Subgroups — #12069362

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3105	C₂	1	1	yes	maximal, characteristic
2	#10614862	C₂	1	1	yes	maximal, characteristic, complemented
3	#10614032	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602543	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602391	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601690	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601688	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601673	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601672	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601671	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×#168	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601546	C₂	1	1	yes	maximal, characteristic, complemented
15	#10601537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#529	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₅×#484	C₄	1	1	yes	characteristic
19	C₅×#481	C₄	1	1	yes	characteristic
20	C₅×#478	C₄	1	1	yes	characteristic
21	C₅×#478	C₄	1	1	yes	characteristic
22	C₅×#463	C₄	1	1	yes	characteristic
23	C₅×#463	C₄	1	1	yes	characteristic
24	C₅×#450	C₄	1	1	yes	characteristic
25	C₅×#447	C₄	1	1	yes	characteristic
26	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊#168	—	2	1	no	—
32	C₂×C₂²⋊#168	—	2	1	no	—
33	#65313	C₂²	1	1	yes	characteristic, complemented
34	Q₈×#168	C₂²	1	1	yes	characteristic, complemented
35	#65301	—	2	1	no	—
36	#65301	C₂²	1	1	yes	characteristic, complemented
37	#65300	—	2	1	no	—
38	D₄×#168	—	2	1	no	—
39	D₄×#168	—	2	1	no	—
40	D₄×#168	C₂²	1	1	yes	characteristic
41	D₄×#168	C₂²	1	1	yes	characteristic
42	D₄×#168	C₂²	1	1	yes	characteristic
43	D₄×#168	C₂²	1	1	yes	characteristic
44	D₄×#168	C₂²	1	1	yes	characteristic, complemented
45	#65289	—	2	1	no	—
46	#65288	—	2	1	no	—
47	#65214	C₂²	1	1	yes	characteristic
48	#65214	C₂²	1	1	yes	characteristic
49	#65214	C₂²	1	1	yes	characteristic
50	#65213	C₂²	1	1	yes	characteristic
51	Q₈⋊#168	C₂²	1	1	yes	characteristic, complemented
52	Q₈⋊#168	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊#168	C₂²	1	1	yes	characteristic
54	D₄⋊#168	C₂²	1	1	yes	characteristic
55	D₄⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
58	D₄⋊#168	C₂²	1	1	yes	characteristic, complemented
59	#64678	C₂²	1	1	yes	characteristic, complemented
60	#64678	C₂²	1	1	yes	characteristic, complemented
61	#64677	C₂²	1	1	yes	characteristic, complemented
62	#64677	C₂²	1	1	yes	characteristic, complemented
63	#64675	C₂²	1	1	yes	characteristic, complemented
64	#64674	C₂²	1	1	yes	characteristic, complemented
65	#64674	C₂²	1	1	yes	characteristic, complemented
66	C₈×#168	C₂²	1	1	yes	characteristic, complemented
67	#17918	—	5	1	no	maximal, Sylow
68	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₅	—	2	1	no	—
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
74	C₅×#126	—	2	1	no	—
75	C₅×#125	C₂×C₄	1	1	yes	characteristic
76	C₅×#124	C₂×C₄	1	1	yes	characteristic
77	C₅×#123	—	2	1	no	—
78	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₅×#121	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₄×C₅×D₄	—	2	1	no	—
82	C₄×C₅×D₄	—	2	1	no	—
83	C₄×C₅×D₄	—	2	1	no	—
84	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
85	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₅×#117	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×#681	—	2	1	no	—
94	C₂×#681	—	2	1	no	—
95	C₂²×#168	—	2	1	no	—
96	C₂²×#168	—	2	1	no	—
97	C₂²×#168	—	2	1	no	—
98	C₂²×#168	—	2	1	no	—
99	C₂²×#168	—	2	1	no	—
100	C₅×#107	C₂×C₄	1	1	yes	characteristic
101	C₅×#107	C₂×C₄	1	1	yes	characteristic
102	C₅×#106	C₂×C₄	1	1	yes	characteristic
103	C₅×#106	C₂×C₄	1	1	yes	characteristic
104	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₅×#103	C₂×C₄	1	1	yes	characteristic
107	C₅×#103	C₂×C₄	1	1	yes	characteristic
108	C₅×#102	C₂×C₄	1	1	yes	characteristic
109	C₅×#102	C₂×C₄	1	1	yes	characteristic
110	C₅×#102	C₂×C₄	1	1	yes	characteristic
111	C₅×#102	C₂×C₄	1	1	yes	characteristic
112	C₅×#102	C₂×C₄	1	1	yes	characteristic
113	C₅×#102	C₂×C₄	1	1	yes	characteristic
114	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
116	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
117	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
118	C₂²⋊#168	—	2	1	no	—
119	C₂²⋊#168	—	2	1	no	—
120	C₂²⋊#168	—	2	1	no	—
121	C₂²⋊#168	—	2	1	no	—
122	C₂²⋊#168	—	2	1	no	—
123	C₂²⋊#168	—	2	1	no	—
124	C₂²⋊#168	—	2	1	no	—
125	C₂²⋊#168	—	2	1	no	—
126	C₂²⋊#168	D₄	1	1	yes	characteristic
127	C₂²⋊#168	D₄	1	1	yes	characteristic
128	C₄⋊#168	—	2	1	no	—
129	C₄⋊#168	—	2	1	no	—
130	C₄⋊#168	—	2	1	no	—
131	C₄⋊#168	—	2	1	no	—
132	C₄⋊#168	D₄	1	1	yes	characteristic
133	C₄⋊#168	D₄	1	1	yes	characteristic
134	C₄⋊#168	C₂³	1	1	yes	characteristic
135	C₄⋊#168	C₂³	1	1	yes	characteristic
136	C₄⋊#168	C₂³	1	1	yes	characteristic
137	C₄⋊#168	C₂³	1	1	yes	characteristic
138	#3935	—	2	1	no	—
139	C₄×#168	—	2	1	no	—
140	C₄×#168	—	2	1	no	—
141	C₄×#168	C₂³	1	1	yes	characteristic
142	C₄×#168	C₂³	1	1	yes	characteristic
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	#3105	D₅	1	1	yes	characteristic
146	#2993	—	5	1	no	—
147	#2972	—	5	1	no	—
148	#1586	—	5	1	no	—
149	#1585	—	5	1	no	—
150	#1582	—	5	1	no	—
151	#1581	—	5	1	no	—
152	#1580	—	5	1	no	—
153	SD₁₆⋊C₈	—	5	1	no	—
154	C₈×SD₁₆	—	5	1	no	—
155	C₈×D₈	—	5	1	no	—
156	#1574	—	5	1	no	—
157	#1486	—	5	1	no	—
158	#1482	—	5	1	no	—
159	#1454	—	5	1	no	—
160	C₂⁴×C₅	—	2	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×D₄	—	2	2	no	—
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	8	1	no	—
176	C₂²×C₄×C₅	—	8	1	no	—
177	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	#41	1	1	yes	characteristic
180	C₅×SD₁₆	—	2	2	no	—
181	C₅×SD₁₆	—	2	2	no	—
182	C₅×D₈	—	2	2	no	—
183	C₅×D₈	—	2	2	no	—
184	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₂²⋊C₄	—	2	1	no	—
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₅×C₂²⋊C₄	—	2	1	no	—
200	C₅×C₂²⋊C₄	—	2	1	no	—
201	C₅×C₂²⋊C₄	—	2	1	no	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₅×C₂²⋊C₄	—	2	1	no	—
204	C₅×C₂²⋊C₄	—	2	1	no	—
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₅	#41	1	1	yes	characteristic
210	C₄²×C₅	C₂⁴	1	1	yes	characteristic
211	#681	—	8	1	no	—
212	#681	—	8	1	no	—
213	C₂×#168	—	2	1	no	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	—	8	1	no	—
220	C₂×#168	—	8	1	no	—
221	C₂×#168	—	8	1	no	—
222	C₂×#168	—	8	1	no	—
223	C₂×#168	—	8	1	no	—
224	C₂×#168	C₂×D₄	1	1	yes	characteristic
225	C₂×#168	C₂×D₄	1	1	yes	characteristic
226	C₂×#168	C₂×D₄	1	1	yes	characteristic
227	C₂×#168	C₂×D₄	1	1	yes	characteristic
228	#529	C₂×D₅	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
230	#484	Dic₅	1	1	yes	characteristic
231	#481	Dic₅	1	1	yes	characteristic
232	#478	Dic₅	1	1	yes	characteristic
233	#478	Dic₅	1	1	yes	characteristic
234	#463	Dic₅	1	1	yes	characteristic
235	#463	Dic₅	1	1	yes	characteristic
236	#450	Dic₅	1	1	yes	characteristic
237	#447	Dic₅	1	1	yes	characteristic
238	#446	—	5	1	no	—
239	C₈×Q₈	—	5	1	no	—
240	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
241	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
242	C₄×D₈	C₂×D₅	1	1	yes	characteristic
243	C₄×D₈	C₂×D₅	1	1	yes	characteristic
244	#436	—	5	1	no	—
245	#436	—	10	1	no	—
246	#435	—	10	1	no	—
247	C₈×D₄	—	5	1	no	—
248	C₈×D₄	—	5	1	no	—
249	C₈×D₄	—	5	1	no	—
250	C₈×D₄	—	5	1	no	—
251	C₈×D₄	—	5	1	no	—
252	C₈×D₄	—	10	1	no	—
253	C₈×D₄	—	10	1	no	—
254	#433	—	10	1	no	—
255	#431	—	5	1	no	—
256	#431	—	5	1	no	—
257	#431	—	5	1	no	—
258	#431	C₂×D₅	1	1	yes	characteristic
259	#424	—	10	1	no	—
260	#423	—	5	1	no	—
261	C₂×C₂²⋊C₈	—	10	1	no	—
262	C₂×C₂²⋊C₈	—	10	1	no	—
263	#335	—	5	1	no	—
264	#335	—	5	1	no	—
265	#334	—	5	1	no	—
266	#334	—	5	1	no	—
267	Q₈⋊C₈	—	5	1	no	—
268	Q₈⋊C₈	—	5	1	no	—
269	D₄⋊C₈	—	5	1	no	—
270	D₄⋊C₈	—	5	1	no	—
271	D₄⋊C₈	—	5	1	no	—
272	D₄⋊C₈	—	5	1	no	—
273	D₄⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	#322	—	5	1	no	—
276	#322	—	5	1	no	—
277	#322	—	5	1	no	—
278	C₈²	—	5	1	no	—
279	C₂³×C₅	—	2	4	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	—	2	1	no	—
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	8	1	no	—
284	C₂³×C₅	—	8	1	no	—
285	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	2	1	no	—
288	C₅×D₄	—	2	4	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	8	1	no	—
294	C₅×D₄	#131	1	2	yes	—
295	C₅×D₄	#131	1	2	yes	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	8	1	no	—
313	C₂×C₄×C₅	—	8	1	no	—
314	C₂×C₄×C₅	—	8	1	no	—
315	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	1	no	—
325	#168	—	2	1	no	—
326	#168	—	2	1	no	—
327	#168	—	2	1	no	—
328	#168	—	2	1	no	—
329	#168	—	4	1	no	—
330	#168	—	4	1	no	—
331	#168	—	4	1	no	—
332	#168	—	4	1	no	—
333	#168	—	4	1	no	—
334	#168	—	4	1	no	—
335	C₂²×D₄	C₂×Dic₅	1	1	yes	characteristic
336	C₂³×C₄	—	2	1	no	—
337	C₂×SD₁₆	C₂×Dic₅	1	1	yes	characteristic
338	C₂×SD₁₆	C₂×Dic₅	1	1	yes	characteristic
339	C₂×D₈	C₂×Dic₅	1	1	yes	characteristic
340	C₂×D₈	C₂×Dic₅	1	1	yes	characteristic
341	C₂×M₁₆	—	10	1	no	—
342	C₂×M₁₆	—	10	1	no	—
343	C₂²×C₈	—	10	1	no	—
344	C₂²×C₈	—	10	1	no	—
345	C₂²×C₈	—	10	1	no	—
346	C₂²×C₈	—	10	1	no	—
347	C₂²×C₈	—	10	1	no	—
348	#126	—	2	1	no	—
349	#125	C₂×Dic₅	1	1	yes	characteristic
350	#124	C₂×Dic₅	1	1	yes	characteristic
351	#123	—	2	1	no	—
352	C₂²⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
353	#121	C₂×Dic₅	1	1	yes	characteristic
354	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
359	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
360	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
361	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
362	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
363	#117	—	2	1	no	—
364	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
367	#107	C₂×Dic₅	1	1	yes	characteristic
368	#107	C₂×Dic₅	1	1	yes	characteristic
369	#106	C₂×Dic₅	1	1	yes	characteristic
370	#106	C₂×Dic₅	1	1	yes	characteristic
371	C₄⋊C₈	—	5	1	no	—
372	C₄⋊C₈	—	5	1	no	—
373	C₄⋊C₈	—	5	1	no	—
374	C₄⋊C₈	—	5	1	no	—
375	C₄⋊C₈	—	5	1	no	—
376	C₄⋊C₈	—	5	1	no	—
377	C₄⋊C₈	—	10	1	no	—
378	C₄⋊C₈	—	10	1	no	—
379	C₄⋊C₈	—	10	1	no	—
380	C₄⋊C₈	—	10	1	no	—
381	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
382	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
383	#103	C₂×Dic₅	1	1	yes	characteristic
384	#103	C₂×Dic₅	1	1	yes	characteristic
385	#102	C₂×Dic₅	1	1	yes	characteristic
386	#102	C₂×Dic₅	1	1	yes	characteristic
387	#102	C₂×Dic₅	1	1	yes	characteristic
388	#102	C₂×Dic₅	1	1	yes	characteristic
389	#102	C₂×Dic₅	1	1	yes	characteristic
390	#102	C₂×Dic₅	1	1	yes	characteristic
391	C₂²⋊C₈	—	5	1	no	—
392	C₂²⋊C₈	—	5	1	no	—
393	C₂²⋊C₈	—	10	1	no	—
394	C₂²⋊C₈	—	10	1	no	—
395	C₂²⋊C₈	—	10	1	no	—
396	C₂²⋊C₈	—	10	1	no	—
397	C₂²⋊C₈	—	10	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	C₂²⋊C₈	C₂×Dic₅	1	1	yes	characteristic
402	C₂²⋊C₈	C₂×Dic₅	1	1	yes	characteristic
403	#97	—	10	1	no	—
404	C₄×C₈	—	5	1	no	—
405	C₄×C₈	—	5	1	no	—
406	C₄×C₈	—	5	1	no	—
407	C₄×C₈	—	5	1	no	—
408	C₄×C₈	—	10	1	no	—
409	C₄×C₈	—	10	1	no	—
410	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	8	4	no	—
425	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	C₂×#131	1	1	yes	characteristic
436	C₄×C₅	C₂×#131	1	1	yes	characteristic
437	C₄×C₅	#576	1	1	yes	characteristic
438	C₄×C₅	#577	1	1	yes	characteristic
439	C₂⁴	—	2	1	no	—
440	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
446	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
447	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	8	1	no	—
455	C₂²×C₄	—	8	1	no	—
456	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
457	C₂²×C₄	#711	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
459	SD₁₆	—	2	2	no	—
460	SD₁₆	—	2	2	no	—
461	D₈	—	2	2	no	—
462	D₈	—	2	2	no	—
463	M₁₆	—	40	1	no	—
464	M₁₆	—	40	1	no	—
465	C₂×C₈	—	5	1	no	—
466	C₂×C₈	—	5	1	no	—
467	C₂×C₈	—	5	1	no	—
468	C₂×C₈	—	5	1	no	—
469	C₂×C₈	—	10	1	no	—
470	C₂×C₈	—	10	1	no	—
471	C₂×C₈	—	10	1	no	—
472	C₂×C₈	—	10	1	no	—
473	C₂×C₈	—	10	1	no	—
474	C₂×C₈	—	10	1	no	—
475	C₂×C₈	—	40	1	no	—
476	C₂×C₈	—	40	1	no	—
477	C₂×C₈	—	40	1	no	—
478	C₂×C₈	—	40	1	no	—
479	C₂×C₈	—	40	1	no	—
480	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
481	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
482	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
483	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	D₄×D₅	1	1	yes	characteristic
504	C₄²	#711	1	1	yes	characteristic
505	C₄²	C₂²×Dic₅	1	1	yes	characteristic
506	C₄²	C₂³×D₅	1	1	yes	characteristic
507	C₂×C₅	—	4	1	no	—
508	C₂×C₅	—	4	2	no	—
509	C₂×C₅	—	4	2	no	—
510	C₂×C₅	—	8	1	no	—
511	C₂×C₅	#2929	1	1	yes	characteristic
512	C₂×C₅	#2946	1	1	yes	characteristic
513	C₂×C₅	#2957	1	1	yes	characteristic
514	C₂³	—	2	4	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	8	1	no	—
519	C₂³	—	8	1	no	—
520	C₂³	D₄×Dic₅	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	D₄	—	2	4	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	8	1	no	—
529	D₄	#4094	1	2	yes	—
530	D₄	#4094	1	2	yes	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
551	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
552	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
553	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
554	C₂×C₄	C₂×#711	1	1	yes	characteristic
555	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	10	1	no	—
561	C₈	—	10	1	no	—
562	C₈	—	10	1	no	—
563	C₈	—	10	1	no	—
564	C₈	—	20	1	no	—
565	C₈	—	20	1	no	—
566	C₈	—	20	1	no	—
567	C₈	—	20	1	no	—
568	C₈	—	20	1	no	—
569	C₈	—	20	1	no	—
570	C₅	#17918	1	1	yes	characteristic, complemented, Sylow
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	4	no	—
584	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	#66108	1	1	yes	characteristic
595	C₄	#66109	1	1	yes	characteristic
596	C₄	C₂×#4094	1	1	yes	characteristic
597	C₄	C₂×#4094	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	#10614647	1	1	yes	characteristic
603	C₂	#10615641	1	1	yes	characteristic
604	C₂	#10615661	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#3105	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#447	C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#3105	D₅
hypocenter	C₅	#17918
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
2. #10614862	C₂	semidirect
3. #10614032	C₂	semidirect
4. #10602543	C₂	semidirect
5. #10602391	C₂	semidirect
6. #10601690	C₂	semidirect
7. #10601688	C₂	semidirect
8. SD₁₆⋊#168	C₂	semidirect
9. SD₁₆×#168	C₂	semidirect
10. #10601673	C₂	semidirect
11. #10601672	C₂	semidirect
12. #10601671	C₂	semidirect
13. D₈×#168	C₂	semidirect
14. #10601546	C₂	semidirect
15. #10601537	C₂	semidirect
33. #65313	C₂²	semidirect
34. Q₈×#168	C₂²	semidirect
36. #65301	C₂²	semidirect
44. D₄×#168	C₂²	semidirect
51. Q₈⋊#168	C₂²	semidirect
52. Q₈⋊#168	C₂²	semidirect
57. D₄⋊#168	C₂²	semidirect
58. D₄⋊#168	C₂²	semidirect
59. #64678	C₂²	semidirect
60. #64678	C₂²	semidirect
61. #64677	C₂²	semidirect
62. #64677	C₂²	semidirect
63. #64675	C₂²	semidirect
64. #64674	C₂²	semidirect
65. #64674	C₂²	semidirect
66. C₈×#168	C₂²	semidirect
570. C₅	#17918	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3105	2
#10614862	2
#10614032	2
#10602543	2
#10602391	2
#10601690	2
#10601688	2
SD₁₆⋊#168	2
SD₁₆×#168	2
#10601673	2
#10601672	2
#10601671	2
D₈×#168	2
#10601546	2
#10601537	2
#17918	5