	—
174	#4085	C₂³	1	12	yes	—
175	#4085	C₂³	1	12	yes	complemented
176	#4085	C₂³	1	12	yes	complemented
177	#4084	C₂³	1	6	yes	—
178	#4084	C₂³	1	12	yes	—
179	#4084	C₂³	1	12	yes	complemented
180	#4083	C₂³	1	6	yes	—
181	#4083	C₂³	1	12	yes	—
182	#4083	C₂³	1	12	yes	complemented
183	#4083	C₂³	1	6	yes	complemented
184	#4082	C₂³	1	3	yes	—
185	#4082	C₂³	1	6	yes	—
186	#4082	C₂³	1	3	yes	complemented
187	#4081	C₂³	1	6	yes	—
188	#4081	C₂³	1	12	yes	complemented
189	#4081	C₂³	1	6	yes	complemented
190	D₄×Dic₅	C₂³	1	6	yes	—
191	D₄×Dic₅	C₂³	1	12	yes	complemented
192	#4076	C₂³	1	6	yes	—
193	#4076	C₂³	1	12	yes	—
194	#4076	C₂³	1	12	yes	complemented
195	#4075	C₂³	1	6	yes	—
196	#4075	C₂³	1	12	yes	complemented
197	#4075	C₂³	1	6	yes	complemented
198	C₄×C₂²⋊D₅	C₂³	1	12	yes	—
199	C₄×C₂²⋊D₅	C₂³	1	12	yes	complemented
200	C₄×C₂²⋊D₅	C₂³	1	12	yes	complemented
201	#4072	C₂³	1	6	yes	complemented
202	#4070	C₂³	1	6	yes	complemented
203	#4070	C₂³	1	12	yes	complemented
204	C₂×C₄×Dic₅	C₂³	1	3	yes	complemented
205	C₂×C₄×Dic₅	C₂³	1	6	yes	complemented
206	#4044	C₂³	1	12	yes	complemented
207	#4044	C₂³	1	12	yes	complemented
208	#4044	C₂³	1	12	yes	complemented
209	#4043	C₂³	1	12	yes	complemented
210	#4043	C₂³	1	6	yes	complemented
211	#4042	C₂³	1	12	yes	complemented
212	#4042	C₂³	1	12	yes	complemented
213	#4042	C₂³	1	12	yes	complemented
214	#4041	C₂³	1	12	yes	—
215	#4041	C₂³	1	6	yes	—
216	#4041	C₂³	1	12	yes	complemented
217	#4040	C₂³	1	12	yes	—
218	#4040	C₂³	1	12	yes	complemented
219	#4040	C₂³	1	12	yes	complemented
220	#4040	C₂³	1	12	yes	complemented
221	#4039	C₂³	1	6	yes	—
222	#4039	C₂³	1	12	yes	complemented
223	#4038	C₂³	1	12	yes	complemented
224	D₅×C₄⋊C₄	C₂³	1	12	yes	—
225	D₅×C₄⋊C₄	C₂³	1	12	yes	—
226	D₅×C₄⋊C₄	C₂³	1	6	yes	—
227	D₅×C₄⋊C₄	C₂³	1	6	yes	—
228	#4036	C₂³	1	6	yes	complemented
229	#4036	C₂³	1	6	yes	complemented
230	#4035	C₂³	1	12	yes	complemented
231	#4035	C₂³	1	12	yes	complemented
232	#4034	C₂³	1	12	yes	complemented
233	#4033	C₂³	1	6	yes	complemented
234	#4032	C₂³	1	6	yes	—
235	#4032	C₂³	1	6	yes	complemented
236	#4032	C₂³	1	12	yes	complemented
237	#4031	C₂³	1	12	yes	—
238	#4031	C₂³	1	12	yes	—
239	#4031	C₂³	1	12	yes	—
240	#4031	C₂³	1	12	yes	complemented
241	#4030	C₂³	1	12	yes	—
242	#4030	C₂³	1	12	yes	—
243	#4030	C₂³	1	12	yes	—
244	#4030	C₂³	1	12	yes	complemented
245	#4030	C₂³	1	12	yes	complemented
246	#4029	C₂³	1	12	yes	—
247	#4029	C₂³	1	12	yes	complemented
248	#4029	C₂³	1	12	yes	complemented
249	#4029	C₂³	1	12	yes	complemented
250	#4028	C₂³	1	6	yes	—
251	#4028	C₂³	1	12	yes	—
252	#4028	C₂³	1	6	yes	complemented
253	#4028	C₂³	1	12	yes	complemented
254	#4027	C₂³	1	12	yes	—
255	#4027	C₂³	1	12	yes	complemented
256	#4027	C₂³	1	12	yes	complemented
257	D₅×C₂²⋊C₄	C₂³	1	6	yes	—
258	D₅×C₂²⋊C₄	C₂³	1	6	yes	—
259	D₅×C₂²⋊C₄	C₂³	1	12	yes	—
260	D₅×C₂²⋊C₄	C₂³	1	12	yes	—
261	D₅×C₂²⋊C₄	C₂³	1	12	yes	—
262	#4025	C₂³	1	12	yes	complemented
263	#4025	C₂³	1	12	yes	complemented
264	#4025	C₂³	1	12	yes	complemented
265	#4024	C₂³	1	12	yes	complemented
266	#4024	C₂³	1	12	yes	complemented
267	#4024	C₂³	1	12	yes	complemented
268	#4023	C₂³	1	6	yes	complemented
269	#4023	C₂³	1	6	yes	complemented
270	#4022	C₂³	1	12	yes	complemented
271	#4021	C₂³	1	3	yes	—
272	#4021	C₂³	1	6	yes	—
273	#4021	C₂³	1	3	yes	complemented
274	#4020	C₂³	1	3	yes	—
275	C₄×D₂₀	C₂³	1	6	yes	—
276	C₄×D₂₀	C₂³	1	12	yes	complemented
277	#4018	C₂³	1	12	yes	complemented
278	C₄²×D₅	C₂³	1	3	yes	—
279	C₄²×D₅	C₂³	1	6	yes	—
280	C₄²×D₅	C₂³	1	3	yes	—
281	C₄²×D₅	C₂³	1	3	yes	complemented
282	C₄²×D₅	C₂³	1	6	yes	complemented
283	C₄²×D₅	C₂³	1	3	yes	complemented
284	#4016	C₂³	1	6	yes	complemented
285	#4015	C₂³	1	3	yes	complemented
286	C₄×Dic₁₀	C₂³	1	6	yes	complemented
287	#3529	—	5	3	no	—
288	#3529	—	5	6	no	—
289	#3529	—	5	1	no	—
290	#3529	—	5	6	no	—
291	#3529	—	5	3	no	—
292	#3529	—	5	6	no	—
293	#3529	—	5	6	no	—
294	#3529	D₅	1	1	yes	characteristic, direct product factor
295	C₂×#563	—	5	3	no	—
296	C₂×#562	—	5	6	no	—
297	C₂×H(3,𝔽₄)	—	5	1	no	—
298	C₂×#560	—	5	6	no	—
299	C₂×#532	—	5	3	no	—
300	C₂×#529	—	5	6	no	—
301	C₂×#525	—	5	6	no	—
302	C₂⁴×C₅	C₂⁴	1	2	yes	—
303	C₂³×D₅	—	4	4	no	—
304	C₂³×D₅	—	4	8	no	—
305	C₂³×D₅	C₂⁴	1	3	yes	—
306	C₂³×D₅	C₂⁴	1	6	yes	—
307	C₂³×D₅	C₂⁴	1	6	yes	—
308	C₅×#41	—	4	6	no	—
309	C₅×#41	—	4	2	no	—
310	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
311	C₂×C₅×Q₈	C₂⁴	1	3	yes	—
312	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
313	C₂×C₅×D₄	C₂⁴	1	6	yes	—
314	C₂×C₅×D₄	C₂⁴	1	12	yes	—
315	C₂×C₅×D₄	C₂⁴	1	3	yes	—
316	C₂×C₅×D₄	C₂⁴	1	6	yes	—
317	C₂×C₅×D₄	C₂⁴	1	3	yes	—
318	C₂²×C₄×C₅	—	4	4	no	—
319	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
321	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
322	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
323	C₂×C₂²⋊D₅	C₂⁴	1	6	yes	—
324	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
325	C₂×C₂²⋊D₅	C₂⁴	1	6	yes	—
326	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
327	C₂×C₂²⋊D₅	C₂⁴	1	6	yes	—
328	C₂×C₂²⋊D₅	C₂⁴	1	6	yes	—
329	C₂×C₂²⋊D₅	C₂⁴	1	12	yes	—
330	C₂²×Dic₅	—	4	4	no	—
331	C₂²×Dic₅	C₂⁴	1	6	yes	—
332	C₂²×Dic₅	C₂⁴	1	3	yes	—
333	C₂²×Dic₅	C₂⁴	1	6	yes	—
334	C₂²×Dic₅	C₂⁴	1	6	yes	—
335	#713	—	4	6	no	—
336	#713	—	4	2	no	—
337	Q₈×D₅	—	4	4	no	—
338	Q₈×D₅	—	4	6	no	—
339	Q₈×D₅	—	4	2	no	—
340	#711	—	4	12	no	—
341	#711	—	4	6	no	—
342	#711	—	4	6	no	—
343	D₄×D₅	—	4	24	no	—
344	D₄×D₅	—	4	12	no	—
345	D₄×D₅	—	4	12	no	—
346	D₄×D₅	—	4	6	no	—
347	D₄×D₅	—	4	6	no	—
348	#709	—	4	6	no	—
349	#709	—	4	12	no	—
350	#709	—	4	6	no	—
351	C₂×D₂₀	C₂⁴	1	3	yes	—
352	C₂×D₂₀	C₂⁴	1	6	yes	—
353	C₂×D₂₀	C₂⁴	1	3	yes	—
354	C₂×D₂₀	C₂⁴	1	6	yes	—
355	C₂×D₂₀	C₂⁴	1	12	yes	—
356	C₂×C₄×D₅	—	2	24	no	—
357	C₂×C₄×D₅	—	2	12	no	—
358	C₂×C₄×D₅	—	4	12	no	—
359	C₂×C₄×D₅	—	4	12	no	—
360	C₂×C₄×D₅	—	4	12	no	—
361	C₂×C₄×D₅	—	4	12	no	—
362	C₂×C₄×D₅	C₂⁴	1	6	yes	—
363	C₂×C₄×D₅	C₂⁴	1	6	yes	—
364	C₂×C₄×D₅	C₂⁴	1	6	yes	—
365	C₂×C₄×D₅	C₂⁴	1	3	yes	—
366	C₂×C₄×D₅	C₂⁴	1	3	yes	—
367	C₂×C₄×D₅	C₂⁴	1	6	yes	—
368	C₂×C₄×D₅	C₂⁴	1	6	yes	—
369	C₂×C₄×D₅	C₂⁴	1	3	yes	—
370	C₂×C₄×D₅	C₂⁴	1	12	yes	—
371	C₂×C₄×D₅	C₂⁴	1	6	yes	—
372	C₂×C₄×D₅	C₂⁴	1	6	yes	—
373	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₁₀	C₂⁴	1	3	yes	—
375	C₂×Dic₁₀	C₂⁴	1	6	yes	—
376	C₂×Dic₁₀	C₂⁴	1	3	yes	—
377	C₂×Dic₁₀	C₂⁴	1	6	yes	—
378	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
379	C₅×C₄⋊C₄	C₂⁴	1	6	yes	—
380	C₅×C₄⋊C₄	C₂⁴	1	12	yes	—
381	C₅×C₄⋊C₄	C₂⁴	1	6	yes	—
382	C₅×C₂²⋊C₄	C₂⁴	1	6	yes	—
383	C₅×C₂²⋊C₄	C₂⁴	1	6	yes	—
384	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	—
385	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	—
386	C₅×C₂²⋊C₄	C₂⁴	1	12	yes	—
387	C₄²×C₅	C₂⁴	1	6	yes	—
388	C₄²×C₅	C₂⁴	1	3	yes	—
389	C₄²×C₅	C₂⁴	1	3	yes	—
390	C₂²⋊Dic₅	C₂⁴	1	6	yes	—
391	C₂²⋊Dic₅	C₂⁴	1	12	yes	—
392	C₂²⋊Dic₅	C₂⁴	1	6	yes	—
393	C₂²⋊Dic₅	C₂⁴	1	12	yes	—
394	C₂²⋊Dic₅	C₂⁴	1	12	yes	—
395	#685	C₂⁴	1	12	yes	—
396	#685	C₂⁴	1	12	yes	—
397	#685	C₂⁴	1	12	yes	—
398	#685	C₂⁴	1	12	yes	—
399	#685	C₂⁴	1	12	yes	—
400	#685	C₂⁴	1	12	yes	—
401	#685	C₂⁴	1	12	yes	—
402	#685	C₂⁴	1	12	yes	—
403	C₄⋊Dic₅	C₂⁴	1	6	yes	—
404	C₄⋊Dic₅	C₂⁴	1	12	yes	—
405	C₄⋊Dic₅	C₂⁴	1	6	yes	—
406	C₄⋊Dic₅	C₂⁴	1	12	yes	—
407	#683	C₂⁴	1	12	yes	—
408	#683	C₂⁴	1	12	yes	—
409	#683	C₂⁴	1	12	yes	—
410	#683	C₂⁴	1	12	yes	—
411	#683	C₂⁴	1	12	yes	—
412	#683	C₂⁴	1	12	yes	—
413	C₄×Dic₅	C₂⁴	1	6	yes	—
414	C₄×Dic₅	C₂⁴	1	6	yes	—
415	C₄×Dic₅	C₂⁴	1	6	yes	—
416	C₄×Dic₅	C₂⁴	1	6	yes	—
417	C₄×Dic₅	C₂⁴	1	3	yes	—
418	C₄×Dic₅	C₂⁴	1	6	yes	—
419	C₄×Dic₅	C₂⁴	1	3	yes	—
420	C₂²×#41	—	5	3	no	—
421	C₂²×#41	—	5	1	no	—
422	C₂⁴×C₄	—	5	2	no	—
423	#563	—	5	6	no	—
424	#563	—	5	12	no	—
425	#563	—	5	6	no	—
426	#563	—	5	3	no	—
427	#563	—	5	6	no	—
428	#563	—	5	12	no	—
429	#563	C₂×D₅	1	3	yes	complemented
430	#562	—	5	6	no	—
431	#562	—	5	6	no	—
432	#562	—	5	6	no	—
433	#562	—	5	12	no	—
434	#562	—	5	12	no	—
435	#562	—	5	12	no	—
436	#562	—	5	12	no	—
437	#562	—	5	12	no	—
438	#562	—	5	12	no	—
439	#562	C₂×D₅	1	6	yes	complemented
440	H(3,𝔽₄)	—	5	6	no	—
441	H(3,𝔽₄)	—	5	3	no	—
442	H(3,𝔽₄)	—	5	6	no	—
443	H(3,𝔽₄)	C₂×D₅	1	1	yes	characteristic, complemented
444	#560	—	5	6	no	—
445	#560	—	5	12	no	—
446	#560	—	5	6	no	—
447	#560	—	5	12	no	—
448	#560	—	5	12	no	—
449	#560	—	5	12	no	—
450	#560	—	5	12	no	—
451	#560	—	5	6	no	—
452	#560	—	5	12	no	—
453	#560	C₂×D₅	1	6	yes	complemented
454	#532	—	5	3	no	—
455	#532	—	5	3	no	—
456	#532	—	5	3	no	—
457	#532	—	5	3	no	—
458	#532	—	5	3	no	—
459	#532	—	5	3	no	—
460	#532	—	5	12	no	—
461	#532	—	5	12	no	—
462	#532	—	5	3	no	—
463	#532	C₂×D₅	1	3	yes	complemented
464	C₂×C₄⋊Q₈	—	5	3	no	—
465	C₂×#127	—	5	3	no	—
466	#529	—	5	12	no	—
467	#529	—	5	6	no	—
468	#529	—	5	6	no	—
469	#529	—	5	12	no	—
470	#529	—	5	6	no	—
471	#529	—	5	6	no	—
472	#529	—	5	6	no	—
473	#529	—	5	6	no	—
474	#529	—	5	12	no	—
475	#529	—	5	12	no	—
476	#529	—	5	6	no	—
477	#529	C₂×D₅	1	6	yes	complemented
478	C₂×#126	—	5	12	no	—
479	C₂×#125	—	5	6	no	—
480	C₂×#124	—	5	6	no	—
481	C₂×#124	—	5	3	no	—
482	C₂×#124	—	5	3	no	—
483	#525	—	5	6	no	—
484	#525	—	5	6	no	—
485	#525	—	5	6	no	—
486	#525	—	5	6	no	—
487	#525	—	5	12	no	—
488	#525	—	5	12	no	—
489	#525	—	5	6	no	—
490	#525	—	5	6	no	—
491	#525	—	5	12	no	—
492	#525	—	5	12	no	—
493	#525	—	5	6	no	—
494	#525	C₂×D₅	1	6	yes	complemented
495	C₂×#123	—	5	6	no	—
496	C₂×#123	—	5	6	no	—
497	C₂×#123	—	5	12	no	—
498	C₂×C₂²⋊Q₈	—	5	12	no	—
499	C₂×C₂²⋊Q₈	—	5	6	no	—
500	C₂×#121	—	5	12	no	—
501	C₂×#121	—	5	6	no	—
502	C₂×#121	—	5	12	no	—
503	C₂×#120	—	5	6	no	—
504	C₂×#120	—	5	6	no	—
505	C₂×C₄×Q₈	—	5	2	no	—
506	C₂×C₄×D₄	—	5	6	no	—
507	C₂×C₄×D₄	—	5	12	no	—
508	C₂×#117	—	5	6	no	—
509	C₂²×C₄²	—	5	3	no	—
510	C₂³×C₅	—	4	2	no	—
511	C₂³×C₅	—	4	4	no	—
512	C₂³×C₅	C₂⁵	1	6	yes	—
513	C₂³×C₅	C₂⁵	1	3	yes	—
514	C₂²×D₅	—	2	12	no	—
515	C₂²×D₅	—	2	6	no	—
516	C₂²×D₅	—	2	12	no	—
517	C₂²×D₅	—	2	24	no	—
518	C₂²×D₅	—	4	6	no	—
519	C₂²×D₅	—	4	12	no	—
520	C₂²×D₅	—	4	32	no	—
521	C₂²×D₅	C₂⁵	1	6	yes	—
522	C₂²×D₅	C₂⁵	1	3	yes	—
523	C₂²×D₅	C₂⁵	1	1	yes	characteristic
524	C₅×Q₈	—	4	1	no	—
525	C₅×Q₈	—	4	3	no	—
526	C₅×Q₈	—	4	2	no	—
527	C₅×D₄	—	4	3	no	—
528	C₅×D₄	—	4	3	no	—
529	C₅×D₄	—	4	6	no	—
530	C₅×D₄	—	4	6	no	—
531	C₅×D₄	—	4	12	no	—
532	C₂×C₄×C₅	—	2	12	no	—
533	C₂×C₄×C₅	—	2	6	no	—
534	C₂×C₄×C₅	—	4	6	no	—
535	C₂×C₄×C₅	—	4	6	no	—
536	C₂×C₄×C₅	C₂⁵	1	6	yes	—
537	C₂×C₄×C₅	C₂⁵	1	3	yes	—
538	C₂×C₄×C₅	C₂⁵	1	6	yes	—
539	C₂×C₄×C₅	C₂⁵	1	6	yes	—
540	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
541	C₂²⋊D₅	—	4	6	no	—
542	C₂²⋊D₅	—	4	6	no	—
543	C₂²⋊D₅	—	4	6	no	—
544	C₂²⋊D₅	—	4	6	no	—
545	C₂²⋊D₅	—	4	12	no	—
546	C₂²⋊D₅	—	4	12	no	—
547	C₂²⋊D₅	—	4	12	no	—
548	C₂×Dic₅	—	2	12	no	—
549	C₂×Dic₅	—	2	6	no	—
550	C₂×Dic₅	—	4	6	no	—
551	C₂×Dic₅	—	4	6	no	—
552	C₂×Dic₅	C₂⁵	1	6	yes	—
553	C₂×Dic₅	C₂⁵	1	6	yes	—
554	C₂×Dic₅	C₂⁵	1	3	yes	—
555	C₂×Dic₅	C₂⁵	1	6	yes	—
556	C₂×Dic₅	C₂⁵	1	1	yes	characteristic
557	D₂₀	—	4	3	no	—
558	D₂₀	—	4	3	no	—
559	D₂₀	—	4	6	no	—
560	D₂₀	—	4	6	no	—
561	D₂₀	—	4	12	no	—
562	C₄×D₅	—	2	12	no	—
563	C₄×D₅	—	2	6	no	—
564	C₄×D₅	—	2	12	no	—
565	C₄×D₅	—	2	12	no	—
566	C₄×D₅	—	2	12	no	—
567	C₄×D₅	—	2	6	no	—
568	C₄×D₅	—	2	12	no	—
569	C₄×D₅	—	2	6	no	—
570	C₄×D₅	—	4	12	no	—
571	C₄×D₅	—	4	6	no	—
572	C₄×D₅	—	4	6	no	—
573	C₄×D₅	H(5,𝔽₂)	1	4	yes	—
574	Dic₁₀	—	4	3	no	—
575	Dic₁₀	—	4	6	no	—
576	Dic₁₀	—	4	3	no	—
577	Dic₁₀	—	4	6	no	—
578	C₂⁵	—	5	2	no	—
579	C₂×#41	—	5	3	no	—
580	C₂×#41	—	5	1	no	—
581	C₂×#41	—	5	6	no	—
582	C₂×#41	—	5	3	no	—
583	C₂×#41	—	5	3	no	—
584	C₂×#41	—	5	6	no	—
585	C₂×#41	—	5	3	no	—
586	C₂×#41	—	5	3	no	—
587	C₂×#41	—	20	12	no	—
588	C₂×#41	—	20	4	no	—
589	C₂×#41	C₂²×D₅	1	3	yes	—
590	C₂×#41	C₂²×D₅	1	1	yes	characteristic, complemented
591	C₂²×Q₈	—	5	2	no	—
592	C₂²×Q₈	—	5	3	no	—
593	C₂²×Q₈	—	5	1	no	—
594	C₂²×D₄	—	5	6	no	—
595	C₂²×D₄	—	5	12	no	—
596	C₂²×D₄	—	5	3	no	—
597	C₂²×D₄	—	5	6	no	—
598	C₂²×D₄	—	5	3	no	—
599	C₂³×C₄	—	5	2	no	—
600	C₂³×C₄	—	5	6	no	—
601	C₂³×C₄	—	5	3	no	—
602	C₂³×C₄	—	5	6	no	—
603	C₂³×C₄	—	5	6	no	—
604	C₂³×C₄	—	5	6	no	—
605	C₂³×C₄	—	5	6	no	—
606	C₂³×C₄	—	20	8	no	—
607	C₂³×C₄	C₂²×D₅	1	2	yes	complemented
608	C₄⋊Q₈	—	5	3	no	—
609	C₄⋊Q₈	—	5	3	no	—
610	C₄⋊Q₈	—	5	12	no	—
611	C₄⋊Q₈	—	5	3	no	—
612	C₄⋊Q₈	C₂²×D₅	1	3	yes	complemented
613	#127	—	5	3	no	—
614	#127	—	5	3	no	—
615	#127	—	5	12	no	—
616	#127	—	5	3	no	—
617	#127	C₂²×D₅	1	3	yes	—
618	#126	—	5	12	no	—
619	#126	—	5	12	no	—
620	#126	—	5	12	no	—
621	#126	—	5	12	no	—
622	#126	—	5	12	no	—
623	#126	—	5	12	no	—
624	#126	—	5	12	no	—
625	#126	C₂²×D₅	1	12	yes	complemented
626	#125	—	5	12	no	—
627	#125	—	5	12	no	—
628	#125	—	5	6	no	—
629	#125	—	5	6	no	—
630	#125	—	5	6	no	—
631	#125	C₂²×D₅	1	6	yes	complemented
632	#124	—	5	6	no	—
633	#124	—	5	3	no	—
634	#124	—	5	3	no	—
635	#124	—	5	6	no	—
636	#124	—	5	3	no	—
637	#124	—	5	3	no	—
638	#124	—	5	12	no	—
639	#124	—	5	12	no	—
640	#124	—	5	12	no	—
641	#124	—	5	12	no	—
642	#124	—	5	6	no	—
643	#124	—	5	3	no	—
644	#124	—	5	3	no	—
645	#124	C₂²×D₅	1	6	yes	—
646	#124	C₂²×D₅	1	3	yes	—
647	#124	C₂²×D₅	1	3	yes	complemented
648	#123	—	5	6	no	—
649	#123	—	5	6	no	—
650	#123	—	5	12	no	—
651	#123	—	5	6	no	—
652	#123	—	5	6	no	—
653	#123	—	5	12	no	—
654	#123	—	5	12	no	—
655	#123	—	5	12	no	—
656	#123	—	5	12	no	—
657	#123	—	5	12	no	—
658	#123	—	5	12	no	—
659	#123	—	5	6	no	—
660	#123	—	5	12	no	—
661	#123	—	5	6	no	—
662	#123	—	5	12	no	—
663	#123	—	5	12	no	—
664	#123	—	5	12	no	—
665	#123	C₂²×D₅	1	6	yes	—
666	#123	C₂²×D₅	1	6	yes	complemented
667	#123	C₂²×D₅	1	12	yes	complemented
668	C₂²⋊Q₈	—	5	12	no	—
669	C₂²⋊Q₈	—	5	6	no	—
670	C₂²⋊Q₈	—	5	12	no	—
671	C₂²⋊Q₈	—	5	6	no	—
672	C₂²⋊Q₈	—	5	12	no	—
673	C₂²⋊Q₈	—	5	12	no	—
674	C₂²⋊Q₈	—	5	12	no	—
675	C₂²⋊Q₈	—	5	12	no	—
676	C₂²⋊Q₈	—	5	6	no	—
677	C₂²⋊Q₈	—	5	12	no	—
678	C₂²⋊Q₈	—	5	12	no	—
679	C₂²⋊Q₈	—	5	12	no	—
680	C₂²⋊Q₈	C₂²×D₅	1	12	yes	complemented
681	C₂²⋊Q₈	C₂²×D₅	1	6	yes	complemented
682	#121	—	5	12	no	—
683	#121	—	5	12	no	—
684	#121	—	5	12	no	—
685	#121	—	5	6	no	—
686	#121	—	5	12	no	—
687	#121	—	5	12	no	—
688	#121	—	5	12	no	—
689	#121	—	5	12	no	—
690	#121	—	5	12	no	—
691	#121	—	5	6	no	—
692	#121	—	5	12	no	—
693	#121	—	5	12	no	—
694	#121	—	5	6	no	—
695	#121	—	5	12	no	—
696	#121	—	5	12	no	—
697	#121	—	5	12	no	—
698	#121	—	5	12	no	—
699	#121	—	5	12	no	—
700	#121	—	5	12	no	—
701	#121	C₂²×D₅	1	12	yes	—
702	#121	C₂²×D₅	1	6	yes	—
703	#121	C₂²×D₅	1	12	yes	complemented
704	#120	—	5	6	no	—
705	#120	—	5	6	no	—
706	#120	—	5	6	no	—
707	#120	—	5	12	no	—
708	#120	—	5	6	no	—
709	#120	—	5	12	no	—
710	#120	—	5	12	no	—
711	#120	—	5	6	no	—
712	#120	—	5	12	no	—
713	#120	—	5	6	no	—
714	#120	C₂²×D₅	1	6	yes	—
715	#120	C₂²×D₅	1	6	yes	complemented
716	C₄×Q₈	—	5	2	no	—
717	C₄×Q₈	—	5	6	no	—
718	C₄×Q₈	—	5	6	no	—
719	C₄×Q₈	C₂²×D₅	1	2	yes	complemented
720	C₄×D₄	—	5	6	no	—
721	C₄×D₄	—	5	12	no	—
722	C₄×D₄	—	5	12	no	—
723	C₄×D₄	—	5	12	no	—
724	C₄×D₄	—	5	12	no	—
725	C₄×D₄	—	5	6	no	—
726	C₄×D₄	—	5	12	no	—
727	C₄×D₄	—	5	12	no	—
728	C₄×D₄	—	5	12	no	—
729	C₄×D₄	—	5	12	no	—
730	C₄×D₄	—	5	6	no	—
731	C₄×D₄	—	5	12	no	—
732	C₄×D₄	C₂²×D₅	1	6	yes	—
733	C₄×D₄	C₂²×D₅	1	12	yes	complemented
734	#117	—	5	6	no	—
735	#117	—	5	12	no	—
736	#117	—	5	6	no	—
737	#117	—	5	6	no	—
738	#117	—	5	12	no	—
739	#117	C₂²×D₅	1	6	yes	complemented
740	C₂×C₄⋊C₄	—	5	12	no	—
741	C₂×C₄⋊C₄	—	5	12	no	—
742	C₂×C₄⋊C₄	—	5	6	no	—
743	C₂×C₄⋊C₄	—	5	6	no	—
744	C₂×C₂²⋊C₄	—	5	6	no	—
745	C₂×C₂²⋊C₄	—	5	6	no	—
746	C₂×C₂²⋊C₄	—	5	12	no	—
747	C₂×C₂²⋊C₄	—	5	12	no	—
748	C₂×C₂²⋊C₄	—	5	12	no	—
749	C₂×C₄²	—	5	6	no	—
750	C₂×C₄²	—	5	3	no	—
751	C₂×C₄²	—	5	6	no	—
752	C₂×C₄²	—	5	3	no	—
753	C₂×C₄²	—	5	3	no	—
754	C₂×C₄²	—	5	3	no	—
755	C₂×C₄²	—	5	3	no	—
756	C₂×C₄²	—	5	6	no	—
757	C₂×C₄²	C₂²×D₅	1	3	yes	complemented
758	C₂²×C₅	—	2	6	no	—
759	C₂²×C₅	—	2	3	no	—
760	C₂²×C₅	—	2	6	no	—
761	C₂²×C₅	—	2	12	no	—
762	C₂²×C₅	—	4	8	no	—
763	C₂²×C₅	C₂⁶	1	1	yes	characteristic
764	C₂×D₅	—	2	6	no	—
765	C₂×D₅	—	2	3	no	—
766	C₂×D₅	—	2	6	no	—
767	C₂×D₅	—	2	12	no	—
768	C₂×D₅	—	4	24	no	—
769	C₂×D₅	—	4	12	no	—
770	C₂×D₅	—	4	24	no	—
771	C₂×D₅	C₂×H(5,𝔽₂)	1	2	yes	—
772	C₂×D₅	#585	1	4	yes	—
773	C₄×C₅	—	2	3	no	—
774	C₄×C₅	—	2	6	no	—
775	C₄×C₅	—	2	6	no	—
776	C₄×C₅	—	2	6	no	—
777	C₄×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
778	Dic₅	—	2	3	no	—
779	Dic₅	—	2	6	no	—
780	Dic₅	—	2	6	no	—
781	Dic₅	—	2	6	no	—
782	Dic₅	C₂×H(5,𝔽₂)	1	2	yes	—
783	C₂⁴	—	5	6	no	—
784	C₂⁴	—	5	3	no	—
785	C₂⁴	—	5	6	no	—
786	C₂⁴	—	20	4	no	—
787	C₂⁴	—	20	8	no	—
788	C₂⁴	C₂³×D₅	1	2	yes	—
789	#41	—	4	6	no	—
790	#41	—	4	2	no	—
791	#41	—	20	12	no	—
792	#41	—	20	6	no	—
793	#41	—	20	6	no	—
794	#41	—	20	12	no	—
795	#41	—	20	6	no	—
796	#41	—	20	6	no	—
797	#41	—	20	6	no	—
798	#41	—	20	2	no	—
799	C₂×Q₈	—	5	6	no	—
800	C₂×Q₈	—	5	6	no	—
801	C₂×Q₈	—	5	3	no	—
802	C₂×Q₈	—	5	3	no	—
803	C₂×Q₈	—	20	6	no	—
804	C₂×Q₈	—	20	2	no	—
805	C₂×Q₈	—	20	4	no	—
806	C₂×Q₈	C₂³×D₅	1	2	yes	—
807	C₂×Q₈	C₂³×D₅	1	3	yes	—
808	C₂×Q₈	C₂³×D₅	1	1	yes	characteristic
809	C₂×D₄	—	5	12	no	—
810	C₂×D₄	—	5	12	no	—
811	C₂×D₄	—	5	12	no	—
812	C₂×D₄	—	5	6	no	—
813	C₂×D₄	—	5	6	no	—
814	C₂×D₄	—	5	6	no	—
815	C₂×D₄	—	5	6	no	—
816	C₂×D₄	—	5	6	no	—
817	C₂×D₄	—	5	12	no	—
818	C₂×D₄	—	5	3	no	—
819	C₂×D₄	—	5	6	no	—
820	C₂×D₄	—	5	3	no	—
821	C₂×D₄	—	20	12	no	—
822	C₂×D₄	—	20	6	no	—
823	C₂×D₄	—	20	6	no	—
824	C₂×D₄	—	20	24	no	—
825	C₂×D₄	—	20	12	no	—
826	C₂×D₄	C₂³×D₅	1	6	yes	—
827	C₂×D₄	C₂³×D₅	1	12	yes	—
828	C₂×D₄	C₂³×D₅	1	3	yes	—
829	C₂×D₄	C₂³×D₅	1	6	yes	—
830	C₂×D₄	C₂³×D₅	1	3	yes	—
831	C₂²×C₄	—	4	4	no	—
832	C₂²×C₄	—	5	1	no	—
833	C₂²×C₄	—	5	3	no	—
834	C₂²×C₄	—	5	6	no	—
835	C₂²×C₄	—	5	6	no	—
836	C₂²×C₄	—	5	6	no	—
837	C₂²×C₄	—	5	6	no	—
838	C₂²×C₄	—	5	6	no	—
839	C₂²×C₄	—	5	3	no	—
840	C₂²×C₄	—	5	3	no	—
841	C₂²×C₄	—	5	6	no	—
842	C₂²×C₄	—	5	6	no	—
843	C₂²×C₄	—	5	3	no	—
844	C₂²×C₄	—	5	6	no	—
845	C₂²×C₄	—	5	6	no	—
846	C₂²×C₄	—	5	6	no	—
847	C₂²×C₄	—	5	12	no	—
848	C₂²×C₄	—	10	24	no	—
849	C₂²×C₄	—	10	12	no	—
850	C₂²×C₄	—	20	12	no	—
851	C₂²×C₄	—	20	12	no	—
852	C₂²×C₄	—	20	12	no	—
853	C₂²×C₄	—	20	12	no	—
854	C₂²×C₄	—	20	4	no	—
855	C₂²×C₄	C₂³×D₅	1	3	yes	—
856	C₂²×C₄	C₂³×D₅	1	6	yes	—
857	C₂²×C₄	C₂³×D₅	1	6	yes	—
858	C₂²×C₄	C₂³×D₅	1	6	yes	—
859	C₄⋊C₄	—	5	12	no	—
860	C₄⋊C₄	—	5	12	no	—
861	C₄⋊C₄	—	5	12	no	—
862	C₄⋊C₄	—	5	12	no	—
863	C₄⋊C₄	—	5	12	no	—
864	C₄⋊C₄	—	5	12	no	—
865	C₄⋊C₄	—	5	12	no	—
866	C₄⋊C₄	—	5	6	no	—
867	C₄⋊C₄	—	5	12	no	—
868	C₄⋊C₄	—	5	6	no	—
869	C₄⋊C₄	C₂³×D₅	1	12	yes	—
870	C₄⋊C₄	C₂³×D₅	1	6	yes	—
871	C₄⋊C₄	C₂³×D₅	1	12	yes	—
872	C₄⋊C₄	C₂³×D₅	1	6	yes	—
873	C₂²⋊C₄	—	5	6	no	—
874	C₂²⋊C₄	—	5	6	no	—
875	C₂²⋊C₄	—	5	12	no	—
876	C₂²⋊C₄	—	5	12	no	—
877	C₂²⋊C₄	—	5	12	no	—
878	C₂²⋊C₄	—	5	12	no	—
879	C₂²⋊C₄	—	5	12	no	—
880	C₂²⋊C₄	—	5	12	no	—
881	C₂²⋊C₄	—	5	12	no	—
882	C₂²⋊C₄	—	5	12	no	—
883	C₂²⋊C₄	—	5	12	no	—
884	C₂²⋊C₄	—	5	12	no	—
885	C₂²⋊C₄	—	5	12	no	—
886	C₂²⋊C₄	C₂³×D₅	1	6	yes	—
887	C₂²⋊C₄	C₂³×D₅	1	6	yes	—
888	C₂²⋊C₄	C₂³×D₅	1	12	yes	—
889	C₂²⋊C₄	C₂³×D₅	1	12	yes	—
890	C₂²⋊C₄	C₂³×D₅	1	12	yes	—
891	C₄²	—	5	6	no	—
892	C₄²	—	5	6	no	—
893	C₄²	—	5	3	no	—
894	C₄²	—	5	6	no	—
895	C₄²	—	5	3	no	—
896	C₄²	—	5	6	no	—
897	C₄²	—	5	6	no	—
898	C₄²	C₂³×D₅	1	3	yes	—
899	C₄²	C₂³×D₅	1	3	yes	—
900	C₄²	C₂³×D₅	1	6	yes	—
901	C₂×C₅	—	4	6	no	—
902	C₂×C₅	—	4	3	no	—
903	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
904	C₂×C₅	C₂×#585	1	2	yes	—
905	D₅	—	4	3	no	—
906	D₅	—	4	6	no	—
907	D₅	#3529	1	4	yes	direct product factor
908	C₂³	—	4	2	no	—
909	C₂³	—	4	4	no	—
910	C₂³	—	5	1	no	—
911	C₂³	—	5	6	no	—
912	C₂³	—	5	3	no	—
913	C₂³	—	10	12	no	—
914	C₂³	—	10	6	no	—
915	C₂³	—	10	12	no	—
916	C₂³	—	10	24	no	—
917	C₂³	—	20	6	no	—
918	C₂³	—	20	12	no	—
919	C₂³	—	20	32	no	—
920	C₂³	C₂⁴×D₅	1	6	yes	—
921	C₂³	C₂⁴×D₅	1	3	yes	—
922	Q₈	—	4	3	no	—
923	Q₈	—	4	1	no	—
924	Q₈	—	4	2	no	—
925	Q₈	—	20	6	no	—
926	Q₈	—	20	3	no	—
927	Q₈	—	20	3	no	—
928	Q₈	—	20	6	no	—
929	D₄	—	4	6	no	—
930	D₄	—	4	3	no	—
931	D₄	—	4	3	no	—
932	D₄	—	4	12	no	—
933	D₄	—	4	6	no	—
934	D₄	—	20	6	no	—
935	D₄	—	20	3	no	—
936	D₄	—	20	3	no	—
937	D₄	—	20	12	no	—
938	D₄	—	20	6	no	—
939	D₄	—	20	6	no	—
940	D₄	—	20	6	no	—
941	D₄	—	20	6	no	—
942	D₄	—	20	6	no	—
943	D₄	—	20	12	no	—
944	D₄	—	20	12	no	—
945	D₄	—	20	12	no	—
946	C₂×C₄	—	2	12	no	—
947	C₂×C₄	—	2	6	no	—
948	C₂×C₄	—	4	6	no	—
949	C₂×C₄	—	4	6	no	—
950	C₂×C₄	—	5	1	no	—
951	C₂×C₄	—	5	4	no	—
952	C₂×C₄	—	5	6	no	—
953	C₂×C₄	—	5	6	no	—
954	C₂×C₄	—	5	3	no	—
955	C₂×C₄	—	5	6	no	—
956	C₂×C₄	—	10	12	no	—
957	C₂×C₄	—	10	6	no	—
958	C₂×C₄	—	10	12	no	—
959	C₂×C₄	—	10	6	no	—
960	C₂×C₄	—	10	12	no	—
961	C₂×C₄	—	10	12	no	—
962	C₂×C₄	—	10	12	no	—
963	C₂×C₄	—	10	6	no	—
964	C₂×C₄	—	10	12	no	—
965	C₂×C₄	—	10	6	no	—
966	C₂×C₄	—	20	12	no	—
967	C₂×C₄	—	20	6	no	—
968	C₂×C₄	—	20	6	no	—
969	C₂×C₄	—	20	6	no	—
970	C₂×C₄	—	20	6	no	—
971	C₂×C₄	C₂⁴×D₅	1	6	yes	—
972	C₂×C₄	C₂⁴×D₅	1	6	yes	—
973	C₂×C₄	C₂⁴×D₅	1	3	yes	—
974	C₂×C₄	C₂⁴×D₅	1	6	yes	—
975	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
976	C₅	C₂×#3529	1	1	yes	characteristic, complemented, Sylow
977	C₂²	—	2	6	no	—
978	C₂²	—	2	3	no	—
979	C₂²	—	2	6	no	—
980	C₂²	—	2	12	no	—
981	C₂²	—	4	8	no	—
982	C₂²	—	5	2	no	—
983	C₂²	—	5	4	no	—
984	C₂²	—	10	6	no	—
985	C₂²	—	10	3	no	—
986	C₂²	—	10	6	no	—
987	C₂²	—	10	12	no	—
988	C₂²	—	20	24	no	—
989	C₂²	—	20	12	no	—
990	C₂²	—	20	24	no	—
991	C₂²	C₂⁵×D₅	1	1	yes	characteristic
992	C₄	—	2	6	no	—
993	C₄	—	2	3	no	—
994	C₄	—	2	6	no	—
995	C₄	—	2	6	no	—
996	C₄	—	5	2	no	—
997	C₄	—	10	6	no	—
998	C₄	—	10	3	no	—
999	C₄	—	10	6	no	—
1000	C₄	—	10	6	no	—
1001	C₄	D₅×H(5,𝔽₂)	1	2	yes	—
1002	C₂	—	4	6	no	—
1003	C₂	—	4	3	no	—
1004	C₂	—	5	4	no	—
1005	C₂	—	20	6	no	—
1006	C₂	—	20	3	no	—
1007	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic
1008	C₂	D₅×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₅×#3529	C₂
hypercenter	#3529	D₅
hypocenter	C₅	C₂×#3529
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #3529

Complements

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

N	H ≅ G/N	type
1. C₅×#3529	C₂	semidirect
2. D₅×#563	C₂	semidirect
3. #10619016	C₂	semidirect
4. D₅×#562	C₂	semidirect
5. #10618994	C₂	semidirect
6. D₅×H(3,𝔽₄)	C₂	semidirect
7. #10618986	C₂	semidirect
8. D₅×#560	C₂	semidirect
9. #10618971	C₂	semidirect
10. #10618149	C₂	semidirect
11. D₅×#532	C₂	semidirect
12. #10618072	C₂	semidirect
13. D₅×#529	C₂	semidirect
14. #10617949	C₂	semidirect
15. D₅×#525	C₂	semidirect
17. C₂×D₅×#41	C₂²	semidirect
18. C₂³×C₄×D₅	C₂²	semidirect
19. C₅×#563	C₂²	semidirect
20. C₅×#562	C₂²	semidirect
21. C₅×H(3,𝔽₄)	C₂²	semidirect
22. C₅×#560	C₂²	semidirect
23. C₅×#532	C₂²	semidirect
24. C₅×#529	C₂²	semidirect
25. C₅×#525	C₂²	semidirect
26. #66166	C₂²	semidirect
27. #66166	C₂²	semidirect
28. #66162	C₂²	semidirect
29. #66125	C₂²	semidirect
30. #66069	C₂²	semidirect
31. #66059	C₂²	semidirect
32. D₅×C₄⋊Q₈	C₂²	semidirect
33. #66054	C₂²	semidirect
34. #66050	C₂²	semidirect
36. #66046	C₂²	semidirect
37. #66045	C₂²	semidirect
38. #66040	C₂²	semidirect
39. D₅×#126	C₂²	semidirect
40. #66034	C₂²	semidirect
41. #66033	C₂²	semidirect
42. #66025	C₂²	semidirect
43. D₅×#125	C₂²	semidirect
44. #66018	C₂²	semidirect
45. #66018	C₂²	semidirect
46. #66017	C₂²	semidirect
47. #66017	C₂²	semidirect
48. #66014	C₂²	semidirect
51. D₅×#124	C₂²	semidirect
52. #66006	C₂²	semidirect
53. #66002	C₂²	semidirect
54. #66002	C₂²	semidirect
55. #66001	C₂²	semidirect
56. #66001	C₂²	semidirect
57. #66000	C₂²	semidirect
58. #66000	C₂²	semidirect
59. #65990	C₂²	semidirect
60. #65990	C₂²	semidirect
62. D₅×#123	C₂²	semidirect
63. D₅×#123	C₂²	semidirect
64. #65985	C₂²	semidirect
65. #65983	C₂²	semidirect
66. #65981	C₂²	semidirect
67. #65981	C₂²	semidirect
68. #65980	C₂²	semidirect
69. #65961	C₂²	semidirect
70. D₅×C₂²⋊Q₈	C₂²	semidirect
71. D₅×C₂²⋊Q₈	C₂²	semidirect
72. #65958	C₂²	semidirect
73. #65955	C₂²	semidirect
74. #65955	C₂²	semidirect
75. #65954	C₂²	semidirect
76. #65954	C₂²	semidirect
77. #65954	C₂²	semidirect
78. #65940	C₂²	semidirect
81. D₅×#121	C₂²	semidirect
82. #65934	C₂²	semidirect
83. #65930	C₂²	semidirect
84. #65929	C₂²	semidirect
85. #65929	C₂²	semidirect
86. #65928	C₂²	semidirect
88. D₅×#120	C₂²	semidirect
89. #65920	C₂²	semidirect
90. #65920	C₂²	semidirect
91. #65914	C₂²	semidirect
92. C₄×Q₈×D₅	C₂²	semidirect
93. #65891	C₂²	semidirect
94. #65882	C₂²	semidirect
95. #65881	C₂²	semidirect
96. #65881	C₂²	semidirect
98. C₄×D₄×D₅	C₂²	semidirect
99. #65872	C₂²	semidirect
100. #65862	C₂²	semidirect
101. #65858	C₂²	semidirect
102. D₅×#117	C₂²	semidirect
103. #65813	C₂²	semidirect
104. #65811	C₂²	semidirect
105. C₂×C₄²×D₅	C₂²	semidirect
109. C₂×C₅×#41	C₂³	semidirect
110. C₂³×C₄×C₅	C₂³	semidirect
111. C₂³×Dic₅	C₂³	semidirect
115. C₂×#713	C₂³	semidirect
121. C₂×#711	C₂³	semidirect
129. C₂×#709	C₂³	semidirect
135. C₂²×C₄×D₅	C₂³	semidirect
136. C₂²×C₄×D₅	C₂³	semidirect
137. C₅×C₄⋊Q₈	C₂³	semidirect
139. C₅×#126	C₂³	semidirect
140. C₅×#125	C₂³	semidirect
143. C₅×#124	C₂³	semidirect
145. C₅×#123	C₂³	semidirect
146. C₅×#123	C₂³	semidirect
147. C₅×C₂²⋊Q₈	C₂³	semidirect
148. C₅×C₂²⋊Q₈	C₂³	semidirect
151. C₅×#121	C₂³	semidirect
153. C₅×#120	C₂³	semidirect
154. C₄×C₅×Q₈	C₂³	semidirect
156. C₄×C₅×D₄	C₂³	semidirect
157. C₅×#117	C₂³	semidirect
158. C₂×C₄²×C₅	C₂³	semidirect
160. #4099	C₂³	semidirect
163. #4093	C₂³	semidirect
164. #4092	C₂³	semidirect
165. #4092	C₂³	semidirect
166. Q₈×Dic₅	C₂³	semidirect
167. #4090	C₂³	semidirect
168. #4090	C₂³	semidirect
175. #4085	C₂³	semidirect
176. #4085	C₂³	semidirect
179. #4084	C₂³	semidirect
182. #4083	C₂³	semidirect
183. #4083	C₂³	semidirect
186. #4082	C₂³	semidirect
188. #4081	C₂³	semidirect
189. #4081	C₂³	semidirect
191. D₄×Dic₅	C₂³	semidirect
194. #4076	C₂³	semidirect
196. #4075	C₂³	semidirect
197. #4075	C₂³	semidirect
199. C₄×C₂²⋊D₅	C₂³	semidirect
200. C₄×C₂²⋊D₅	C₂³	semidirect
201. #4072	C₂³	semidirect
202. #4070	C₂³	semidirect
203. #4070	C₂³	semidirect
204. C₂×C₄×Dic₅	C₂³	semidirect
205. C₂×C₄×Dic₅	C₂³	semidirect
206. #4044	C₂³	semidirect
207. #4044	C₂³	semidirect
208. #4044	C₂³	semidirect
209. #4043	C₂³	semidirect
210. #4043	C₂³	semidirect
211. #4042	C₂³	semidirect
212. #4042	C₂³	semidirect
213. #4042	C₂³	semidirect
216. #4041	C₂³	semidirect
218. #4040	C₂³	semidirect
219. #4040	C₂³	semidirect
220. #4040	C₂³	semidirect
222. #4039	C₂³	semidirect
223. #4038	C₂³	semidirect
228. #4036	C₂³	semidirect
229. #4036	C₂³	semidirect
230. #4035	C₂³	semidirect
231. #4035	C₂³	semidirect
232. #4034	C₂³	semidirect
233. #4033	C₂³	semidirect
235. #4032	C₂³	semidirect
236. #4032	C₂³	semidirect
240. #4031	C₂³	semidirect
244. #4030	C₂³	semidirect
245. #4030	C₂³	semidirect
247. #4029	C₂³	semidirect
248. #4029	C₂³	semidirect
249. #4029	C₂³	semidirect
252. #4028	C₂³	semidirect
253. #4028	C₂³	semidirect
255. #4027	C₂³	semidirect
256. #4027	C₂³	semidirect
262. #4025	C₂³	semidirect
263. #4025	C₂³	semidirect
264. #4025	C₂³	semidirect
265. #4024	C₂³	semidirect
266. #4024	C₂³	semidirect
267. #4024	C₂³	semidirect
268. #4023	C₂³	semidirect
269. #4023	C₂³	semidirect
270. #4022	C₂³	semidirect
273. #4021	C₂³	semidirect
276. C₄×D₂₀	C₂³	semidirect
277. #4018	C₂³	semidirect
281. C₄²×D₅	C₂³	semidirect
282. C₄²×D₅	C₂³	semidirect
283. C₄²×D₅	C₂³	semidirect
284. #4016	C₂³	semidirect
285. #4015	C₂³	semidirect
286. C₄×Dic₁₀	C₂³	semidirect
294. #3529	D₅	direct (N × H)
429. #563	C₂×D₅	semidirect
439. #562	C₂×D₅	semidirect
443. H(3,𝔽₄)	C₂×D₅	semidirect
453. #560	C₂×D₅	semidirect
463. #532	C₂×D₅	semidirect
477. #529	C₂×D₅	semidirect
494. #525	C₂×D₅	semidirect
590. C₂×#41	C₂²×D₅	semidirect
607. C₂³×C₄	C₂²×D₅	semidirect
612. C₄⋊Q₈	C₂²×D₅	semidirect
625. #126	C₂²×D₅	semidirect
631. #125	C₂²×D₅	semidirect
647. #124	C₂²×D₅	semidirect
666. #123	C₂²×D₅	semidirect
667. #123	C₂²×D₅	semidirect
680. C₂²⋊Q₈	C₂²×D₅	semidirect
681. C₂²⋊Q₈	C₂²×D₅	semidirect
703. #121	C₂²×D₅	semidirect
715. #120	C₂²×D₅	semidirect
719. C₄×Q₈	C₂²×D₅	semidirect
733. C₄×D₄	C₂²×D₅	semidirect
739. #117	C₂²×D₅	semidirect
757. C₂×C₄²	C₂²×D₅	semidirect
907. D₅	#3529	direct (N × H)
976. C₅	C₂×#3529	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3529	2
D₅×#563	2
#10619016	2
D₅×#562	2
#10618994	2
D₅×H(3,𝔽₄)	2
#10618986	2
D₅×#560	2
#10618971	2
#10618149	2
D₅×#532	2
#10618072	2
D₅×#529	2
#10617949	2
D₅×#525	2
C₂×#3529	5

Subgroups — D5×#3529 #13006187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#3529 #13006187