Subgroups — #12068241

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617731	C₂	1	1	yes	maximal, characteristic
2	C₅×#2990	C₂	1	1	yes	maximal, characteristic
3	#10614253	C₂	1	1	yes	maximal, characteristic
4	#10601618	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601617	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601614	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601613	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601574	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601569	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601303	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601302	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601232	C₂	1	1	yes	maximal, characteristic, complemented
13	#10601231	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601230	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#64701	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	#66159	C₄	1	2	yes	—
18	#65901	—	2	1	no	—
19	#65901	—	2	1	no	—
20	#65876	—	2	1	no	—
21	#65876	—	2	1	no	—
22	#65875	—	2	1	no	—
23	#65875	—	2	1	no	—
24	#65875	—	2	1	no	—
25	#65875	—	2	1	no	—
26	#65852	C₄	1	2	yes	—
27	#65852	C₄	1	2	yes	—
28	#65850	C₄	1	2	yes	—
29	#65804	C₂²	1	1	yes	characteristic
30	#65804	C₂²	1	1	yes	characteristic
31	#65804	C₂²	1	1	yes	characteristic
32	#65804	C₂²	1	1	yes	characteristic
33	#65804	C₂²	1	1	yes	characteristic
34	C₂×#4015	C₂²	1	1	yes	characteristic
35	C₅×#446	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×#435	—	2	1	no	—
38	C₅×C₈×D₄	—	2	1	no	—
39	C₅×#432	C₂²	1	1	yes	characteristic
40	C₅×#432	C₂²	1	1	yes	characteristic
41	C₅×#431	C₂²	1	1	yes	characteristic
42	C₅×#423	C₂²	1	1	yes	characteristic
43	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	#65313	—	2	1	no	—
46	#65300	—	2	1	no	—
47	#65300	—	2	1	no	—
48	D₄×#168	—	2	1	no	—
49	#65215	C₂²	1	1	yes	characteristic
50	#65215	C₂²	1	1	yes	characteristic
51	#65214	C₂²	1	1	yes	characteristic
52	#65213	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
55	#64706	C₂²	1	1	yes	characteristic
56	#64706	C₂²	1	1	yes	characteristic
57	#64706	C₂²	1	1	yes	characteristic
58	#64706	C₂²	1	1	yes	characteristic
59	#64702	C₂²	1	1	yes	characteristic
60	#64702	C₂²	1	1	yes	characteristic
61	#64702	C₂²	1	1	yes	characteristic
62	#64702	C₂²	1	1	yes	characteristic
63	#64701	C₂²	1	1	yes	characteristic
64	#64701	C₂²	1	1	yes	characteristic
65	#64701	C₂²	1	1	yes	characteristic
66	#64701	C₂²	1	1	yes	characteristic
67	#64701	C₂²	1	1	yes	characteristic
68	#64701	C₂²	1	1	yes	characteristic
69	#64701	C₂²	1	1	yes	characteristic
70	#64701	C₂²	1	1	yes	characteristic
71	#17780	—	5	1	no	maximal, Sylow
72	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
73	C₂²×Dic₁₀	C₂×C₄	1	2	yes	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂²×C₅×C₈	—	2	1	no	—
76	C₂²×C₅×C₈	—	2	1	no	—
77	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
78	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
79	C₄×C₅×D₄	D₄	1	1	yes	characteristic
80	C₄×C₅×D₄	D₄	1	1	yes	characteristic
81	C₄×C₅×D₄	D₄	1	1	yes	characteristic
82	C₄×C₅×D₄	D₄	1	1	yes	characteristic
83	C₄×C₅×D₄	D₄	1	1	yes	characteristic
84	C₄×C₅×D₄	D₄	1	1	yes	characteristic
85	C₅×#117	C₂×C₄	1	1	yes	characteristic
86	C₅×#117	C₂×C₄	1	1	yes	characteristic
87	C₅×#117	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	#4090	—	2	2	no	—
92	#4082	—	2	2	no	—
93	#4081	—	2	2	no	—
94	#4081	—	2	2	no	—
95	#4072	—	2	1	no	—
96	#4072	—	2	1	no	—
97	#4072	—	2	1	no	—
98	#4072	—	2	1	no	—
99	#4072	C₂×C₄	1	2	yes	—
100	C₂×C₄⋊Dic₅	—	2	1	no	—
101	C₂×C₄⋊Dic₅	—	2	1	no	—
102	#4070	—	2	1	no	—
103	#4070	—	2	1	no	—
104	#4070	—	2	1	no	—
105	#4070	—	2	1	no	—
106	#4070	—	2	1	no	—
107	#4070	—	2	1	no	—
108	#4070	C₂×C₄	1	2	yes	—
109	#4070	C₂×C₄	1	2	yes	—
110	#4070	C₂×C₄	1	2	yes	—
111	#4070	C₂×C₄	1	2	yes	—
112	C₂×#681	—	2	1	no	—
113	C₂²×#168	—	2	1	no	—
114	C₂²×#168	—	2	1	no	—
115	#4035	—	2	2	no	—
116	#4035	—	2	2	no	—
117	#4035	—	2	2	no	—
118	#4035	—	2	2	no	—
119	#4033	—	2	2	no	—
120	#4033	—	2	2	no	—
121	#4025	—	2	2	no	—
122	#4025	—	2	2	no	—
123	#4025	—	2	2	no	—
124	#4025	—	2	2	no	—
125	#4023	—	2	2	no	—
126	#4023	—	2	2	no	—
127	#4016	—	2	1	no	—
128	#4016	—	2	1	no	—
129	#4016	—	2	1	no	—
130	#4016	—	2	1	no	—
131	#4016	C₂×C₄	1	2	yes	—
132	#4015	—	2	1	no	—
133	#4015	—	2	1	no	—
134	#4015	C₂×C₄	1	2	yes	—
135	#4015	C₂³	1	1	yes	characteristic
136	#4015	C₂³	1	1	yes	characteristic
137	#4015	C₂³	1	1	yes	characteristic
138	#4015	C₂³	1	1	yes	characteristic
139	C₄×Dic₁₀	—	2	1	no	—
140	C₄×Dic₁₀	—	2	1	no	—
141	C₄×Dic₁₀	—	2	1	no	—
142	C₄×Dic₁₀	—	2	1	no	—
143	C₄×Dic₁₀	—	2	1	no	—
144	C₄×Dic₁₀	—	2	1	no	—
145	C₄×Dic₁₀	C₂×C₄	1	2	yes	—
146	C₄×Dic₁₀	C₂×C₄	1	2	yes	—
147	C₄×Dic₁₀	C₂×C₄	1	2	yes	—
148	C₄×Dic₁₀	C₂×C₄	1	2	yes	—
149	C₅×C₄⋊C₈	—	2	1	no	—
150	C₅×C₄⋊C₈	—	2	1	no	—
151	C₅×C₄⋊C₈	—	2	1	no	—
152	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₅×C₂²⋊C₈	—	2	1	no	—
157	C₅×C₂²⋊C₈	—	2	1	no	—
158	C₅×C₂²⋊C₈	—	2	1	no	—
159	C₅×#97	—	2	1	no	—
160	C₅×#97	—	2	1	no	—
161	C₄×C₅×C₈	—	2	1	no	—
162	C₂²⋊#168	—	2	1	no	—
163	C₂²⋊#168	—	2	1	no	—
164	C₂²⋊#168	—	2	1	no	—
165	C₄⋊#168	—	2	1	no	—
166	C₄⋊#168	—	2	1	no	—
167	C₄⋊#168	—	2	1	no	—
168	C₄⋊#168	C₂³	1	1	yes	characteristic
169	C₄⋊#168	C₂³	1	1	yes	characteristic
170	C₄⋊#168	C₂³	1	1	yes	characteristic
171	C₄⋊#168	C₂³	1	1	yes	characteristic
172	#3935	—	2	1	no	—
173	#3935	—	2	1	no	—
174	C₄×#168	—	2	1	no	—
175	#3509	—	5	1	no	—
176	#2990	—	5	1	no	—
177	#2990	D₅	1	1	yes	characteristic
178	#1559	—	5	1	no	—
179	#1559	—	5	1	no	—
180	#1558	—	5	1	no	—
181	#1554	—	5	1	no	—
182	#1554	—	5	1	no	—
183	#1552	—	5	1	no	—
184	#1552	—	5	1	no	—
185	#1550	—	5	1	no	—
186	#1550	—	5	1	no	—
187	#1542	—	5	1	no	—
188	#1542	—	5	1	no	—
189	C₂×#333	—	5	1	no	—
190	C₅×#41	—	4	2	no	—
191	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×Dic₅	—	2	2	no	—
205	C₂×Dic₁₀	—	2	2	no	—
206	C₂×Dic₁₀	—	2	1	no	—
207	C₂×Dic₁₀	—	2	1	no	—
208	C₂×Dic₁₀	—	4	4	no	—
209	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
210	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
211	C₅×M₁₆	—	8	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	2	1	no	—
215	C₂×C₅×C₈	—	2	1	no	—
216	C₂×C₅×C₈	—	8	1	no	—
217	C₂×C₅×C₈	—	8	1	no	—
218	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
223	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
224	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
226	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
227	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
228	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
229	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
230	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
231	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
232	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
233	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
239	C₄²×C₅	C₂⁴	1	1	yes	characteristic
240	C₂²⋊Dic₅	—	2	2	no	—
241	C₂²⋊Dic₅	—	2	2	no	—
242	C₂²⋊Dic₅	—	2	2	no	—
243	C₂²⋊Dic₅	—	2	2	no	—
244	C₂²⋊Dic₅	—	2	2	no	—
245	C₄⋊Dic₅	—	2	2	no	—
246	C₄⋊Dic₅	—	2	2	no	—
247	C₄⋊Dic₅	—	2	1	no	—
248	C₄⋊Dic₅	—	2	1	no	—
249	C₄⋊Dic₅	—	2	1	no	—
250	C₄⋊Dic₅	—	2	1	no	—
251	C₄⋊Dic₅	—	2	1	no	—
252	C₄⋊Dic₅	—	2	1	no	—
253	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
254	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
255	#683	—	2	2	no	—
256	#683	—	2	2	no	—
257	#683	—	2	2	no	—
258	#683	—	2	2	no	—
259	#683	—	2	2	no	—
260	#683	—	2	2	no	—
261	#683	—	2	2	no	—
262	#683	—	2	2	no	—
263	#683	—	2	2	no	—
264	#683	—	2	2	no	—
265	C₄×Dic₅	—	2	2	no	—
266	C₄×Dic₅	—	2	2	no	—
267	C₄×Dic₅	—	2	2	no	—
268	C₄×Dic₅	—	2	2	no	—
269	C₄×Dic₅	—	2	2	no	—
270	#681	—	8	1	no	—
271	C₂×#168	—	2	1	no	—
272	C₂×#168	—	2	1	no	—
273	C₂×#168	—	2	1	no	—
274	C₂×#168	—	2	1	no	—
275	C₂×#168	—	8	1	no	—
276	C₂×#168	—	8	1	no	—
277	#557	—	10	1	no	—
278	#557	—	10	1	no	—
279	#556	—	10	1	no	—
280	#556	—	10	1	no	—
281	#552	—	10	1	no	—
282	#552	—	10	1	no	—
283	#552	—	10	1	no	—
284	#552	—	10	1	no	—
285	#541	—	5	2	no	—
286	#541	—	5	2	no	—
287	#536	—	5	2	no	—
288	#533	—	5	1	no	—
289	#533	—	5	1	no	—
290	#533	—	5	1	no	—
291	#533	—	5	1	no	—
292	#533	—	5	1	no	—
293	C₂×C₄⋊Q₈	—	5	1	no	—
294	#519	—	5	2	no	—
295	C₄×#41	C₂×D₅	1	1	yes	characteristic
296	#446	—	2	1	no	—
297	#446	—	10	1	no	—
298	#435	—	2	1	no	—
299	#435	—	2	1	no	—
300	#435	—	10	1	no	—
301	#435	—	10	1	no	—
302	C₈×D₄	—	2	1	no	—
303	C₈×D₄	—	10	1	no	—
304	#432	—	5	1	no	—
305	#432	—	5	1	no	—
306	#432	C₂×D₅	1	1	yes	characteristic
307	#432	C₂×D₅	1	1	yes	characteristic
308	#431	—	5	1	no	—
309	#431	C₂×D₅	1	1	yes	characteristic
310	#423	—	5	1	no	—
311	#423	C₂×D₅	1	1	yes	characteristic
312	C₂×C₄⋊C₈	—	5	1	no	—
313	C₂×C₄⋊C₈	—	5	1	no	—
314	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
316	#333	—	5	1	no	—
317	#333	—	5	1	no	—
318	#333	—	5	1	no	—
319	#333	—	5	1	no	—
320	#333	—	5	1	no	—
321	#333	—	5	1	no	—
322	#333	—	5	1	no	—
323	#333	—	5	1	no	—
324	#332	—	5	1	no	—
325	#332	—	5	1	no	—
326	#332	—	5	1	no	—
327	#332	—	5	1	no	—
328	#332	—	5	1	no	—
329	#332	—	5	1	no	—
330	#332	—	5	1	no	—
331	#332	—	5	1	no	—
332	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
333	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₅×Q₈	—	4	1	no	—
336	C₅×D₄	—	2	2	no	—
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	4	1	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
366	C₂×Dic₅	—	2	2	no	—
367	C₂×Dic₅	—	2	2	no	—
368	C₂×Dic₅	—	2	2	no	—
369	C₂×Dic₅	—	2	2	no	—
370	C₂×Dic₅	—	4	4	no	—
371	Dic₁₀	—	4	4	no	—
372	Dic₁₀	—	4	1	no	—
373	Dic₁₀	—	4	1	no	—
374	Dic₁₀	—	4	1	no	—
375	Dic₁₀	—	4	1	no	—
376	Dic₁₀	—	4	2	no	—
377	Dic₁₀	—	4	2	no	—
378	C₅×C₈	—	4	1	no	—
379	C₅×C₈	—	4	1	no	—
380	C₅×C₈	—	4	1	no	—
381	C₅×C₈	—	4	1	no	—
382	#168	—	4	1	no	—
383	#168	—	4	1	no	—
384	#168	—	4	1	no	—
385	#168	—	4	1	no	—
386	C₂×#41	C₄×D₅	1	1	yes	characteristic
387	C₂²×Q₈	—	5	2	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	10	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	10	1	no	—
393	C₂²×C₈	—	10	1	no	—
394	C₄⋊Q₈	—	5	2	no	—
395	C₄⋊Q₈	—	5	1	no	—
396	C₄⋊Q₈	—	5	1	no	—
397	C₄⋊Q₈	—	5	1	no	—
398	C₄⋊Q₈	—	5	1	no	—
399	C₄⋊Q₈	—	10	2	no	—
400	C₄⋊Q₈	—	10	1	no	—
401	C₄⋊Q₈	—	10	1	no	—
402	#126	—	10	2	no	—
403	#126	—	10	2	no	—
404	#126	—	10	2	no	—
405	#126	—	10	2	no	—
406	#125	—	5	2	no	—
407	#125	—	10	2	no	—
408	#125	—	10	2	no	—
409	#125	—	10	2	no	—
410	#125	—	10	2	no	—
411	#125	—	10	1	no	—
412	#125	—	10	1	no	—
413	#125	—	10	1	no	—
414	#125	—	10	1	no	—
415	#124	—	10	2	no	—
416	#123	—	10	2	no	—
417	#123	—	10	2	no	—
418	C₂²⋊Q₈	—	5	2	no	—
419	C₂²⋊Q₈	—	5	2	no	—
420	C₂²⋊Q₈	—	5	2	no	—
421	C₂²⋊Q₈	—	5	2	no	—
422	C₂²⋊Q₈	—	10	1	no	—
423	C₂²⋊Q₈	—	10	1	no	—
424	C₂²⋊Q₈	—	10	1	no	—
425	C₂²⋊Q₈	—	10	1	no	—
426	C₂²⋊Q₈	—	10	1	no	—
427	C₂²⋊Q₈	—	10	1	no	—
428	C₄×Q₈	—	5	2	no	—
429	C₄×Q₈	—	5	2	no	—
430	C₄×Q₈	—	5	2	no	—
431	C₄×Q₈	—	5	2	no	—
432	C₄×Q₈	—	10	2	no	—
433	C₄×Q₈	—	10	2	no	—
434	C₄×Q₈	—	10	1	no	—
435	C₄×Q₈	—	10	1	no	—
436	C₄×Q₈	—	10	1	no	—
437	C₄×Q₈	—	10	1	no	—
438	C₄×Q₈	—	10	1	no	—
439	C₄×Q₈	—	10	1	no	—
440	C₄×Q₈	D₂₀	1	1	yes	characteristic
441	C₄×Q₈	C₂²⋊D₅	1	1	yes	characteristic
442	C₄×D₄	D₂₀	1	1	yes	characteristic
443	C₄×D₄	D₂₀	1	1	yes	characteristic
444	C₄×D₄	D₂₀	1	1	yes	characteristic
445	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
446	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
447	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
448	#117	—	5	2	no	—
449	#117	—	10	1	no	—
450	#117	—	10	1	no	—
451	#117	—	10	1	no	—
452	#117	—	10	1	no	—
453	#117	—	10	2	no	—
454	#117	—	10	2	no	—
455	#117	C₄×D₅	1	1	yes	characteristic
456	#117	C₄×D₅	1	1	yes	characteristic
457	#117	C₄×D₅	1	1	yes	characteristic
458	C₂×C₄⋊C₄	—	10	1	no	—
459	C₂×C₄⋊C₄	—	10	1	no	—
460	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
461	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
462	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
463	C₄⋊C₈	—	2	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	5	1	no	—
467	C₄⋊C₈	—	5	1	no	—
468	C₄⋊C₈	—	5	1	no	—
469	C₄⋊C₈	—	5	1	no	—
470	C₄⋊C₈	—	10	1	no	—
471	C₄⋊C₈	—	10	1	no	—
472	C₄⋊C₈	—	10	1	no	—
473	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
474	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
475	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
476	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	C₂²⋊C₈	—	2	1	no	—
480	C₂²⋊C₈	—	10	1	no	—
481	C₂²⋊C₈	—	10	1	no	—
482	C₂²⋊C₈	—	10	1	no	—
483	#97	—	2	1	no	—
484	#97	—	2	1	no	—
485	#97	—	10	1	no	—
486	#97	—	10	1	no	—
487	C₄×C₈	—	2	1	no	—
488	C₄×C₈	—	10	1	no	—
489	C₂²×C₅	—	2	1	no	—
490	C₂²×C₅	—	2	1	no	—
491	C₂²×C₅	—	2	1	no	—
492	C₂²×C₅	—	2	1	no	—
493	C₂²×C₅	—	2	1	no	—
494	C₂²×C₅	—	2	1	no	—
495	C₂²×C₅	—	2	1	no	—
496	C₂²×C₅	—	2	1	no	—
497	C₂²×C₅	#413	1	2	yes	—
498	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
499	C₄×C₅	—	2	1	no	—
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	—	2	1	no	—
504	C₄×C₅	—	2	1	no	—
505	C₄×C₅	—	2	1	no	—
506	C₄×C₅	—	2	1	no	—
507	C₄×C₅	—	2	1	no	—
508	C₄×C₅	—	2	1	no	—
509	C₄×C₅	#577	1	1	yes	characteristic
510	C₄×C₅	#577	1	1	yes	characteristic
511	C₄×C₅	#578	1	1	yes	characteristic
512	C₄×C₅	#578	1	1	yes	characteristic
513	Dic₅	—	4	2	no	—
514	Dic₅	—	4	2	no	—
515	Dic₅	—	4	2	no	—
516	Dic₅	—	4	2	no	—
517	#41	—	4	2	no	—
518	C₂×Q₈	—	5	2	no	—
519	C₂×Q₈	—	5	2	no	—
520	C₂×Q₈	—	10	1	no	—
521	C₂×Q₈	—	10	1	no	—
522	C₂×Q₈	—	10	2	no	—
523	C₂×Q₈	—	20	4	no	—
524	C₂×Q₈	#685	1	1	yes	characteristic
525	C₂×D₄	#685	1	1	yes	characteristic
526	C₂×D₄	#685	1	1	yes	characteristic
527	C₂×D₄	#685	1	1	yes	characteristic
528	C₂²×C₄	—	10	2	no	—
529	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
530	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
531	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
535	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
538	M₁₆	—	8	1	no	—
539	M₁₆	—	40	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	8	1	no	—
545	C₂×C₈	—	8	1	no	—
546	C₂×C₈	—	10	1	no	—
547	C₂×C₈	—	10	1	no	—
548	C₂×C₈	—	10	1	no	—
549	C₂×C₈	—	10	1	no	—
550	C₂×C₈	—	40	1	no	—
551	C₂×C₈	—	40	1	no	—
552	C₄⋊C₄	—	5	2	no	—
553	C₄⋊C₄	—	5	2	no	—
554	C₄⋊C₄	—	10	1	no	—
555	C₄⋊C₄	—	10	1	no	—
556	C₄⋊C₄	—	10	1	no	—
557	C₄⋊C₄	—	10	1	no	—
558	C₄⋊C₄	—	10	1	no	—
559	C₄⋊C₄	—	10	1	no	—
560	C₄⋊C₄	—	10	2	no	—
561	C₄⋊C₄	—	10	2	no	—
562	C₄⋊C₄	—	10	2	no	—
563	C₄⋊C₄	—	10	2	no	—
564	C₄⋊C₄	—	10	2	no	—
565	C₄⋊C₄	—	10	2	no	—
566	C₄⋊C₄	—	10	2	no	—
567	C₄⋊C₄	—	10	2	no	—
568	C₄⋊C₄	—	10	2	no	—
569	C₄⋊C₄	—	10	2	no	—
570	C₄⋊C₄	—	10	2	no	—
571	C₄⋊C₄	—	10	2	no	—
572	C₄⋊C₄	#685	1	1	yes	characteristic
573	C₄⋊C₄	#685	1	1	yes	characteristic
574	C₄⋊C₄	#685	1	1	yes	characteristic
575	C₄⋊C₄	#685	1	1	yes	characteristic
576	C₄⋊C₄	#685	1	1	yes	characteristic
577	C₄⋊C₄	#685	1	1	yes	characteristic
578	C₂²⋊C₄	—	10	2	no	—
579	C₂²⋊C₄	—	10	2	no	—
580	C₂²⋊C₄	—	10	2	no	—
581	C₂²⋊C₄	—	10	2	no	—
582	C₂²⋊C₄	—	10	2	no	—
583	C₂²⋊C₄	#685	1	1	yes	characteristic
584	C₂²⋊C₄	#685	1	1	yes	characteristic
585	C₂²⋊C₄	#685	1	1	yes	characteristic
586	C₂²⋊C₄	#685	1	1	yes	characteristic
587	C₂²⋊C₄	#685	1	1	yes	characteristic
588	C₂²⋊C₄	#685	1	1	yes	characteristic
589	C₄²	—	10	2	no	—
590	C₄²	—	10	2	no	—
591	C₄²	—	10	2	no	—
592	C₄²	—	10	2	no	—
593	C₄²	—	10	2	no	—
594	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
595	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
596	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
597	C₄²	C₂×D₂₀	1	1	yes	characteristic
598	C₄²	C₂×D₂₀	1	1	yes	characteristic
599	C₄²	C₂×D₂₀	1	1	yes	characteristic
600	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
601	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
602	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
603	C₄²	C₂³×D₅	1	1	yes	characteristic
604	C₂×C₅	—	2	2	no	—
605	C₂×C₅	—	4	1	no	—
606	C₂×C₅	—	4	1	no	—
607	C₂×C₅	C₂×#413	1	1	yes	characteristic
608	C₂×C₅	#2898	1	1	yes	characteristic
609	C₂×C₅	#2898	1	1	yes	characteristic
610	C₂³	C₂×#685	1	1	yes	characteristic
611	C₂³	C₂×#685	1	1	yes	characteristic
612	C₂³	C₂×#685	1	1	yes	characteristic
613	Q₈	—	4	1	no	—
614	Q₈	—	20	2	no	—
615	Q₈	—	20	2	no	—
616	Q₈	—	20	4	no	—
617	Q₈	—	20	1	no	—
618	Q₈	—	20	1	no	—
619	Q₈	—	20	1	no	—
620	Q₈	—	20	1	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	10	2	no	—
640	C₂×C₄	—	10	2	no	—
641	C₂×C₄	—	10	2	no	—
642	C₂×C₄	—	10	2	no	—
643	C₂×C₄	—	20	4	no	—
644	C₂×C₄	C₂×#685	1	1	yes	characteristic
645	C₂×C₄	C₂×#685	1	1	yes	characteristic
646	C₂×C₄	C₂×#685	1	1	yes	characteristic
647	C₂×C₄	C₂×#685	1	1	yes	characteristic
648	C₂×C₄	C₂×#685	1	1	yes	characteristic
649	C₂×C₄	C₂×#685	1	1	yes	characteristic
650	C₂×C₄	C₂×#685	1	1	yes	characteristic
651	C₂×C₄	C₂×#685	1	1	yes	characteristic
652	C₂×C₄	C₂×#685	1	1	yes	characteristic
653	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
654	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
655	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	20	1	no	—
661	C₈	—	20	1	no	—
662	C₈	—	20	1	no	—
663	C₈	—	20	1	no	—
664	C₅	#17780	1	1	yes	characteristic, complemented, Sylow
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	#65421	1	2	yes	—
674	C₂²	C₂²×#685	1	1	yes	characteristic
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	20	2	no	—
686	C₄	—	20	2	no	—
687	C₄	—	20	2	no	—
688	C₄	—	20	2	no	—
689	C₄	#66085	1	1	yes	characteristic
690	C₄	#66087	1	1	yes	characteristic
691	C₄	#66170	1	1	yes	characteristic
692	C₄	#66172	1	1	yes	characteristic
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	1	no	—
696	C₂	#10614301	1	1	yes	characteristic
697	C₂	C₂×#65421	1	1	yes	characteristic
698	C₂	#10615537	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#685
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2990	C₂
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#41	C₂×C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2990	D₅
hypocenter	C₅	#17780
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
4. #10601618	C₂	semidirect
5. #10601617	C₂	semidirect
6. #10601614	C₂	semidirect
7. #10601613	C₂	semidirect
8. #10601574	C₂	semidirect
9. #10601569	C₂	semidirect
10. #10601303	C₂	semidirect
11. #10601302	C₂	semidirect
12. #10601232	C₂	semidirect
13. #10601231	C₂	semidirect
14. #10601230	C₂	semidirect
15. C₂×#64701	C₂	semidirect
664. C₅	#17780	semidirect

Maximal subgroups

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

subgroup	index
#10617731	2
C₅×#2990	2
#10614253	2
#10601618	2
#10601617	2
#10601614	2
#10601613	2
#10601574	2
#10601569	2
#10601303	2
#10601302	2
#10601232	2
#10601231	2
#10601230	2
C₂×#64701	2
#17780	5