Subgroups — #28404609

Order 14464.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299309	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299292	C₂	1	2	yes	maximal, complemented
3	#20299292	C₂	1	2	yes	maximal, complemented
4	#20299269	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299245	C₂	1	2	yes	maximal, complemented
6	#20299241	C₂	1	4	yes	maximal, complemented
7	D₄×D₄₅₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299232	C₂	1	2	yes	maximal, complemented
9	#20299201	C₂	1	2	yes	maximal, complemented
10	#20299182	C₂	1	4	yes	maximal, complemented
11	#20299149	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299130	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299110	C₂	1	2	yes	maximal, complemented
14	#121×D₁₁₃	C₂	1	2	yes	maximal, complemented
15	#20299072	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#555×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	complemented
19	C₂×#14268647	C₂²	1	2	yes	complemented
20	C₂²×D₄₅₂	C₂²	1	2	yes	—
21	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₁₁₃	C₂²	1	4	yes	complemented
23	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
24	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
25	#16813619	C₂²	1	1	yes	characteristic, complemented
26	#16813618	C₂²	1	2	yes	complemented
27	#16813616	C₂²	1	4	yes	complemented
28	#16813615	C₂²	1	2	yes	complemented
29	#16813613	C₂²	1	1	yes	characteristic, complemented
30	#16813613	C₂²	1	2	yes	complemented
31	#16813611	C₂²	1	2	yes	complemented
32	#16813609	C₂²	1	1	yes	characteristic, complemented
33	#16813606	C₂²	1	4	yes	complemented
34	#16813604	C₂²	1	4	yes	complemented
35	#16813604	C₂²	1	4	yes	complemented
36	#16813604	C₂²	1	2	yes	complemented
37	#16813602	C₂²	1	2	yes	complemented
38	#16813602	C₂²	1	1	yes	characteristic, complemented
39	#16813598	C₂²	1	4	yes	complemented
40	#16813597	C₂²	1	2	yes	complemented
41	#16813597	C₂²	1	2	yes	complemented
42	#16813597	C₂²	1	2	yes	complemented
43	#16813596	C₂²	1	2	yes	complemented
44	#16813596	C₂²	1	2	yes	complemented
45	#16813595	C₂²	1	4	yes	complemented
46	#16813595	C₂²	1	4	yes	complemented
47	#16813595	C₂²	1	4	yes	complemented
48	#16813594	C₂²	1	4	yes	complemented
49	#16813593	C₂²	1	1	yes	characteristic
50	#16813593	C₂²	1	4	yes	complemented
51	#16813592	C₂²	1	4	yes	complemented
52	#16813592	C₂²	1	4	yes	complemented
53	#16813590	C₂²	1	4	yes	complemented
54	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
56	C₄×D₄₅₂	C₂²	1	4	yes	complemented
57	C₄×D₄₅₂	C₂²	1	4	yes	complemented
58	C₄×D₄₅₂	C₂²	1	4	yes	complemented
59	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
60	#16813584	C₂²	1	2	yes	—
61	#16813584	C₂²	1	1	yes	characteristic
62	#16813584	C₂²	1	2	yes	complemented
63	#16813584	C₂²	1	2	yes	complemented
64	#16813584	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
67	#16813582	C₂²	1	2	yes	complemented
68	#16813581	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
70	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
72	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
74	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
76	#124×C₁₁₃	C₂²	1	4	yes	complemented
77	#121×C₁₁₃	C₂²	1	2	yes	complemented
78	#121×C₁₁₃	C₂²	1	2	yes	complemented
79	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
81	#117×C₁₁₃	C₂²	1	2	yes	complemented
82	#117×C₁₁₃	C₂²	1	2	yes	complemented
83	C₂³×D₁₁₃	C₂³	1	2	yes	—
84	C₂³×D₁₁₃	C₂³	1	4	yes	—
85	#14268648	—	4	4	no	—
86	#14268647	—	4	4	no	—
87	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
88	C₂×D₄₅₂	—	2	8	no	—
89	C₂×D₄₅₂	C₂³	1	2	yes	—
90	C₂×D₄₅₂	C₂³	1	2	yes	—
91	C₂×D₄₅₂	C₂³	1	4	yes	—
92	C₂×D₄₅₂	C₂³	1	4	yes	—
93	C₂×D₄₅₂	C₂³	1	2	yes	—
94	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
100	D₄×D₁₁₃	—	2	4	no	—
101	D₄×D₁₁₃	—	4	4	no	—
102	D₄×D₁₁₃	—	4	8	no	—
103	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₁₃	—	4	4	no	—
105	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
109	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
110	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
111	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
113	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
114	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
117	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
118	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
119	#14268626	C₂³	1	2	yes	—
120	#14268626	C₂³	1	4	yes	—
121	#14268626	C₂³	1	2	yes	—
122	#14268626	C₂³	1	2	yes	—
123	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
127	#14268624	C₂³	1	2	yes	—
128	#14268624	C₂³	1	2	yes	—
129	#14268624	C₂³	1	4	yes	—
130	#14268624	C₂³	1	4	yes	—
131	#14268624	C₂³	1	4	yes	—
132	#14268624	C₂³	1	2	yes	—
133	#14268624	C₂³	1	4	yes	—
134	#14268624	C₂³	1	4	yes	—
135	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
136	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
137	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
138	C₄×Dic₁₁₃	C₂³	1	2	yes	—
139	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
140	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
143	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
153	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
154	C₄²×C₁₁₃	C₂³	1	4	yes	—
155	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
156	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
157	C₂²×D₁₁₃	—	2	4	no	—
158	C₂²×D₁₁₃	—	2	4	no	—
159	C₂²×D₁₁₃	—	2	8	no	—
160	C₂²×D₁₁₃	—	4	2	no	—
161	C₂²×D₁₁₃	—	4	4	no	—
162	C₂²×D₁₁₃	—	4	4	no	—
163	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
164	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
165	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
166	Q₈×C₁₁₃	—	4	2	no	—
167	D₄×C₁₁₃	—	2	2	no	—
168	D₄×C₁₁₃	—	2	2	no	—
169	D₄×C₁₁₃	—	4	4	no	—
170	C₂×C₄×C₁₁₃	—	2	4	no	—
171	C₂×C₄×C₁₁₃	—	2	4	no	—
172	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
176	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₁₁₃	—	2	4	no	—
179	C₂²⋊D₁₁₃	—	2	4	no	—
180	C₂²⋊D₁₁₃	—	4	4	no	—
181	C₂²⋊D₁₁₃	—	4	4	no	—
182	C₂²⋊D₁₁₃	—	4	4	no	—
183	C₂×Dic₁₁₃	—	4	2	no	—
184	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
188	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
189	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
190	D₄₅₂	—	2	8	no	—
191	D₄₅₂	—	2	8	no	—
192	D₄₅₂	—	2	4	no	—
193	D₄₅₂	—	2	4	no	—
194	D₄₅₂	—	4	2	no	—
195	D₄₅₂	#41	1	4	yes	complemented
196	C₄×D₁₁₃	—	2	2	no	—
197	C₄×D₁₁₃	—	2	2	no	—
198	C₄×D₁₁₃	—	2	2	no	—
199	C₄×D₁₁₃	—	2	4	no	—
200	C₄×D₁₁₃	—	4	2	no	—
201	C₄×D₁₁₃	—	4	2	no	—
202	C₄×D₁₁₃	—	4	4	no	—
203	C₄×D₁₁₃	—	4	4	no	—
204	C₄×D₁₁₃	—	4	4	no	—
205	Dic₂₂₆	—	2	2	no	—
206	C₂²×C₁₁₃	—	2	2	no	—
207	C₂²×C₁₁₃	—	2	2	no	—
208	C₂²×C₁₁₃	—	2	2	no	—
209	C₂²×C₁₁₃	—	2	2	no	—
210	C₂²×C₁₁₃	—	2	2	no	—
211	C₂²×C₁₁₃	—	2	2	no	—
212	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
213	C₂×D₁₁₃	—	2	1	no	—
214	C₂×D₁₁₃	—	2	1	no	—
215	C₂×D₁₁₃	—	2	2	no	—
216	C₂×D₁₁₃	—	2	2	no	—
217	C₂×D₁₁₃	—	2	4	no	—
218	C₂×D₁₁₃	—	2	4	no	—
219	C₂×D₁₁₃	—	2	4	no	—
220	C₂×D₁₁₃	—	4	8	no	—
221	C₂×D₁₁₃	—	8	8	no	—
222	C₂×D₁₁₃	C₂×#41	1	4	yes	—
223	C₂×D₁₁₃	H(5,𝔽₂)	1	2	yes	—
224	C₄×C₁₁₃	—	2	2	no	—
225	C₄×C₁₁₃	—	2	1	no	—
226	C₄×C₁₁₃	—	2	2	no	—
227	C₄×C₁₁₃	—	2	4	no	—
228	C₄×C₁₁₃	C₂×#41	1	2	yes	—
229	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
230	Dic₁₁₃	—	2	1	no	—
231	Dic₁₁₃	—	2	2	no	—
232	Dic₁₁₃	—	2	1	no	—
233	Dic₁₁₃	—	2	1	no	—
234	Dic₁₁₃	—	2	2	no	—
235	Dic₁₁₃	—	2	2	no	—
236	C₂×C₁₁₃	—	4	2	no	—
237	C₂×C₁₁₃	—	4	2	no	—
238	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
239	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	D₁₁₃	—	2	2	no	—
242	D₁₁₃	—	2	4	no	—
243	D₁₁₃	—	4	4	no	—
244	#3519	—	113	1	no	maximal, Sylow
245	C₁₁₃	#3519	1	1	yes	characteristic, complemented, Sylow
246	#555	D₁₁₃	1	1	yes	characteristic, complemented
247	#554	—	113	1	no	—
248	#553	—	113	2	no	—
249	#553	—	113	2	no	—
250	#550	—	113	1	no	—
251	#546	—	113	4	no	—
252	#546	—	113	2	no	—
253	D₄²	—	113	2	no	—
254	D₄²	—	113	1	no	—
255	#540	—	113	2	no	—
256	#538	—	113	4	no	—
257	#532	—	113	1	no	—
258	#529	—	113	1	no	—
259	#525	—	113	2	no	—
260	C₂×#121	—	113	2	no	—
261	#518	—	113	2	no	—
262	C₂×C₄×D₄	—	113	1	no	—
263	C₂×#41	—	113	2	no	—
264	C₂×#41	—	113	2	no	—
265	C₂²×D₄	—	113	4	no	—
266	C₂²×D₄	—	113	2	no	—
267	C₂²×D₄	—	113	1	no	—
268	C₂²×D₄	—	113	2	no	—
269	C₂³×C₄	—	113	2	no	—
270	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
271	#127	—	113	2	no	—
272	#127	—	113	1	no	—
273	#126	—	113	2	no	—
274	#126	—	113	4	no	—
275	#125	—	113	1	no	—
276	#125	—	113	2	no	—
277	#124	—	113	2	no	—
278	#124	—	113	1	no	—
279	#124	C₂×D₁₁₃	1	4	yes	complemented
280	#123	—	113	4	no	—
281	#123	—	113	2	no	—
282	#123	—	113	4	no	—
283	#123	—	113	4	no	—
284	C₂²⋊Q₈	—	113	4	no	—
285	C₂²⋊Q₈	—	113	1	no	—
286	C₂²⋊Q₈	—	113	2	no	—
287	#121	—	113	1	no	—
288	#121	—	113	4	no	—
289	#121	—	113	4	no	—
290	#121	—	113	2	no	—
291	#121	—	113	2	no	—
292	#121	—	113	2	no	—
293	#121	—	113	2	no	—
294	#121	—	113	2	no	—
295	#121	—	113	4	no	—
296	#121	—	113	4	no	—
297	#121	—	113	4	no	—
298	#121	C₂×D₁₁₃	1	2	yes	complemented
299	#121	C₂×D₁₁₃	1	2	yes	complemented
300	#120	—	113	4	no	—
301	#120	—	113	4	no	—
302	#120	—	113	4	no	—
303	C₄×Q₈	—	113	1	no	—
304	C₄×D₄	—	113	1	no	—
305	C₄×D₄	—	113	2	no	—
306	C₄×D₄	—	113	2	no	—
307	C₄×D₄	—	113	1	no	—
308	C₄×D₄	—	113	2	no	—
309	C₄×D₄	—	113	2	no	—
310	C₄×D₄	—	113	2	no	—
311	C₄×D₄	—	113	2	no	—
312	C₄×D₄	—	113	2	no	—
313	C₄×D₄	—	113	1	no	—
314	C₄×D₄	—	113	4	no	—
315	C₄×D₄	—	113	4	no	—
316	C₄×D₄	—	113	4	no	—
317	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
318	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
319	#117	—	113	2	no	—
320	#117	C₂×D₁₁₃	1	2	yes	complemented
321	#117	C₂×D₁₁₃	1	2	yes	complemented
322	C₂×C₄⋊C₄	—	113	1	no	—
323	C₂×C₄⋊C₄	—	113	2	no	—
324	C₂×C₂²⋊C₄	—	113	2	no	—
325	C₂×C₂²⋊C₄	—	113	4	no	—
326	C₂×C₂²⋊C₄	—	113	4	no	—
327	C₂×C₄²	—	113	1	no	—
328	C₂⁴	—	113	4	no	—
329	C₂⁴	—	113	2	no	—
330	#41	—	452	4	no	—
331	#41	—	452	4	no	—
332	C₂×Q₈	—	113	1	no	—
333	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
334	C₂×D₄	—	113	4	no	—
335	C₂×D₄	—	113	4	no	—
336	C₂×D₄	—	113	4	no	—
337	C₂×D₄	—	113	2	no	—
338	C₂×D₄	—	113	2	no	—
339	C₂×D₄	—	113	1	no	—
340	C₂×D₄	—	113	2	no	—
341	C₂×D₄	—	113	4	no	—
342	C₂×D₄	—	113	2	no	—
343	C₂×D₄	—	113	4	no	—
344	C₂×D₄	—	113	2	no	—
345	C₂×D₄	—	452	8	no	—
346	C₂×D₄	—	452	4	no	—
347	C₂×D₄	—	226	8	no	—
348	C₂×D₄	—	226	4	no	—
349	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
350	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
351	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
352	C₂²×C₄	—	113	2	no	—
353	C₂²×C₄	—	113	2	no	—
354	C₂²×C₄	—	113	2	no	—
355	C₂²×C₄	—	113	4	no	—
356	C₂²×C₄	—	113	4	no	—
357	C₂²×C₄	—	113	4	no	—
358	C₂²×C₄	—	113	1	no	—
359	C₂²×C₄	—	113	1	no	—
360	C₂²×C₄	—	113	1	no	—
361	C₂²×C₄	—	113	2	no	—
362	C₂²×C₄	—	452	4	no	—
363	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
364	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
365	C₄⋊C₄	—	113	1	no	—
366	C₄⋊C₄	—	113	1	no	—
367	C₄⋊C₄	—	113	2	no	—
368	C₄⋊C₄	—	113	4	no	—
369	C₄⋊C₄	—	113	2	no	—
370	C₄⋊C₄	—	113	2	no	—
371	C₄⋊C₄	—	113	2	no	—
372	C₄⋊C₄	—	113	4	no	—
373	C₄⋊C₄	—	113	2	no	—
374	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
375	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
376	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
378	C₂²⋊C₄	—	113	2	no	—
379	C₂²⋊C₄	—	113	2	no	—
380	C₂²⋊C₄	—	113	2	no	—
381	C₂²⋊C₄	—	113	2	no	—
382	C₂²⋊C₄	—	113	2	no	—
383	C₂²⋊C₄	—	113	4	no	—
384	C₂²⋊C₄	—	113	2	no	—
385	C₂²⋊C₄	—	113	4	no	—
386	C₂²⋊C₄	—	113	4	no	—
387	C₂²⋊C₄	—	113	2	no	—
388	C₂²⋊C₄	—	113	4	no	—
389	C₂²⋊C₄	—	113	4	no	—
390	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
391	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
393	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
394	C₄²	—	113	1	no	—
395	C₄²	—	113	1	no	—
396	C₄²	—	113	1	no	—
397	C₄²	—	113	2	no	—
398	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
399	C₄²	C₂²×D₁₁₃	1	4	yes	—
400	C₂³	—	113	2	no	—
401	C₂³	—	113	1	no	—
402	C₂³	—	113	4	no	—
403	C₂³	—	452	4	no	—
404	C₂³	—	452	4	no	—
405	C₂³	—	452	2	no	—
406	C₂³	—	226	8	no	—
407	C₂³	—	226	4	no	—
408	C₂³	—	226	4	no	—
409	C₂³	C₂³×D₁₁₃	1	2	yes	—
410	C₂³	C₂³×D₁₁₃	1	2	yes	—
411	Q₈	—	4	2	no	—
412	Q₈	—	226	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	113	4	no	—
417	D₄	—	452	2	no	—
418	D₄	—	452	4	no	—
419	D₄	—	452	4	no	—
420	D₄	—	452	4	no	—
421	D₄	—	226	8	no	—
422	D₄	—	226	8	no	—
423	D₄	—	226	4	no	—
424	D₄	—	226	4	no	—
425	D₄	—	226	4	no	—
426	D₄	—	226	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	113	1	no	—
430	C₂×C₄	—	113	1	no	—
431	C₂×C₄	—	113	1	no	—
432	C₂×C₄	—	113	2	no	—
433	C₂×C₄	—	113	2	no	—
434	C₂×C₄	—	113	2	no	—
435	C₂×C₄	—	452	2	no	—
436	C₂×C₄	—	452	2	no	—
437	C₂×C₄	—	452	4	no	—
438	C₂×C₄	—	452	4	no	—
439	C₂×C₄	—	452	4	no	—
440	C₂×C₄	—	452	2	no	—
441	C₂×C₄	—	226	2	no	—
442	C₂×C₄	—	226	2	no	—
443	C₂×C₄	—	226	2	no	—
444	C₂×C₄	—	226	4	no	—
445	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
447	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
448	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
449	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	113	4	no	—
458	C₂²	—	113	2	no	—
459	C₂²	—	904	8	no	—
460	C₂²	—	452	8	no	—
461	C₂²	—	226	4	no	—
462	C₂²	—	226	4	no	—
463	C₂²	—	226	4	no	—
464	C₂²	—	226	1	no	—
465	C₂²	—	226	2	no	—
466	C₂²	—	226	1	no	—
467	C₂²	—	226	2	no	—
468	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	226	1	no	—
474	C₄	—	226	1	no	—
475	C₄	—	226	2	no	—
476	C₄	—	226	1	no	—
477	C₄	—	226	2	no	—
478	C₄	—	226	2	no	—
479	C₄	#41×D₁₁₃	1	2	yes	—
480	C₄	#16813668	1	2	yes	—
481	C₂	—	4	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	452	4	no	—
484	C₂	—	226	4	no	—
485	C₂	—	226	2	no	—
486	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
487	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
488	C₂	C₂×#16813668	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#555×C₁₁₃	C₂
hypercenter	#555	D₁₁₃
hypocenter	C₁₁₃	#3519
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #20299309	C₂	semidirect
2. #20299292	C₂	semidirect
3. #20299292	C₂	semidirect
4. #20299269	C₂	semidirect
5. #20299245	C₂	semidirect
6. #20299241	C₂	semidirect
7. D₄×D₄₅₂	C₂	semidirect
8. #20299232	C₂	semidirect
9. #20299201	C₂	semidirect
10. #20299182	C₂	semidirect
11. #20299149	C₂	semidirect
12. #20299130	C₂	semidirect
13. #20299110	C₂	semidirect
14. #121×D₁₁₃	C₂	semidirect
15. #20299072	C₂	semidirect
16. C₄×D₄×D₁₁₃	C₂	semidirect
17. #555×C₁₁₃	C₂	semidirect
18. C₂×#14268648	C₂²	semidirect
19. C₂×#14268647	C₂²	semidirect
22. C₂×D₄×D₁₁₃	C₂²	semidirect
23. C₂×D₄×D₁₁₃	C₂²	semidirect
24. C₂²×C₄×D₁₁₃	C₂²	semidirect
25. #16813619	C₂²	semidirect
26. #16813618	C₂²	semidirect
27. #16813616	C₂²	semidirect
28. #16813615	C₂²	semidirect
29. #16813613	C₂²	semidirect
30. #16813613	C₂²	semidirect
31. #16813611	C₂²	semidirect
32. #16813609	C₂²	semidirect
33. #16813606	C₂²	semidirect
34. #16813604	C₂²	semidirect
35. #16813604	C₂²	semidirect
36. #16813604	C₂²	semidirect
37. #16813602	C₂²	semidirect
38. #16813602	C₂²	semidirect
39. #16813598	C₂²	semidirect
40. #16813597	C₂²	semidirect
41. #16813597	C₂²	semidirect
42. #16813597	C₂²	semidirect
43. #16813596	C₂²	semidirect
44. #16813596	C₂²	semidirect
45. #16813595	C₂²	semidirect
46. #16813595	C₂²	semidirect
47. #16813595	C₂²	semidirect
48. #16813594	C₂²	semidirect
50. #16813593	C₂²	semidirect
51. #16813592	C₂²	semidirect
52. #16813592	C₂²	semidirect
53. #16813590	C₂²	semidirect
54. C₄×Dic₂₂₆	C₂²	semidirect
56. C₄×D₄₅₂	C₂²	semidirect
57. C₄×D₄₅₂	C₂²	semidirect
58. C₄×D₄₅₂	C₂²	semidirect
59. D₄×Dic₁₁₃	C₂²	semidirect
62. #16813584	C₂²	semidirect
63. #16813584	C₂²	semidirect
64. #16813584	C₂²	semidirect
65. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
66. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
67. #16813582	C₂²	semidirect
68. #16813581	C₂²	semidirect
69. C₄⋊C₄×D₁₁₃	C₂²	semidirect
70. C₄⋊C₄×D₁₁₃	C₂²	semidirect
71. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
72. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
73. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
74. C₄²×D₁₁₃	C₂²	semidirect
75. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
76. #124×C₁₁₃	C₂²	semidirect
77. #121×C₁₁₃	C₂²	semidirect
78. #121×C₁₁₃	C₂²	semidirect
79. C₄×D₄×C₁₁₃	C₂²	semidirect
80. C₄×D₄×C₁₁₃	C₂²	semidirect
81. #117×C₁₁₃	C₂²	semidirect
82. #117×C₁₁₃	C₂²	semidirect
195. D₄₅₂	#41	semidirect
245. C₁₁₃	#3519	semidirect
246. #555	D₁₁₃	semidirect
270. C₄⋊Q₈	C₂×D₁₁₃	semidirect
279. #124	C₂×D₁₁₃	semidirect
298. #121	C₂×D₁₁₃	semidirect
299. #121	C₂×D₁₁₃	semidirect
317. C₄×D₄	C₂×D₁₁₃	semidirect
318. C₄×D₄	C₂×D₁₁₃	semidirect
320. #117	C₂×D₁₁₃	semidirect
321. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299309	2
#20299292	2
#20299269	2
#20299245	2
#20299241	2
D₄×D₄₅₂	2
#20299232	2
#20299201	2
#20299182	2
#20299149	2
#20299130	2
#20299110	2
#121×D₁₁₃	2
#20299072	2
C₄×D₄×D₁₁₃	2
#555×C₁₁₃	2
#3519	113