Subgroups — #28404667

Order 14464.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 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	#20299325	C₂	1	2	yes	maximal, complemented
3	#20299321	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299320	C₂	1	2	yes	maximal, complemented
5	#20299289	C₂	1	2	yes	maximal, complemented
6	#20299280	C₂	1	4	yes	maximal, complemented
7	#20299263	C₂	1	2	yes	maximal, complemented
8	#20299263	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299209	C₂	1	2	yes	maximal, complemented
10	#20299207	C₂	1	4	yes	maximal, complemented
11	#20299153	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299152	C₂	1	2	yes	maximal, complemented
13	#20299135	C₂	1	1	yes	maximal, characteristic
14	#20299133	C₂	1	2	yes	maximal
15	#20299074	C₂	1	2	yes	maximal, complemented
16	C₄×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#557×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
20	#16813622	C₂²	1	1	yes	characteristic
21	#16813621	C₂²	1	2	yes	—
22	#16813621	C₂²	1	4	yes	—
23	#16813620	C₂²	1	2	yes	—
24	#16813617	C₂²	1	4	yes	—
25	#16813617	C₂²	1	4	yes	—
26	#16813617	C₂²	1	4	yes	—
27	#16813617	C₂²	1	2	yes	—
28	#16813616	C₂²	1	4	yes	—
29	#16813614	C₂²	1	2	yes	—
30	#16813613	C₂²	1	1	yes	characteristic
31	#16813613	C₂²	1	2	yes	—
32	#16813612	C₂²	1	4	yes	—
33	#16813612	C₂²	1	4	yes	—
34	#16813612	C₂²	1	4	yes	—
35	#16813612	C₂²	1	4	yes	—
36	#16813611	C₂²	1	1	yes	characteristic
37	#16813610	C₂²	1	2	yes	—
38	#16813607	C₂²	1	2	yes	—
39	#16813607	C₂²	1	4	yes	—
40	#16813602	C₂²	1	2	yes	—
41	#16813600	C₂²	1	4	yes	—
42	#16813600	C₂²	1	4	yes	—
43	#16813600	C₂²	1	4	yes	—
44	#16813598	C₂²	1	2	yes	—
45	#16813598	C₂²	1	2	yes	—
46	#16813598	C₂²	1	2	yes	—
47	#16813598	C₂²	1	1	yes	characteristic
48	#16813597	C₂²	1	1	yes	characteristic
49	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
50	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
51	C₄×Dic₂₂₆	C₂²	1	2	yes	—
52	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
53	C₄×Dic₂₂₆	C₂²	1	2	yes	—
54	C₄×Dic₂₂₆	C₂²	1	2	yes	—
55	C₄×Dic₂₂₆	C₂²	1	4	yes	—
56	#16813587	C₂²	1	4	yes	—
57	#16813587	C₂²	1	1	yes	characteristic
58	#16813587	C₂²	1	2	yes	—
59	#16813587	C₂²	1	2	yes	—
60	#16813587	C₂²	1	2	yes	—
61	C₄×D₄₅₂	C₂²	1	2	yes	—
62	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
63	#16813584	C₂²	1	4	yes	—
64	#16813584	C₂²	1	2	yes	—
65	#16813580	C₂²	1	2	yes	—
66	#16813580	C₂²	1	2	yes	—
67	#16813580	C₂²	1	4	yes	—
68	#16813579	C₂²	1	4	yes	—
69	#16813579	C₂²	1	4	yes	—
70	#16813579	C₂²	1	2	yes	—
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
73	C₄²×D₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
76	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
77	#125×C₁₁₃	C₂²	1	4	yes	—
78	#125×C₁₁₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
80	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
81	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
82	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
83	C₂×Dic₂₂₆	C₂³	1	2	yes	—
84	C₂×Dic₂₂₆	C₂³	1	4	yes	—
85	C₂×Dic₂₂₆	C₂³	1	2	yes	—
86	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
87	Q₈×D₁₁₃	—	2	4	no	—
88	Q₈×D₁₁₃	—	2	8	no	—
89	C₂×D₄₅₂	C₂³	1	2	yes	—
90	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
100	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
105	#14268626	C₂³	1	2	yes	—
106	#14268626	C₂³	1	2	yes	—
107	#14268626	C₂³	1	2	yes	—
108	#14268626	C₂³	1	2	yes	—
109	#14268626	C₂³	1	2	yes	—
110	#14268626	C₂³	1	4	yes	—
111	#14268626	C₂³	1	4	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	4	yes	—
114	#14268626	C₂³	1	4	yes	—
115	#14268626	C₂³	1	4	yes	—
116	#14268624	C₂³	1	2	yes	—
117	#14268624	C₂³	1	2	yes	—
118	#14268624	C₂³	1	2	yes	—
119	#14268624	C₂³	1	4	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	#14268624	C₂³	1	4	yes	—
123	#14268624	C₂³	1	2	yes	—
124	#14268624	C₂³	1	2	yes	—
125	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
126	C₄×Dic₁₁₃	C₂³	1	2	yes	—
127	C₄×Dic₁₁₃	C₂³	1	2	yes	—
128	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
129	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
130	C₄×Dic₁₁₃	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	4	yes	—
132	C₄×Dic₁₁₃	C₂³	1	4	yes	—
133	C₄×Dic₁₁₃	C₂³	1	4	yes	—
134	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₄²×C₁₁₃	C₂³	1	2	yes	—
148	C₄²×C₁₁₃	C₂³	1	4	yes	—
149	C₄²×C₁₁₃	C₂³	1	2	yes	—
150	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
151	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
152	Q₈×C₁₁₃	—	2	2	no	—
153	Q₈×C₁₁₃	—	2	4	no	—
154	Q₈×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
158	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
166	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
167	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
169	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
170	D₄₅₂	—	2	4	no	—
171	D₄₅₂	—	2	2	no	—
172	C₄×D₁₁₃	—	2	4	no	—
173	C₄×D₁₁₃	—	2	2	no	—
174	C₄×D₁₁₃	—	2	2	no	—
175	C₄×D₁₁₃	—	2	4	no	—
176	C₄×D₁₁₃	—	2	2	no	—
177	C₄×D₁₁₃	—	2	4	no	—
178	C₄×D₁₁₃	—	2	8	no	—
179	Dic₂₂₆	—	2	4	no	—
180	Dic₂₂₆	—	2	4	no	—
181	Dic₂₂₆	—	2	8	no	—
182	Dic₂₂₆	#41	1	4	yes	—
183	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
184	C₂×D₁₁₃	—	2	1	no	—
185	C₂×D₁₁₃	—	2	1	no	—
186	C₂×D₁₁₃	—	2	2	no	—
187	C₂×D₁₁₃	—	2	2	no	—
188	C₂×D₁₁₃	—	2	2	no	—
189	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
190	C₄×C₁₁₃	—	2	2	no	—
191	C₄×C₁₁₃	—	2	4	no	—
192	C₄×C₁₁₃	—	2	2	no	—
193	C₄×C₁₁₃	—	2	1	no	—
194	C₄×C₁₁₃	—	2	2	no	—
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	C₂×#41	1	2	yes	—
197	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
198	Dic₁₁₃	—	2	1	no	—
199	Dic₁₁₃	—	2	2	no	—
200	Dic₁₁₃	—	2	4	no	—
201	Dic₁₁₃	—	2	1	no	—
202	Dic₁₁₃	—	2	2	no	—
203	Dic₁₁₃	—	2	1	no	—
204	Dic₁₁₃	C₂×#41	1	4	yes	—
205	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
206	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
208	D₁₁₃	—	2	2	no	—
209	D₁₁₃	—	4	2	no	—
210	#3523	—	113	1	no	maximal, Sylow
211	C₁₁₃	#3523	1	1	yes	characteristic, complemented, Sylow
212	#557	—	113	2	no	—
213	#557	—	113	1	no	—
214	#557	D₁₁₃	1	1	yes	characteristic, complemented
215	#556	—	113	2	no	—
216	#556	—	113	1	no	—
217	#552	—	113	4	no	—
218	#552	—	113	2	no	—
219	D₄×Q₈	—	113	2	no	—
220	D₄×Q₈	—	113	1	no	—
221	#541	—	113	2	no	—
222	#541	—	113	4	no	—
223	#533	—	113	1	no	—
224	#533	—	113	2	no	—
225	#529	—	113	2	no	—
226	#529	—	113	1	no	—
227	#519	—	113	2	no	—
228	C₂×C₄×Q₈	—	113	1	no	—
229	C₂²×Q₈	—	113	1	no	—
230	C₂²×Q₈	—	113	2	no	—
231	C₄⋊Q₈	—	113	2	no	—
232	C₄⋊Q₈	—	113	2	no	—
233	C₄⋊Q₈	—	113	4	no	—
234	C₄⋊Q₈	—	113	1	no	—
235	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
236	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	—
237	#126	—	113	2	no	—
238	#126	—	113	4	no	—
239	#126	—	113	4	no	—
240	#126	—	113	4	no	—
241	#126	—	113	4	no	—
242	#125	—	113	1	no	—
243	#125	—	113	4	no	—
244	#125	—	113	2	no	—
245	#125	—	113	4	no	—
246	#125	—	113	4	no	—
247	#125	—	113	4	no	—
248	#125	—	113	2	no	—
249	#125	C₂×D₁₁₃	1	2	yes	—
250	#125	C₂×D₁₁₃	1	4	yes	—
251	#124	—	113	1	no	—
252	#124	—	113	2	no	—
253	#123	—	113	2	no	—
254	#123	—	113	4	no	—
255	C₂²⋊Q₈	—	113	1	no	—
256	C₂²⋊Q₈	—	113	2	no	—
257	C₂²⋊Q₈	—	113	2	no	—
258	C₂²⋊Q₈	—	113	2	no	—
259	C₂²⋊Q₈	—	113	2	no	—
260	C₂²⋊Q₈	—	113	4	no	—
261	C₂²⋊Q₈	—	113	4	no	—
262	C₂²⋊Q₈	—	113	4	no	—
263	#121	—	113	1	no	—
264	C₄×Q₈	—	113	1	no	—
265	C₄×Q₈	—	113	2	no	—
266	C₄×Q₈	—	113	1	no	—
267	C₄×Q₈	—	113	2	no	—
268	C₄×Q₈	—	113	4	no	—
269	C₄×Q₈	—	113	2	no	—
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	1	no	—
272	C₄×Q₈	—	113	2	no	—
273	C₄×Q₈	—	113	4	no	—
274	C₄×Q₈	—	113	2	no	—
275	C₄×Q₈	—	113	2	no	—
276	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
277	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
278	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
279	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
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	#117	—	113	4	no	—
285	#117	—	113	2	no	—
286	#117	—	113	2	no	—
287	#117	—	113	2	no	—
288	#117	—	113	4	no	—
289	#117	—	113	4	no	—
290	C₂×C₄⋊C₄	—	113	2	no	—
291	C₂×C₄⋊C₄	—	113	1	no	—
292	C₂×C₄²	—	113	2	no	—
293	C₂×C₄²	—	113	1	no	—
294	C₂×Q₈	—	113	1	no	—
295	C₂×Q₈	—	113	2	no	—
296	C₂×Q₈	—	113	2	no	—
297	C₂×Q₈	—	113	4	no	—
298	C₂×Q₈	—	226	4	no	—
299	C₂×Q₈	—	226	8	no	—
300	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
301	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
302	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
303	C₂×D₄	—	113	2	no	—
304	C₂×D₄	—	113	1	no	—
305	C₂²×C₄	—	113	1	no	—
306	C₂²×C₄	—	113	1	no	—
307	C₂²×C₄	—	113	2	no	—
308	C₂²×C₄	—	113	2	no	—
309	C₂²×C₄	—	113	1	no	—
310	C₂²×C₄	—	113	4	no	—
311	C₂²×C₄	—	113	2	no	—
312	C₄⋊C₄	—	113	2	no	—
313	C₄⋊C₄	—	113	2	no	—
314	C₄⋊C₄	—	113	1	no	—
315	C₄⋊C₄	—	113	2	no	—
316	C₄⋊C₄	—	113	2	no	—
317	C₄⋊C₄	—	113	4	no	—
318	C₄⋊C₄	—	113	2	no	—
319	C₄⋊C₄	—	113	2	no	—
320	C₄⋊C₄	—	113	4	no	—
321	C₄⋊C₄	—	113	2	no	—
322	C₄⋊C₄	—	113	4	no	—
323	C₄⋊C₄	—	113	4	no	—
324	C₄⋊C₄	—	113	2	no	—
325	C₄⋊C₄	—	113	1	no	—
326	C₄⋊C₄	—	113	2	no	—
327	C₄⋊C₄	—	113	4	no	—
328	C₄⋊C₄	—	113	4	no	—
329	C₄⋊C₄	—	113	4	no	—
330	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
332	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
333	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
334	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
335	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
336	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
338	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
339	C₂²⋊C₄	—	113	2	no	—
340	C₂²⋊C₄	—	113	2	no	—
341	C₂²⋊C₄	—	113	4	no	—
342	C₂²⋊C₄	—	113	4	no	—
343	C₂²⋊C₄	—	113	2	no	—
344	C₂²⋊C₄	—	113	4	no	—
345	C₂²⋊C₄	—	113	2	no	—
346	C₂²⋊C₄	—	113	4	no	—
347	C₂²⋊C₄	—	113	2	no	—
348	C₄²	—	113	2	no	—
349	C₄²	—	113	1	no	—
350	C₄²	—	113	2	no	—
351	C₄²	—	113	1	no	—
352	C₄²	—	113	2	no	—
353	C₄²	—	113	1	no	—
354	C₄²	—	113	4	no	—
355	C₄²	—	113	4	no	—
356	C₄²	—	113	4	no	—
357	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
358	C₄²	C₂²×D₁₁₃	1	2	yes	—
359	C₄²	C₂²×D₁₁₃	1	4	yes	—
360	C₄²	C₂²×D₁₁₃	1	2	yes	—
361	C₂³	—	113	1	no	—
362	C₂³	—	113	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	113	4	no	—
367	Q₈	—	226	4	no	—
368	Q₈	—	226	8	no	—
369	Q₈	—	226	4	no	—
370	D₄	—	226	4	no	—
371	D₄	—	226	2	no	—
372	C₂×C₄	—	113	2	no	—
373	C₂×C₄	—	113	1	no	—
374	C₂×C₄	—	113	1	no	—
375	C₂×C₄	—	113	4	no	—
376	C₂×C₄	—	113	2	no	—
377	C₂×C₄	—	113	1	no	—
378	C₂×C₄	—	113	2	no	—
379	C₂×C₄	—	226	8	no	—
380	C₂×C₄	—	226	4	no	—
381	C₂×C₄	—	226	4	no	—
382	C₂×C₄	—	226	2	no	—
383	C₂×C₄	—	226	4	no	—
384	C₂×C₄	—	226	2	no	—
385	C₂×C₄	—	226	2	no	—
386	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
387	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
388	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
390	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
391	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
392	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
394	C₂²	—	113	2	no	—
395	C₂²	—	226	2	no	—
396	C₂²	—	226	2	no	—
397	C₂²	—	226	2	no	—
398	C₂²	—	226	1	no	—
399	C₂²	—	226	1	no	—
400	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	113	4	no	—
408	C₄	—	226	1	no	—
409	C₄	—	226	2	no	—
410	C₄	—	226	1	no	—
411	C₄	—	226	2	no	—
412	C₄	—	226	1	no	—
413	C₄	—	226	4	no	—
414	C₄	#41×D₁₁₃	1	2	yes	—
415	C₄	#16813670	1	2	yes	—
416	C₂	—	452	2	no	—
417	C₂	—	226	2	no	—
418	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
419	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic
420	C₂	C₂×#16813670	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#557×C₁₁₃	C₂
prime radical	#16813597	C₂²
hypercenter	#557	D₁₁₃
hypocenter	C₁₁₃	#3523
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #20299326	C₂	semidirect
2. #20299325	C₂	semidirect
3. #20299321	C₂	semidirect
4. #20299320	C₂	semidirect
5. #20299289	C₂	semidirect
6. #20299280	C₂	semidirect
7. #20299263	C₂	semidirect
8. #20299263	C₂	semidirect
9. #20299209	C₂	semidirect
10. #20299207	C₂	semidirect
11. #20299153	C₂	semidirect
12. #20299152	C₂	semidirect
15. #20299074	C₂	semidirect
16. C₄×Q₈×D₁₁₃	C₂	semidirect
17. #557×C₁₁₃	C₂	semidirect
211. C₁₁₃	#3523	semidirect
214. #557	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
#20299325	2
#20299321	2
#20299320	2
#20299289	2
#20299280	2
#20299263	2
#20299209	2
#20299207	2
#20299153	2
#20299152	2
#20299135	2
#20299133	2
#20299074	2
C₄×Q₈×D₁₁₃	2
#557×C₁₁₃	2
#3523	113