Subgroups — #14415254

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5548	C₂	1	1	yes	maximal, characteristic
2	C₂×#91286	C₂	1	2	yes	maximal, complemented
3	#11751113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748490	C₂	1	2	yes	maximal, complemented
6	#67×#168	C₂	1	2	yes	maximal, complemented
7	#11748314	C₂	1	2	yes	maximal, complemented
8	#11747014	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747011	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615006	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	2	yes	—
14	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×#6710	C₂²	1	2	yes	—
16	C₅×#940	C₄	1	1	yes	characteristic
17	C₅×#938	C₄	1	1	yes	characteristic
18	C₄×C₅×#67	C₂²	1	2	yes	—
19	C₅×#895	C₄	1	1	yes	characteristic
20	C₅×#888	C₄	1	1	yes	characteristic
21	C₅×#885	C₄	1	2	yes	—
22	C₅×#884	C₄	1	2	yes	—
23	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	C₂²	1	2	yes	—
26	C₂×#6650	C₂²	1	2	yes	—
27	C₂×#6650	C₂²	1	2	yes	—
28	#91286	—	2	8	no	—
29	C₂×D₃×#168	C₂²	1	2	yes	—
30	C₂×D₃×#168	C₂²	1	1	yes	characteristic
31	C₂×D₃×#168	C₂²	1	1	yes	characteristic
32	#91114	C₂²	1	2	yes	—
33	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
34	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊#168	C₂²	1	2	yes	—
36	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic
38	Dic₃⋊#168	C₂²	1	2	yes	—
39	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
40	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
41	Dic₃×#168	C₂²	1	1	yes	characteristic
42	Dic₃×#168	C₂²	1	1	yes	characteristic
43	#79422	—	5	1	no	maximal, Hall
44	C₅×#532	—	3	1	no	—
45	C₂×#4094	—	3	2	no	—
46	#65523	—	3	2	no	—
47	#65301	—	3	2	no	—
48	#65301	—	3	1	no	—
49	#65301	—	3	1	no	—
50	D₄×#168	—	3	2	no	—
51	D₄×#168	—	3	1	no	—
52	D₄×#168	D₃	1	1	yes	characteristic, complemented
53	#65213	—	3	1	no	—
54	C₂×C₄×#168	—	3	1	no	—
55	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂×C₅×#67	C₂×C₄	1	2	yes	—
58	C₂×C₅×#67	C₂×C₄	1	2	yes	—
59	C₂×C₅×#67	C₂×C₄	1	2	yes	—
60	C₅×#235	—	2	4	no	—
61	C₅×#235	—	2	4	no	—
62	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	#6710	—	2	4	no	—
73	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
74	C₂×C₃⋊#168	C₂³	1	2	yes	—
75	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
76	C₅×#217	C₂×C₄	1	2	yes	—
77	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
78	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
79	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
81	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	—	2	4	no	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	2	yes	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	#6650	—	2	4	no	—
89	#6650	—	2	4	no	—
90	D₃×#168	—	2	2	no	—
91	D₃×#168	—	2	4	no	—
92	D₃×#168	D₄	1	4	yes	complemented
93	C₂×#901	—	5	2	no	—
94	#5548	D₅	1	1	yes	characteristic
95	C₃×C₈×D₄	—	5	1	no	—
96	C₈×#67	—	5	2	no	—
97	#5012	—	5	1	no	—
98	#4838	—	5	1	no	—
99	#4837	—	5	1	no	—
100	#4729	—	5	2	no	—
101	#4727	—	5	2	no	—
102	C₈×D₁₂	—	5	1	no	—
103	C₄×D₃×C₈	—	5	1	no	—
104	C₂×C₅×#41	—	3	2	no	—
105	C₅×C₄⋊Q₈	—	3	1	no	—
106	C₅×#127	—	3	1	no	—
107	C₅×#124	—	3	2	no	—
108	C₅×#121	—	3	1	no	—
109	C₅×#121	—	3	1	no	—
110	C₅×#121	—	3	2	no	—
111	C₄×C₅×D₄	—	3	2	no	—
112	C₄×C₅×D₄	—	3	1	no	—
113	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
114	C₂×C₄²×C₅	—	3	1	no	—
115	#4094	—	6	8	no	—
116	C₂×#681	—	3	2	no	—
117	C₂×#681	—	3	2	no	—
118	C₂×#681	—	3	2	no	—
119	C₂²×#168	—	3	1	no	—
120	C₂²×#168	—	3	2	no	—
121	C₂²×#168	—	3	1	no	—
122	C₂²×#168	C₂×D₃	1	2	yes	—
123	C₂²⋊#168	—	3	2	no	—
124	C₂²⋊#168	—	3	2	no	—
125	C₂²⋊#168	—	3	2	no	—
126	C₂²⋊#168	C₂×D₃	1	2	yes	—
127	C₄⋊#168	—	3	1	no	—
128	C₄⋊#168	—	3	2	no	—
129	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
130	C₄×#168	—	3	1	no	—
131	C₄×#168	—	3	1	no	—
132	C₄×#168	—	3	1	no	—
133	C₄×#168	C₂×D₃	1	1	yes	characteristic
134	#2931	—	15	1	no	Sylow
135	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
136	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
138	C₃×C₅×D₄	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×#67	—	2	4	no	—
146	C₅×#67	—	2	4	no	—
147	C₅×#67	—	2	4	no	—
148	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
150	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
152	C₅×D₁₂	—	2	4	no	—
153	C₅×D₁₂	—	2	2	no	—
154	C₄×C₅×D₃	—	2	2	no	—
155	C₄×C₅×D₃	—	2	2	no	—
156	C₄×C₅×D₃	—	2	2	no	—
157	C₄×C₅×D₃	—	2	2	no	—
158	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
159	C₄×C₅×D₃	#41	1	2	yes	—
160	C₅×Dic₆	—	2	4	no	—
161	C₃⋊#168	—	2	2	no	—
162	C₃⋊#168	—	2	1	no	—
163	C₃⋊#168	C₂×D₄	1	2	yes	—
164	C₃×#168	—	2	2	no	—
165	C₃×#168	—	2	1	no	—
166	C₃×#168	C₂×D₄	1	2	yes	—
167	C₂×#235	C₂×D₅	1	2	yes	—
168	C₂²×C₃×C₈	—	5	2	no	—
169	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
170	#940	Dic₅	1	1	yes	characteristic
171	#938	Dic₅	1	1	yes	characteristic
172	C₄×#67	C₂×D₅	1	2	yes	—
173	C₂×#208	—	5	2	no	—
174	#901	—	10	8	no	—
175	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
176	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
177	C₂×D₃×C₈	—	5	1	no	—
178	C₂×D₃×C₈	—	5	1	no	—
179	C₂×D₃×C₈	—	5	2	no	—
180	#895	Dic₅	1	1	yes	characteristic
181	#888	Dic₅	1	1	yes	characteristic
182	#885	Dic₅	1	2	yes	—
183	#884	Dic₅	1	2	yes	—
184	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
185	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
186	C₃×C₄⋊C₈	—	5	1	no	—
187	C₃×C₂²⋊C₈	—	5	2	no	—
188	C₃×C₄×C₈	—	5	1	no	—
189	#830	—	5	2	no	—
190	(C₂×D₃)⋊C₈	—	5	2	no	—
191	(C₂×D₃)⋊C₈	—	5	2	no	—
192	Dic₃⋊C₈	—	5	2	no	—
193	C₈×Dic₃	—	5	1	no	—
194	C₈×Dic₃	—	5	1	no	—
195	C₄⋊(C₃⋊C₈)	—	5	1	no	—
196	C₄×C₃⋊C₈	—	5	1	no	—
197	C₅×#41	—	6	4	no	—
198	C₅×#41	—	6	4	no	—
199	C₂×C₅×Q₈	—	3	2	no	—
200	C₂×C₅×D₄	—	3	2	no	—
201	C₂×C₅×D₄	—	3	2	no	—
202	C₂×C₅×D₄	—	3	2	no	—
203	C₂×C₅×D₄	—	3	1	no	—
204	C₂×C₅×D₄	—	3	2	no	—
205	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	3	1	no	—
209	C₂²×C₄×C₅	—	3	2	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
211	C₅×C₄⋊C₄	—	3	2	no	—
212	C₅×C₄⋊C₄	—	3	1	no	—
213	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
214	C₅×C₂²⋊C₄	—	3	2	no	—
215	C₅×C₂²⋊C₄	—	3	2	no	—
216	C₅×C₂²⋊C₄	—	3	2	no	—
217	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
218	C₄²×C₅	—	3	1	no	—
219	C₄²×C₅	—	3	1	no	—
220	C₄²×C₅	—	3	1	no	—
221	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
222	#681	—	6	4	no	—
223	#681	—	6	4	no	—
224	#681	—	6	4	no	—
225	C₂×#168	—	2	4	no	—
226	C₂×#168	—	3	1	no	—
227	C₂×#168	—	3	4	no	—
228	C₂×#168	—	3	1	no	—
229	C₂×#168	—	3	2	no	—
230	C₂×#168	—	6	2	no	—
231	C₂×#168	—	6	4	no	—
232	C₂×#168	C₂²×D₃	1	1	yes	characteristic
233	C₂×#168	C₂²×D₃	1	2	yes	—
234	C₂×#168	C₂²×D₃	1	1	yes	characteristic
235	C₂×#131	—	15	2	no	—
236	#532	—	3	1	no	—
237	#436	—	15	2	no	—
238	#436	—	15	1	no	—
239	#436	—	15	1	no	—
240	C₈×D₄	—	5	1	no	—
241	C₈×D₄	—	15	1	no	—
242	C₈×D₄	—	15	2	no	—
243	#423	—	15	1	no	—
244	#408	—	15	2	no	—
245	C₂×C₄×C₈	—	15	1	no	—
246	C₂²×C₃×C₅	—	2	2	no	—
247	C₂²×C₃×C₅	—	2	2	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	1	no	—
251	C₂×C₅×D₃	—	2	1	no	—
252	C₂×C₅×D₃	—	2	2	no	—
253	C₂×C₅×D₃	—	2	2	no	—
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	1	no	—
258	C₃×C₄×C₅	#131	1	2	yes	complemented
259	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×Dic₃	—	2	2	no	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	C₄×D₄	1	2	yes	—
264	C₅×Dic₃	#131	1	2	yes	complemented
265	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
267	C₂×#67	C₂×Dic₅	1	2	yes	—
268	C₂×#67	C₂×Dic₅	1	2	yes	—
269	C₂×#67	C₂×Dic₅	1	2	yes	—
270	#235	—	2	4	no	—
271	#235	—	2	4	no	—
272	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
273	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
274	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
277	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
278	C₂×Dic₆	C₂×Dic₅	1	2	yes	—
279	C₂×C₃×C₈	—	5	1	no	—
280	C₂×C₃×C₈	—	5	1	no	—
281	C₂×C₃×C₈	—	5	2	no	—
282	C₂×C₃×C₈	—	10	4	no	—
283	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
284	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
285	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
286	#217	C₂×Dic₅	1	2	yes	—
287	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
288	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
289	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
290	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
291	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
292	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
293	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
294	#208	—	10	4	no	—
295	C₂×C₃⋊C₈	—	5	1	no	—
296	C₂×C₃⋊C₈	—	5	1	no	—
297	C₂×C₃⋊C₈	—	5	2	no	—
298	ΓL(1,𝔽₂₅)	—	10	4	no	—
299	ΓL(1,𝔽₂₅)	—	10	4	no	—
300	D₃×C₈	—	5	4	no	—
301	D₃×C₈	—	10	4	no	—
302	D₃×C₈	—	10	2	no	—
303	C₂³×C₅	—	3	1	no	—
304	C₂³×C₅	—	3	2	no	—
305	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
306	C₅×Q₈	—	6	4	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	6	4	no	—
309	C₅×D₄	—	6	4	no	—
310	C₅×D₄	—	6	4	no	—
311	C₅×D₄	—	6	4	no	—
312	C₅×D₄	—	6	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	3	1	no	—
316	C₂×C₄×C₅	—	3	1	no	—
317	C₂×C₄×C₅	—	3	2	no	—
318	C₂×C₄×C₅	—	3	2	no	—
319	C₂×C₄×C₅	—	3	1	no	—
320	C₂×C₄×C₅	—	3	2	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
327	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
329	#168	—	2	2	no	—
330	#168	—	2	1	no	—
331	#168	—	3	2	no	—
332	#168	—	6	2	no	—
333	#168	—	6	1	no	—
334	#168	D₃×D₄	1	2	yes	—
335	C₂×#41	—	3	2	no	—
336	#131	—	30	8	no	—
337	C₂×M₁₆	—	15	2	no	—
338	C₂×M₁₆	—	15	2	no	—
339	C₂×M₁₆	—	15	2	no	—
340	C₂²×C₈	—	5	2	no	—
341	C₂²×C₈	—	15	1	no	—
342	C₂²×C₈	—	15	2	no	—
343	C₂²×C₈	—	15	1	no	—
344	C₄⋊Q₈	—	3	1	no	—
345	#127	—	3	1	no	—
346	#124	—	3	2	no	—
347	#121	—	3	1	no	—
348	#121	—	3	1	no	—
349	#121	—	3	2	no	—
350	C₄×D₄	—	3	2	no	—
351	C₄×D₄	—	3	1	no	—
352	C₄×D₄	D₃×D₅	1	1	yes	characteristic
353	C₂×C₄²	—	3	1	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	15	2	no	—
356	C₄⋊C₈	—	15	1	no	—
357	C₂²⋊C₈	—	5	2	no	—
358	C₂²⋊C₈	—	15	2	no	—
359	C₂²⋊C₈	—	15	2	no	—
360	C₂²⋊C₈	—	15	2	no	—
361	C₄×C₈	—	5	1	no	—
362	C₄×C₈	—	15	1	no	—
363	C₄×C₈	—	15	1	no	—
364	C₄×C₈	—	15	1	no	—
365	C₂×C₃×C₅	—	4	2	no	—
366	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
368	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
369	C₅×D₃	—	2	2	no	—
370	C₅×D₃	—	4	2	no	—
371	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
372	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
373	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
374	C₃×D₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
379	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
381	#67	—	2	4	no	—
382	#67	—	2	4	no	—
383	#67	—	2	4	no	—
384	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
385	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
386	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
387	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
388	D₁₂	—	2	4	no	—
389	D₁₂	—	2	2	no	—
390	C₄×D₃	—	2	2	no	—
391	C₄×D₃	—	2	2	no	—
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	D₄×D₅	1	2	yes	—
395	C₄×D₃	#711	1	2	yes	—
396	Dic₆	—	2	4	no	—
397	C₃×C₈	—	5	2	no	—
398	C₃×C₈	—	10	2	no	—
399	C₃×C₈	—	10	1	no	—
400	C₃⋊C₈	—	5	2	no	—
401	C₃⋊C₈	—	10	2	no	—
402	C₃⋊C₈	—	10	1	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	3	2	no	—
407	C₂²×C₅	—	6	1	no	—
408	C₂²×C₅	—	6	1	no	—
409	C₂²×C₅	—	6	2	no	—
410	C₂²×C₅	—	6	2	no	—
411	C₂²×C₅	—	6	2	no	—
412	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	—	3	2	no	—
416	C₄×C₅	—	3	2	no	—
417	C₄×C₅	—	6	1	no	—
418	C₄×C₅	—	6	2	no	—
419	C₄×C₅	#901	1	2	yes	complemented
420	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
421	C₄×C₅	D₃×#41	1	1	yes	characteristic
422	#41	—	6	4	no	—
423	#41	—	6	4	no	—
424	C₂×Q₈	—	3	2	no	—
425	C₂×D₄	—	3	2	no	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	2	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	1	no	—
434	C₂²×C₄	—	3	2	no	—
435	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
436	M₁₆	—	30	4	no	—
437	M₁₆	—	30	4	no	—
438	M₁₆	—	30	4	no	—
439	C₂×C₈	—	5	1	no	—
440	C₂×C₈	—	5	1	no	—
441	C₂×C₈	—	5	2	no	—
442	C₂×C₈	—	10	4	no	—
443	C₂×C₈	—	15	4	no	—
444	C₂×C₈	—	15	1	no	—
445	C₂×C₈	—	15	1	no	—
446	C₂×C₈	—	15	2	no	—
447	C₂×C₈	—	30	4	no	—
448	C₂×C₈	—	30	2	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	1	no	—
451	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
452	C₂²⋊C₄	—	3	2	no	—
453	C₂²⋊C₄	—	3	2	no	—
454	C₂²⋊C₄	—	3	2	no	—
455	C₂²⋊C₄	D₃×Dic₅	1	2	yes	—
456	C₄²	—	3	1	no	—
457	C₄²	—	3	1	no	—
458	C₄²	—	3	1	no	—
459	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
460	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
465	C₂×D₃	—	2	1	no	—
466	C₂×D₃	—	2	1	no	—
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	2	2	no	—
469	C₂×D₃	—	2	2	no	—
470	C₂×D₃	D₄×Dic₅	1	2	yes	—
471	C₃×C₄	—	2	2	no	—
472	C₃×C₄	—	2	1	no	—
473	C₃×C₄	#4094	1	2	yes	complemented
474	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
475	C₃×C₄	C₂×#711	1	1	yes	characteristic
476	Dic₃	—	2	2	no	—
477	Dic₃	—	2	1	no	—
478	Dic₃	D₄×Dic₅	1	2	yes	—
479	Dic₃	#4094	1	2	yes	complemented
480	C₂×C₅	—	4	2	no	—
481	C₂×C₅	—	6	2	no	—
482	C₂×C₅	—	12	2	no	—
483	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
484	C₂×C₅	C₂×#901	1	1	yes	characteristic
485	C₂×C₅	D₃×#131	1	1	yes	characteristic
486	C₂³	—	3	1	no	—
487	C₂³	—	3	2	no	—
488	C₂³	C₂×D₃×Dic₅	1	2	yes	—
489	Q₈	—	6	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	6	4	no	—
492	D₄	—	6	4	no	—
493	D₄	—	6	4	no	—
494	D₄	—	6	4	no	—
495	D₄	—	6	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	3	1	no	—
499	C₂×C₄	—	3	1	no	—
500	C₂×C₄	—	3	2	no	—
501	C₂×C₄	—	3	2	no	—
502	C₂×C₄	—	3	1	no	—
503	C₂×C₄	—	3	2	no	—
504	C₂×C₄	—	6	2	no	—
505	C₂×C₄	—	6	2	no	—
506	C₂×C₄	—	6	2	no	—
507	C₂×C₄	—	6	2	no	—
508	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
509	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
510	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
512	C₈	—	5	2	no	—
513	C₈	—	10	2	no	—
514	C₈	—	10	1	no	—
515	C₈	—	15	2	no	—
516	C₈	—	30	2	no	—
517	C₈	—	30	1	no	—
518	C₂×C₃	—	4	2	no	—
519	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
520	C₂×C₃	C₂×#4094	1	1	yes	characteristic
521	C₂×C₃	C₂×#4094	1	1	yes	characteristic
522	D₃	—	2	2	no	—
523	D₃	—	4	2	no	—
524	C₅	#79422	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	2	2	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	3	2	no	—
529	C₂²	—	6	1	no	—
530	C₂²	—	6	1	no	—
531	C₂²	—	6	2	no	—
532	C₂²	—	6	2	no	—
533	C₂²	—	6	2	no	—
534	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	3	2	no	—
538	C₄	—	3	2	no	—
539	C₄	—	6	2	no	—
540	C₄	—	6	1	no	—
541	C₄	#91286	1	2	yes	complemented
542	C₄	D₃×D₄×D₅	1	1	yes	characteristic
543	C₄	D₃×#711	1	1	yes	characteristic
544	C₃	#10615006	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	4	2	no	—
546	C₂	—	6	2	no	—
547	C₂	—	12	2	no	—
548	C₂	C₂×#91286	1	1	yes	characteristic
549	C₂	D₃×D₄×Dic₅	1	1	yes	characteristic
550	C₂	D₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×D₄	C₂²
prime radical	C₅×#5548	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	#2931
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#91286	C₂	semidirect
3. #11751113	C₂	semidirect
4. C₃×D₄×#168	C₂	semidirect
5. #11748490	C₂	semidirect
6. #67×#168	C₂	semidirect
7. #11748314	C₂	semidirect
8. #11747014	C₂	semidirect
9. #11747011	C₂	semidirect
10. D₁₂×#168	C₂	semidirect
11. C₄×D₃×#168	C₂	semidirect
52. D₄×#168	D₃	semidirect
92. D₃×#168	D₄	semidirect
258. C₃×C₄×C₅	#131	semidirect
264. C₅×Dic₃	#131	semidirect
419. C₄×C₅	#901	semidirect
460. C₃×C₅	#2931	semidirect
473. C₃×C₄	#4094	semidirect
479. Dic₃	#4094	semidirect
524. C₅	#79422	semidirect
541. C₄	#91286	semidirect
544. C₃	#10615006	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5548	2
C₂×#91286	2
#11751113	2
C₃×D₄×#168	2
#11748490	2
#67×#168	2
#11748314	2
#11747014	2
#11747011	2
D₁₂×#168	2
C₄×D₃×#168	2
#10615006	3
#79422	5