Subgroups — #14414966

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5791	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91286	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751308	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748500	C₂	1	4	yes	maximal, complemented
6	#67×#168	C₂	1	4	yes	maximal, complemented
7	#11748439	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748345	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748323	C₂	1	1	yes	maximal, characteristic, complemented
10	#10614647	—	3	1	no	maximal, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×#235	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	1	yes	characteristic
14	C₂×#6710	C₂²	1	1	yes	characteristic
15	C₅×#953	C₄	1	2	yes	—
16	C₅×#930	C₄	1	2	yes	—
17	C₅×#929	C₄	1	2	yes	—
18	C₄×C₅×#67	C₂²	1	4	yes	—
19	C₅×#926	C₂²	1	1	yes	characteristic
20	C₅×#924	C₄	1	2	yes	—
21	C₂²×C₃×#168	—	2	4	no	—
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	2	yes	—
24	C₂²×C₃×#168	C₂²	1	2	yes	—
25	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
26	C₂×#6650	C₂²	1	2	yes	complemented
27	#91286	—	2	4	no	—
28	C₂×D₃×#168	C₂²	1	2	yes	complemented
29	#91114	C₂²	1	4	yes	—
30	Dic₃⋊#168	C₂²	1	4	yes	complemented
31	(C₂×D₃)⋊#168	C₂²	1	4	yes	complemented
32	#90953	C₂²	1	2	yes	complemented
33	Dic₃×#168	C₂²	1	2	yes	complemented
34	#83734	—	5	1	no	maximal, Hall
35	C₅×#525	—	3	1	no	—
36	C₂×#4094	—	3	1	no	—
37	C₂³×#168	D₃	1	1	yes	characteristic, complemented
38	#65523	—	3	1	no	—
39	#65496	—	3	1	no	—
40	#65300	—	3	4	no	—
41	D₄×#168	—	3	4	no	—
42	#65288	—	3	1	no	—
43	#65286	—	3	1	no	—
44	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	C₂×C₄	1	4	yes	—
52	C₂×C₅×#67	C₂×C₄	1	2	yes	—
53	C₅×#235	—	2	2	no	—
54	C₅×#235	—	2	2	no	—
55	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
58	#6710	—	2	2	no	—
59	#6710	—	2	2	no	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₂×C₃⋊#168	C₂³	1	2	yes	—
62	C₅×#217	C₂×C₄	1	4	yes	—
63	C₅×#217	C₂×C₄	1	2	yes	—
64	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
65	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
66	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
67	C₄×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂×C₃×#168	—	2	2	no	—
69	C₂×C₃×#168	—	2	4	no	—
70	C₂×C₃×#168	—	2	4	no	—
71	C₂×C₃×#168	D₄	1	4	yes	complemented
72	C₂×C₃×#168	C₂³	1	2	yes	—
73	C₂×C₃×#168	C₂³	1	1	yes	characteristic
74	C₂×C₃×#168	C₂³	1	1	yes	characteristic
75	#6650	—	2	4	no	—
76	D₃×#168	—	2	4	no	—
77	C₂³×C₃×C₈	—	5	1	no	—
78	#5791	D₅	1	1	yes	characteristic
79	C₂×#901	—	5	1	no	—
80	#5207	—	5	1	no	—
81	#5111	—	5	4	no	—
82	#5110	—	5	1	no	—
83	C₈×#67	—	5	4	no	—
84	#5102	—	5	1	no	—
85	#5101	—	5	1	no	—
86	C₂×C₅×#41	—	3	1	no	—
87	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
88	C₅×#123	—	3	2	no	—
89	C₅×C₂²⋊Q₈	—	3	2	no	—
90	C₅×#121	—	3	2	no	—
91	C₅×#120	—	3	2	no	—
92	C₄×C₅×D₄	—	3	4	no	—
93	C₅×#117	—	3	1	no	—
94	#4094	—	6	4	no	—
95	C₂×#681	—	3	1	no	—
96	C₂×#681	—	3	1	no	—
97	C₂×#681	—	3	2	no	—
98	C₂²×#168	—	2	4	no	—
99	C₂²×#168	—	3	2	no	—
100	C₂²×#168	C₂×D₃	1	1	yes	characteristic
101	C₂²×#168	C₂×D₃	1	2	yes	—
102	C₂²×#168	C₂×D₃	1	2	yes	—
103	C₂²×#168	C₂×D₃	1	1	yes	characteristic
104	C₂²⋊#168	—	3	4	no	—
105	C₂²⋊#168	—	3	4	no	—
106	C₄⋊#168	—	3	4	no	—
107	#3935	—	3	2	no	—
108	C₄×#168	—	3	2	no	—
109	#2929	—	15	1	no	Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₅×#67	—	2	4	no	—
125	C₅×#67	—	2	8	no	—
126	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
127	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
128	C₅×D₁₂	—	2	2	no	—
129	C₄×C₅×D₃	—	2	2	no	—
130	C₄×C₅×D₃	—	2	2	no	—
131	C₅×Dic₆	—	2	2	no	—
132	C₃⋊#168	—	2	2	no	—
133	C₃⋊#168	—	2	2	no	—
134	C₃×#168	—	2	2	no	—
135	C₃×#168	C₂×D₄	1	2	yes	—
136	C₃×#168	C₂×D₄	1	2	yes	—
137	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
138	C₂×#235	C₂×D₅	1	1	yes	characteristic
139	C₂²×C₃×C₈	—	5	1	no	—
140	C₂²×C₃×C₈	—	5	1	no	—
141	C₂²×C₃×C₈	—	5	2	no	—
142	C₂²×C₃×C₈	—	5	2	no	—
143	C₂²×C₃×C₈	—	10	4	no	—
144	#953	Dic₅	1	2	yes	—
145	#930	Dic₅	1	2	yes	—
146	#929	Dic₅	1	2	yes	—
147	C₄×#67	C₂×D₅	1	4	yes	—
148	#926	C₂×D₅	1	1	yes	characteristic
149	#924	Dic₅	1	2	yes	—
150	C₂×#208	—	5	1	no	—
151	C₂×#208	—	5	1	no	—
152	#901	—	10	4	no	—
153	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
154	C₂×D₃×C₈	—	5	2	no	—
155	#830	—	5	4	no	—
156	(C₂×D₃)⋊C₈	—	5	4	no	—
157	#815	—	5	2	no	—
158	Dic₃⋊C₈	—	5	4	no	—
159	C₈×Dic₃	—	5	2	no	—
160	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
161	C₅×#41	—	6	2	no	—
162	C₅×#41	—	6	2	no	—
163	C₂×C₅×Q₈	—	3	1	no	—
164	C₂×C₅×D₄	—	3	4	no	—
165	C₂×C₅×D₄	—	3	2	no	—
166	C₂×C₅×D₄	—	3	1	no	—
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	3	2	no	—
170	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
171	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×C₄⋊C₄	—	3	2	no	—
175	C₅×C₄⋊C₄	—	3	4	no	—
176	C₅×C₂²⋊C₄	—	3	2	no	—
177	C₅×C₂²⋊C₄	—	3	4	no	—
178	C₅×C₂²⋊C₄	—	3	4	no	—
179	C₄²×C₅	—	3	2	no	—
180	#681	—	6	2	no	—
181	#681	—	6	2	no	—
182	#681	—	6	4	no	—
183	C₂×#168	—	2	2	no	—
184	C₂×#168	—	2	4	no	—
185	C₂×#168	—	2	4	no	—
186	C₂×#168	—	3	2	no	—
187	C₂×#168	—	3	2	no	—
188	C₂×#168	—	6	4	no	—
189	C₂×#168	#67	1	4	yes	complemented
190	C₂×#168	C₂²×D₃	1	2	yes	—
191	C₂×#168	C₂²×D₃	1	1	yes	characteristic
192	C₂×#168	C₂²×D₃	1	1	yes	characteristic
193	C₂×#131	—	15	1	no	—
194	C₂³×C₈	—	5	1	no	—
195	#525	—	3	1	no	—
196	#435	—	15	4	no	—
197	C₈×D₄	—	15	4	no	—
198	#424	—	15	1	no	—
199	#408	—	15	1	no	—
200	#407	—	15	1	no	—
201	#405	—	15	1	no	—
202	C₂²×C₃×C₅	—	2	8	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	2	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	#131	1	4	yes	complemented
208	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₅×D₃	—	2	2	no	—
210	C₂×C₅×D₃	—	2	4	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
213	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
215	C₅×Dic₃	—	2	2	no	—
216	C₅×Dic₃	—	2	4	no	—
217	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	2	2	no	—
219	C₂²×C₃×C₄	—	2	2	no	—
220	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
224	C₂×#67	C₂×Dic₅	1	4	yes	—
225	C₂×#67	C₂×Dic₅	1	2	yes	—
226	#235	—	2	2	no	—
227	#235	—	2	2	no	—
228	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
229	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
230	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
231	C₂×C₃×C₈	—	5	4	no	—
232	C₂×C₃×C₈	—	5	1	no	—
233	C₂×C₃×C₈	—	5	1	no	—
234	C₂×C₃×C₈	—	5	2	no	—
235	C₂×C₃×C₈	—	10	4	no	—
236	C₂×C₃×C₈	—	10	4	no	—
237	C₂×C₃×C₈	—	10	2	no	—
238	#217	C₂×Dic₅	1	4	yes	—
239	#217	C₂×Dic₅	1	2	yes	—
240	(C₂×D₃)⋊C₄	C₂×Dic₅	1	4	yes	—
241	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
242	Dic₃⋊C₄	C₂×Dic₅	1	4	yes	—
243	C₄×Dic₃	C₂²×D₅	1	2	yes	—
244	#208	—	10	2	no	—
245	#208	—	10	2	no	—
246	C₂×C₃⋊C₈	—	5	2	no	—
247	C₂×C₃⋊C₈	—	5	2	no	—
248	ΓL(1,𝔽₂₅)	—	10	4	no	—
249	D₃×C₈	—	10	4	no	—
250	C₂³×C₅	—	2	4	no	—
251	C₂³×C₅	—	2	2	no	—
252	C₂³×C₅	—	3	2	no	—
253	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
254	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
255	C₅×Q₈	—	6	2	no	—
256	C₅×D₄	—	6	8	no	—
257	C₅×D₄	—	6	4	no	—
258	C₅×D₄	—	6	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	3	4	no	—
264	C₂×C₄×C₅	—	3	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂×C₄×C₅	#235	1	2	yes	—
270	C₂×C₄×C₅	C₂×#67	1	2	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	#168	—	2	2	no	—
273	#168	—	6	2	no	—
274	#168	—	6	2	no	—
275	#168	C₂×#67	1	2	yes	—
276	#168	C₂×#67	1	2	yes	—
277	C₂×#41	—	3	1	no	—
278	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
279	#131	—	30	4	no	—
280	C₂×M₁₆	—	15	2	no	—
281	C₂×M₁₆	—	15	1	no	—
282	C₂×M₁₆	—	15	1	no	—
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	1	no	—
285	C₂²×C₈	—	5	2	no	—
286	C₂²×C₈	—	5	2	no	—
287	C₂²×C₈	—	10	4	no	—
288	C₂²×C₈	—	15	2	no	—
289	#123	—	3	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	#121	—	3	2	no	—
292	#120	—	3	2	no	—
293	C₄×D₄	—	3	4	no	—
294	#117	—	3	1	no	—
295	C₄⋊C₈	—	15	4	no	—
296	C₂²⋊C₈	—	15	4	no	—
297	C₂²⋊C₈	—	15	4	no	—
298	#97	—	15	2	no	—
299	C₄×C₈	—	15	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	2	4	no	—
302	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	2	yes	—
304	C₅×D₃	—	4	2	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	4	no	—
307	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
308	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
309	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
315	C₂×C₃×C₄	#711	1	2	yes	—
316	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
317	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
319	#67	—	2	4	no	—
320	#67	—	2	8	no	—
321	C₂×Dic₃	C₂²×Dic₅	1	4	yes	—
322	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
323	D₁₂	—	2	2	no	—
324	C₄×D₃	—	2	2	no	—
325	C₄×D₃	—	2	2	no	—
326	Dic₆	—	2	2	no	—
327	C₃×C₈	—	5	2	no	—
328	C₃×C₈	—	5	2	no	—
329	C₃×C₈	—	10	2	no	—
330	C₃⋊C₈	—	10	2	no	—
331	C₃⋊C₈	—	10	2	no	—
332	C₂²×C₅	—	2	8	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	6	4	no	—
337	C₂²×C₅	—	6	2	no	—
338	C₂²×C₅	#901	1	4	yes	complemented
339	C₂²×C₅	C₄×#67	1	2	yes	—
340	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	6	4	no	—
343	C₄×C₅	—	6	2	no	—
344	C₄×C₅	C₄×#67	1	2	yes	—
345	C₄×C₅	C₂×#235	1	1	yes	characteristic
346	C₄×C₅	C₂²×#67	1	1	yes	characteristic
347	C₂⁴	D₃×Dic₅	1	1	yes	characteristic
348	#41	—	6	2	no	—
349	#41	—	6	2	no	—
350	C₂×Q₈	—	3	1	no	—
351	C₂×D₄	—	3	4	no	—
352	C₂×D₄	—	3	2	no	—
353	C₂×D₄	—	3	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	3	2	no	—
357	C₂²×C₄	D₃×Dic₅	1	2	yes	—
358	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
360	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
361	M₁₆	—	30	4	no	—
362	M₁₆	—	30	2	no	—
363	M₁₆	—	30	2	no	—
364	C₂×C₈	—	5	4	no	—
365	C₂×C₈	—	5	1	no	—
366	C₂×C₈	—	5	1	no	—
367	C₂×C₈	—	5	2	no	—
368	C₂×C₈	—	10	4	no	—
369	C₂×C₈	—	10	4	no	—
370	C₂×C₈	—	10	2	no	—
371	C₂×C₈	—	15	2	no	—
372	C₂×C₈	—	15	2	no	—
373	C₂×C₈	—	30	4	no	—
374	C₄⋊C₄	—	3	2	no	—
375	C₄⋊C₄	—	3	4	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₂²⋊C₄	—	3	4	no	—
378	C₂²⋊C₄	—	3	4	no	—
379	C₄²	—	3	2	no	—
380	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	2	8	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	D₄×Dic₅	1	2	yes	—
386	C₂²×C₃	#4094	1	4	yes	complemented
387	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	—	2	4	no	—
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	D₄×Dic₅	1	2	yes	—
392	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
393	C₃×C₄	C₂×#711	1	1	yes	characteristic
394	Dic₃	—	2	2	no	—
395	Dic₃	—	2	4	no	—
396	C₂×C₅	—	2	4	no	—
397	C₂×C₅	—	2	2	no	—
398	C₂×C₅	—	12	2	no	—
399	C₂×C₅	C₂×#901	1	2	yes	—
400	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	3	2	no	—
404	C₂³	C₂×D₃×Dic₅	1	2	yes	—
405	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
406	Q₈	—	6	2	no	—
407	D₄	—	6	8	no	—
408	D₄	—	6	4	no	—
409	D₄	—	6	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	3	4	no	—
415	C₂×C₄	—	3	2	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
419	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
420	C₂×C₄	#6782	1	2	yes	—
421	C₂×C₄	D₅×#67	1	2	yes	—
422	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
423	C₈	—	5	2	no	—
424	C₈	—	5	2	no	—
425	C₈	—	10	2	no	—
426	C₈	—	30	2	no	—
427	C₈	—	30	2	no	—
428	C₂×C₃	—	2	2	no	—
429	C₂×C₃	—	2	4	no	—
430	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
431	C₂×C₃	C₂×#4094	1	2	yes	—
432	D₃	—	4	2	no	—
433	C₅	#83734	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	6	2	no	—
439	C₂²	—	6	4	no	—
440	C₂²	#91286	1	4	yes	complemented
441	C₂²	Dic₅×#67	1	2	yes	—
442	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	6	2	no	—
445	C₄	—	6	4	no	—
446	C₄	Dic₅×#67	1	2	yes	—
447	C₄	C₂×#6782	1	1	yes	characteristic
448	C₄	C₂×D₅×#67	1	1	yes	characteristic
449	C₃	#10614647	1	1	yes	characteristic, complemented, Sylow
450	C₂	—	2	4	no	—
451	C₂	—	2	2	no	—
452	C₂	—	12	2	no	—
453	C₂	C₂×#91286	1	2	yes	—
454	C₂	C₂×Dic₅×#67	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂³×C₃×C₄×C₅	C₂²
prime radical	C₅×#5791	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	#2929
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×#168	C₂	semidirect
3. C₂×#91286	C₂	semidirect
4. #11751308	C₂	semidirect
5. #11748500	C₂	semidirect
6. #67×#168	C₂	semidirect
7. #11748439	C₂	semidirect
8. #11748345	C₂	semidirect
9. #11748323	C₂	semidirect
26. C₂×#6650	C₂²	semidirect
28. C₂×D₃×#168	C₂²	semidirect
30. Dic₃⋊#168	C₂²	semidirect
31. (C₂×D₃)⋊#168	C₂²	semidirect
32. #90953	C₂²	semidirect
33. Dic₃×#168	C₂²	semidirect
37. C₂³×#168	D₃	semidirect
71. C₂×C₃×#168	D₄	semidirect
189. C₂×#168	#67	semidirect
207. C₂²×C₃×C₅	#131	semidirect
338. C₂²×C₅	#901	semidirect
380. C₃×C₅	#2929	semidirect
386. C₂²×C₃	#4094	semidirect
433. C₅	#83734	semidirect
440. C₂²	#91286	semidirect
449. C₃	#10614647	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5791	2
C₂³×C₃×#168	2
C₂×#91286	2
#11751308	2
#11748500	2
#67×#168	2
#11748439	2
#11748345	2
#11748323	2
#10614647	3
#83734	5