Subgroups — #28404578

Order 14464.

1122 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299326	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299299	C₂	1	4	yes	maximal, complemented
3	#20299294	C₂	1	2	yes	maximal, complemented
4	#20299270	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299269	C₂	1	2	yes	maximal, complemented
6	#20299269	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299266	C₂	1	2	yes	maximal, complemented
8	#20299252	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299250	C₂	1	2	yes	maximal, complemented
10	#20299203	C₂	1	2	yes	maximal, complemented
11	#20299200	C₂	1	4	yes	maximal, complemented
12	#20299148	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299147	C₂	1	2	yes	maximal, complemented
14	#20299133	C₂	1	2	yes	maximal, complemented
15	#20299078	C₂	1	2	yes	maximal, complemented
16	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	—
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	C₂×#14268647	C₂²	1	2	yes	—
21	C₂×#14268647	C₂²	1	2	yes	—
22	C₂×#14268646	C₂²	1	2	yes	—
23	#16813622	C₂²	1	1	yes	characteristic
24	#16813620	C₂²	1	2	yes	—
25	#16813619	C₂²	1	1	yes	characteristic
26	#16813619	C₂²	1	2	yes	—
27	#16813618	C₂²	1	2	yes	—
28	#16813618	C₂²	1	4	yes	—
29	#16813617	C₂²	1	4	yes	—
30	#16813614	C₂²	1	2	yes	—
31	#16813612	C₂²	1	4	yes	—
32	#16813610	C₂²	1	2	yes	—
33	#16813607	C₂²	1	4	yes	—
34	#16813607	C₂²	1	4	yes	—
35	#16813606	C₂²	1	4	yes	—
36	#16813604	C₂²	1	4	yes	—
37	#16813602	C₂²	1	2	yes	—
38	#16813597	C₂²	1	2	yes	—
39	#16813597	C₂²	1	4	yes	—
40	#16813596	C₂²	1	2	yes	—
41	#16813596	C₂²	1	2	yes	—
42	#16813596	C₂²	1	2	yes	—
43	#16813596	C₂²	1	2	yes	—
44	#16813595	C₂²	1	4	yes	—
45	#16813595	C₂²	1	4	yes	—
46	#16813595	C₂²	1	4	yes	—
47	#16813595	C₂²	1	4	yes	—
48	#16813595	C₂²	1	4	yes	—
49	#16813594	C₂²	1	4	yes	—
50	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
51	C₄×Dic₂₂₆	C₂²	1	2	yes	—
52	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
53	#16813587	C₂²	1	2	yes	—
54	C₄×D₄₅₂	C₂²	1	2	yes	—
55	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
56	C₄×D₄₅₂	C₂²	1	2	yes	—
57	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
58	C₄×D₄₅₂	C₂²	1	2	yes	—
59	#16813584	C₂²	1	4	yes	—
60	#16813584	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
63	#16813582	C₂²	1	4	yes	—
64	#16813582	C₂²	1	4	yes	—
65	#16813582	C₂²	1	4	yes	—
66	#16813581	C₂²	1	1	yes	characteristic
67	#16813580	C₂²	1	4	yes	—
68	#16813579	C₂²	1	2	yes	—
69	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
70	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
71	C₄²×D₁₁₃	C₂²	1	2	yes	—
72	#126×C₁₁₃	C₂²	1	2	yes	—
73	#125×C₁₁₃	C₂²	1	1	yes	characteristic
74	#124×C₁₁₃	C₂²	1	1	yes	characteristic
75	#123×C₁₁₃	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
77	#121×C₁₁₃	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
80	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
81	#117×C₁₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
83	#14268648	—	4	4	no	—
84	#14268647	—	2	4	no	—
85	#14268647	—	2	8	no	—
86	#14268647	—	4	4	no	—
87	#14268646	—	4	4	no	—
88	C₂×Dic₂₂₆	C₂³	1	2	yes	—
89	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
90	C₂×D₄₅₂	C₂³	1	2	yes	—
91	C₂×D₄₅₂	C₂³	1	2	yes	—
92	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
93	C₂×D₄₅₂	C₂³	1	4	yes	—
94	C₂×D₄₅₂	C₂³	1	2	yes	—
95	C₂×D₄₅₂	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
101	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
102	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
105	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
106	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
107	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
108	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
109	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
111	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
113	#14268626	C₂³	1	2	yes	—
114	#14268626	C₂³	1	4	yes	—
115	#14268626	C₂³	1	2	yes	—
116	#14268626	C₂³	1	4	yes	—
117	#14268626	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
119	#14268624	C₂³	1	2	yes	—
120	#14268624	C₂³	1	2	yes	—
121	#14268624	C₂³	1	4	yes	—
122	#14268624	C₂³	1	4	yes	—
123	#14268624	C₂³	1	4	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	4	yes	—
126	C₄×Dic₁₁₃	C₂³	1	2	yes	—
127	C₄×Dic₁₁₃	C₂³	1	2	yes	—
128	C₄×Dic₁₁₃	C₂³	1	2	yes	—
129	C₄×Dic₁₁₃	C₂³	1	4	yes	—
130	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
138	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₁₃	C₂³	1	2	yes	—
152	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
153	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
156	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
157	Q₈×C₁₁₃	—	2	2	no	—
158	D₄×C₁₁₃	—	2	2	no	—
159	D₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	—	2	4	no	—
161	C₂×C₄×C₁₁₃	—	2	2	no	—
162	C₂×C₄×C₁₁₃	—	2	2	no	—
163	C₂×C₄×C₁₁₃	—	4	1	no	—
164	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₁₁₃	—	2	8	no	—
174	C₂²⋊D₁₁₃	—	2	4	no	—
175	C₂²⋊D₁₁₃	—	4	4	no	—
176	C₂²⋊D₁₁₃	—	4	4	no	—
177	C₂²⋊D₁₁₃	—	4	4	no	—
178	C₂×Dic₁₁₃	—	4	4	no	—
179	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	D₄₅₂	—	2	4	no	—
184	D₄₅₂	—	2	2	no	—
185	D₄₅₂	—	2	4	no	—
186	D₄₅₂	—	4	2	no	—
187	D₄₅₂	—	4	4	no	—
188	D₄₅₂	—	4	4	no	—
189	C₄×D₁₁₃	—	2	4	no	—
190	C₄×D₁₁₃	—	2	4	no	—
191	C₄×D₁₁₃	—	2	8	no	—
192	C₄×D₁₁₃	—	4	2	no	—
193	C₄×D₁₁₃	—	4	4	no	—
194	C₄×D₁₁₃	—	4	4	no	—
195	Dic₂₂₆	—	2	4	no	—
196	Dic₂₂₆	#41	1	4	yes	complemented
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	—	2	1	no	—
199	C₂²×C₁₁₃	—	2	2	no	—
200	C₂²×C₁₁₃	—	2	1	no	—
201	C₂²×C₁₁₃	—	2	2	no	—
202	C₂²×C₁₁₃	—	2	1	no	—
203	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
204	C₂×D₁₁₃	—	2	2	no	—
205	C₂×D₁₁₃	—	2	4	no	—
206	C₂×D₁₁₃	—	2	2	no	—
207	C₂×D₁₁₃	—	2	4	no	—
208	C₂×D₁₁₃	—	2	2	no	—
209	C₂×D₁₁₃	—	2	4	no	—
210	C₄×C₁₁₃	—	2	1	no	—
211	C₄×C₁₁₃	—	2	2	no	—
212	C₄×C₁₁₃	—	2	1	no	—
213	C₄×C₁₁₃	—	2	2	no	—
214	C₄×C₁₁₃	—	2	1	no	—
215	C₄×C₁₁₃	—	2	1	no	—
216	C₄×C₁₁₃	—	2	2	no	—
217	C₄×C₁₁₃	C₂×#41	1	2	yes	—
218	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
219	Dic₁₁₃	—	2	4	no	—
220	Dic₁₁₃	—	2	2	no	—
221	Dic₁₁₃	—	2	2	no	—
222	Dic₁₁₃	C₂×#41	1	4	yes	—
223	C₂×C₁₁₃	—	4	2	no	—
224	C₂×C₁₁₃	—	4	1	no	—
225	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₁₁₃	#585	1	1	yes	characteristic
228	D₁₁₃	—	4	2	no	—
229	D₁₁₃	—	4	4	no	—
230	#3517	—	113	1	no	maximal, Sylow
231	C₁₁₃	#3517	1	1	yes	characteristic, complemented, Sylow
232	#557	—	113	1	no	—
233	#553	—	113	4	no	—
234	#553	—	113	2	no	—
235	#550	—	113	2	no	—
236	#550	—	113	1	no	—
237	#550	—	113	1	no	—
238	#550	—	113	2	no	—
239	#547	—	113	2	no	—
240	#547	—	113	1	no	—
241	#540	—	113	4	no	—
242	#540	—	113	2	no	—
243	#532	—	113	2	no	—
244	#532	—	113	1	no	—
245	#529	—	113	2	no	—
246	#529	D₁₁₃	1	1	yes	characteristic, complemented
247	#520	—	113	2	no	—
248	C₄×#41	—	113	1	no	—
249	C₂×#41	—	113	2	no	—
250	C₂×#41	—	113	2	no	—
251	C₂×#41	—	113	2	no	—
252	C₂×#41	—	113	1	no	—
253	C₂×#41	—	113	2	no	—
254	C₄⋊Q₈	—	113	2	no	—
255	C₄⋊Q₈	—	113	1	no	—
256	#127	—	113	2	no	—
257	#127	—	113	4	no	—
258	#127	—	113	1	no	—
259	#127	—	113	2	no	—
260	#126	—	113	4	no	—
261	#126	C₂×D₁₁₃	1	2	yes	—
262	#125	—	113	4	no	—
263	#125	—	113	2	no	—
264	#125	C₂×D₁₁₃	1	1	yes	characteristic
265	#124	—	113	2	no	—
266	#124	C₂×D₁₁₃	1	1	yes	characteristic
267	#123	—	113	4	no	—
268	#123	—	113	4	no	—
269	#123	—	113	4	no	—
270	#123	—	113	4	no	—
271	#123	C₂×D₁₁₃	1	2	yes	—
272	C₂²⋊Q₈	—	113	2	no	—
273	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
274	#121	—	113	4	no	—
275	#121	—	113	2	no	—
276	#121	—	113	2	no	—
277	#121	—	113	2	no	—
278	#121	—	113	2	no	—
279	#121	—	113	2	no	—
280	#121	—	113	4	no	—
281	#121	—	113	4	no	—
282	#121	—	113	4	no	—
283	#121	—	113	4	no	—
284	#121	—	113	4	no	—
285	#121	—	113	4	no	—
286	#121	C₂×D₁₁₃	1	1	yes	characteristic
287	C₄×Q₈	—	113	2	no	—
288	C₄×Q₈	—	113	1	no	—
289	C₄×Q₈	—	113	1	no	—
290	C₄×Q₈	—	113	2	no	—
291	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
292	C₄×D₄	—	113	2	no	—
293	C₄×D₄	—	113	2	no	—
294	C₄×D₄	—	113	2	no	—
295	C₄×D₄	—	113	4	no	—
296	C₄×D₄	—	113	4	no	—
297	C₄×D₄	—	113	4	no	—
298	C₄×D₄	—	113	4	no	—
299	C₄×D₄	—	113	1	no	—
300	C₄×D₄	—	113	1	no	—
301	C₄×D₄	—	113	2	no	—
302	C₄×D₄	—	113	2	no	—
303	C₄×D₄	—	113	2	no	—
304	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
305	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
306	#117	—	113	1	no	—
307	#117	—	113	4	no	—
308	#117	—	113	2	no	—
309	#117	C₂×D₁₁₃	1	2	yes	—
310	C₂×C₄⋊C₄	—	113	2	no	—
311	C₂×C₄⋊C₄	—	113	4	no	—
312	C₂×C₄²	—	113	2	no	—
313	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
314	#41	—	452	4	no	—
315	#41	—	452	4	no	—
316	#41	—	452	4	no	—
317	#41	—	226	4	no	—
318	#41	—	226	8	no	—
319	C₂×Q₈	—	113	1	no	—
320	C₂×Q₈	—	113	2	no	—
321	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
322	C₂×D₄	—	113	4	no	—
323	C₂×D₄	—	113	4	no	—
324	C₂×D₄	—	113	4	no	—
325	C₂×D₄	—	113	2	no	—
326	C₂×D₄	—	113	4	no	—
327	C₂×D₄	—	113	2	no	—
328	C₂×D₄	—	113	4	no	—
329	C₂×D₄	—	113	4	no	—
330	C₂×D₄	—	113	1	no	—
331	C₂×D₄	—	113	2	no	—
332	C₂×D₄	—	113	2	no	—
333	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
334	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
335	C₂²×C₄	—	113	4	no	—
336	C₂²×C₄	—	113	2	no	—
337	C₂²×C₄	—	113	4	no	—
338	C₂²×C₄	—	113	4	no	—
339	C₂²×C₄	—	113	2	no	—
340	C₂²×C₄	—	113	2	no	—
341	C₂²×C₄	—	113	4	no	—
342	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
345	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
346	C₄⋊C₄	—	113	2	no	—
347	C₄⋊C₄	—	113	1	no	—
348	C₄⋊C₄	—	113	4	no	—
349	C₄⋊C₄	—	113	4	no	—
350	C₄⋊C₄	—	113	2	no	—
351	C₄⋊C₄	—	113	2	no	—
352	C₄⋊C₄	—	113	1	no	—
353	C₄⋊C₄	—	113	4	no	—
354	C₄⋊C₄	—	113	2	no	—
355	C₄⋊C₄	—	113	4	no	—
356	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
360	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
361	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
362	C₂²⋊C₄	—	113	2	no	—
363	C₂²⋊C₄	—	113	4	no	—
364	C₂²⋊C₄	—	113	2	no	—
365	C₂²⋊C₄	—	113	2	no	—
366	C₂²⋊C₄	—	113	4	no	—
367	C₂²⋊C₄	—	113	4	no	—
368	C₂²⋊C₄	—	113	4	no	—
369	C₂²⋊C₄	—	113	4	no	—
370	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
372	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
373	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
375	C₄²	—	113	2	no	—
376	C₄²	—	113	2	no	—
377	C₄²	—	113	2	no	—
378	C₄²	—	113	4	no	—
379	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
380	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
381	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
382	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
383	C₄²	C₂²×D₁₁₃	1	2	yes	—
384	C₂³	—	113	4	no	—
385	C₂³	—	113	2	no	—
386	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
387	C₂³	C₂³×D₁₁₃	1	2	yes	—
388	Q₈	—	2	2	no	—
389	Q₈	—	113	4	no	—
390	Q₈	—	226	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	452	4	no	—
394	D₄	—	452	2	no	—
395	D₄	—	452	4	no	—
396	D₄	—	452	4	no	—
397	D₄	—	452	4	no	—
398	D₄	—	452	4	no	—
399	D₄	—	226	4	no	—
400	D₄	—	226	8	no	—
401	D₄	—	226	2	no	—
402	D₄	—	226	4	no	—
403	D₄	—	226	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	113	2	no	—
409	C₂×C₄	—	113	2	no	—
410	C₂×C₄	—	113	2	no	—
411	C₂×C₄	—	113	4	no	—
412	C₂×C₄	—	452	4	no	—
413	C₂×C₄	—	452	4	no	—
414	C₂×C₄	—	452	2	no	—
415	C₂×C₄	—	452	4	no	—
416	C₂×C₄	—	226	4	no	—
417	C₂×C₄	—	226	8	no	—
418	C₂×C₄	—	226	4	no	—
419	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
422	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
425	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
426	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	226	4	no	—
435	C₂²	—	226	2	no	—
436	C₂²	—	226	4	no	—
437	C₂²	—	226	2	no	—
438	C₂²	—	226	2	no	—
439	C₂²	—	226	4	no	—
440	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	2	no	—
448	C₄	—	113	4	no	—
449	C₄	—	226	2	no	—
450	C₄	—	226	4	no	—
451	C₄	—	226	2	no	—
452	C₄	#41×D₁₁₃	1	2	yes	—
453	C₄	#16813668	1	2	yes	—
454	C₂	—	4	1	no	—
455	C₂	—	4	2	no	—
456	C₂	—	452	4	no	—
457	C₂	—	452	2	no	—
458	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
459	C₂	C₂×#16813668	1	1	yes	characteristic
460	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#529×C₁₁₃	C₂
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3517
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #20299326	C₂	semidirect
2. #20299299	C₂	semidirect
3. #20299294	C₂	semidirect
4. #20299270	C₂	semidirect
5. #20299269	C₂	semidirect
6. #20299269	C₂	semidirect
7. #20299266	C₂	semidirect
8. #20299252	C₂	semidirect
9. #20299250	C₂	semidirect
10. #20299203	C₂	semidirect
11. #20299200	C₂	semidirect
12. #20299148	C₂	semidirect
13. #20299147	C₂	semidirect
14. #20299133	C₂	semidirect
15. #20299078	C₂	semidirect
16. C₄×#14268647	C₂	semidirect
17. #529×C₁₁₃	C₂	semidirect
196. Dic₂₂₆	#41	semidirect
231. C₁₁₃	#3517	semidirect
246. #529	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299326	2
#20299299	2
#20299294	2
#20299270	2
#20299269	2
#20299266	2
#20299252	2
#20299250	2
#20299203	2
#20299200	2
#20299148	2
#20299147	2
#20299133	2
#20299078	2
C₄×#14268647	2
#529×C₁₁₃	2
#3517	113