Subgroups — #13013152

Order 1280.

10836 conjugacy classes of subgroups.

The subgroup lattice has 876 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	#10619112	C₂	1	8	yes	maximal, complemented
5	#10619109	C₂	1	8	yes	maximal, complemented
6	#10619108	C₂	1	8	yes	maximal, complemented
7	#10619105	C₂	1	8	yes	maximal, complemented
8	#10619100	C₂	1	6	yes	maximal, complemented
9	D₅×#575	C₂	1	6	yes	maximal, complemented
10	#10619088	C₂	1	6	yes	maximal, complemented
11	C₂×#66102	C₂	1	6	yes	maximal, complemented
12	#10619064	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#66084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#585	C₂²	1	2	yes	complemented
15	#66287	—	2	2	no	—
16	#66287	C₂²	1	8	yes	complemented
17	D₅×2₋¹⁺⁴	—	2	2	no	—
18	D₅×2₋¹⁺⁴	C₂²	1	8	yes	complemented
19	#66285	—	2	6	no	—
20	#66285	C₂²	1	8	yes	complemented
21	D₅×H(5,𝔽₂)	—	2	6	no	—
22	D₅×H(5,𝔽₂)	C₂²	1	8	yes	complemented
23	#66283	—	2	8	no	—
24	#66283	C₂²	1	12	yes	complemented
25	#66283	C₂²	1	2	yes	complemented
26	C₂×D₅×#41	—	2	8	no	—
27	C₂×D₅×#41	C₂²	1	1	yes	characteristic
28	C₂×D₅×#41	C₂²	1	12	yes	complemented
29	C₅×#578	C₂²	1	4	yes	complemented
30	C₅×#577	C₂²	1	8	yes	complemented
31	C₅×#576	C₂²	1	4	yes	complemented
32	C₅×#575	C₂²	1	6	yes	complemented
33	C₂×C₅×#135	C₂²	1	6	yes	complemented
34	C₂×C₅×#131	C₂²	1	1	yes	characteristic, complemented
35	#66172	C₂²	1	8	yes	complemented
36	#66171	C₂²	1	8	yes	complemented
37	#66170	C₂²	1	8	yes	complemented
38	#66169	C₂²	1	8	yes	complemented
39	#66156	C₂²	1	12	yes	complemented
40	C₂×#4096	C₂²	1	12	yes	complemented
41	C₂×#4094	C₂²	1	1	yes	characteristic, complemented
42	#66113	C₂²	1	24	yes	complemented
43	#66112	C₂²	1	24	yes	complemented
44	#66111	C₂²	1	24	yes	complemented
45	D₅×#137	C₂²	1	24	yes	complemented
46	#66109	C₂²	1	24	yes	complemented
47	#66108	C₂²	1	24	yes	complemented
48	#66107	C₂²	1	24	yes	complemented
49	D₅×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
50	#66105	C₂²	1	12	yes	complemented
51	#66104	C₂²	1	24	yes	complemented
52	#66103	C₂²	1	12	yes	complemented
53	#66102	C₂²	1	4	yes	complemented
54	#66102	C₂²	1	12	yes	complemented
55	#66102	C₂²	1	24	yes	complemented
56	#66102	C₂²	1	24	yes	complemented
57	#66102	C₂²	1	12	yes	complemented
58	#66102	C₂²	1	12	yes	complemented
59	D₅×#135	C₂²	1	24	yes	complemented
60	#66100	C₂²	1	12	yes	complemented
61	C₂×#4064	C₂²	1	12	yes	complemented
62	#66096	C₂²	1	24	yes	complemented
63	C₂×#4061	C₂²	1	12	yes	complemented
64	C₂×#4060	C₂²	1	12	yes	complemented
65	#66091	C₂²	1	12	yes	complemented
66	C₂×#4057	C₂²	1	12	yes	complemented
67	#66087	C₂²	1	4	yes	complemented
68	#66086	C₂²	1	4	yes	complemented
69	#66085	C₂²	1	8	yes	complemented
70	#66084	C₂²	1	8	yes	complemented
71	#66084	C₂²	1	8	yes	complemented
72	#66082	C₂²	1	6	yes	complemented
73	C₂×#4053	C₂²	1	3	yes	complemented
74	C₂×D₅×M₁₆	C₂²	1	3	yes	complemented
75	C₂×#4050	C₂²	1	6	yes	complemented
76	C₂×#4047	C₂²	1	3	yes	complemented
77	C₂²×#676	C₂²	1	3	yes	complemented
78	#63090	—	5	1	no	maximal, Sylow
79	C₅×2₋¹⁺⁴	—	2	2	no	—
80	C₅×2₋¹⁺⁴	C₂³	1	8	yes	complemented
81	C₅×H(5,𝔽₂)	—	2	6	no	—
82	C₅×H(5,𝔽₂)	C₂³	1	8	yes	complemented
83	C₂×C₅×#41	—	2	8	no	—
84	C₂×C₅×#41	C₂³	1	1	yes	characteristic
85	C₂×C₅×#41	C₂³	1	12	yes	complemented
86	#4150	—	2	8	no	—
87	#4150	—	2	24	no	—
88	#4150	—	2	12	no	—
89	#4150	C₂³	1	24	yes	complemented
90	#4150	C₂³	1	8	yes	complemented
91	#4149	—	2	8	no	—
92	#4149	—	2	24	no	—
93	#4149	—	2	12	no	—
94	#4149	C₂³	1	24	yes	complemented
95	#4149	C₂³	1	8	yes	complemented
96	D₅×#41	—	2	8	no	—
97	D₅×#41	—	2	8	no	—
98	D₅×#41	—	2	8	no	—
99	D₅×#41	—	2	24	no	—
100	D₅×#41	—	2	24	no	—
101	D₅×#41	—	2	24	no	—
102	D₅×#41	—	2	12	no	—
103	D₅×#41	—	2	12	no	—
104	D₅×#41	—	2	12	no	—
105	D₅×#41	—	2	12	no	—
106	D₅×#41	D₄	1	8	yes	—
107	D₅×#41	C₂³	1	8	yes	—
108	D₅×#41	C₂³	1	24	yes	—
109	D₅×#41	C₂³	1	8	yes	—
110	D₅×#41	C₂³	1	24	yes	complemented
111	D₅×#41	C₂³	1	24	yes	complemented
112	#4147	—	2	2	no	—
113	#4147	—	2	8	no	—
114	#4147	—	2	8	no	—
115	#4147	C₂³	1	24	yes	complemented
116	C₂×#713	—	2	8	no	—
117	C₂×#713	D₄	1	1	yes	characteristic
118	C₂×#713	C₂³	1	12	yes	—
119	C₂×Q₈×D₅	—	2	8	no	—
120	C₂×Q₈×D₅	D₄	1	1	yes	characteristic
121	C₂×Q₈×D₅	C₂³	1	12	yes	complemented
122	#4144	—	2	6	no	—
123	#4144	—	2	24	no	—
124	#4144	—	2	24	no	—
125	#4144	—	2	24	no	—
126	#4144	C₂³	1	24	yes	complemented
127	C₂×#711	—	2	12	no	—
128	C₂×#711	—	2	24	no	—
129	C₂×#711	D₄	1	3	yes	—
130	C₂×#711	C₂³	1	12	yes	—
131	C₂×D₄×D₅	—	2	12	no	—
132	C₂×D₄×D₅	—	2	24	no	—
133	C₂×D₄×D₅	D₄	1	3	yes	—
134	C₂×D₄×D₅	C₂³	1	12	yes	complemented
135	C₂×#709	—	2	24	no	—
136	C₂×#709	—	2	12	no	—
137	C₂×#709	C₂³	1	3	yes	—
138	C₂×#709	C₂³	1	12	yes	complemented
139	C₂²×C₄×D₅	—	2	12	no	—
140	C₂²×C₄×D₅	C₂³	1	3	yes	—
141	C₅×#137	C₂³	1	24	yes	complemented
142	C₅×AGL(1,ℤ/8)	C₂³	1	24	yes	complemented
143	C₅×#135	C₂³	1	12	yes	complemented
144	C₅×#135	C₂³	1	4	yes	complemented
145	C₅×#135	C₂³	1	12	yes	complemented
146	C₅×#135	C₂³	1	12	yes	complemented
147	C₂×C₅×Q₁₆	C₂³	1	6	yes	complemented
148	C₂×C₅×SD₁₆	C₂³	1	12	yes	complemented
149	C₂×C₅×D₈	C₂³	1	6	yes	complemented
150	C₅×#131	C₂³	1	4	yes	complemented
151	C₅×#131	C₂³	1	4	yes	complemented
152	C₂×C₅×M₁₆	C₂³	1	3	yes	complemented
153	C₂²×C₅×C₈	C₂³	1	3	yes	complemented
154	#4097	C₂³	1	24	yes	complemented
155	#4096	C₂³	1	24	yes	complemented
156	#4096	C₂³	1	8	yes	complemented
157	#4096	C₂³	1	24	yes	complemented
158	#4096	C₂³	1	24	yes	complemented
159	#4095	C₂³	1	24	yes	complemented
160	#4094	C₂³	1	8	yes	complemented
161	C₂×#689	C₂³	1	12	yes	complemented
162	#4088	C₂³	1	24	yes	complemented
163	C₂×#688	C₂³	1	12	yes	complemented
164	C₂×#687	C₂³	1	12	yes	complemented
165	#4078	C₂³	1	24	yes	complemented
166	C₂×#686	C₂³	1	12	yes	complemented
167	C₂×#681	C₂³	1	3	yes	complemented
168	C₂²×#168	C₂³	1	3	yes	complemented
169	#4065	C₂³	1	24	yes	complemented
170	#4064	C₂³	1	8	yes	complemented
171	#4064	C₂³	1	24	yes	complemented
172	#4064	C₂³	1	24	yes	complemented
173	#4064	C₂³	1	24	yes	complemented
174	D₅×Q₁₆	C₂³	1	24	yes	complemented
175	#4062	C₂³	1	48	yes	complemented
176	#4061	C₂³	1	8	yes	complemented
177	#4061	C₂³	1	24	yes	complemented
178	#4061	C₂³	1	24	yes	complemented
179	#4061	C₂³	1	24	yes	complemented
180	#4060	C₂³	1	8	yes	complemented
181	#4060	C₂³	1	24	yes	complemented
182	#4060	C₂³	1	24	yes	complemented
183	#4060	C₂³	1	24	yes	complemented
184	D₅×SD₁₆	C₂³	1	48	yes	complemented
185	#4058	C₂³	1	24	yes	complemented
186	#4057	C₂³	1	8	yes	complemented
187	#4057	C₂³	1	24	yes	complemented
188	#4057	C₂³	1	24	yes	complemented
189	#4057	C₂³	1	24	yes	complemented
190	D₅×D₈	C₂³	1	24	yes	complemented
191	#4055	C₂³	1	24	yes	complemented
192	#4054	C₂³	1	24	yes	complemented
193	#4053	C₂³	1	24	yes	complemented
194	D₅×M₁₆	C₂³	1	24	yes	complemented
195	C₂×Dic₂₀	C₂³	1	6	yes	complemented
196	#4050	C₂³	1	4	yes	complemented
197	#4050	C₂³	1	12	yes	complemented
198	#4050	C₂³	1	12	yes	complemented
199	#4050	C₂³	1	12	yes	complemented
200	C₂×D₄₀	C₂³	1	6	yes	complemented
201	C₂×#677	C₂³	1	12	yes	complemented
202	#4047	C₂³	1	12	yes	complemented
203	#4047	C₂³	1	12	yes	complemented
204	C₂×#676	C₂³	1	1	yes	characteristic
205	C₂×#676	C₂³	1	3	yes	—
206	C₂×#676	C₂³	1	3	yes	complemented
207	C₂×#676	C₂³	1	3	yes	complemented
208	C₂×#676	C₂³	1	12	yes	complemented
209	C₂×#676	C₂³	1	12	yes	complemented
210	C₂×C₈×D₅	C₂³	1	6	yes	complemented
211	C₂×#585	—	5	2	no	—
212	#3586	—	5	8	no	—
213	#3586	—	5	8	no	—
214	#3585	—	5	8	no	—
215	#3585	—	5	8	no	—
216	#3584	—	5	2	no	—
217	#3584	—	5	6	no	—
218	#3584	—	5	6	no	—
219	#3584	—	5	1	no	—
220	#3584	D₅	1	1	yes	characteristic, complemented
221	C₂×#575	—	5	6	no	—
222	C₂×#575	—	5	6	no	—
223	C₂×#568	—	5	1	no	—
224	C₂³×D₅	—	2	12	no	—
225	C₂³×D₅	C₂×D₄	1	3	yes	—
226	C₅×#41	—	2	8	no	—
227	C₅×#41	—	2	24	no	—
228	C₅×#41	—	2	12	no	—
229	C₅×#41	—	2	12	no	—
230	C₅×#41	C₂×D₄	1	4	yes	—
231	C₅×#41	C₂⁴	1	8	yes	—
232	C₅×#41	C₂⁴	1	24	yes	—
233	C₅×#41	C₂⁴	1	4	yes	—
234	C₂×C₅×Q₈	—	2	8	no	—
235	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
236	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
237	C₂×C₅×D₄	—	2	12	no	—
238	C₂×C₅×D₄	—	2	24	no	—
239	C₂×C₅×D₄	C₂×D₄	1	3	yes	—
240	C₂×C₅×D₄	C₂⁴	1	12	yes	—
241	C₂²×C₄×C₅	—	2	12	no	—
242	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
243	C₂×C₂²⋊D₅	—	2	12	no	—
244	C₂×C₂²⋊D₅	—	2	12	no	—
245	C₂×C₂²⋊D₅	—	2	48	no	—
246	C₂×C₂²⋊D₅	—	2	12	no	—
247	C₂×C₂²⋊D₅	C₂×D₄	1	6	yes	—
248	C₂²×Dic₅	—	2	12	no	—
249	C₂²×Dic₅	C₂×D₄	1	3	yes	—
250	#713	—	2	8	no	—
251	#713	—	2	24	no	—
252	#713	—	2	12	no	—
253	#713	—	2	12	no	—
254	#713	C₂×D₄	1	8	yes	—
255	#713	C₂⁴	1	8	yes	—
256	#713	C₂⁴	1	24	yes	—
257	Q₈×D₅	—	2	8	no	—
258	Q₈×D₅	—	2	12	no	—
259	Q₈×D₅	—	2	12	no	—
260	Q₈×D₅	—	2	24	no	—
261	Q₈×D₅	C₂×D₄	1	8	yes	—
262	Q₈×D₅	C₂⁴	1	8	yes	—
263	Q₈×D₅	C₂⁴	1	24	yes	—
264	#711	—	2	24	no	—
265	#711	—	2	48	no	—
266	#711	—	2	24	no	—
267	#711	—	2	8	no	—
268	#711	—	2	24	no	—
269	#711	—	2	24	no	—
270	#711	—	2	12	no	—
271	#711	—	2	12	no	—
272	#711	—	2	24	no	—
273	#711	C₂×D₄	1	24	yes	—
274	#711	C₂⁴	1	8	yes	—
275	#711	C₂⁴	1	24	yes	—
276	D₄×D₅	—	2	8	no	—
277	D₄×D₅	—	2	24	no	—
278	D₄×D₅	—	2	24	no	—
279	D₄×D₅	—	2	24	no	—
280	D₄×D₅	—	2	24	no	—
281	D₄×D₅	—	2	48	no	—
282	D₄×D₅	—	2	24	no	—
283	D₄×D₅	—	2	12	no	—
284	D₄×D₅	—	2	12	no	—
285	D₄×D₅	C₂×D₄	1	24	yes	—
286	D₄×D₅	C₂⁴	1	8	yes	—
287	D₄×D₅	C₂⁴	1	24	yes	—
288	#709	—	2	12	no	—
289	#709	—	2	12	no	—
290	#709	—	2	48	no	—
291	#709	—	2	24	no	—
292	#709	—	2	8	no	—
293	#709	—	2	24	no	—
294	#709	—	2	24	no	—
295	#709	—	2	24	no	—
296	#709	—	2	24	no	—
297	#709	C₂×D₄	1	12	yes	—
298	#709	C₂⁴	1	12	yes	—
299	#709	C₂⁴	1	8	yes	—
300	#709	C₂⁴	1	24	yes	—
301	C₂×D₂₀	—	2	12	no	—
302	C₂×D₂₀	—	2	24	no	—
303	C₂×D₂₀	C₂×D₄	1	3	yes	—
304	C₂×D₂₀	C₂⁴	1	12	yes	—
305	C₂×C₄×D₅	—	2	12	no	—
306	C₂×C₄×D₅	—	2	12	no	—
307	C₂×C₄×D₅	—	2	12	no	—
308	C₂×C₄×D₅	—	2	8	no	—
309	C₂×C₄×D₅	—	2	24	no	—
310	C₂×C₄×D₅	—	2	24	no	—
311	C₂×C₄×D₅	—	2	24	no	—
312	C₂×C₄×D₅	C₂×D₄	1	12	yes	—
313	C₂×C₄×D₅	C₂×D₄	1	3	yes	—
314	C₂×C₄×D₅	C₂×D₄	1	3	yes	—
315	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
316	C₂×C₄×D₅	C₂⁴	1	3	yes	—
317	C₂×C₄×D₅	C₂⁴	1	12	yes	—
318	C₂×Dic₁₀	—	2	12	no	—
319	C₂×Dic₁₀	—	2	24	no	—
320	C₂×Dic₁₀	C₂×D₄	1	3	yes	—
321	C₂×Dic₁₀	C₂⁴	1	12	yes	—
322	C₅×Q₁₆	C₂⁴	1	4	yes	—
323	C₅×Q₁₆	C₂⁴	1	12	yes	—
324	C₅×SD₁₆	C₂⁴	1	8	yes	—
325	C₅×SD₁₆	C₂⁴	1	24	yes	—
326	C₅×D₈	C₂⁴	1	4	yes	—
327	C₅×D₈	C₂⁴	1	12	yes	—
328	C₅×M₁₆	C₂⁴	1	12	yes	—
329	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
330	C₂×C₅×C₈	C₂⁴	1	3	yes	—
331	C₂×C₅×C₈	C₂⁴	1	6	yes	—
332	C₂×C₅×C₈	C₂⁴	1	6	yes	—
333	#689	C₂⁴	1	8	yes	—
334	#689	C₂⁴	1	24	yes	—
335	#688	C₂⁴	1	8	yes	—
336	#688	C₂⁴	1	24	yes	—
337	#687	C₂⁴	1	8	yes	—
338	#687	C₂⁴	1	24	yes	—
339	#686	C₂⁴	1	8	yes	—
340	#686	C₂⁴	1	24	yes	—
341	#681	C₂⁴	1	12	yes	—
342	C₂×#168	C₂⁴	1	3	yes	—
343	C₂×#168	C₂⁴	1	1	yes	characteristic
344	C₂×#168	C₂⁴	1	12	yes	—
345	Dic₂₀	C₂⁴	1	4	yes	—
346	Dic₂₀	C₂⁴	1	12	yes	—
347	D₄₀	C₂⁴	1	4	yes	—
348	D₄₀	C₂⁴	1	12	yes	—
349	#677	C₂⁴	1	8	yes	—
350	#677	C₂⁴	1	24	yes	—
351	#676	C₂⁴	1	2	yes	—
352	#676	C₂⁴	1	2	yes	—
353	#676	C₂⁴	1	12	yes	—
354	#676	C₂⁴	1	6	yes	—
355	#676	C₂⁴	1	6	yes	—
356	#676	C₂⁴	1	12	yes	—
357	C₈×D₅	C₂⁴	1	24	yes	—
358	#585	—	5	8	no	—
359	#585	—	5	8	no	—
360	#585	—	5	2	no	—
361	#585	—	5	12	no	—
362	#585	—	10	8	no	—
363	#585	—	10	6	no	—
364	#585	—	10	2	no	—
365	#585	C₂×D₅	1	2	yes	complemented
366	C₂×2₋¹⁺⁴	—	5	8	no	—
367	C₂×2₋¹⁺⁴	—	10	2	no	—
368	C₂×H(5,𝔽₂)	—	5	8	no	—
369	C₂×H(5,𝔽₂)	—	10	6	no	—
370	C₂²×#41	—	5	1	no	—
371	C₂²×#41	—	5	12	no	—
372	C₂²×#41	—	10	8	no	—
373	#578	—	5	8	no	—
374	#578	—	5	24	no	—
375	#578	—	5	12	no	—
376	#578	—	5	12	no	—
377	#578	—	5	4	no	—
378	#578	C₂×D₅	1	4	yes	complemented
379	#577	—	5	8	no	—
380	#577	—	5	8	no	—
381	#577	—	5	24	no	—
382	#577	—	5	24	no	—
383	#577	—	5	24	no	—
384	#577	—	5	24	no	—
385	#577	—	5	8	no	—
386	#577	C₂×D₅	1	8	yes	complemented
387	#576	—	5	8	no	—
388	#576	—	5	24	no	—
389	#576	—	5	12	no	—
390	#576	—	5	12	no	—
391	#576	—	5	4	no	—
392	#576	C₂×D₅	1	4	yes	complemented
393	#575	—	5	12	no	—
394	#575	—	5	24	no	—
395	#575	—	5	24	no	—
396	#575	—	5	12	no	—
397	#575	—	5	12	no	—
398	#575	—	5	24	no	—
399	#575	—	5	24	no	—
400	#575	—	5	12	no	—
401	#575	—	5	4	no	—
402	#575	—	5	6	no	—
403	#575	C₂×D₅	1	6	yes	complemented
404	C₂×#137	—	5	24	no	—
405	C₂×#137	—	5	12	no	—
406	C₂×#137	—	5	12	no	—
407	C₂×AGL(1,ℤ/8)	—	5	24	no	—
408	C₂×AGL(1,ℤ/8)	—	5	12	no	—
409	C₂×AGL(1,ℤ/8)	—	5	12	no	—
410	C₂×#135	—	5	12	no	—
411	C₂×#135	—	5	24	no	—
412	C₂×#135	—	5	6	no	—
413	C₂×#135	C₂×D₅	1	6	yes	complemented
414	#568	—	5	8	no	—
415	#568	—	5	8	no	—
416	C₂×#131	—	5	1	no	—
417	C₂×#131	—	5	3	no	—
418	C₂×#131	—	5	3	no	—
419	C₂×#131	C₂×D₅	1	1	yes	characteristic, complemented
420	C₂²×M₁₆	—	5	3	no	—
421	C₂²×M₁₆	—	5	3	no	—
422	C₂³×C₅	—	2	12	no	—
423	C₂³×C₅	C₂²×D₄	1	3	yes	—
424	C₂²×D₅	—	2	12	no	—
425	C₂²×D₅	—	2	8	no	—
426	C₂²×D₅	—	2	24	no	—
427	C₂²×D₅	—	8	3	no	—
428	C₂²×D₅	—	8	24	no	—
429	C₂²×D₅	C₂²×D₄	1	12	yes	—
430	C₂²×D₅	C₂²×D₄	1	1	yes	characteristic
431	C₂²×D₅	C₂²×D₄	1	3	yes	—
432	C₅×Q₈	—	2	12	no	—
433	C₅×Q₈	C₂²×D₄	1	4	yes	—
434	C₅×Q₈	C₂⁵	1	8	yes	—
435	C₅×D₄	—	2	24	no	—
436	C₅×D₄	—	2	8	no	—
437	C₅×D₄	—	2	12	no	—
438	C₅×D₄	C₂²×D₄	1	12	yes	—
439	C₅×D₄	C₂⁵	1	8	yes	—
440	C₂×C₄×C₅	—	2	12	no	—
441	C₂×C₄×C₅	—	2	24	no	—
442	C₂×C₄×C₅	—	2	8	no	—
443	C₂×C₄×C₅	C₂²×D₄	1	3	yes	—
444	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
445	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
446	C₂×C₄×C₅	C₂⁵	1	6	yes	—
447	C₂²⋊D₅	—	2	24	no	—
448	C₂²⋊D₅	—	2	8	no	—
449	C₂²⋊D₅	—	2	8	no	—
450	C₂²⋊D₅	—	2	24	no	—
451	C₂²⋊D₅	—	2	24	no	—
452	C₂²⋊D₅	—	2	8	no	—
453	C₂²⋊D₅	C₂²×D₄	1	24	yes	—
454	C₂×Dic₅	—	2	12	no	—
455	C₂×Dic₅	—	2	24	no	—
456	C₂×Dic₅	—	2	8	no	—
457	C₂×Dic₅	C₂²×D₄	1	12	yes	—
458	C₂×Dic₅	C₂²×D₄	1	3	yes	—
459	C₂×Dic₅	C₂²×D₄	1	1	yes	characteristic
460	D₂₀	—	2	8	no	—
461	D₂₀	—	2	24	no	—
462	D₂₀	—	2	12	no	—
463	D₂₀	C₂²×D₄	1	12	yes	—
464	D₂₀	C₂⁵	1	8	yes	—
465	C₄×D₅	—	2	8	no	—
466	C₄×D₅	—	2	24	no	—
467	C₄×D₅	—	2	8	no	—
468	C₄×D₅	—	2	24	no	—
469	C₄×D₅	—	2	8	no	—
470	C₄×D₅	—	2	24	no	—
471	C₄×D₅	C₂²×D₄	1	2	yes	—
472	C₄×D₅	C₂²×D₄	1	6	yes	—
473	C₄×D₅	C₂²×D₄	1	12	yes	—
474	C₄×D₅	C₂²×D₄	1	12	yes	—
475	C₄×D₅	C₂⁵	1	6	yes	—
476	C₄×D₅	C₂⁵	1	2	yes	—
477	Dic₁₀	—	2	12	no	—
478	Dic₁₀	—	2	24	no	—
479	Dic₁₀	—	2	8	no	—
480	Dic₁₀	C₂²×D₄	1	12	yes	—
481	Dic₁₀	C₂⁵	1	8	yes	—
482	C₅×C₈	C₂⁵	1	6	yes	—
483	C₅×C₈	C₂⁵	1	1	yes	characteristic
484	C₅×C₈	C₂⁵	1	1	yes	characteristic
485	#168	C₂⁵	1	6	yes	—
486	#168	C₂⁵	1	2	yes	—
487	2₋¹⁺⁴	—	2	2	no	—
488	2₋¹⁺⁴	—	5	24	no	—
489	2₋¹⁺⁴	—	5	8	no	—
490	2₋¹⁺⁴	—	5	24	no	—
491	2₋¹⁺⁴	—	10	8	no	—
492	2₋¹⁺⁴	—	10	8	no	—
493	2₋¹⁺⁴	—	10	8	no	—
494	2₋¹⁺⁴	—	10	12	no	—
495	2₋¹⁺⁴	—	10	24	no	—
496	2₋¹⁺⁴	—	10	2	no	—
497	2₋¹⁺⁴	C₂²×D₅	1	8	yes	complemented
498	H(5,𝔽₂)	—	2	6	no	—
499	H(5,𝔽₂)	—	5	24	no	—
500	H(5,𝔽₂)	—	5	8	no	—
501	H(5,𝔽₂)	—	5	24	no	—
502	H(5,𝔽₂)	—	10	24	no	—
503	H(5,𝔽₂)	—	10	24	no	—
504	H(5,𝔽₂)	—	10	24	no	—
505	H(5,𝔽₂)	—	10	24	no	—
506	H(5,𝔽₂)	—	10	12	no	—
507	H(5,𝔽₂)	—	10	8	no	—
508	H(5,𝔽₂)	—	10	6	no	—
509	H(5,𝔽₂)	C₂²×D₅	1	8	yes	complemented
510	C₂×#41	—	2	8	no	—
511	C₂×#41	—	5	8	no	—
512	C₂×#41	—	5	8	no	—
513	C₂×#41	—	5	1	no	—
514	C₂×#41	—	5	3	no	—
515	C₂×#41	—	5	3	no	—
516	C₂×#41	—	5	24	no	—
517	C₂×#41	—	5	8	no	—
518	C₂×#41	—	5	24	no	—
519	C₂×#41	—	5	24	no	—
520	C₂×#41	—	5	12	no	—
521	C₂×#41	—	5	12	no	—
522	C₂×#41	—	5	12	no	—
523	C₂×#41	—	10	12	no	—
524	C₂×#41	—	10	24	no	—
525	C₂×#41	—	10	12	no	—
526	C₂×#41	—	10	12	no	—
527	C₂×#41	—	10	12	no	—
528	C₂×#41	—	10	12	no	—
529	C₂×#41	—	10	12	no	—
530	C₂×#41	—	10	24	no	—
531	C₂×#41	—	10	24	no	—
532	C₂×#41	—	10	8	no	—
533	C₂×#41	—	10	8	no	—
534	C₂×#41	—	10	8	no	—
535	C₂×#41	—	10	24	no	—
536	C₂×#41	—	10	24	no	—
537	C₂×#41	—	10	8	no	—
538	C₂×#41	C₂²×D₅	1	1	yes	characteristic
539	C₂×#41	C₂²×D₅	1	12	yes	complemented
540	C₂²×Q₈	—	5	1	no	—
541	C₂²×Q₈	—	5	12	no	—
542	C₂²×Q₈	—	10	8	no	—
543	C₂²×D₄	—	5	3	no	—
544	C₂²×D₄	—	5	12	no	—
545	C₂²×D₄	—	10	24	no	—
546	C₂²×D₄	—	10	12	no	—
547	C₂³×C₄	—	5	3	no	—
548	C₂³×C₄	—	10	12	no	—
549	#137	—	5	24	no	—
550	#137	—	5	24	no	—
551	#137	—	5	24	no	—
552	#137	—	5	8	no	—
553	#137	—	5	24	no	—
554	#137	—	5	24	no	—
555	#137	—	5	24	no	—
556	#137	—	5	8	no	—
557	#137	—	5	24	no	—
558	#137	—	5	24	no	—
559	#137	—	5	24	no	—
560	#137	C₂²×D₅	1	24	yes	complemented
561	AGL(1,ℤ/8)	—	5	24	no	—
562	AGL(1,ℤ/8)	—	5	24	no	—
563	AGL(1,ℤ/8)	—	5	24	no	—
564	AGL(1,ℤ/8)	—	5	8	no	—
565	AGL(1,ℤ/8)	—	5	24	no	—
566	AGL(1,ℤ/8)	—	5	24	no	—
567	AGL(1,ℤ/8)	—	5	24	no	—
568	AGL(1,ℤ/8)	—	5	8	no	—
569	AGL(1,ℤ/8)	—	5	24	no	—
570	AGL(1,ℤ/8)	—	5	24	no	—
571	AGL(1,ℤ/8)	—	5	24	no	—
572	AGL(1,ℤ/8)	C₂²×D₅	1	24	yes	complemented
573	#135	—	5	24	no	—
574	#135	—	5	8	no	—
575	#135	—	5	24	no	—
576	#135	—	5	24	no	—
577	#135	—	5	24	no	—
578	#135	—	5	48	no	—
579	#135	—	5	24	no	—
580	#135	—	5	12	no	—
581	#135	—	5	4	no	—
582	#135	—	5	12	no	—
583	#135	—	5	12	no	—
584	#135	C₂²×D₅	1	12	yes	complemented
585	#135	C₂²×D₅	1	4	yes	complemented
586	#135	C₂²×D₅	1	12	yes	complemented
587	#135	C₂²×D₅	1	12	yes	complemented
588	C₂×Q₁₆	—	5	12	no	—
589	C₂×Q₁₆	—	5	24	no	—
590	C₂×Q₁₆	—	5	6	no	—
591	C₂×Q₁₆	C₂²×D₅	1	6	yes	complemented
592	C₂×SD₁₆	—	5	12	no	—
593	C₂×SD₁₆	—	5	12	no	—
594	C₂×SD₁₆	—	5	48	no	—
595	C₂×SD₁₆	—	5	12	no	—
596	C₂×SD₁₆	C₂²×D₅	1	12	yes	complemented
597	C₂×D₈	—	5	12	no	—
598	C₂×D₈	—	5	24	no	—
599	C₂×D₈	—	5	6	no	—
600	C₂×D₈	C₂²×D₅	1	6	yes	complemented
601	#131	—	5	8	no	—
602	#131	—	5	24	no	—
603	#131	—	5	12	no	—
604	#131	—	5	12	no	—
605	#131	C₂²×D₅	1	4	yes	complemented
606	#131	C₂²×D₅	1	4	yes	complemented
607	C₂×M₁₆	—	5	3	no	—
608	C₂×M₁₆	—	5	24	no	—
609	C₂×M₁₆	—	5	3	no	—
610	C₂×M₁₆	—	5	1	no	—
611	C₂×M₁₆	—	5	3	no	—
612	C₂×M₁₆	—	5	3	no	—
613	C₂×M₁₆	—	5	12	no	—
614	C₂×M₁₆	—	5	12	no	—
615	C₂×M₁₆	C₂²×D₅	1	3	yes	complemented
616	C₂²×C₈	—	5	3	no	—
617	C₂²×C₈	—	5	6	no	—
618	C₂²×C₈	C₂²×D₅	1	3	yes	complemented
619	C₂²×C₅	—	2	8	no	—
620	C₂²×C₅	—	4	3	no	—
621	C₂²×C₅	—	8	12	no	—
622	C₂²×C₅	C₂³×D₄	1	6	yes	—
623	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
624	C₂×D₅	—	2	8	no	—
625	C₂×D₅	—	4	1	no	—
626	C₂×D₅	—	4	12	no	—
627	C₂×D₅	—	4	3	no	—
628	C₂×D₅	—	4	16	no	—
629	C₂×D₅	—	8	24	no	—
630	C₂×D₅	—	8	12	no	—
631	C₂×D₅	C₂³×D₄	1	2	yes	—
632	C₂×D₅	C₂³×D₄	1	6	yes	—
633	C₄×C₅	—	2	8	no	—
634	C₄×C₅	C₂³×D₄	1	6	yes	—
635	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
636	C₄×C₅	C₂⁶	1	1	yes	characteristic
637	Dic₅	—	2	8	no	—
638	Dic₅	C₂³×D₄	1	6	yes	—
639	Dic₅	C₂³×D₄	1	2	yes	—
640	C₂⁴	—	5	3	no	—
641	C₂⁴	—	10	12	no	—
642	#41	—	2	8	no	—
643	#41	—	2	24	no	—
644	#41	—	2	12	no	—
645	#41	—	2	12	no	—
646	#41	—	5	8	no	—
647	#41	—	5	24	no	—
648	#41	—	5	12	no	—
649	#41	—	5	12	no	—
650	#41	—	5	24	no	—
651	#41	—	5	8	no	—
652	#41	—	5	24	no	—
653	#41	—	5	8	no	—
654	#41	—	5	8	no	—
655	#41	—	5	24	no	—
656	#41	—	10	8	no	—
657	#41	—	10	24	no	—
658	#41	—	10	24	no	—
659	#41	—	10	24	no	—
660	#41	—	10	48	no	—
661	#41	—	10	24	no	—
662	#41	—	10	24	no	—
663	#41	—	10	8	no	—
664	#41	—	10	24	no	—
665	#41	—	10	12	no	—
666	#41	—	10	24	no	—
667	#41	—	10	24	no	—
668	#41	—	10	12	no	—
669	#41	—	10	12	no	—
670	#41	—	10	12	no	—
671	#41	—	10	48	no	—
672	#41	—	10	24	no	—
673	#41	—	10	24	no	—
674	#41	—	10	8	no	—
675	#41	—	10	24	no	—
676	#41	—	10	12	no	—
677	#41	—	10	12	no	—
678	#41	D₄×D₅	1	4	yes	—
679	#41	C₂³×D₅	1	8	yes	—
680	#41	C₂³×D₅	1	24	yes	—
681	#41	C₂³×D₅	1	4	yes	—
682	C₂×Q₈	—	2	8	no	—
683	C₂×Q₈	—	5	8	no	—
684	C₂×Q₈	—	5	3	no	—
685	C₂×Q₈	—	5	24	no	—
686	C₂×Q₈	—	5	8	no	—
687	C₂×Q₈	—	5	12	no	—
688	C₂×Q₈	—	10	12	no	—
689	C₂×Q₈	—	10	24	no	—
690	C₂×Q₈	—	10	12	no	—
691	C₂×Q₈	—	10	12	no	—
692	C₂×Q₈	—	10	24	no	—
693	C₂×Q₈	—	10	8	no	—
694	C₂×Q₈	D₄×D₅	1	1	yes	characteristic
695	C₂×Q₈	C₂³×D₅	1	12	yes	—
696	C₂×D₄	—	2	12	no	—
697	C₂×D₄	—	2	24	no	—
698	C₂×D₄	—	5	6	no	—
699	C₂×D₄	—	5	24	no	—
700	C₂×D₄	—	5	24	no	—
701	C₂×D₄	—	5	8	no	—
702	C₂×D₄	—	5	3	no	—
703	C₂×D₄	—	5	12	no	—
704	C₂×D₄	—	10	24	no	—
705	C₂×D₄	—	10	12	no	—
706	C₂×D₄	—	10	12	no	—
707	C₂×D₄	—	10	12	no	—
708	C₂×D₄	—	10	12	no	—
709	C₂×D₄	—	10	48	no	—
710	C₂×D₄	—	10	24	no	—
711	C₂×D₄	—	10	8	no	—
712	C₂×D₄	—	10	24	no	—
713	C₂×D₄	—	10	24	no	—
714	C₂×D₄	—	10	24	no	—
715	C₂×D₄	—	10	48	no	—
716	C₂×D₄	—	10	12	no	—
717	C₂×D₄	—	10	12	no	—
718	C₂×D₄	—	10	24	no	—
719	C₂×D₄	D₄×D₅	1	3	yes	—
720	C₂×D₄	C₂³×D₅	1	12	yes	—
721	C₂²×C₄	—	2	12	no	—
722	C₂²×C₄	—	5	3	no	—
723	C₂²×C₄	—	5	12	no	—
724	C₂²×C₄	—	5	3	no	—
725	C₂²×C₄	—	5	3	no	—
726	C₂²×C₄	—	5	3	no	—
727	C₂²×C₄	—	5	1	no	—
728	C₂²×C₄	—	5	12	no	—
729	C₂²×C₄	—	10	8	no	—
730	C₂²×C₄	—	10	24	no	—
731	C₂²×C₄	—	10	12	no	—
732	C₂²×C₄	—	10	24	no	—
733	C₂²×C₄	—	10	24	no	—
734	C₂²×C₄	—	10	12	no	—
735	C₂²×C₄	—	10	12	no	—
736	C₂²×C₄	—	10	12	no	—
737	C₂²×C₄	C₂³×D₅	1	3	yes	—
738	Q₁₆	—	5	8	no	—
739	Q₁₆	—	5	24	no	—
740	Q₁₆	—	5	12	no	—
741	Q₁₆	—	5	4	no	—
742	Q₁₆	C₂³×D₅	1	12	yes	—
743	Q₁₆	C₂³×D₅	1	4	yes	—
744	SD₁₆	—	5	8	no	—
745	SD₁₆	—	5	24	no	—
746	SD₁₆	—	5	8	no	—
747	SD₁₆	—	5	24	no	—
748	SD₁₆	—	5	24	no	—
749	SD₁₆	—	5	8	no	—
750	SD₁₆	C₂³×D₅	1	24	yes	—
751	SD₁₆	C₂³×D₅	1	8	yes	—
752	D₈	—	5	8	no	—
753	D₈	—	5	24	no	—
754	D₈	—	5	12	no	—
755	D₈	—	5	4	no	—
756	D₈	C₂³×D₅	1	12	yes	—
757	D₈	C₂³×D₅	1	4	yes	—
758	M₁₆	—	5	12	no	—
759	M₁₆	—	5	12	no	—
760	M₁₆	—	5	2	no	—
761	M₁₆	—	5	2	no	—
762	M₁₆	—	5	12	no	—
763	M₁₆	—	5	6	no	—
764	M₁₆	—	5	6	no	—
765	M₁₆	C₂³×D₅	1	12	yes	—
766	C₂×C₈	—	5	1	no	—
767	C₂×C₈	—	5	3	no	—
768	C₂×C₈	—	5	12	no	—
769	C₂×C₈	—	5	24	no	—
770	C₂×C₈	C₂³×D₅	1	3	yes	—
771	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
772	C₂×C₈	C₂³×D₅	1	6	yes	—
773	C₂×C₈	C₂³×D₅	1	6	yes	—
774	C₂×C₅	—	2	1	no	—
775	C₂×C₅	—	2	6	no	—
776	C₂×C₅	—	4	8	no	—
777	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
778	D₅	—	2	2	no	—
779	D₅	—	2	6	no	—
780	D₅	—	4	8	no	—
781	C₂³	—	2	12	no	—
782	C₂³	—	5	1	no	—
783	C₂³	—	5	12	no	—
784	C₂³	—	5	3	no	—
785	C₂³	—	10	8	no	—
786	C₂³	—	10	24	no	—
787	C₂³	—	10	12	no	—
788	C₂³	—	40	3	no	—
789	C₂³	—	40	24	no	—
790	C₂³	C₂×D₄×D₅	1	3	yes	—
791	Q₈	—	2	12	no	—
792	Q₈	—	5	12	no	—
793	Q₈	—	5	8	no	—
794	Q₈	—	10	8	no	—
795	Q₈	—	10	24	no	—
796	Q₈	—	10	12	no	—
797	Q₈	C₂×D₄×D₅	1	4	yes	—
798	Q₈	C₂⁴×D₅	1	8	yes	—
799	D₄	—	2	24	no	—
800	D₄	—	2	8	no	—
801	D₄	—	2	12	no	—
802	D₄	—	5	24	no	—
803	D₄	—	5	12	no	—
804	D₄	—	5	8	no	—
805	D₄	—	10	8	no	—
806	D₄	—	10	24	no	—
807	D₄	—	10	8	no	—
808	D₄	—	10	24	no	—
809	D₄	—	10	8	no	—
810	D₄	—	10	24	no	—
811	D₄	—	10	24	no	—
812	D₄	—	10	8	no	—
813	D₄	—	10	12	no	—
814	D₄	C₂×D₄×D₅	1	12	yes	—
815	D₄	C₂⁴×D₅	1	8	yes	—
816	C₂×C₄	—	2	12	no	—
817	C₂×C₄	—	2	24	no	—
818	C₂×C₄	—	2	8	no	—
819	C₂×C₄	—	5	1	no	—
820	C₂×C₄	—	5	12	no	—
821	C₂×C₄	—	5	3	no	—
822	C₂×C₄	—	5	12	no	—
823	C₂×C₄	—	5	12	no	—
824	C₂×C₄	—	5	2	no	—
825	C₂×C₄	—	5	6	no	—
826	C₂×C₄	—	5	6	no	—
827	C₂×C₄	—	5	2	no	—
828	C₂×C₄	—	10	8	no	—
829	C₂×C₄	—	10	24	no	—
830	C₂×C₄	—	10	8	no	—
831	C₂×C₄	—	10	24	no	—
832	C₂×C₄	—	10	8	no	—
833	C₂×C₄	—	10	24	no	—
834	C₂×C₄	—	10	12	no	—
835	C₂×C₄	—	10	24	no	—
836	C₂×C₄	—	10	8	no	—
837	C₂×C₄	C₂×D₄×D₅	1	3	yes	—
838	C₂×C₄	C₂×D₄×D₅	1	6	yes	—
839	C₂×C₄	C₂⁴×D₅	1	6	yes	—
840	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
841	C₈	—	5	2	no	—
842	C₈	—	5	6	no	—
843	C₈	C₂⁴×D₅	1	6	yes	—
844	C₈	C₂⁴×D₅	1	1	yes	characteristic
845	C₈	C₂⁴×D₅	1	1	yes	characteristic
846	C₅	#63090	1	1	yes	characteristic, complemented, Sylow
847	C₂²	—	2	8	no	—
848	C₂²	—	4	3	no	—
849	C₂²	—	5	2	no	—
850	C₂²	—	5	6	no	—
851	C₂²	—	8	12	no	—
852	C₂²	—	10	8	no	—
853	C₂²	—	20	1	no	—
854	C₂²	—	20	12	no	—
855	C₂²	—	20	3	no	—
856	C₂²	—	20	16	no	—
857	C₂²	—	40	12	no	—
858	C₂²	—	40	24	no	—
859	C₂²	C₂²×D₄×D₅	1	6	yes	—
860	C₂²	C₂²×D₄×D₅	1	1	yes	characteristic
861	C₄	—	2	8	no	—
862	C₄	—	5	2	no	—
863	C₄	—	5	6	no	—
864	C₄	—	10	8	no	—
865	C₄	C₂²×D₄×D₅	1	6	yes	—
866	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
867	C₄	C₂⁵×D₅	1	1	yes	characteristic
868	C₂	—	2	1	no	—
869	C₂	—	2	6	no	—
870	C₂	—	4	8	no	—
871	C₂	—	10	2	no	—
872	C₂	—	10	6	no	—
873	C₂	—	20	8	no	—
874	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	#63090
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. #10619112	C₂	semidirect
5. #10619109	C₂	semidirect
6. #10619108	C₂	semidirect
7. #10619105	C₂	semidirect
8. #10619100	C₂	semidirect
9. D₅×#575	C₂	semidirect
10. #10619088	C₂	semidirect
11. C₂×#66102	C₂	semidirect
12. #10619064	C₂	semidirect
13. C₂×#66084	C₂	semidirect
14. C₅×#585	C₂²	semidirect
16. #66287	C₂²	semidirect
18. D₅×2₋¹⁺⁴	C₂²	semidirect
20. #66285	C₂²	semidirect
22. D₅×H(5,𝔽₂)	C₂²	semidirect
24. #66283	C₂²	semidirect
25. #66283	C₂²	semidirect
28. C₂×D₅×#41	C₂²	semidirect
29. C₅×#578	C₂²	semidirect
30. C₅×#577	C₂²	semidirect
31. C₅×#576	C₂²	semidirect
32. C₅×#575	C₂²	semidirect
33. C₂×C₅×#135	C₂²	semidirect
34. C₂×C₅×#131	C₂²	semidirect
35. #66172	C₂²	semidirect
36. #66171	C₂²	semidirect
37. #66170	C₂²	semidirect
38. #66169	C₂²	semidirect
39. #66156	C₂²	semidirect
40. C₂×#4096	C₂²	semidirect
41. C₂×#4094	C₂²	semidirect
42. #66113	C₂²	semidirect
43. #66112	C₂²	semidirect
44. #66111	C₂²	semidirect
45. D₅×#137	C₂²	semidirect
46. #66109	C₂²	semidirect
47. #66108	C₂²	semidirect
48. #66107	C₂²	semidirect
49. D₅×AGL(1,ℤ/8)	C₂²	semidirect
50. #66105	C₂²	semidirect
51. #66104	C₂²	semidirect
52. #66103	C₂²	semidirect
53. #66102	C₂²	semidirect
54. #66102	C₂²	semidirect
55. #66102	C₂²	semidirect
56. #66102	C₂²	semidirect
57. #66102	C₂²	semidirect
58. #66102	C₂²	semidirect
59. D₅×#135	C₂²	semidirect
60. #66100	C₂²	semidirect
61. C₂×#4064	C₂²	semidirect
62. #66096	C₂²	semidirect
63. C₂×#4061	C₂²	semidirect
64. C₂×#4060	C₂²	semidirect
65. #66091	C₂²	semidirect
66. C₂×#4057	C₂²	semidirect
67. #66087	C₂²	semidirect
68. #66086	C₂²	semidirect
69. #66085	C₂²	semidirect
70. #66084	C₂²	semidirect
71. #66084	C₂²	semidirect
72. #66082	C₂²	semidirect
73. C₂×#4053	C₂²	semidirect
74. C₂×D₅×M₁₆	C₂²	semidirect
75. C₂×#4050	C₂²	semidirect
76. C₂×#4047	C₂²	semidirect
77. C₂²×#676	C₂²	semidirect
80. C₅×2₋¹⁺⁴	C₂³	semidirect
82. C₅×H(5,𝔽₂)	C₂³	semidirect
85. C₂×C₅×#41	C₂³	semidirect
89. #4150	C₂³	semidirect
90. #4150	C₂³	semidirect
94. #4149	C₂³	semidirect
95. #4149	C₂³	semidirect
110. D₅×#41	C₂³	semidirect
111. D₅×#41	C₂³	semidirect
115. #4147	C₂³	semidirect
121. C₂×Q₈×D₅	C₂³	semidirect
126. #4144	C₂³	semidirect
134. C₂×D₄×D₅	C₂³	semidirect
138. C₂×#709	C₂³	semidirect
141. C₅×#137	C₂³	semidirect
142. C₅×AGL(1,ℤ/8)	C₂³	semidirect
143. C₅×#135	C₂³	semidirect
144. C₅×#135	C₂³	semidirect
145. C₅×#135	C₂³	semidirect
146. C₅×#135	C₂³	semidirect
147. C₂×C₅×Q₁₆	C₂³	semidirect
148. C₂×C₅×SD₁₆	C₂³	semidirect
149. C₂×C₅×D₈	C₂³	semidirect
150. C₅×#131	C₂³	semidirect
151. C₅×#131	C₂³	semidirect
152. C₂×C₅×M₁₆	C₂³	semidirect
153. C₂²×C₅×C₈	C₂³	semidirect
154. #4097	C₂³	semidirect
155. #4096	C₂³	semidirect
156. #4096	C₂³	semidirect
157. #4096	C₂³	semidirect
158. #4096	C₂³	semidirect
159. #4095	C₂³	semidirect
160. #4094	C₂³	semidirect
161. C₂×#689	C₂³	semidirect
162. #4088	C₂³	semidirect
163. C₂×#688	C₂³	semidirect
164. C₂×#687	C₂³	semidirect
165. #4078	C₂³	semidirect
166. C₂×#686	C₂³	semidirect
167. C₂×#681	C₂³	semidirect
168. C₂²×#168	C₂³	semidirect
169. #4065	C₂³	semidirect
170. #4064	C₂³	semidirect
171. #4064	C₂³	semidirect
172. #4064	C₂³	semidirect
173. #4064	C₂³	semidirect
174. D₅×Q₁₆	C₂³	semidirect
175. #4062	C₂³	semidirect
176. #4061	C₂³	semidirect
177. #4061	C₂³	semidirect
178. #4061	C₂³	semidirect
179. #4061	C₂³	semidirect
180. #4060	C₂³	semidirect
181. #4060	C₂³	semidirect
182. #4060	C₂³	semidirect
183. #4060	C₂³	semidirect
184. D₅×SD₁₆	C₂³	semidirect
185. #4058	C₂³	semidirect
186. #4057	C₂³	semidirect
187. #4057	C₂³	semidirect
188. #4057	C₂³	semidirect
189. #4057	C₂³	semidirect
190. D₅×D₈	C₂³	semidirect
191. #4055	C₂³	semidirect
192. #4054	C₂³	semidirect
193. #4053	C₂³	semidirect
194. D₅×M₁₆	C₂³	semidirect
195. C₂×Dic₂₀	C₂³	semidirect
196. #4050	C₂³	semidirect
197. #4050	C₂³	semidirect
198. #4050	C₂³	semidirect
199. #4050	C₂³	semidirect
200. C₂×D₄₀	C₂³	semidirect
201. C₂×#677	C₂³	semidirect
202. #4047	C₂³	semidirect
203. #4047	C₂³	semidirect
206. C₂×#676	C₂³	semidirect
207. C₂×#676	C₂³	semidirect
208. C₂×#676	C₂³	semidirect
209. C₂×#676	C₂³	semidirect
210. C₂×C₈×D₅	C₂³	semidirect
220. #3584	D₅	semidirect
365. #585	C₂×D₅	semidirect
378. #578	C₂×D₅	semidirect
386. #577	C₂×D₅	semidirect
392. #576	C₂×D₅	semidirect
403. #575	C₂×D₅	semidirect
413. C₂×#135	C₂×D₅	semidirect
419. C₂×#131	C₂×D₅	semidirect
497. 2₋¹⁺⁴	C₂²×D₅	semidirect
509. H(5,𝔽₂)	C₂²×D₅	semidirect
539. C₂×#41	C₂²×D₅	semidirect
560. #137	C₂²×D₅	semidirect
572. AGL(1,ℤ/8)	C₂²×D₅	semidirect
584. #135	C₂²×D₅	semidirect
585. #135	C₂²×D₅	semidirect
586. #135	C₂²×D₅	semidirect
587. #135	C₂²×D₅	semidirect
591. C₂×Q₁₆	C₂²×D₅	semidirect
596. C₂×SD₁₆	C₂²×D₅	semidirect
600. C₂×D₈	C₂²×D₅	semidirect
605. #131	C₂²×D₅	semidirect
606. #131	C₂²×D₅	semidirect
615. C₂×M₁₆	C₂²×D₅	semidirect
618. C₂²×C₈	C₂²×D₅	semidirect
846. C₅	#63090	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
#10619112	2
#10619109	2
#10619108	2
#10619105	2
#10619100	2
D₅×#575	2
#10619088	2
C₂×#66102	2
#10619064	2
C₂×#66084	2
#63090	5