Subgroups — #28404418

Order 14464.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299334	C₂	1	2	yes	maximal, complemented
2	#20299331	C₂	1	2	yes	maximal, complemented
3	#20299321	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299318	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299312	C₂	1	2	yes	maximal, complemented
6	#20299291	C₂	1	4	yes	maximal, complemented
7	#20299268	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299247	C₂	1	2	yes	maximal, complemented
9	#20299180	C₂	1	4	yes	maximal, complemented
10	#20299161	C₂	1	2	yes	maximal, complemented
11	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299146	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299108	C₂	1	2	yes	maximal, complemented
14	#20299105	C₂	1	2	yes	maximal, complemented
15	#20299077	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268646	C₂²	1	2	yes	—
19	C₂×#14268646	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
22	#16813622	C₂²	1	1	yes	characteristic, complemented
23	#16813621	C₂²	1	1	yes	characteristic, complemented
24	#16813620	C₂²	1	1	yes	characteristic, complemented
25	#16813618	C₂²	1	2	yes	—
26	#16813617	C₂²	1	4	yes	complemented
27	#16813615	C₂²	1	4	yes	complemented
28	#16813612	C₂²	1	2	yes	complemented
29	#16813610	C₂²	1	2	yes	—
30	#16813609	C₂²	1	2	yes	—
31	#16813609	C₂²	1	4	yes	complemented
32	#16813609	C₂²	1	2	yes	complemented
33	#16813608	C₂²	1	4	yes	complemented
34	#16813605	C₂²	1	4	yes	complemented
35	#16813604	C₂²	1	4	yes	complemented
36	#16813603	C₂²	1	4	yes	complemented
37	#16813603	C₂²	1	4	yes	complemented
38	#16813602	C₂²	1	1	yes	characteristic
39	#16813601	C₂²	1	2	yes	complemented
40	#16813600	C₂²	1	2	yes	—
41	#16813598	C₂²	1	1	yes	characteristic
42	#16813598	C₂²	1	2	yes	complemented
43	#16813594	C₂²	1	4	yes	—
44	#16813594	C₂²	1	4	yes	—
45	#16813594	C₂²	1	4	yes	complemented
46	#16813593	C₂²	1	2	yes	—
47	#16813593	C₂²	1	2	yes	—
48	#16813593	C₂²	1	2	yes	complemented
49	#16813590	C₂²	1	4	yes	—
50	#16813590	C₂²	1	4	yes	—
51	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
52	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
53	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
54	#16813587	C₂²	1	2	yes	complemented
55	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
56	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
57	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
58	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
59	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
60	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
61	#16813584	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
64	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
65	#16813582	C₂²	1	2	yes	—
66	#16813582	C₂²	1	4	yes	—
67	#16813581	C₂²	1	2	yes	complemented
68	#16813580	C₂²	1	2	yes	complemented
69	#16813579	C₂²	1	2	yes	—
70	#16813578	C₂²	1	4	yes	complemented
71	C₂×#14268626	C₂²	1	4	yes	complemented
72	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
73	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₁₃	C₂²	1	2	yes	complemented
76	#127×C₁₁₃	C₂²	1	2	yes	—
77	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
78	#121×C₁₁₃	C₂²	1	4	yes	complemented
79	#121×C₁₁₃	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
83	C₂³×D₁₁₃	C₂³	1	2	yes	—
84	#14268646	—	2	8	no	—
85	#14268646	—	4	4	no	—
86	C₂×Dic₂₂₆	C₂³	1	2	yes	—
87	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
88	C₂×Dic₂₂₆	C₂³	1	2	yes	—
89	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
94	D₄×D₁₁₃	—	2	4	no	—
95	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
96	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
97	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₁₃	—	4	4	no	—
99	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
101	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
107	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
109	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
110	#14268626	C₂³	1	2	yes	—
111	#14268626	C₂³	1	2	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	4	yes	—
114	#14268626	C₂³	1	2	yes	—
115	#14268626	C₂³	1	2	yes	—
116	#14268626	C₂³	1	2	yes	—
117	#14268626	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
124	#14268624	C₂³	1	2	yes	—
125	#14268624	C₂³	1	2	yes	—
126	#14268624	C₂³	1	2	yes	—
127	#14268624	C₂³	1	2	yes	—
128	#14268624	C₂³	1	4	yes	—
129	#14268624	C₂³	1	4	yes	—
130	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
133	C₄×Dic₁₁₃	C₂³	1	4	yes	—
134	C₄×Dic₁₁₃	C₂³	1	4	yes	—
135	C₄×Dic₁₁₃	C₂³	1	2	yes	—
136	#41×C₁₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
140	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
141	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
142	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
143	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
144	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
146	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
151	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
152	C₄²×C₁₁₃	C₂³	1	2	yes	—
153	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
155	C₂²×D₁₁₃	—	2	4	no	—
156	C₂²×D₁₁₃	—	4	2	no	—
157	C₂²×D₁₁₃	—	4	2	no	—
158	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
159	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₁₃	—	2	2	no	—
161	D₄×C₁₁₃	—	2	2	no	—
162	D₄×C₁₁₃	—	2	4	no	—
163	D₄×C₁₁₃	—	2	4	no	—
164	D₄×C₁₁₃	—	4	4	no	—
165	D₄×C₁₁₃	—	4	2	no	—
166	D₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	2	4	no	—
168	C₂×C₄×C₁₁₃	—	4	4	no	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²⋊D₁₁₃	—	2	8	no	—
176	C₂²⋊D₁₁₃	—	2	4	no	—
177	C₂²⋊D₁₁₃	—	4	4	no	—
178	C₂²⋊D₁₁₃	—	4	4	no	—
179	C₂×Dic₁₁₃	—	2	8	no	—
180	C₂×Dic₁₁₃	—	4	2	no	—
181	C₂×Dic₁₁₃	—	4	4	no	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
185	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
186	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
188	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
189	D₄₅₂	—	2	2	no	—
190	C₄×D₁₁₃	—	2	2	no	—
191	C₄×D₁₁₃	—	2	4	no	—
192	C₄×D₁₁₃	—	4	2	no	—
193	C₄×D₁₁₃	—	4	2	no	—
194	C₄×D₁₁₃	—	4	1	no	—
195	C₄×D₁₁₃	#41	1	4	yes	complemented
196	Dic₂₂₆	—	2	4	no	—
197	Dic₂₂₆	—	2	2	no	—
198	Dic₂₂₆	—	4	2	no	—
199	C₂²×C₁₁₃	—	2	4	no	—
200	C₂²×C₁₁₃	—	2	2	no	—
201	C₂²×C₁₁₃	—	2	4	no	—
202	C₂²×C₁₁₃	—	2	2	no	—
203	C₂²×C₁₁₃	—	2	4	no	—
204	C₂²×C₁₁₃	—	2	2	no	—
205	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₁₁₃	—	2	1	no	—
207	C₂×D₁₁₃	—	2	1	no	—
208	C₂×D₁₁₃	—	2	2	no	—
209	C₂×D₁₁₃	—	2	2	no	—
210	C₂×D₁₁₃	—	2	2	no	—
211	C₂×D₁₁₃	—	4	8	no	—
212	C₂×D₁₁₃	C₂×#41	1	2	yes	—
213	C₄×C₁₁₃	—	2	2	no	—
214	C₄×C₁₁₃	—	2	2	no	—
215	C₄×C₁₁₃	—	2	2	no	—
216	C₄×C₁₁₃	—	2	1	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	1	no	—
222	Dic₁₁₃	—	2	2	no	—
223	Dic₁₁₃	—	2	1	no	—
224	Dic₁₁₃	—	2	2	no	—
225	Dic₁₁₃	C₂×#41	1	2	yes	—
226	C₂×C₁₁₃	—	4	2	no	—
227	C₂×C₁₁₃	—	4	4	no	—
228	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
229	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₁₁₃	#585	1	1	yes	characteristic
231	D₁₁₃	—	2	2	no	—
232	D₁₁₃	—	4	2	no	—
233	#3506	—	113	1	no	maximal, Sylow
234	C₁₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
235	#559	—	113	2	no	—
236	#559	—	113	2	no	—
237	#556	—	113	1	no	—
238	#556	—	113	1	no	—
239	#555	—	113	2	no	—
240	#553	—	113	4	no	—
241	#550	—	113	1	no	—
242	#550	D₁₁₃	1	1	yes	characteristic, complemented
243	#547	—	113	2	no	—
244	#538	—	113	4	no	—
245	#535	—	113	2	no	—
246	#533	—	113	1	no	—
247	#532	—	113	1	no	—
248	#525	—	113	2	no	—
249	#525	—	113	2	no	—
250	#520	—	113	2	no	—
251	C₂×C₄×D₄	—	113	1	no	—
252	C₂×#41	—	113	2	no	—
253	C₂×#41	—	113	2	no	—
254	C₂×#41	C₂×D₁₁₃	1	2	yes	complemented
255	C₂²×D₄	—	113	1	no	—
256	C₂³×C₄	—	113	2	no	—
257	C₄⋊Q₈	—	113	1	no	—
258	C₄⋊Q₈	—	113	1	no	—
259	C₄⋊Q₈	—	113	1	no	—
260	#127	—	113	2	no	—
261	#127	C₂×D₁₁₃	1	2	yes	—
262	#127	C₂×D₁₁₃	1	1	yes	characteristic, complemented
263	#126	—	113	4	no	—
264	#126	—	113	4	no	—
265	#125	—	113	2	no	—
266	#124	—	113	2	no	—
267	#124	—	113	2	no	—
268	#124	—	113	4	no	—
269	#124	—	113	4	no	—
270	#124	—	113	2	no	—
271	#123	—	113	4	no	—
272	#123	—	113	4	no	—
273	#123	—	113	4	no	—
274	#123	—	113	4	no	—
275	C₂²⋊Q₈	—	113	1	no	—
276	C₂²⋊Q₈	—	113	2	no	—
277	C₂²⋊Q₈	—	113	2	no	—
278	C₂²⋊Q₈	—	113	1	no	—
279	C₂²⋊Q₈	—	113	2	no	—
280	#121	—	113	2	no	—
281	#121	—	113	2	no	—
282	#121	—	113	2	no	—
283	#121	—	113	4	no	—
284	#121	—	113	4	no	—
285	#121	—	113	4	no	—
286	#121	C₂×D₁₁₃	1	2	yes	complemented
287	#121	C₂×D₁₁₃	1	4	yes	complemented
288	#120	—	113	4	no	—
289	#120	—	113	4	no	—
290	C₄×Q₈	—	113	2	no	—
291	C₄×Q₈	—	113	2	no	—
292	C₄×Q₈	—	113	1	no	—
293	C₄×Q₈	—	113	2	no	—
294	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
295	C₄×D₄	—	113	1	no	—
296	C₄×D₄	—	113	2	no	—
297	C₄×D₄	—	113	4	no	—
298	C₄×D₄	—	113	2	no	—
299	C₄×D₄	—	113	2	no	—
300	C₄×D₄	—	113	2	no	—
301	C₄×D₄	—	113	4	no	—
302	C₄×D₄	—	113	4	no	—
303	C₄×D₄	—	113	1	no	—
304	C₄×D₄	—	113	2	no	—
305	C₄×D₄	—	113	4	no	—
306	C₄×D₄	—	113	1	no	—
307	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
308	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
309	#117	—	113	2	no	—
310	#117	—	113	2	no	—
311	#117	—	113	4	no	—
312	#117	—	113	2	no	—
313	C₂×C₄⋊C₄	—	113	4	no	—
314	C₂×C₄⋊C₄	—	113	1	no	—
315	C₂×C₂²⋊C₄	—	113	2	no	—
316	C₂×C₄²	—	113	1	no	—
317	C₂⁴	—	113	2	no	—
318	#41	—	4	4	no	—
319	#41	—	452	4	no	—
320	#41	—	226	8	no	—
321	C₂×Q₈	—	113	2	no	—
322	C₂×Q₈	—	113	2	no	—
323	C₂×Q₈	—	113	1	no	—
324	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
325	C₂×D₄	—	113	4	no	—
326	C₂×D₄	—	113	4	no	—
327	C₂×D₄	—	113	4	no	—
328	C₂×D₄	—	113	2	no	—
329	C₂×D₄	—	113	1	no	—
330	C₂×D₄	—	226	4	no	—
331	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
333	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
334	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
335	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
336	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
337	C₂²×C₄	—	113	1	no	—
338	C₂²×C₄	—	113	4	no	—
339	C₂²×C₄	—	113	2	no	—
340	C₂²×C₄	—	113	4	no	—
341	C₂²×C₄	—	113	1	no	—
342	C₂²×C₄	—	113	2	no	—
343	C₂²×C₄	—	113	2	no	—
344	C₂²×C₄	—	113	1	no	—
345	C₂²×C₄	—	113	2	no	—
346	C₂²×C₄	—	452	4	no	—
347	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
348	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
349	C₄⋊C₄	—	113	2	no	—
350	C₄⋊C₄	—	113	2	no	—
351	C₄⋊C₄	—	113	1	no	—
352	C₄⋊C₄	—	113	4	no	—
353	C₄⋊C₄	—	113	4	no	—
354	C₄⋊C₄	—	113	2	no	—
355	C₄⋊C₄	—	113	2	no	—
356	C₄⋊C₄	—	113	1	no	—
357	C₄⋊C₄	—	113	2	no	—
358	C₄⋊C₄	—	113	2	no	—
359	C₄⋊C₄	—	113	2	no	—
360	C₄⋊C₄	—	113	2	no	—
361	C₄⋊C₄	—	113	2	no	—
362	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	—	113	4	no	—
371	C₂²⋊C₄	—	113	2	no	—
372	C₂²⋊C₄	—	113	2	no	—
373	C₂²⋊C₄	—	113	2	no	—
374	C₂²⋊C₄	—	113	2	no	—
375	C₂²⋊C₄	—	113	4	no	—
376	C₂²⋊C₄	—	113	4	no	—
377	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
379	C₄²	—	113	1	no	—
380	C₄²	—	113	1	no	—
381	C₄²	—	113	1	no	—
382	C₄²	—	113	4	no	—
383	C₄²	—	113	4	no	—
384	C₄²	—	113	2	no	—
385	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
386	C₄²	C₂²×D₁₁₃	1	2	yes	—
387	C₂³	—	113	1	no	—
388	C₂³	—	113	2	no	—
389	C₂³	—	452	2	no	—
390	C₂³	—	452	2	no	—
391	C₂³	—	226	4	no	—
392	C₂³	C₂³×D₁₁₃	1	2	yes	—
393	C₂³	C₂³×D₁₁₃	1	4	yes	—
394	Q₈	—	2	2	no	—
395	Q₈	—	452	2	no	—
396	Q₈	—	226	4	no	—
397	Q₈	—	226	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	4	no	—
404	D₄	—	452	4	no	—
405	D₄	—	452	4	no	—
406	D₄	—	226	4	no	—
407	D₄	—	226	8	no	—
408	D₄	—	226	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	113	1	no	—
412	C₂×C₄	—	113	4	no	—
413	C₂×C₄	—	113	2	no	—
414	C₂×C₄	—	113	1	no	—
415	C₂×C₄	—	113	4	no	—
416	C₂×C₄	—	113	1	no	—
417	C₂×C₄	—	113	2	no	—
418	C₂×C₄	—	113	2	no	—
419	C₂×C₄	—	452	2	no	—
420	C₂×C₄	—	452	2	no	—
421	C₂×C₄	—	452	1	no	—
422	C₂×C₄	—	452	2	no	—
423	C₂×C₄	—	452	4	no	—
424	C₂×C₄	—	226	8	no	—
425	C₂×C₄	—	226	2	no	—
426	C₂×C₄	—	226	4	no	—
427	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
428	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
429	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
431	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	113	2	no	—
440	C₂²	—	452	8	no	—
441	C₂²	—	226	2	no	—
442	C₂²	—	226	2	no	—
443	C₂²	—	226	2	no	—
444	C₂²	—	226	1	no	—
445	C₂²	—	226	1	no	—
446	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	113	2	no	—
452	C₄	—	226	4	no	—
453	C₄	—	226	1	no	—
454	C₄	—	226	2	no	—
455	C₄	—	226	2	no	—
456	C₄	—	226	1	no	—
457	C₄	—	226	2	no	—
458	C₄	#41×D₁₁₃	1	2	yes	—
459	C₄	#16813667	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	4	4	no	—
462	C₂	—	452	2	no	—
463	C₂	—	226	2	no	—
464	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
465	C₂	C₂×#16813667	1	1	yes	characteristic
466	C₂	#20299433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#550×C₁₁₃	C₂
hypercenter	#550	D₁₁₃
hypocenter	C₁₁₃	#3506
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #20299334	C₂	semidirect
2. #20299331	C₂	semidirect
3. #20299321	C₂	semidirect
4. #20299318	C₂	semidirect
5. #20299312	C₂	semidirect
6. #20299291	C₂	semidirect
7. #20299268	C₂	semidirect
8. #20299247	C₂	semidirect
9. #20299180	C₂	semidirect
10. #20299161	C₂	semidirect
11. #20299152	C₂	semidirect
12. #20299146	C₂	semidirect
13. #20299108	C₂	semidirect
14. #20299105	C₂	semidirect
15. #20299077	C₂	semidirect
16. C₄×D₄×D₁₁₃	C₂	semidirect
17. #550×C₁₁₃	C₂	semidirect
19. C₂×#14268646	C₂²	semidirect
22. #16813622	C₂²	semidirect
23. #16813621	C₂²	semidirect
24. #16813620	C₂²	semidirect
26. #16813617	C₂²	semidirect
27. #16813615	C₂²	semidirect
28. #16813612	C₂²	semidirect
31. #16813609	C₂²	semidirect
32. #16813609	C₂²	semidirect
33. #16813608	C₂²	semidirect
34. #16813605	C₂²	semidirect
35. #16813604	C₂²	semidirect
36. #16813603	C₂²	semidirect
37. #16813603	C₂²	semidirect
39. #16813601	C₂²	semidirect
42. #16813598	C₂²	semidirect
45. #16813594	C₂²	semidirect
48. #16813593	C₂²	semidirect
51. C₄×Dic₂₂₆	C₂²	semidirect
52. C₄×Dic₂₂₆	C₂²	semidirect
53. C₄×Dic₂₂₆	C₂²	semidirect
54. #16813587	C₂²	semidirect
57. D₄×Dic₁₁₃	C₂²	semidirect
58. D₄×Dic₁₁₃	C₂²	semidirect
59. D₄×Dic₁₁₃	C₂²	semidirect
60. D₄×Dic₁₁₃	C₂²	semidirect
64. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
67. #16813581	C₂²	semidirect
68. #16813580	C₂²	semidirect
70. #16813578	C₂²	semidirect
71. C₂×#14268626	C₂²	semidirect
75. C₂×#41×C₁₁₃	C₂²	semidirect
77. #127×C₁₁₃	C₂²	semidirect
78. #121×C₁₁₃	C₂²	semidirect
79. #121×C₁₁₃	C₂²	semidirect
80. C₄×Q₈×C₁₁₃	C₂²	semidirect
82. C₄×D₄×C₁₁₃	C₂²	semidirect
195. C₄×D₁₁₃	#41	semidirect
234. C₁₁₃	#3506	semidirect
242. #550	D₁₁₃	semidirect
254. C₂×#41	C₂×D₁₁₃	semidirect
262. #127	C₂×D₁₁₃	semidirect
286. #121	C₂×D₁₁₃	semidirect
287. #121	C₂×D₁₁₃	semidirect
294. C₄×Q₈	C₂×D₁₁₃	semidirect
308. C₄×D₄	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299334	2
#20299331	2
#20299321	2
#20299318	2
#20299312	2
#20299291	2
#20299268	2
#20299247	2
#20299180	2
#20299161	2
#20299152	2
#20299146	2
#20299108	2
#20299105	2
#20299077	2
C₄×D₄×D₁₁₃	2
#550×C₁₁₃	2
#3506	113