Subgroups — #28404547

Order 14464.

1014 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299323	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299309	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299309	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299292	C₂	1	2	yes	maximal, complemented
5	#20299289	C₂	1	4	yes	maximal, complemented
6	#20299287	C₂	1	2	yes	maximal, complemented
7	#20299282	C₂	1	2	yes	maximal, complemented
8	#20299251	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299250	C₂	1	2	yes	maximal, complemented
10	#20299206	C₂	1	2	yes	maximal, complemented
11	#20299194	C₂	1	4	yes	maximal, complemented
12	#20299133	C₂	1	2	yes	maximal, complemented
13	#20299132	C₂	1	1	yes	maximal, characteristic, complemented
14	#125×D₁₁₃	C₂	1	2	yes	maximal, complemented
15	#20299080	C₂	1	2	yes	maximal, complemented
16	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
17	#533×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	—
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	#16813620	C₂²	1	2	yes	—
21	#16813617	C₂²	1	4	yes	—
22	#16813616	C₂²	1	2	yes	—
23	#16813616	C₂²	1	4	yes	—
24	#16813615	C₂²	1	4	yes	—
25	#16813614	C₂²	1	4	yes	—
26	#16813614	C₂²	1	1	yes	characteristic
27	#16813613	C₂²	1	2	yes	—
28	#16813613	C₂²	1	2	yes	—
29	#16813613	C₂²	1	2	yes	—
30	#16813612	C₂²	1	4	yes	—
31	#16813612	C₂²	1	4	yes	—
32	#16813612	C₂²	1	4	yes	—
33	#16813610	C₂²	1	1	yes	characteristic
34	#16813607	C₂²	1	4	yes	—
35	#16813607	C₂²	1	4	yes	—
36	#16813605	C₂²	1	2	yes	—
37	#16813604	C₂²	1	4	yes	—
38	#16813604	C₂²	1	4	yes	—
39	#16813602	C₂²	1	2	yes	—
40	#16813602	C₂²	1	2	yes	—
41	#16813601	C₂²	1	1	yes	characteristic
42	#16813598	C₂²	1	2	yes	—
43	#16813598	C₂²	1	4	yes	—
44	#16813598	C₂²	1	4	yes	—
45	#16813597	C₂²	1	2	yes	—
46	#16813596	C₂²	1	1	yes	characteristic
47	#16813595	C₂²	1	4	yes	—
48	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
49	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
50	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
51	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
52	#16813587	C₂²	1	2	yes	—
53	C₄×D₄₅₂	C₂²	1	4	yes	—
54	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
55	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
56	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
57	#16813584	C₂²	1	2	yes	—
58	#16813584	C₂²	1	2	yes	—
59	#16813584	C₂²	1	4	yes	—
60	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
63	#16813581	C₂²	1	1	yes	characteristic
64	#16813580	C₂²	1	4	yes	—
65	#16813579	C₂²	1	4	yes	—
66	#16813579	C₂²	1	2	yes	—
67	#16813579	C₂²	1	2	yes	—
68	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
70	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
73	C₄²×D₁₁₃	C₂²	1	2	yes	—
74	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
76	#125×C₁₁₃	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
80	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
81	#117×C₁₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
83	#14268648	—	2	8	no	—
84	#14268647	—	2	4	no	—
85	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
87	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
88	C₂×D₄₅₂	C₂³	1	4	yes	—
89	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
104	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
105	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
106	#14268626	C₂³	1	4	yes	—
107	#14268626	C₂³	1	2	yes	—
108	#14268626	C₂³	1	2	yes	—
109	#14268626	C₂³	1	4	yes	—
110	#14268626	C₂³	1	4	yes	—
111	#14268626	C₂³	1	4	yes	—
112	#14268626	C₂³	1	2	yes	—
113	#14268626	C₂³	1	2	yes	—
114	#14268626	C₂³	1	2	yes	—
115	#14268626	C₂³	1	4	yes	—
116	#14268626	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₁₃	C₂³	1	2	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	2	yes	—
123	#14268624	C₂³	1	2	yes	—
124	#14268624	C₂³	1	2	yes	—
125	#14268624	C₂³	1	4	yes	—
126	#14268624	C₂³	1	4	yes	—
127	#14268624	C₂³	1	2	yes	—
128	C₄×Dic₁₁₃	C₂³	1	2	yes	—
129	C₄×Dic₁₁₃	C₂³	1	2	yes	—
130	C₄×Dic₁₁₃	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	4	yes	—
132	C₄×Dic₁₁₃	C₂³	1	2	yes	—
133	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
134	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
139	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
142	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
145	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₁₃	C₂³	1	4	yes	—
149	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
150	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
152	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
153	Q₈×C₁₁₃	—	2	4	no	—
154	Q₈×C₁₁₃	—	4	2	no	—
155	C₂×C₄×C₁₁₃	—	2	2	no	—
156	C₂×C₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	4	1	no	—
158	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
163	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
164	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₁₁₃	—	2	4	no	—
167	C₂²⋊D₁₁₃	—	4	2	no	—
168	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
169	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
170	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
171	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	D₄₅₂	—	2	8	no	—
175	D₄₅₂	—	2	2	no	—
176	D₄₅₂	#41	1	4	yes	—
177	C₄×D₁₁₃	—	2	4	no	—
178	C₄×D₁₁₃	—	2	8	no	—
179	C₄×D₁₁₃	—	2	4	no	—
180	C₄×D₁₁₃	—	2	4	no	—
181	C₄×D₁₁₃	—	4	2	no	—
182	C₄×D₁₁₃	—	4	4	no	—
183	C₄×D₁₁₃	—	4	4	no	—
184	Dic₂₂₆	—	2	2	no	—
185	Dic₂₂₆	—	2	2	no	—
186	C₂²×C₁₁₃	—	2	1	no	—
187	C₂²×C₁₁₃	—	2	1	no	—
188	C₂²×C₁₁₃	—	2	1	no	—
189	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
190	C₂×D₁₁₃	—	2	2	no	—
191	C₂×D₁₁₃	—	2	2	no	—
192	C₂×D₁₁₃	—	2	2	no	—
193	C₂×D₁₁₃	—	2	2	no	—
194	C₂×D₁₁₃	—	2	2	no	—
195	C₂×D₁₁₃	C₂×#41	1	4	yes	—
196	C₄×C₁₁₃	—	2	1	no	—
197	C₄×C₁₁₃	—	2	4	no	—
198	C₄×C₁₁₃	—	2	1	no	—
199	C₄×C₁₁₃	—	2	1	no	—
200	C₄×C₁₁₃	—	2	4	no	—
201	C₄×C₁₁₃	—	2	1	no	—
202	C₄×C₁₁₃	C₂×#41	1	2	yes	—
203	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
204	Dic₁₁₃	—	2	2	no	—
205	Dic₁₁₃	—	2	2	no	—
206	Dic₁₁₃	—	2	2	no	—
207	Dic₁₁₃	—	2	2	no	—
208	Dic₁₁₃	—	2	2	no	—
209	Dic₁₁₃	—	2	2	no	—
210	C₂×C₁₁₃	—	4	1	no	—
211	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
212	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
213	C₂×C₁₁₃	#585	1	1	yes	characteristic
214	D₁₁₃	—	2	4	no	—
215	D₁₁₃	—	4	2	no	—
216	#3515	—	113	1	no	maximal, Sylow
217	C₁₁₃	#3515	1	1	yes	characteristic, complemented, Sylow
218	#557	—	113	1	no	—
219	#554	—	113	1	no	—
220	#554	—	113	1	no	—
221	#553	—	113	2	no	—
222	#552	—	113	2	no	—
223	#552	—	113	4	no	—
224	#552	—	113	2	no	—
225	#547	—	113	1	no	—
226	#547	—	113	2	no	—
227	#541	—	113	2	no	—
228	#539	—	113	4	no	—
229	#533	D₁₁₃	1	1	yes	characteristic, complemented
230	#529	—	113	2	no	—
231	#529	—	113	1	no	—
232	C₂×#125	—	113	2	no	—
233	#520	—	113	2	no	—
234	C₄×#41	—	113	1	no	—
235	C₂×#41	—	113	2	no	—
236	C₂×#41	—	113	1	no	—
237	C₄⋊Q₈	—	113	2	no	—
238	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
239	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
240	#126	—	113	4	no	—
241	#126	—	113	4	no	—
242	#126	—	113	2	no	—
243	#126	—	113	4	no	—
244	#125	—	113	4	no	—
245	#125	—	113	4	no	—
246	#125	—	113	2	no	—
247	#125	—	113	2	no	—
248	#125	—	113	4	no	—
249	#125	—	113	2	no	—
250	#125	—	113	1	no	—
251	#125	—	113	4	no	—
252	#125	C₂×D₁₁₃	1	2	yes	—
253	#124	—	113	1	no	—
254	#123	—	113	2	no	—
255	#123	—	113	4	no	—
256	#123	—	113	4	no	—
257	#123	—	113	4	no	—
258	#123	—	113	4	no	—
259	C₂²⋊Q₈	—	113	4	no	—
260	C₂²⋊Q₈	—	113	4	no	—
261	C₂²⋊Q₈	—	113	2	no	—
262	C₂²⋊Q₈	—	113	1	no	—
263	C₂²⋊Q₈	—	113	2	no	—
264	C₂²⋊Q₈	—	113	2	no	—
265	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
266	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
267	#121	—	113	1	no	—
268	#121	—	113	2	no	—
269	#121	—	113	4	no	—
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	2	no	—
272	C₄×Q₈	—	113	1	no	—
273	C₄×Q₈	—	113	1	no	—
274	C₄×Q₈	—	113	1	no	—
275	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
276	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
277	C₄×D₄	—	113	2	no	—
278	C₄×D₄	—	113	2	no	—
279	C₄×D₄	—	113	2	no	—
280	C₄×D₄	—	113	4	no	—
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	1	no	—
284	C₄×D₄	—	113	1	no	—
285	C₄×D₄	—	113	4	no	—
286	C₄×D₄	—	113	1	no	—
287	#117	—	113	1	no	—
288	#117	—	113	4	no	—
289	#117	—	113	2	no	—
290	#117	—	113	2	no	—
291	#117	—	113	4	no	—
292	#117	C₂×D₁₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	—	113	4	no	—
294	C₂×C₄⋊C₄	—	113	2	no	—
295	C₂×C₄⋊C₄	—	113	2	no	—
296	C₂×C₄⋊C₄	—	113	4	no	—
297	C₂×C₄⋊C₄	—	113	2	no	—
298	C₂×C₄²	—	113	2	no	—
299	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
300	#41	—	226	4	no	—
301	#41	—	226	8	no	—
302	C₂×Q₈	—	113	1	no	—
303	C₂×Q₈	—	113	1	no	—
304	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
305	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
306	C₂×D₄	—	113	2	no	—
307	C₂×D₄	—	113	2	no	—
308	C₂×D₄	—	113	1	no	—
309	C₂×D₄	—	113	1	no	—
310	C₂×D₄	—	113	4	no	—
311	C₂²×C₄	—	113	2	no	—
312	C₂²×C₄	—	113	4	no	—
313	C₂²×C₄	—	113	4	no	—
314	C₂²×C₄	—	113	2	no	—
315	C₂²×C₄	—	113	2	no	—
316	C₂²×C₄	—	113	4	no	—
317	C₂²×C₄	—	113	2	no	—
318	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
321	C₄⋊C₄	—	113	1	no	—
322	C₄⋊C₄	—	113	4	no	—
323	C₄⋊C₄	—	113	2	no	—
324	C₄⋊C₄	—	113	1	no	—
325	C₄⋊C₄	—	113	2	no	—
326	C₄⋊C₄	—	113	1	no	—
327	C₄⋊C₄	—	113	4	no	—
328	C₄⋊C₄	—	113	4	no	—
329	C₄⋊C₄	—	113	4	no	—
330	C₄⋊C₄	—	113	4	no	—
331	C₄⋊C₄	—	113	4	no	—
332	C₄⋊C₄	—	113	2	no	—
333	C₄⋊C₄	—	113	2	no	—
334	C₄⋊C₄	—	113	1	no	—
335	C₄⋊C₄	—	113	2	no	—
336	C₄⋊C₄	—	113	4	no	—
337	C₄⋊C₄	—	113	2	no	—
338	C₄⋊C₄	—	113	4	no	—
339	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
340	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
341	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
342	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
343	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
344	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
345	C₂²⋊C₄	—	113	2	no	—
346	C₂²⋊C₄	—	113	2	no	—
347	C₂²⋊C₄	—	113	2	no	—
348	C₂²⋊C₄	—	113	2	no	—
349	C₂²⋊C₄	—	113	2	no	—
350	C₂²⋊C₄	—	113	4	no	—
351	C₂²⋊C₄	—	113	2	no	—
352	C₂²⋊C₄	—	113	2	no	—
353	C₂²⋊C₄	—	113	4	no	—
354	C₂²⋊C₄	—	113	4	no	—
355	C₂²⋊C₄	—	113	2	no	—
356	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
357	C₄²	—	113	2	no	—
358	C₄²	—	113	2	no	—
359	C₄²	—	113	2	no	—
360	C₄²	—	113	4	no	—
361	C₄²	—	113	2	no	—
362	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
363	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
364	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
365	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
366	C₄²	C₂²×D₁₁₃	1	4	yes	—
367	C₂³	—	113	2	no	—
368	C₂³	—	113	2	no	—
369	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	226	2	no	—
373	Q₈	—	226	2	no	—
374	D₄	—	113	4	no	—
375	D₄	—	452	2	no	—
376	D₄	—	226	8	no	—
377	D₄	—	226	4	no	—
378	D₄	—	226	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	113	2	no	—
383	C₂×C₄	—	113	2	no	—
384	C₂×C₄	—	113	2	no	—
385	C₂×C₄	—	113	2	no	—
386	C₂×C₄	—	113	2	no	—
387	C₂×C₄	—	113	2	no	—
388	C₂×C₄	—	452	2	no	—
389	C₂×C₄	—	452	4	no	—
390	C₂×C₄	—	452	4	no	—
391	C₂×C₄	—	226	4	no	—
392	C₂×C₄	—	226	8	no	—
393	C₂×C₄	—	226	4	no	—
394	C₂×C₄	—	226	4	no	—
395	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
398	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
401	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	113	4	no	—
407	C₂²	—	226	2	no	—
408	C₂²	—	226	2	no	—
409	C₂²	—	226	2	no	—
410	C₂²	—	226	2	no	—
411	C₂²	—	226	2	no	—
412	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	4	no	—
419	C₄	—	226	2	no	—
420	C₄	—	226	2	no	—
421	C₄	—	226	2	no	—
422	C₄	—	226	2	no	—
423	C₄	—	226	2	no	—
424	C₄	—	226	2	no	—
425	C₄	#41×D₁₁₃	1	2	yes	—
426	C₄	#16813670	1	2	yes	—
427	C₂	—	4	1	no	—
428	C₂	—	452	2	no	—
429	C₂	—	226	4	no	—
430	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
431	C₂	C₂×#16813670	1	1	yes	characteristic
432	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#533×C₁₁₃	C₂
hypercenter	#533	D₁₁₃
hypocenter	C₁₁₃	#3515
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #20299323	C₂	semidirect
2. #20299309	C₂	semidirect
3. #20299309	C₂	semidirect
4. #20299292	C₂	semidirect
5. #20299289	C₂	semidirect
6. #20299287	C₂	semidirect
7. #20299282	C₂	semidirect
8. #20299251	C₂	semidirect
9. #20299250	C₂	semidirect
10. #20299206	C₂	semidirect
11. #20299194	C₂	semidirect
12. #20299133	C₂	semidirect
13. #20299132	C₂	semidirect
14. #125×D₁₁₃	C₂	semidirect
15. #20299080	C₂	semidirect
16. C₄×#14268647	C₂	semidirect
17. #533×C₁₁₃	C₂	semidirect
217. C₁₁₃	#3515	semidirect
229. #533	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299323	2
#20299309	2
#20299292	2
#20299289	2
#20299287	2
#20299282	2
#20299251	2
#20299250	2
#20299206	2
#20299194	2
#20299133	2
#20299132	2
#125×D₁₁₃	2
#20299080	2
C₄×#14268647	2
#533×C₁₁₃	2
#3515	113