Subgroups — #14282385

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 472 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	#11747011	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745837	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745836	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602595	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	—	2	1	no	—
10	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₅×#940	C₄	1	1	yes	characteristic
12	C₅×#938	C₄	1	1	yes	characteristic
13	C₄×C₅×#67	—	2	1	no	—
14	C₅×#895	C₄	1	1	yes	characteristic
15	C₅×#888	C₄	1	1	yes	characteristic
16	C₅×#885	—	2	1	no	—
17	C₅×#884	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×#6650	—	2	1	no	—
21	C₂×D₃×#168	—	2	1	no	—
22	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
23	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
25	C₃×C₄×#168	C₂²	1	1	yes	characteristic
26	Dic₃⋊#168	—	2	1	no	—
27	Dic₃×#168	—	2	1	no	—
28	#68176	—	5	1	no	maximal, Hall
29	C₅×#532	—	3	1	no	—
30	#65213	—	3	1	no	—
31	C₂×C₄×#168	—	3	1	no	—
32	D₄⋊#168	—	3	1	no	—
33	D₄⋊#168	—	3	1	no	—
34	D₄⋊#168	—	3	1	no	—
35	D₄⋊#168	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂×C₅×#67	—	2	1	no	—
39	C₂×C₅×#67	—	2	1	no	—
40	C₂×C₅×#67	—	2	1	no	—
41	C₅×#235	—	4	2	no	—
42	C₅×#235	—	4	2	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
49	C₂×C₅×Dic₆	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃⋊#168	—	2	1	no	—
54	C₂×C₃⋊#168	—	2	1	no	—
55	C₅×#217	—	2	1	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
58	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₅×Dic₃⋊C₄	—	2	1	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₃×#168	—	2	1	no	—
64	C₂×C₃×#168	—	2	1	no	—
65	#6650	—	4	2	no	—
66	D₃×#168	—	2	4	no	—
67	#5548	D₅	1	1	yes	characteristic
68	#4837	—	5	1	no	—
69	C₄×D₃×C₈	—	5	1	no	—
70	C₃×D₄⋊C₈	—	5	1	no	—
71	D₄⋊(C₃⋊C₈)	—	5	1	no	—
72	#4483	—	5	1	no	—
73	#4459	—	5	1	no	—
74	C₂×C₅×#41	—	6	1	no	—
75	C₅×C₄⋊Q₈	—	3	1	no	—
76	C₅×#127	—	3	1	no	—
77	C₅×#124	—	6	1	no	—
78	C₅×#121	—	3	1	no	—
79	C₅×#121	—	3	1	no	—
80	C₅×#121	—	6	1	no	—
81	C₄×C₅×D₄	—	3	1	no	—
82	C₄×C₅×D₄	—	6	1	no	—
83	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₂×#681	—	6	1	no	—
86	C₂²×#168	—	6	1	no	—
87	C₄⋊#168	—	3	1	no	—
88	C₄⋊#168	—	6	1	no	—
89	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
90	C₄×#168	—	3	1	no	—
91	C₄×#168	—	6	1	no	—
92	C₄×#168	C₂×D₃	1	1	yes	characteristic
93	#1492	—	15	1	no	Sylow
94	C₂³×C₃×C₅	—	2	1	no	—
95	C₂²×C₅×D₃	—	2	1	no	—
96	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₃×C₅×D₄	—	2	1	no	—
98	C₃×C₅×D₄	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₅×#67	—	4	2	no	—
106	C₅×#67	—	4	2	no	—
107	C₅×#67	—	4	2	no	—
108	C₂×C₅×Dic₃	—	2	1	no	—
109	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₅×D₁₂	—	2	1	no	—
113	C₅×D₁₂	—	2	1	no	—
114	C₅×D₁₂	—	4	2	no	—
115	C₄×C₅×D₃	—	2	1	no	—
116	C₄×C₅×D₃	—	2	1	no	—
117	C₄×C₅×D₃	—	2	2	no	—
118	C₄×C₅×D₃	—	4	1	no	—
119	C₄×C₅×D₃	—	4	1	no	—
120	C₄×C₅×D₃	D₈	1	2	yes	—
121	C₄×C₅×D₃	SD₁₆	1	2	yes	—
122	C₅×Dic₆	—	4	2	no	—
123	C₃⋊#168	—	2	2	no	—
124	C₃⋊#168	—	4	1	no	—
125	C₃×#168	—	2	2	no	—
126	C₃×#168	—	4	1	no	—
127	C₂×#235	—	2	1	no	—
128	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
129	#940	Dic₅	1	1	yes	characteristic
130	#938	Dic₅	1	1	yes	characteristic
131	C₄×#67	—	2	1	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
133	C₂×D₃×C₈	—	10	1	no	—
134	#895	Dic₅	1	1	yes	characteristic
135	#888	Dic₅	1	1	yes	characteristic
136	#885	—	2	1	no	—
137	#884	—	2	1	no	—
138	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
139	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
140	C₃×C₄⋊C₈	—	5	1	no	—
141	C₃×C₄×C₈	—	5	1	no	—
142	Dic₃⋊C₈	—	10	1	no	—
143	C₈×Dic₃	—	10	1	no	—
144	C₄⋊(C₃⋊C₈)	—	5	1	no	—
145	C₄×C₃⋊C₈	—	5	1	no	—
146	C₅×#41	—	12	2	no	—
147	C₅×#41	—	12	2	no	—
148	C₂×C₅×Q₈	—	6	1	no	—
149	C₂×C₅×D₄	—	3	1	no	—
150	C₂×C₅×D₄	—	6	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₅×C₄⋊C₄	—	3	1	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	6	1	no	—
165	C₅×C₂²⋊C₄	—	6	1	no	—
166	C₅×C₂²⋊C₄	—	6	1	no	—
167	C₄²×C₅	—	3	1	no	—
168	C₄²×C₅	—	3	1	no	—
169	C₄²×C₅	—	3	1	no	—
170	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
171	#681	—	12	2	no	—
172	C₂×#168	—	2	1	no	—
173	C₂×#168	—	2	1	no	—
174	C₂×#168	—	6	4	no	—
175	C₂×#168	—	6	1	no	—
176	C₂×#168	—	6	1	no	—
177	#532	—	3	1	no	—
178	#423	—	15	1	no	—
179	C₂×C₄×C₈	—	15	1	no	—
180	D₄⋊C₈	—	5	1	no	—
181	D₄⋊C₈	—	15	1	no	—
182	D₄⋊C₈	—	15	1	no	—
183	D₄⋊C₈	—	15	1	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	—	4	1	no	—
186	C₂²×C₃×C₅	—	4	1	no	—
187	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₅×D₃	—	2	1	no	—
189	C₂×C₅×D₃	—	2	1	no	—
190	C₂×C₅×D₃	—	4	1	no	—
191	C₂×C₅×D₃	—	4	1	no	—
192	C₂×C₅×D₃	—	4	1	no	—
193	C₂×C₅×D₃	#102	1	2	yes	—
194	C₃×C₄×C₅	—	2	1	no	—
195	C₃×C₄×C₅	—	4	1	no	—
196	C₃×C₄×C₅	#131	1	1	yes	characteristic
197	C₃×C₄×C₅	#131	1	1	yes	characteristic
198	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
200	C₅×Dic₃	—	2	1	no	—
201	C₅×Dic₃	—	4	1	no	—
202	C₅×Dic₃	#102	1	2	yes	—
203	C₅×Dic₃	#104	1	2	yes	—
204	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂×#67	—	2	1	no	—
207	C₂×#67	—	2	1	no	—
208	C₂×#67	—	2	1	no	—
209	#235	—	4	2	no	—
210	#235	—	4	2	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
213	C₂×C₄×D₃	—	2	1	no	—
214	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
215	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
216	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
217	C₂×Dic₆	—	2	1	no	—
218	C₂×C₃×C₈	—	10	1	no	—
219	C₂×C₃×C₈	—	10	1	no	—
220	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
221	C₃×C₂²⋊C₄	—	2	1	no	—
222	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
223	#217	—	2	1	no	—
224	(C₂×D₃)⋊C₄	—	2	1	no	—
225	(C₂×D₃)⋊C₄	—	2	1	no	—
226	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
227	Dic₃⋊C₄	—	2	1	no	—
228	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
229	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
230	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
231	C₂×C₃⋊C₈	—	10	1	no	—
232	C₂×C₃⋊C₈	—	10	1	no	—
233	ΓL(1,𝔽₂₅)	—	20	2	no	—
234	D₃×C₈	—	10	4	no	—
235	C₂³×C₅	—	2	1	no	—
236	C₂³×C₅	—	3	1	no	—
237	C₂³×C₅	—	6	1	no	—
238	C₅×Q₈	—	12	2	no	—
239	C₅×D₄	—	2	1	no	—
240	C₅×D₄	—	2	1	no	—
241	C₅×D₄	—	6	1	no	—
242	C₅×D₄	—	6	1	no	—
243	C₅×D₄	—	12	2	no	—
244	C₅×D₄	—	12	2	no	—
245	C₅×D₄	—	12	2	no	—
246	C₅×D₄	—	12	2	no	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	3	1	no	—
249	C₂×C₄×C₅	—	3	1	no	—
250	C₂×C₄×C₅	—	3	2	no	—
251	C₂×C₄×C₅	—	3	2	no	—
252	C₂×C₄×C₅	—	3	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	1	no	—
257	C₂×C₄×C₅	—	6	1	no	—
258	C₂×C₄×C₅	—	6	1	no	—
259	C₂×C₄×C₅	—	12	1	no	—
260	C₂×C₄×C₅	—	12	1	no	—
261	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
264	#168	—	2	2	no	—
265	#168	—	4	1	no	—
266	#168	—	6	2	no	—
267	#168	—	12	1	no	—
268	C₂×#41	—	6	1	no	—
269	C₂×M₁₆	—	30	1	no	—
270	C₂²×C₈	—	30	1	no	—
271	C₄⋊Q₈	—	3	1	no	—
272	#127	—	3	1	no	—
273	#124	—	6	1	no	—
274	#121	—	3	1	no	—
275	#121	—	3	1	no	—
276	#121	—	6	1	no	—
277	C₄×D₄	—	3	1	no	—
278	C₄×D₄	—	6	1	no	—
279	C₄×D₄	D₃×D₅	1	1	yes	characteristic
280	C₂×C₄²	—	3	1	no	—
281	C₄⋊C₈	—	5	1	no	—
282	C₄⋊C₈	—	15	1	no	—
283	C₄⋊C₈	—	30	1	no	—
284	C₄×C₈	—	5	1	no	—
285	C₄×C₈	—	15	1	no	—
286	C₄×C₈	—	30	1	no	—
287	C₂×C₃×C₅	—	8	1	no	—
288	C₂×C₃×C₅	#408	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
290	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
291	C₅×D₃	—	2	2	no	—
292	C₅×D₃	—	8	1	no	—
293	C₂³×C₃	—	2	1	no	—
294	C₂²×D₃	—	2	1	no	—
295	C₂²×D₃	C₂²⋊Dic₅	1	1	yes	characteristic
296	C₃×D₄	—	2	1	no	—
297	C₃×D₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	—	4	1	no	—
301	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
304	#67	—	4	2	no	—
305	#67	—	4	2	no	—
306	#67	—	4	2	no	—
307	C₂×Dic₃	—	2	1	no	—
308	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
309	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
310	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
311	D₁₂	—	2	1	no	—
312	D₁₂	—	2	1	no	—
313	D₁₂	—	4	2	no	—
314	C₄×D₃	—	2	1	no	—
315	C₄×D₃	—	2	1	no	—
316	C₄×D₃	—	2	2	no	—
317	C₄×D₃	—	4	1	no	—
318	C₄×D₃	—	4	1	no	—
319	C₄×D₃	#686	1	2	yes	—
320	C₄×D₃	#687	1	2	yes	—
321	Dic₆	—	4	2	no	—
322	C₃×C₈	—	10	2	no	—
323	C₃×C₈	—	20	1	no	—
324	C₃⋊C₈	—	10	2	no	—
325	C₃⋊C₈	—	20	1	no	—
326	C₂²×C₅	—	3	2	no	—
327	C₂²×C₅	—	4	1	no	—
328	C₂²×C₅	—	4	1	no	—
329	C₂²×C₅	—	4	1	no	—
330	C₂²×C₅	—	6	1	no	—
331	C₂²×C₅	—	6	1	no	—
332	C₂²×C₅	—	12	1	no	—
333	C₂²×C₅	—	12	1	no	—
334	C₂²×C₅	—	12	1	no	—
335	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	3	2	no	—
338	C₄×C₅	—	3	2	no	—
339	C₄×C₅	—	4	1	no	—
340	C₄×C₅	—	6	1	no	—
341	C₄×C₅	—	12	1	no	—
342	C₄×C₅	#901	1	1	yes	characteristic
343	C₄×C₅	#907	1	1	yes	characteristic
344	C₄×C₅	D₃×D₈	1	1	yes	characteristic
345	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
346	#41	—	12	2	no	—
347	#41	—	12	2	no	—
348	C₂×Q₈	—	6	1	no	—
349	C₂×D₄	—	3	1	no	—
350	C₂×D₄	—	6	1	no	—
351	C₂×D₄	—	6	1	no	—
352	C₂×D₄	—	6	1	no	—
353	C₂×D₄	—	6	1	no	—
354	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	3	1	no	—
357	C₂²×C₄	—	3	1	no	—
358	C₂²×C₄	—	3	1	no	—
359	C₂²×C₄	—	6	1	no	—
360	M₁₆	—	60	2	no	—
361	C₂×C₈	—	10	1	no	—
362	C₂×C₈	—	10	1	no	—
363	C₂×C₈	—	30	4	no	—
364	C₂×C₈	—	30	1	no	—
365	C₂×C₈	—	30	1	no	—
366	C₄⋊C₄	—	3	1	no	—
367	C₄⋊C₄	—	6	1	no	—
368	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	6	1	no	—
371	C₂²⋊C₄	—	6	1	no	—
372	C₂²⋊C₄	—	6	1	no	—
373	C₄²	—	3	1	no	—
374	C₄²	—	3	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
377	C₃×C₅	#1492	1	1	yes	characteristic, complemented, Hall
378	C₂²×C₃	—	4	1	no	—
379	C₂²×C₃	—	4	1	no	—
380	C₂²×C₃	—	4	1	no	—
381	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
382	C₂×D₃	—	2	1	no	—
383	C₂×D₃	—	2	1	no	—
384	C₂×D₃	—	4	1	no	—
385	C₂×D₃	—	4	1	no	—
386	C₂×D₃	—	4	1	no	—
387	C₂×D₃	#3964	1	2	yes	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	4	1	no	—
390	C₃×C₄	C₂×#686	1	1	yes	characteristic
391	C₃×C₄	C₂×#687	1	1	yes	characteristic
392	C₃×C₄	#4094	1	1	yes	characteristic
393	C₃×C₄	#4094	1	1	yes	characteristic
394	Dic₃	—	2	1	no	—
395	Dic₃	—	4	1	no	—
396	Dic₃	#3964	1	2	yes	—
397	Dic₃	#3969	1	2	yes	—
398	C₂×C₅	—	6	2	no	—
399	C₂×C₅	—	8	1	no	—
400	C₂×C₅	—	24	1	no	—
401	C₂×C₅	#4727	1	1	yes	characteristic
402	C₂×C₅	D₃×#102	1	1	yes	characteristic
403	C₂×C₅	D₃×#104	1	1	yes	characteristic
404	C₂³	—	2	1	no	—
405	C₂³	—	3	1	no	—
406	C₂³	—	6	1	no	—
407	Q₈	—	12	2	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	1	no	—
410	D₄	—	6	1	no	—
411	D₄	—	6	1	no	—
412	D₄	—	12	2	no	—
413	D₄	—	12	2	no	—
414	D₄	—	12	2	no	—
415	D₄	—	12	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	3	1	no	—
418	C₂×C₄	—	3	1	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	6	1	no	—
426	C₂×C₄	—	6	1	no	—
427	C₂×C₄	—	6	1	no	—
428	C₂×C₄	—	12	1	no	—
429	C₂×C₄	—	12	1	no	—
430	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
431	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
432	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
433	C₈	—	10	2	no	—
434	C₈	—	20	1	no	—
435	C₈	—	30	2	no	—
436	C₈	—	60	1	no	—
437	C₂×C₃	—	8	1	no	—
438	C₂×C₃	C₂×#3964	1	1	yes	characteristic
439	C₂×C₃	#65523	1	1	yes	characteristic
440	C₂×C₃	C₂×#3969	1	1	yes	characteristic
441	D₃	—	2	2	no	—
442	D₃	—	8	1	no	—
443	C₅	#68176	1	1	yes	characteristic, complemented, Sylow
444	C₂²	—	3	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	6	1	no	—
449	C₂²	—	6	1	no	—
450	C₂²	—	12	1	no	—
451	C₂²	—	12	1	no	—
452	C₂²	—	12	1	no	—
453	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	3	2	no	—
456	C₄	—	3	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	6	1	no	—
459	C₄	—	12	1	no	—
460	C₄	#91286	1	1	yes	characteristic
461	C₄	#91288	1	1	yes	characteristic
462	C₄	D₃×#686	1	1	yes	characteristic
463	C₄	D₃×#687	1	1	yes	characteristic
464	C₃	#10602595	1	1	yes	characteristic, complemented, Sylow
465	C₂	—	6	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	24	1	no	—
468	C₂	#11748490	1	1	yes	characteristic
469	C₂	D₃×#3964	1	1	yes	characteristic
470	C₂	D₃×#3969	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₄×C₅×D₄	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#5548	C₂
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	#1492
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #11747011	C₂	semidirect
3. C₄×D₃×#168	C₂	semidirect
4. D₄⋊(C₃⋊#168)	C₂	semidirect
5. C₃×D₄⋊#168	C₂	semidirect
6. #11745837	C₂	semidirect
7. #11745836	C₂	semidirect
35. D₄⋊#168	D₃	semidirect
377. C₃×C₅	#1492	semidirect
443. C₅	#68176	semidirect
464. C₃	#10602595	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
#11747011	2
C₄×D₃×#168	2
D₄⋊(C₃⋊#168)	2
C₃×D₄⋊#168	2
#11745837	2
#11745836	2
#10602595	3
#68176	5