Subgroups — D₅×#3584 #13013127

Order 1280.

10858 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#585	C₂	1	2	yes	maximal, complemented
2	C₅×#3584	C₂	1	1	yes	maximal, characteristic, complemented
3	#10619198	C₂	1	2	yes	maximal, complemented
4	#10619111	C₂	1	4	yes	maximal, complemented
5	D₅×#578	C₂	1	4	yes	maximal, complemented
6	#10619107	C₂	1	8	yes	maximal, complemented
7	D₅×#577	C₂	1	8	yes	maximal, complemented
8	#10619104	C₂	1	4	yes	maximal, complemented
9	D₅×#576	C₂	1	4	yes	maximal, complemented
10	#10619100	C₂	1	6	yes	maximal, complemented
11	D₅×#575	C₂	1	6	yes	maximal, complemented
12	#10619088	C₂	1	6	yes	maximal, complemented
13	C₂×D₅×#135	C₂	1	6	yes	maximal, complemented
14	#10619064	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#585	C₂²	1	2	yes	complemented
17	#66287	—	2	2	no	—
18	#66287	C₂²	1	8	yes	complemented
19	D₅×2₋¹⁺⁴	—	2	2	no	—
20	D₅×2₋¹⁺⁴	C₂²	1	8	yes	complemented
21	#66285	—	2	6	no	—
22	#66285	C₂²	1	8	yes	complemented
23	D₅×H(5,𝔽₂)	—	2	6	no	—
24	D₅×H(5,𝔽₂)	C₂²	1	8	yes	complemented
25	#66283	—	2	8	no	—
26	#66283	C₂²	1	12	yes	complemented
27	#66283	C₂²	1	2	yes	complemented
28	C₂×D₅×#41	—	2	8	no	—
29	C₂×D₅×#41	C₂²	1	1	yes	characteristic
30	C₂×D₅×#41	C₂²	1	12	yes	complemented
31	C₅×#578	C₂²	1	4	yes	complemented
32	C₅×#577	C₂²	1	8	yes	complemented
33	C₅×#576	C₂²	1	4	yes	complemented
34	C₅×#575	C₂²	1	6	yes	complemented
35	C₂×C₅×#135	C₂²	1	6	yes	complemented
36	C₂×C₅×#131	C₂²	1	1	yes	characteristic, complemented
37	#66172	C₂²	1	8	yes	complemented
38	#66171	C₂²	1	8	yes	complemented
39	#66170	C₂²	1	8	yes	complemented
40	#66169	C₂²	1	8	yes	complemented
41	#66156	C₂²	1	12	yes	complemented
42	C₂×#4096	C₂²	1	12	yes	complemented
43	C₂×#4094	C₂²	1	1	yes	characteristic, complemented
44	#66113	C₂²	1	24	yes	complemented
45	#66112	C₂²	1	24	yes	complemented
46	#66111	C₂²	1	24	yes	complemented
47	D₅×#137	C₂²	1	24	yes	complemented
48	#66109	C₂²	1	24	yes	complemented
49	#66108	C₂²	1	24	yes	complemented
50	#66107	C₂²	1	24	yes	complemented
51	D₅×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
52	#66105	C₂²	1	12	yes	complemented
53	#66104	C₂²	1	24	yes	complemented
54	#66103	C₂²	1	12	yes	complemented
55	#66102	C₂²	1	24	yes	complemented
56	D₅×#135	C₂²	1	4	yes	complemented
57	D₅×#135	C₂²	1	12	yes	complemented
58	D₅×#135	C₂²	1	12	yes	complemented
59	D₅×#135	C₂²	1	12	yes	complemented
60	D₅×#135	C₂²	1	12	yes	complemented
61	D₅×#135	C₂²	1	12	yes	complemented
62	D₅×#135	C₂²	1	12	yes	complemented
63	D₅×#135	C₂²	1	12	yes	complemented
64	#66100	C₂²	1	12	yes	complemented
65	C₂×#4065	C₂²	1	6	yes	complemented
66	C₂×D₅×Q₁₆	C₂²	1	6	yes	complemented
67	#66096	C₂²	1	24	yes	complemented
68	C₂×#4062	C₂²	1	12	yes	complemented
69	C₂×D₅×SD₁₆	C₂²	1	12	yes	complemented
70	#66091	C₂²	1	12	yes	complemented
71	C₂×#4058	C₂²	1	6	yes	complemented
72	C₂×D₅×D₈	C₂²	1	6	yes	complemented
73	#66087	C₂²	1	4	yes	complemented
74	#66086	C₂²	1	4	yes	complemented
75	#66085	C₂²	1	8	yes	complemented
76	D₅×#131	C₂²	1	4	yes	complemented
77	D₅×#131	C₂²	1	4	yes	complemented
78	D₅×#131	C₂²	1	4	yes	complemented
79	D₅×#131	C₂²	1	4	yes	complemented
80	#66082	C₂²	1	6	yes	complemented
81	C₂×#4053	C₂²	1	3	yes	complemented
82	C₂×D₅×M₁₆	C₂²	1	3	yes	complemented
83	C₂×#4050	C₂²	1	6	yes	complemented
84	C₂×#4047	C₂²	1	3	yes	complemented
85	C₂²×C₈×D₅	C₂²	1	3	yes	complemented
86	C₂×#3584	—	5	1	no	maximal, Sylow
87	C₅×2₋¹⁺⁴	—	2	2	no	—
88	C₅×2₋¹⁺⁴	C₂³	1	8	yes	complemented
89	C₅×H(5,𝔽₂)	—	2	6	no	—
90	C₅×H(5,𝔽₂)	C₂³	1	8	yes	complemented
91	C₂×C₅×#41	—	2	8	no	—
92	C₂×C₅×#41	C₂³	1	1	yes	characteristic
93	C₂×C₅×#41	C₂³	1	12	yes	complemented
94	#4150	—	2	8	no	—
95	#4150	—	2	24	no	—
96	#4150	—	2	12	no	—
97	#4150	C₂³	1	24	yes	complemented
98	#4150	C₂³	1	8	yes	complemented
99	#4149	—	2	8	no	—
100	#4149	—	2	24	no	—
101	#4149	—	2	12	no	—
102	#4149	C₂³	1	24	yes	complemented
103	#4149	C₂³	1	8	yes	complemented
104	D₅×#41	—	2	8	no	—
105	D₅×#41	—	2	8	no	—
106	D₅×#41	—	2	8	no	—
107	D₅×#41	—	2	24	no	—
108	D₅×#41	—	2	24	no	—
109	D₅×#41	—	2	24	no	—
110	D₅×#41	—	2	12	no	—
111	D₅×#41	—	2	12	no	—
112	D₅×#41	—	2	12	no	—
113	D₅×#41	—	2	12	no	—
114	D₅×#41	D₄	1	4	yes	—
115	D₅×#41	D₄	1	4	yes	—
116	D₅×#41	C₂³	1	8	yes	—
117	D₅×#41	C₂³	1	24	yes	—
118	D₅×#41	C₂³	1	4	yes	—
119	D₅×#41	C₂³	1	4	yes	—
120	D₅×#41	C₂³	1	24	yes	complemented
121	D₅×#41	C₂³	1	24	yes	complemented
122	#4147	—	2	2	no	—
123	#4147	—	2	8	no	—
124	#4147	—	2	8	no	—
125	#4147	C₂³	1	24	yes	complemented
126	C₂×#713	—	2	8	no	—
127	C₂×#713	D₄	1	1	yes	characteristic
128	C₂×#713	C₂³	1	12	yes	complemented
129	C₂×Q₈×D₅	—	2	8	no	—
130	C₂×Q₈×D₅	D₄	1	1	yes	characteristic
131	C₂×Q₈×D₅	C₂³	1	12	yes	—
132	#4144	—	2	6	no	—
133	#4144	—	2	24	no	—
134	#4144	—	2	24	no	—
135	#4144	—	2	24	no	—
136	#4144	C₂³	1	24	yes	complemented
137	C₂×#711	—	2	12	no	—
138	C₂×#711	—	2	24	no	—
139	C₂×#711	D₄	1	3	yes	—
140	C₂×#711	C₂³	1	12	yes	complemented
141	C₂×D₄×D₅	—	2	12	no	—
142	C₂×D₄×D₅	—	2	24	no	—
143	C₂×D₄×D₅	D₄	1	3	yes	—
144	C₂×D₄×D₅	C₂³	1	12	yes	—
145	C₂×#709	—	2	24	no	—
146	C₂×#709	—	2	12	no	—
147	C₂×#709	C₂³	1	3	yes	—
148	C₂×#709	C₂³	1	12	yes	complemented
149	C₂²×C₄×D₅	—	2	12	no	—
150	C₂²×C₄×D₅	C₂³	1	3	yes	—
151	C₅×#137	C₂³	1	24	yes	complemented
152	C₅×AGL(1,ℤ/8)	C₂³	1	24	yes	complemented
153	C₅×#135	C₂³	1	4	yes	complemented
154	C₅×#135	C₂³	1	12	yes	complemented
155	C₅×#135	C₂³	1	12	yes	complemented
156	C₅×#135	C₂³	1	12	yes	complemented
157	C₂×C₅×Q₁₆	C₂³	1	6	yes	complemented
158	C₂×C₅×SD₁₆	C₂³	1	12	yes	complemented
159	C₂×C₅×D₈	C₂³	1	6	yes	complemented
160	C₅×#131	C₂³	1	4	yes	complemented
161	C₅×#131	C₂³	1	4	yes	complemented
162	C₂×C₅×M₁₆	C₂³	1	3	yes	complemented
163	C₂²×C₅×C₈	C₂³	1	3	yes	complemented
164	#4097	C₂³	1	24	yes	complemented
165	#4096	C₂³	1	8	yes	complemented
166	#4096	C₂³	1	24	yes	complemented
167	#4096	C₂³	1	24	yes	complemented
168	#4096	C₂³	1	24	yes	complemented
169	#4095	C₂³	1	24	yes	complemented
170	#4094	C₂³	1	4	yes	complemented
171	#4094	C₂³	1	4	yes	complemented
172	C₂×#689	C₂³	1	12	yes	complemented
173	#4088	C₂³	1	24	yes	complemented
174	C₂×#688	C₂³	1	12	yes	complemented
175	C₂×#687	C₂³	1	12	yes	complemented
176	#4078	C₂³	1	24	yes	complemented
177	C₂×#686	C₂³	1	12	yes	complemented
178	C₂×#681	C₂³	1	3	yes	complemented
179	C₂²×#168	C₂³	1	3	yes	complemented
180	#4065	C₂³	1	4	yes	complemented
181	#4065	C₂³	1	12	yes	complemented
182	#4065	C₂³	1	12	yes	complemented
183	#4065	C₂³	1	12	yes	complemented
184	#4064	C₂³	1	48	yes	complemented
185	D₅×Q₁₆	C₂³	1	4	yes	—
186	D₅×Q₁₆	C₂³	1	12	yes	—
187	D₅×Q₁₆	C₂³	1	12	yes	complemented
188	D₅×Q₁₆	C₂³	1	12	yes	complemented
189	#4062	C₂³	1	8	yes	complemented
190	#4062	C₂³	1	24	yes	complemented
191	#4062	C₂³	1	24	yes	complemented
192	#4062	C₂³	1	24	yes	complemented
193	#4061	C₂³	1	48	yes	complemented
194	#4060	C₂³	1	48	yes	complemented
195	D₅×SD₁₆	C₂³	1	8	yes	—
196	D₅×SD₁₆	C₂³	1	24	yes	—
197	D₅×SD₁₆	C₂³	1	24	yes	complemented
198	D₅×SD₁₆	C₂³	1	24	yes	complemented
199	#4058	C₂³	1	4	yes	complemented
200	#4058	C₂³	1	12	yes	complemented
201	#4058	C₂³	1	12	yes	complemented
202	#4058	C₂³	1	12	yes	complemented
203	#4057	C₂³	1	48	yes	complemented
204	D₅×D₈	C₂³	1	4	yes	—
205	D₅×D₈	C₂³	1	12	yes	—
206	D₅×D₈	C₂³	1	12	yes	complemented
207	D₅×D₈	C₂³	1	12	yes	complemented
208	#4055	C₂³	1	24	yes	complemented
209	#4054	C₂³	1	24	yes	complemented
210	#4053	C₂³	1	12	yes	complemented
211	#4053	C₂³	1	12	yes	complemented
212	D₅×M₁₆	C₂³	1	12	yes	—
213	D₅×M₁₆	C₂³	1	12	yes	complemented
214	C₂×Dic₂₀	C₂³	1	6	yes	complemented
215	#4050	C₂³	1	4	yes	complemented
216	#4050	C₂³	1	12	yes	complemented
217	#4050	C₂³	1	12	yes	complemented
218	#4050	C₂³	1	12	yes	complemented
219	C₂×D₄₀	C₂³	1	6	yes	complemented
220	C₂×#677	C₂³	1	12	yes	complemented
221	#4047	C₂³	1	12	yes	complemented
222	#4047	C₂³	1	12	yes	complemented
223	C₂×#676	C₂³	1	6	yes	complemented
224	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
225	C₂×C₈×D₅	C₂³	1	3	yes	—
226	C₂×C₈×D₅	C₂³	1	6	yes	—
227	C₂×C₈×D₅	C₂³	1	6	yes	—
228	C₂×C₈×D₅	C₂³	1	3	yes	complemented
229	C₂×C₈×D₅	C₂³	1	3	yes	complemented
230	C₂×C₈×D₅	C₂³	1	6	yes	complemented
231	C₂×C₈×D₅	C₂³	1	6	yes	complemented
232	C₂×#585	—	5	2	no	—
233	#3584	—	5	2	no	—
234	#3584	—	5	4	no	—
235	#3584	—	5	8	no	—
236	#3584	—	5	4	no	—
237	#3584	—	5	6	no	—
238	#3584	—	5	6	no	—
239	#3584	—	5	1	no	—
240	#3584	D₅	1	1	yes	characteristic, direct product factor
241	C₂×#578	—	5	4	no	—
242	C₂×#577	—	5	8	no	—
243	C₂×#576	—	5	4	no	—
244	C₂×#575	—	5	6	no	—
245	C₂²×#135	—	5	6	no	—
246	C₂²×#131	—	5	1	no	—
247	C₂³×D₅	—	2	12	no	—
248	C₂³×D₅	C₂×D₄	1	3	yes	—
249	C₅×#41	—	2	8	no	—
250	C₅×#41	—	2	24	no	—
251	C₅×#41	—	2	12	no	—
252	C₅×#41	—	2	12	no	—
253	C₅×#41	C₂×D₄	1	4	yes	—
254	C₅×#41	C₂⁴	1	8	yes	—
255	C₅×#41	C₂⁴	1	24	yes	—
256	C₅×#41	C₂⁴	1	4	yes	—
257	C₂×C₅×Q₈	—	2	8	no	—
258	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
259	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
260	C₂×C₅×D₄	—	2	12	no	—
261	C₂×C₅×D₄	—	2	24	no	—
262	C₂×C₅×D₄	C₂×D₄	1	3	yes	—
263	C₂×C₅×D₄	C₂⁴	1	12	yes	—
264	C₂²×C₄×C₅	—	2	12	no	—
265	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
266	C₂×C₂²⋊D₅	—	2	12	no	—
267	C₂×C₂²⋊D₅	—	2	12	no	—
268	C₂×C₂²⋊D₅	—	2	48	no	—
269	C₂×C₂²⋊D₅	—	2	12	no	—
270	C₂×C₂²⋊D₅	C₂×D₄	1	6	yes	—
271	C₂²×Dic₅	—	2	12	no	—
272	C₂²×Dic₅	C₂×D₄	1	3	yes	—
273	#713	—	2	8	no	—
274	#713	—	2	24	no	—
275	#713	—	2	12	no	—
276	#713	—	2	12	no	—
277	#713	C₂×D₄	1	4	yes	—
278	#713	C₂×D₄	1	4	yes	—
279	#713	C₂⁴	1	8	yes	—
280	#713	C₂⁴	1	24	yes	—
281	Q₈×D₅	—	2	8	no	—
282	Q₈×D₅	—	2	12	no	—
283	Q₈×D₅	—	2	12	no	—
284	Q₈×D₅	—	2	24	no	—
285	Q₈×D₅	C₂×D₄	1	4	yes	—
286	Q₈×D₅	C₂×D₄	1	4	yes	—
287	Q₈×D₅	C₂⁴	1	8	yes	—
288	Q₈×D₅	C₂⁴	1	24	yes	—
289	#711	—	2	24	no	—
290	#711	—	2	48	no	—
291	#711	—	2	8	no	—
292	#711	—	2	24	no	—
293	#711	—	2	24	no	—
294	#711	—	2	24	no	—
295	#711	—	2	12	no	—
296	#711	—	2	12	no	—
297	#711	—	2	24	no	—
298	#711	C₂×D₄	1	12	yes	—
299	#711	C₂×D₄	1	12	yes	—
300	#711	C₂⁴	1	8	yes	—
301	#711	C₂⁴	1	24	yes	—
302	D₄×D₅	—	2	24	no	—
303	D₄×D₅	—	2	8	no	—
304	D₄×D₅	—	2	24	no	—
305	D₄×D₅	—	2	24	no	—
306	D₄×D₅	—	2	24	no	—
307	D₄×D₅	—	2	48	no	—
308	D₄×D₅	—	2	24	no	—
309	D₄×D₅	—	2	12	no	—
310	D₄×D₅	—	2	12	no	—
311	D₄×D₅	C₂×D₄	1	12	yes	—
312	D₄×D₅	C₂×D₄	1	12	yes	—
313	D₄×D₅	C₂⁴	1	8	yes	—
314	D₄×D₅	C₂⁴	1	24	yes	—
315	#709	—	2	12	no	—
316	#709	—	2	12	no	—
317	#709	—	2	48	no	—
318	#709	—	2	24	no	—
319	#709	—	2	8	no	—
320	#709	—	2	24	no	—
321	#709	—	2	24	no	—
322	#709	—	2	24	no	—
323	#709	—	2	24	no	—
324	#709	C₂×D₄	1	12	yes	—
325	#709	C₂⁴	1	12	yes	—
326	#709	C₂⁴	1	8	yes	—
327	#709	C₂⁴	1	24	yes	—
328	C₂×D₂₀	—	2	12	no	—
329	C₂×D₂₀	—	2	24	no	—
330	C₂×D₂₀	C₂×D₄	1	3	yes	—
331	C₂×D₂₀	C₂⁴	1	12	yes	—
332	C₂×C₄×D₅	—	2	12	no	—
333	C₂×C₄×D₅	—	2	12	no	—
334	C₂×C₄×D₅	—	2	12	no	—
335	C₂×C₄×D₅	—	2	8	no	—
336	C₂×C₄×D₅	—	2	24	no	—
337	C₂×C₄×D₅	—	2	24	no	—
338	C₂×C₄×D₅	—	2	24	no	—
339	C₂×C₄×D₅	C₂×D₄	1	6	yes	—
340	C₂×C₄×D₅	C₂×D₄	1	6	yes	—
341	C₂×C₄×D₅	C₂×D₄	1	3	yes	—
342	C₂×C₄×D₅	C₂×D₄	1	3	yes	—
343	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
344	C₂×C₄×D₅	C₂⁴	1	3	yes	—
345	C₂×C₄×D₅	C₂⁴	1	6	yes	—
346	C₂×C₄×D₅	C₂⁴	1	6	yes	—
347	C₂×Dic₁₀	—	2	12	no	—
348	C₂×Dic₁₀	—	2	24	no	—
349	C₂×Dic₁₀	C₂×D₄	1	3	yes	—
350	C₂×Dic₁₀	C₂⁴	1	12	yes	—
351	C₅×Q₁₆	C₂⁴	1	4	yes	—
352	C₅×Q₁₆	C₂⁴	1	12	yes	—
353	C₅×SD₁₆	C₂⁴	1	8	yes	—
354	C₅×SD₁₆	C₂⁴	1	24	yes	—
355	C₅×D₈	C₂⁴	1	4	yes	—
356	C₅×D₈	C₂⁴	1	12	yes	—
357	C₅×M₁₆	C₂⁴	1	12	yes	—
358	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
359	C₂×C₅×C₈	C₂⁴	1	3	yes	—
360	C₂×C₅×C₈	C₂⁴	1	6	yes	—
361	C₂×C₅×C₈	C₂⁴	1	6	yes	—
362	#689	C₂⁴	1	8	yes	—
363	#689	C₂⁴	1	24	yes	—
364	#688	C₂⁴	1	8	yes	—
365	#688	C₂⁴	1	24	yes	—
366	#687	C₂⁴	1	8	yes	—
367	#687	C₂⁴	1	24	yes	—
368	#686	C₂⁴	1	8	yes	—
369	#686	C₂⁴	1	24	yes	—
370	#681	C₂⁴	1	12	yes	—
371	C₂×#168	C₂⁴	1	1	yes	characteristic
372	C₂×#168	C₂⁴	1	3	yes	—
373	C₂×#168	C₂⁴	1	6	yes	—
374	C₂×#168	C₂⁴	1	6	yes	—
375	Dic₂₀	C₂⁴	1	4	yes	—
376	Dic₂₀	C₂⁴	1	12	yes	—
377	D₄₀	C₂⁴	1	4	yes	—
378	D₄₀	C₂⁴	1	12	yes	—
379	#677	C₂⁴	1	8	yes	—
380	#677	C₂⁴	1	24	yes	—
381	#676	C₂⁴	1	24	yes	—
382	C₈×D₅	C₂⁴	1	1	yes	characteristic
383	C₈×D₅	C₂⁴	1	1	yes	characteristic
384	C₈×D₅	C₂⁴	1	6	yes	—
385	C₈×D₅	C₂⁴	1	1	yes	characteristic
386	C₈×D₅	C₂⁴	1	1	yes	characteristic
387	C₈×D₅	C₂⁴	1	6	yes	—
388	C₈×D₅	C₂⁴	1	6	yes	—
389	C₈×D₅	C₂⁴	1	6	yes	—
390	C₈×D₅	C₂⁴	1	6	yes	—
391	C₈×D₅	C₂⁴	1	6	yes	—
392	#585	—	5	8	no	—
393	#585	—	5	8	no	—
394	#585	—	5	2	no	—
395	#585	—	5	12	no	—
396	#585	—	10	8	no	—
397	#585	—	10	6	no	—
398	#585	—	10	2	no	—
399	#585	C₂×D₅	1	2	yes	complemented
400	C₂×2₋¹⁺⁴	—	5	8	no	—
401	C₂×2₋¹⁺⁴	—	10	2	no	—
402	C₂×H(5,𝔽₂)	—	5	8	no	—
403	C₂×H(5,𝔽₂)	—	10	6	no	—
404	C₂²×#41	—	5	1	no	—
405	C₂²×#41	—	5	12	no	—
406	C₂²×#41	—	10	8	no	—
407	#578	—	5	8	no	—
408	#578	—	5	24	no	—
409	#578	—	5	12	no	—
410	#578	—	5	12	no	—
411	#578	—	5	4	no	—
412	#578	C₂×D₅	1	4	yes	complemented
413	#577	—	5	8	no	—
414	#577	—	5	8	no	—
415	#577	—	5	24	no	—
416	#577	—	5	24	no	—
417	#577	—	5	24	no	—
418	#577	—	5	24	no	—
419	#577	—	5	8	no	—
420	#577	C₂×D₅	1	8	yes	complemented
421	#576	—	5	8	no	—
422	#576	—	5	24	no	—
423	#576	—	5	12	no	—
424	#576	—	5	12	no	—
425	#576	—	5	4	no	—
426	#576	C₂×D₅	1	4	yes	complemented
427	#575	—	5	12	no	—
428	#575	—	5	24	no	—
429	#575	—	5	24	no	—
430	#575	—	5	24	no	—
431	#575	—	5	6	no	—
432	#575	C₂×D₅	1	6	yes	complemented
433	C₂×#137	—	5	24	no	—
434	C₂×AGL(1,ℤ/8)	—	5	24	no	—
435	C₂×#135	—	5	12	no	—
436	C₂×#135	—	5	12	no	—
437	C₂×#135	—	5	12	no	—
438	C₂×#135	—	5	12	no	—
439	C₂×#135	—	5	12	no	—
440	C₂×#135	—	5	4	no	—
441	C₂×#135	—	5	12	no	—
442	C₂×#135	—	5	12	no	—
443	C₂×#135	—	5	12	no	—
444	C₂×#135	—	5	6	no	—
445	C₂×#135	—	5	12	no	—
446	C₂×#135	—	5	6	no	—
447	C₂×#135	—	5	6	no	—
448	C₂×#135	C₂×D₅	1	6	yes	complemented
449	C₂²×Q₁₆	—	5	6	no	—
450	C₂²×SD₁₆	—	5	12	no	—
451	C₂²×D₈	—	5	6	no	—
452	C₂×#131	—	5	1	no	—
453	C₂×#131	—	5	4	no	—
454	C₂×#131	—	5	4	no	—
455	C₂×#131	—	5	4	no	—
456	C₂×#131	—	5	4	no	—
457	C₂×#131	—	5	3	no	—
458	C₂×#131	—	5	3	no	—
459	C₂×#131	C₂×D₅	1	1	yes	characteristic, complemented
460	C₂²×M₁₆	—	5	3	no	—
461	C₂³×C₈	—	5	3	no	—
462	C₂³×C₅	—	2	12	no	—
463	C₂³×C₅	C₂²×D₄	1	3	yes	—
464	C₂²×D₅	—	2	12	no	—
465	C₂²×D₅	—	2	8	no	—
466	C₂²×D₅	—	2	24	no	—
467	C₂²×D₅	—	4	6	no	—
468	C₂²×D₅	—	8	24	no	—
469	C₂²×D₅	C₂²×D₄	1	6	yes	—
470	C₂²×D₅	C₂²×D₄	1	1	yes	characteristic
471	C₂²×D₅	C₂²×D₄	1	6	yes	—
472	C₂²×D₅	C₂²×D₄	1	3	yes	—
473	C₅×Q₈	—	2	12	no	—
474	C₅×Q₈	C₂²×D₄	1	4	yes	—
475	C₅×Q₈	C₂⁵	1	8	yes	—
476	C₅×D₄	—	2	24	no	—
477	C₅×D₄	—	2	8	no	—
478	C₅×D₄	—	2	12	no	—
479	C₅×D₄	C₂²×D₄	1	12	yes	—
480	C₅×D₄	C₂⁵	1	8	yes	—
481	C₂×C₄×C₅	—	2	12	no	—
482	C₂×C₄×C₅	—	2	24	no	—
483	C₂×C₄×C₅	—	2	8	no	—
484	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
485	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
486	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
487	C₂×C₄×C₅	C₂⁵	1	6	yes	—
488	C₂²⋊D₅	—	2	24	no	—
489	C₂²⋊D₅	—	2	8	no	—
490	C₂²⋊D₅	—	2	24	no	—
491	C₂²⋊D₅	—	2	8	no	—
492	C₂²⋊D₅	—	2	8	no	—
493	C₂²⋊D₅	—	2	24	no	—
494	C₂²⋊D₅	C₂²×D₄	1	24	yes	—
495	C₂×Dic₅	—	2	12	no	—
496	C₂×Dic₅	—	2	24	no	—
497	C₂×Dic₅	—	2	8	no	—
498	C₂×Dic₅	C₂²×D₄	1	6	yes	—
499	C₂×Dic₅	C₂²×D₄	1	3	yes	—
500	C₂×Dic₅	C₂²×D₄	1	6	yes	—
501	C₂×Dic₅	C₂²×D₄	1	1	yes	characteristic
502	D₂₀	—	2	24	no	—
503	D₂₀	—	2	8	no	—
504	D₂₀	—	2	12	no	—
505	D₂₀	C₂²×D₄	1	12	yes	—
506	D₂₀	C₂⁵	1	8	yes	—
507	C₄×D₅	—	2	8	no	—
508	C₄×D₅	—	2	24	no	—
509	C₄×D₅	—	2	8	no	—
510	C₄×D₅	—	2	24	no	—
511	C₄×D₅	—	2	8	no	—
512	C₄×D₅	—	2	24	no	—
513	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
514	C₄×D₅	C₂²×D₄	1	6	yes	—
515	C₄×D₅	C₂²×D₄	1	6	yes	—
516	C₄×D₅	C₂²×D₄	1	6	yes	—
517	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
518	C₄×D₅	C₂²×D₄	1	6	yes	—
519	C₄×D₅	C₂²×D₄	1	6	yes	—
520	C₄×D₅	C₂⁵	1	1	yes	characteristic
521	C₄×D₅	C₂⁵	1	1	yes	characteristic
522	C₄×D₅	C₂⁵	1	6	yes	—
523	Dic₁₀	—	2	12	no	—
524	Dic₁₀	—	2	8	no	—
525	Dic₁₀	—	2	24	no	—
526	Dic₁₀	C₂²×D₄	1	12	yes	—
527	Dic₁₀	C₂⁵	1	8	yes	—
528	C₅×C₈	C₂⁵	1	1	yes	characteristic
529	C₅×C₈	C₂⁵	1	1	yes	characteristic
530	C₅×C₈	C₂⁵	1	6	yes	—
531	#168	C₂⁵	1	1	yes	characteristic
532	#168	C₂⁵	1	1	yes	characteristic
533	#168	C₂⁵	1	6	yes	—
534	2₋¹⁺⁴	—	2	2	no	—
535	2₋¹⁺⁴	—	5	24	no	—
536	2₋¹⁺⁴	—	5	8	no	—
537	2₋¹⁺⁴	—	5	24	no	—
538	2₋¹⁺⁴	—	10	8	no	—
539	2₋¹⁺⁴	—	10	8	no	—
540	2₋¹⁺⁴	—	10	8	no	—
541	2₋¹⁺⁴	—	10	12	no	—
542	2₋¹⁺⁴	—	10	24	no	—
543	2₋¹⁺⁴	—	10	2	no	—
544	2₋¹⁺⁴	C₂²×D₅	1	8	yes	complemented
545	H(5,𝔽₂)	—	2	6	no	—
546	H(5,𝔽₂)	—	5	24	no	—
547	H(5,𝔽₂)	—	5	8	no	—
548	H(5,𝔽₂)	—	5	24	no	—
549	H(5,𝔽₂)	—	10	24	no	—
550	H(5,𝔽₂)	—	10	24	no	—
551	H(5,𝔽₂)	—	10	24	no	—
552	H(5,𝔽₂)	—	10	24	no	—
553	H(5,𝔽₂)	—	10	12	no	—
554	H(5,𝔽₂)	—	10	8	no	—
555	H(5,𝔽₂)	—	10	6	no	—
556	H(5,𝔽₂)	C₂²×D₅	1	8	yes	complemented
557	C₂×#41	—	2	8	no	—
558	C₂×#41	—	5	4	no	—
559	C₂×#41	—	5	4	no	—
560	C₂×#41	—	5	4	no	—
561	C₂×#41	—	5	4	no	—
562	C₂×#41	—	5	1	no	—
563	C₂×#41	—	5	3	no	—
564	C₂×#41	—	5	3	no	—
565	C₂×#41	—	5	8	no	—
566	C₂×#41	—	5	24	no	—
567	C₂×#41	—	5	24	no	—
568	C₂×#41	—	5	24	no	—
569	C₂×#41	—	5	12	no	—
570	C₂×#41	—	5	12	no	—
571	C₂×#41	—	5	12	no	—
572	C₂×#41	—	10	12	no	—
573	C₂×#41	—	10	24	no	—
574	C₂×#41	—	10	12	no	—
575	C₂×#41	—	10	12	no	—
576	C₂×#41	—	10	12	no	—
577	C₂×#41	—	10	12	no	—
578	C₂×#41	—	10	12	no	—
579	C₂×#41	—	10	24	no	—
580	C₂×#41	—	10	24	no	—
581	C₂×#41	—	10	8	no	—
582	C₂×#41	—	10	8	no	—
583	C₂×#41	—	10	8	no	—
584	C₂×#41	—	10	24	no	—
585	C₂×#41	—	10	24	no	—
586	C₂×#41	—	10	8	no	—
587	C₂×#41	C₂²×D₅	1	1	yes	characteristic
588	C₂×#41	C₂²×D₅	1	12	yes	complemented
589	C₂²×Q₈	—	5	1	no	—
590	C₂²×Q₈	—	5	12	no	—
591	C₂²×Q₈	—	10	8	no	—
592	C₂²×D₄	—	5	3	no	—
593	C₂²×D₄	—	5	12	no	—
594	C₂²×D₄	—	10	24	no	—
595	C₂²×D₄	—	10	12	no	—
596	C₂³×C₄	—	5	3	no	—
597	C₂³×C₄	—	10	12	no	—
598	#137	—	5	24	no	—
599	#137	—	5	24	no	—
600	#137	—	5	48	no	—
601	#137	—	5	48	no	—
602	#137	—	5	24	no	—
603	#137	C₂²×D₅	1	24	yes	complemented
604	AGL(1,ℤ/8)	—	5	24	no	—
605	AGL(1,ℤ/8)	—	5	24	no	—
606	AGL(1,ℤ/8)	—	5	48	no	—
607	AGL(1,ℤ/8)	—	5	48	no	—
608	AGL(1,ℤ/8)	—	5	24	no	—
609	AGL(1,ℤ/8)	C₂²×D₅	1	24	yes	complemented
610	#135	—	5	8	no	—
611	#135	—	5	24	no	—
612	#135	—	5	24	no	—
613	#135	—	5	24	no	—
614	#135	—	5	4	no	—
615	#135	—	5	12	no	—
616	#135	—	5	12	no	—
617	#135	—	5	12	no	—
618	#135	—	5	8	no	—
619	#135	—	5	24	no	—
620	#135	—	5	24	no	—
621	#135	—	5	24	no	—
622	#135	—	5	4	no	—
623	#135	—	5	12	no	—
624	#135	—	5	12	no	—
625	#135	—	5	12	no	—
626	#135	—	5	4	no	—
627	#135	—	5	12	no	—
628	#135	—	5	12	no	—
629	#135	—	5	12	no	—
630	#135	C₂²×D₅	1	4	yes	complemented
631	#135	C₂²×D₅	1	12	yes	complemented
632	#135	C₂²×D₅	1	12	yes	complemented
633	#135	C₂²×D₅	1	12	yes	complemented
634	C₂×Q₁₆	—	5	12	no	—
635	C₂×Q₁₆	—	5	4	no	—
636	C₂×Q₁₆	—	5	12	no	—
637	C₂×Q₁₆	—	5	12	no	—
638	C₂×Q₁₆	—	5	12	no	—
639	C₂×Q₁₆	—	5	6	no	—
640	C₂×Q₁₆	C₂²×D₅	1	6	yes	complemented
641	C₂×SD₁₆	—	5	12	no	—
642	C₂×SD₁₆	—	5	12	no	—
643	C₂×SD₁₆	—	5	8	no	—
644	C₂×SD₁₆	—	5	24	no	—
645	C₂×SD₁₆	—	5	24	no	—
646	C₂×SD₁₆	—	5	24	no	—
647	C₂×SD₁₆	—	5	12	no	—
648	C₂×SD₁₆	C₂²×D₅	1	12	yes	complemented
649	C₂×D₈	—	5	12	no	—
650	C₂×D₈	—	5	4	no	—
651	C₂×D₈	—	5	12	no	—
652	C₂×D₈	—	5	12	no	—
653	C₂×D₈	—	5	12	no	—
654	C₂×D₈	—	5	6	no	—
655	C₂×D₈	C₂²×D₅	1	6	yes	complemented
656	#131	—	5	4	no	—
657	#131	—	5	4	no	—
658	#131	—	5	12	no	—
659	#131	—	5	12	no	—
660	#131	—	5	12	no	—
661	#131	—	5	12	no	—
662	#131	C₂²×D₅	1	4	yes	complemented
663	#131	C₂²×D₅	1	4	yes	complemented
664	C₂×M₁₆	—	5	3	no	—
665	C₂×M₁₆	—	5	12	no	—
666	C₂×M₁₆	—	5	12	no	—
667	C₂×M₁₆	—	5	6	no	—
668	C₂×M₁₆	C₂²×D₅	1	3	yes	complemented
669	C₂²×C₈	—	5	3	no	—
670	C₂²×C₈	—	5	1	no	—
671	C₂²×C₈	—	5	3	no	—
672	C₂²×C₈	—	5	6	no	—
673	C₂²×C₈	—	5	6	no	—
674	C₂²×C₈	—	5	3	no	—
675	C₂²×C₈	—	5	3	no	—
676	C₂²×C₈	—	5	6	no	—
677	C₂²×C₈	—	5	6	no	—
678	C₂²×C₈	C₂²×D₅	1	3	yes	complemented
679	C₂²×C₅	—	2	8	no	—
680	C₂²×C₅	—	4	3	no	—
681	C₂²×C₅	—	8	12	no	—
682	C₂²×C₅	C₂³×D₄	1	6	yes	—
683	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
684	C₂×D₅	—	2	2	no	—
685	C₂×D₅	—	2	12	no	—
686	C₂×D₅	—	2	8	no	—
687	C₂×D₅	—	4	6	no	—
688	C₂×D₅	—	4	3	no	—
689	C₂×D₅	—	4	16	no	—
690	C₂×D₅	—	8	24	no	—
691	C₂×D₅	—	8	12	no	—
692	C₂×D₅	C₂³×D₄	1	6	yes	—
693	C₂×D₅	C₂³×D₄	1	1	yes	characteristic
694	C₂×D₅	C₂³×D₄	1	1	yes	characteristic
695	C₄×C₅	—	2	8	no	—
696	C₄×C₅	C₂³×D₄	1	6	yes	—
697	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
698	C₄×C₅	C₂⁶	1	1	yes	characteristic
699	Dic₅	—	2	8	no	—
700	Dic₅	C₂³×D₄	1	1	yes	characteristic
701	Dic₅	C₂³×D₄	1	6	yes	—
702	Dic₅	C₂³×D₄	1	1	yes	characteristic
703	C₂⁴	—	5	3	no	—
704	C₂⁴	—	10	12	no	—
705	#41	—	2	8	no	—
706	#41	—	2	24	no	—
707	#41	—	2	12	no	—
708	#41	—	2	12	no	—
709	#41	—	5	4	no	—
710	#41	—	5	4	no	—
711	#41	—	5	12	no	—
712	#41	—	5	12	no	—
713	#41	—	5	12	no	—
714	#41	—	5	12	no	—
715	#41	—	5	8	no	—
716	#41	—	5	24	no	—
717	#41	—	5	8	no	—
718	#41	—	5	24	no	—
719	#41	—	5	8	no	—
720	#41	—	5	24	no	—
721	#41	—	10	8	no	—
722	#41	—	10	24	no	—
723	#41	—	10	24	no	—
724	#41	—	10	24	no	—
725	#41	—	10	48	no	—
726	#41	—	10	24	no	—
727	#41	—	10	24	no	—
728	#41	—	10	8	no	—
729	#41	—	10	24	no	—
730	#41	—	10	12	no	—
731	#41	—	10	24	no	—
732	#41	—	10	24	no	—
733	#41	—	10	12	no	—
734	#41	—	10	12	no	—
735	#41	—	10	12	no	—
736	#41	—	10	48	no	—
737	#41	—	10	24	no	—
738	#41	—	10	24	no	—
739	#41	—	10	8	no	—
740	#41	—	10	24	no	—
741	#41	—	10	12	no	—
742	#41	—	10	12	no	—
743	#41	D₄×D₅	1	4	yes	—
744	#41	C₂³×D₅	1	8	yes	—
745	#41	C₂³×D₅	1	24	yes	—
746	#41	C₂³×D₅	1	4	yes	—
747	C₂×Q₈	—	2	8	no	—
748	C₂×Q₈	—	5	4	no	—
749	C₂×Q₈	—	5	4	no	—
750	C₂×Q₈	—	5	3	no	—
751	C₂×Q₈	—	5	8	no	—
752	C₂×Q₈	—	5	24	no	—
753	C₂×Q₈	—	5	12	no	—
754	C₂×Q₈	—	10	12	no	—
755	C₂×Q₈	—	10	24	no	—
756	C₂×Q₈	—	10	12	no	—
757	C₂×Q₈	—	10	12	no	—
758	C₂×Q₈	—	10	24	no	—
759	C₂×Q₈	—	10	8	no	—
760	C₂×Q₈	D₄×D₅	1	1	yes	characteristic
761	C₂×Q₈	C₂³×D₅	1	12	yes	—
762	C₂×D₄	—	2	12	no	—
763	C₂×D₄	—	2	24	no	—
764	C₂×D₄	—	5	6	no	—
765	C₂×D₄	—	5	12	no	—
766	C₂×D₄	—	5	12	no	—
767	C₂×D₄	—	5	8	no	—
768	C₂×D₄	—	5	24	no	—
769	C₂×D₄	—	5	3	no	—
770	C₂×D₄	—	5	12	no	—
771	C₂×D₄	—	10	24	no	—
772	C₂×D₄	—	10	12	no	—
773	C₂×D₄	—	10	12	no	—
774	C₂×D₄	—	10	12	no	—
775	C₂×D₄	—	10	12	no	—
776	C₂×D₄	—	10	48	no	—
777	C₂×D₄	—	10	24	no	—
778	C₂×D₄	—	10	8	no	—
779	C₂×D₄	—	10	24	no	—
780	C₂×D₄	—	10	24	no	—
781	C₂×D₄	—	10	24	no	—
782	C₂×D₄	—	10	48	no	—
783	C₂×D₄	—	10	12	no	—
784	C₂×D₄	—	10	12	no	—
785	C₂×D₄	—	10	24	no	—
786	C₂×D₄	D₄×D₅	1	3	yes	—
787	C₂×D₄	C₂³×D₅	1	12	yes	—
788	C₂²×C₄	—	2	12	no	—
789	C₂²×C₄	—	5	3	no	—
790	C₂²×C₄	—	5	6	no	—
791	C₂²×C₄	—	5	3	no	—
792	C₂²×C₄	—	5	3	no	—
793	C₂²×C₄	—	5	6	no	—
794	C₂²×C₄	—	5	1	no	—
795	C₂²×C₄	—	5	6	no	—
796	C₂²×C₄	—	5	6	no	—
797	C₂²×C₄	—	5	3	no	—
798	C₂²×C₄	—	10	8	no	—
799	C₂²×C₄	—	10	24	no	—
800	C₂²×C₄	—	10	12	no	—
801	C₂²×C₄	—	10	24	no	—
802	C₂²×C₄	—	10	24	no	—
803	C₂²×C₄	—	10	12	no	—
804	C₂²×C₄	—	10	12	no	—
805	C₂²×C₄	—	10	12	no	—
806	C₂²×C₄	C₂³×D₅	1	3	yes	—
807	Q₁₆	—	5	8	no	—
808	Q₁₆	—	5	24	no	—
809	Q₁₆	—	5	4	no	—
810	Q₁₆	—	5	12	no	—
811	Q₁₆	C₂³×D₅	1	4	yes	—
812	Q₁₆	C₂³×D₅	1	12	yes	—
813	SD₁₆	—	5	8	no	—
814	SD₁₆	—	5	24	no	—
815	SD₁₆	—	5	8	no	—
816	SD₁₆	—	5	24	no	—
817	SD₁₆	—	5	8	no	—
818	SD₁₆	—	5	24	no	—
819	SD₁₆	C₂³×D₅	1	8	yes	—
820	SD₁₆	C₂³×D₅	1	24	yes	—
821	D₈	—	5	8	no	—
822	D₈	—	5	24	no	—
823	D₈	—	5	4	no	—
824	D₈	—	5	12	no	—
825	D₈	C₂³×D₅	1	4	yes	—
826	D₈	C₂³×D₅	1	12	yes	—
827	M₁₆	—	5	12	no	—
828	M₁₆	—	5	24	no	—
829	M₁₆	C₂³×D₅	1	12	yes	—
830	C₂×C₈	—	5	1	no	—
831	C₂×C₈	—	5	3	no	—
832	C₂×C₈	—	5	6	no	—
833	C₂×C₈	—	5	6	no	—
834	C₂×C₈	—	5	1	no	—
835	C₂×C₈	—	5	1	no	—
836	C₂×C₈	—	5	1	no	—
837	C₂×C₈	—	5	1	no	—
838	C₂×C₈	—	5	6	no	—
839	C₂×C₈	—	5	6	no	—
840	C₂×C₈	—	5	6	no	—
841	C₂×C₈	—	5	6	no	—
842	C₂×C₈	—	5	6	no	—
843	C₂×C₈	—	5	6	no	—
844	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
845	C₂×C₈	C₂³×D₅	1	3	yes	—
846	C₂×C₈	C₂³×D₅	1	6	yes	—
847	C₂×C₈	C₂³×D₅	1	6	yes	—
848	C₂×C₅	—	2	1	no	—
849	C₂×C₅	—	2	6	no	—
850	C₂×C₅	—	4	8	no	—
851	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
852	D₅	—	2	1	no	—
853	D₅	—	2	6	no	—
854	D₅	—	4	8	no	—
855	D₅	#3584	1	2	yes	direct product factor
856	C₂³	—	2	12	no	—
857	C₂³	—	5	1	no	—
858	C₂³	—	5	6	no	—
859	C₂³	—	5	6	no	—
860	C₂³	—	5	3	no	—
861	C₂³	—	10	8	no	—
862	C₂³	—	10	24	no	—
863	C₂³	—	10	12	no	—
864	C₂³	—	20	6	no	—
865	C₂³	—	40	24	no	—
866	C₂³	C₂×D₄×D₅	1	3	yes	—
867	Q₈	—	2	12	no	—
868	Q₈	—	5	12	no	—
869	Q₈	—	5	8	no	—
870	Q₈	—	10	8	no	—
871	Q₈	—	10	24	no	—
872	Q₈	—	10	12	no	—
873	Q₈	C₂×D₄×D₅	1	4	yes	—
874	Q₈	C₂⁴×D₅	1	8	yes	—
875	D₄	—	2	24	no	—
876	D₄	—	2	8	no	—
877	D₄	—	2	12	no	—
878	D₄	—	5	24	no	—
879	D₄	—	5	12	no	—
880	D₄	—	5	8	no	—
881	D₄	—	10	8	no	—
882	D₄	—	10	24	no	—
883	D₄	—	10	8	no	—
884	D₄	—	10	24	no	—
885	D₄	—	10	8	no	—
886	D₄	—	10	24	no	—
887	D₄	—	10	24	no	—
888	D₄	—	10	8	no	—
889	D₄	—	10	12	no	—
890	D₄	C₂×D₄×D₅	1	12	yes	—
891	D₄	C₂⁴×D₅	1	8	yes	—
892	C₂×C₄	—	2	12	no	—
893	C₂×C₄	—	2	24	no	—
894	C₂×C₄	—	2	8	no	—
895	C₂×C₄	—	5	1	no	—
896	C₂×C₄	—	5	6	no	—
897	C₂×C₄	—	5	3	no	—
898	C₂×C₄	—	5	6	no	—
899	C₂×C₄	—	5	6	no	—
900	C₂×C₄	—	5	6	no	—
901	C₂×C₄	—	5	6	no	—
902	C₂×C₄	—	5	6	no	—
903	C₂×C₄	—	5	1	no	—
904	C₂×C₄	—	5	1	no	—
905	C₂×C₄	—	5	6	no	—
906	C₂×C₄	—	5	1	no	—
907	C₂×C₄	—	5	1	no	—
908	C₂×C₄	—	5	6	no	—
909	C₂×C₄	—	10	8	no	—
910	C₂×C₄	—	10	24	no	—
911	C₂×C₄	—	10	8	no	—
912	C₂×C₄	—	10	24	no	—
913	C₂×C₄	—	10	8	no	—
914	C₂×C₄	—	10	24	no	—
915	C₂×C₄	—	10	12	no	—
916	C₂×C₄	—	10	24	no	—
917	C₂×C₄	—	10	8	no	—
918	C₂×C₄	C₂×D₄×D₅	1	3	yes	—
919	C₂×C₄	C₂×D₄×D₅	1	6	yes	—
920	C₂×C₄	C₂⁴×D₅	1	6	yes	—
921	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
922	C₈	—	5	1	no	—
923	C₈	—	5	1	no	—
924	C₈	—	5	6	no	—
925	C₈	C₂⁴×D₅	1	1	yes	characteristic
926	C₈	C₂⁴×D₅	1	1	yes	characteristic
927	C₈	C₂⁴×D₅	1	6	yes	—
928	C₅	C₂×#3584	1	1	yes	characteristic, complemented, Sylow
929	C₂²	—	2	8	no	—
930	C₂²	—	4	3	no	—
931	C₂²	—	5	1	no	—
932	C₂²	—	5	1	no	—
933	C₂²	—	5	6	no	—
934	C₂²	—	8	12	no	—
935	C₂²	—	10	2	no	—
936	C₂²	—	10	12	no	—
937	C₂²	—	10	8	no	—
938	C₂²	—	20	3	no	—
939	C₂²	—	20	6	no	—
940	C₂²	—	20	16	no	—
941	C₂²	—	40	12	no	—
942	C₂²	—	40	24	no	—
943	C₂²	C₂²×D₄×D₅	1	6	yes	—
944	C₂²	C₂²×D₄×D₅	1	1	yes	characteristic
945	C₄	—	2	8	no	—
946	C₄	—	5	1	no	—
947	C₄	—	5	1	no	—
948	C₄	—	5	6	no	—
949	C₄	—	10	8	no	—
950	C₄	C₂²×D₄×D₅	1	6	yes	—
951	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
952	C₄	C₂⁵×D₅	1	1	yes	characteristic
953	C₂	—	2	1	no	—
954	C₂	—	2	6	no	—
955	C₂	—	4	8	no	—
956	C₂	—	5	2	no	—
957	C₂	—	10	1	no	—
958	C₂	—	10	6	no	—
959	C₂	—	20	8	no	—
960	C₂	C₂³×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁶
Frattini	C₄	C₂⁵×D₅
Fitting	C₅×#3584	C₂
socle	C₂×C₅	C₂⁴×D₄
hypercenter	#3584	D₅
hypocenter	C₅	C₂×#3584
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. D₅×#585	C₂	semidirect
2. C₅×#3584	C₂	semidirect
3. #10619198	C₂	semidirect
4. #10619111	C₂	semidirect
5. D₅×#578	C₂	semidirect
6. #10619107	C₂	semidirect
7. D₅×#577	C₂	semidirect
8. #10619104	C₂	semidirect
9. D₅×#576	C₂	semidirect
10. #10619100	C₂	semidirect
11. D₅×#575	C₂	semidirect
12. #10619088	C₂	semidirect
13. C₂×D₅×#135	C₂	semidirect
14. #10619064	C₂	semidirect
15. C₂×D₅×#131	C₂	semidirect
16. C₅×#585	C₂²	semidirect
18. #66287	C₂²	semidirect
20. D₅×2₋¹⁺⁴	C₂²	semidirect
22. #66285	C₂²	semidirect
24. D₅×H(5,𝔽₂)	C₂²	semidirect
26. #66283	C₂²	semidirect
27. #66283	C₂²	semidirect
30. C₂×D₅×#41	C₂²	semidirect
31. C₅×#578	C₂²	semidirect
32. C₅×#577	C₂²	semidirect
33. C₅×#576	C₂²	semidirect
34. C₅×#575	C₂²	semidirect
35. C₂×C₅×#135	C₂²	semidirect
36. C₂×C₅×#131	C₂²	semidirect
37. #66172	C₂²	semidirect
38. #66171	C₂²	semidirect
39. #66170	C₂²	semidirect
40. #66169	C₂²	semidirect
41. #66156	C₂²	semidirect
42. C₂×#4096	C₂²	semidirect
43. C₂×#4094	C₂²	semidirect
44. #66113	C₂²	semidirect
45. #66112	C₂²	semidirect
46. #66111	C₂²	semidirect
47. D₅×#137	C₂²	semidirect
48. #66109	C₂²	semidirect
49. #66108	C₂²	semidirect
50. #66107	C₂²	semidirect
51. D₅×AGL(1,ℤ/8)	C₂²	semidirect
52. #66105	C₂²	semidirect
53. #66104	C₂²	semidirect
54. #66103	C₂²	semidirect
55. #66102	C₂²	semidirect
56. D₅×#135	C₂²	semidirect
57. D₅×#135	C₂²	semidirect
58. D₅×#135	C₂²	semidirect
59. D₅×#135	C₂²	semidirect
60. D₅×#135	C₂²	semidirect
61. D₅×#135	C₂²	semidirect
62. D₅×#135	C₂²	semidirect
63. D₅×#135	C₂²	semidirect
64. #66100	C₂²	semidirect
65. C₂×#4065	C₂²	semidirect
66. C₂×D₅×Q₁₆	C₂²	semidirect
67. #66096	C₂²	semidirect
68. C₂×#4062	C₂²	semidirect
69. C₂×D₅×SD₁₆	C₂²	semidirect
70. #66091	C₂²	semidirect
71. C₂×#4058	C₂²	semidirect
72. C₂×D₅×D₈	C₂²	semidirect
73. #66087	C₂²	semidirect
74. #66086	C₂²	semidirect
75. #66085	C₂²	semidirect
76. D₅×#131	C₂²	semidirect
77. D₅×#131	C₂²	semidirect
78. D₅×#131	C₂²	semidirect
79. D₅×#131	C₂²	semidirect
80. #66082	C₂²	semidirect
81. C₂×#4053	C₂²	semidirect
82. C₂×D₅×M₁₆	C₂²	semidirect
83. C₂×#4050	C₂²	semidirect
84. C₂×#4047	C₂²	semidirect
85. C₂²×C₈×D₅	C₂²	semidirect
88. C₅×2₋¹⁺⁴	C₂³	semidirect
90. C₅×H(5,𝔽₂)	C₂³	semidirect
93. C₂×C₅×#41	C₂³	semidirect
97. #4150	C₂³	semidirect
98. #4150	C₂³	semidirect
102. #4149	C₂³	semidirect
103. #4149	C₂³	semidirect
120. D₅×#41	C₂³	semidirect
121. D₅×#41	C₂³	semidirect
125. #4147	C₂³	semidirect
128. C₂×#713	C₂³	semidirect
136. #4144	C₂³	semidirect
140. C₂×#711	C₂³	semidirect
148. C₂×#709	C₂³	semidirect
151. C₅×#137	C₂³	semidirect
152. C₅×AGL(1,ℤ/8)	C₂³	semidirect
153. C₅×#135	C₂³	semidirect
154. C₅×#135	C₂³	semidirect
155. C₅×#135	C₂³	semidirect
156. C₅×#135	C₂³	semidirect
157. C₂×C₅×Q₁₆	C₂³	semidirect
158. C₂×C₅×SD₁₆	C₂³	semidirect
159. C₂×C₅×D₈	C₂³	semidirect
160. C₅×#131	C₂³	semidirect
161. C₅×#131	C₂³	semidirect
162. C₂×C₅×M₁₆	C₂³	semidirect
163. C₂²×C₅×C₈	C₂³	semidirect
164. #4097	C₂³	semidirect
165. #4096	C₂³	semidirect
166. #4096	C₂³	semidirect
167. #4096	C₂³	semidirect
168. #4096	C₂³	semidirect
169. #4095	C₂³	semidirect
170. #4094	C₂³	semidirect
171. #4094	C₂³	semidirect
172. C₂×#689	C₂³	semidirect
173. #4088	C₂³	semidirect
174. C₂×#688	C₂³	semidirect
175. C₂×#687	C₂³	semidirect
176. #4078	C₂³	semidirect
177. C₂×#686	C₂³	semidirect
178. C₂×#681	C₂³	semidirect
179. C₂²×#168	C₂³	semidirect
180. #4065	C₂³	semidirect
181. #4065	C₂³	semidirect
182. #4065	C₂³	semidirect
183. #4065	C₂³	semidirect
184. #4064	C₂³	semidirect
187. D₅×Q₁₆	C₂³	semidirect
188. D₅×Q₁₆	C₂³	semidirect
189. #4062	C₂³	semidirect
190. #4062	C₂³	semidirect
191. #4062	C₂³	semidirect
192. #4062	C₂³	semidirect
193. #4061	C₂³	semidirect
194. #4060	C₂³	semidirect
197. D₅×SD₁₆	C₂³	semidirect
198. D₅×SD₁₆	C₂³	semidirect
199. #4058	C₂³	semidirect
200. #4058	C₂³	semidirect
201. #4058	C₂³	semidirect
202. #4058	C₂³	semidirect
203. #4057	C₂³	semidirect
206. D₅×D₈	C₂³	semidirect
207. D₅×D₈	C₂³	semidirect
208. #4055	C₂³	semidirect
209. #4054	C₂³	semidirect
210. #4053	C₂³	semidirect
211. #4053	C₂³	semidirect
213. D₅×M₁₆	C₂³	semidirect
214. C₂×Dic₂₀	C₂³	semidirect
215. #4050	C₂³	semidirect
216. #4050	C₂³	semidirect
217. #4050	C₂³	semidirect
218. #4050	C₂³	semidirect
219. C₂×D₄₀	C₂³	semidirect
220. C₂×#677	C₂³	semidirect
221. #4047	C₂³	semidirect
222. #4047	C₂³	semidirect
223. C₂×#676	C₂³	semidirect
228. C₂×C₈×D₅	C₂³	semidirect
229. C₂×C₈×D₅	C₂³	semidirect
230. C₂×C₈×D₅	C₂³	semidirect
231. C₂×C₈×D₅	C₂³	semidirect
240. #3584	D₅	direct (N × H)
399. #585	C₂×D₅	semidirect
412. #578	C₂×D₅	semidirect
420. #577	C₂×D₅	semidirect
426. #576	C₂×D₅	semidirect
432. #575	C₂×D₅	semidirect
448. C₂×#135	C₂×D₅	semidirect
459. C₂×#131	C₂×D₅	semidirect
544. 2₋¹⁺⁴	C₂²×D₅	semidirect
556. H(5,𝔽₂)	C₂²×D₅	semidirect
588. C₂×#41	C₂²×D₅	semidirect
603. #137	C₂²×D₅	semidirect
609. AGL(1,ℤ/8)	C₂²×D₅	semidirect
630. #135	C₂²×D₅	semidirect
631. #135	C₂²×D₅	semidirect
632. #135	C₂²×D₅	semidirect
633. #135	C₂²×D₅	semidirect
640. C₂×Q₁₆	C₂²×D₅	semidirect
648. C₂×SD₁₆	C₂²×D₅	semidirect
655. C₂×D₈	C₂²×D₅	semidirect
662. #131	C₂²×D₅	semidirect
663. #131	C₂²×D₅	semidirect
668. C₂×M₁₆	C₂²×D₅	semidirect
678. C₂²×C₈	C₂²×D₅	semidirect
855. D₅	#3584	direct (N × H)
928. C₅	C₂×#3584	semidirect

Maximal subgroups

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

subgroup	index
D₅×#585	2
C₅×#3584	2
#10619198	2
#10619111	2
D₅×#578	2
#10619107	2
D₅×#577	2
#10619104	2
D₅×#576	2
#10619100	2
D₅×#575	2
#10619088	2
C₂×D₅×#135	2
#10619064	2
C₂×D₅×#131	2
C₂×#3584	5

Subgroups — D5×#3584 #13013127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#3584 #13013127