Subgroups — #15757166

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
2	#13115599	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114964	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114837	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718051	C₂	1	1	yes	maximal, characteristic
6	#13112720	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₄×D₁₃	—	2	1	no	—
9	C₂×C₄×D₅₂	—	2	1	no	—
10	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×#88061	—	2	1	no	—
15	#11718648	—	2	1	no	—
16	C₂×#88048	—	2	1	no	—
17	#11718596	C₂²	1	1	yes	characteristic
18	#11718596	C₂²	1	1	yes	characteristic
19	#11718589	—	2	1	no	—
20	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
21	#11718329	—	2	2	no	—
22	#11718143	—	2	2	no	—
23	#11718143	—	2	1	no	—
24	#11718121	—	2	1	no	—
25	#11718051	C₄	1	4	yes	complemented
26	C₂²×D₅₂	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₁₃	—	2	1	no	—
28	C₂²×C₄×D₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	2	1	no	—
30	C₂²×C₈×C₁₃	—	2	1	no	—
31	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	—	2	1	no	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×#6103	—	2	1	no	—
36	C₂×#6103	—	2	2	no	—
37	C₂×C₄⋊Dic₁₃	—	2	1	no	—
38	C₂×C₄⋊Dic₁₃	—	2	1	no	—
39	C₂×C₄⋊Dic₁₃	—	2	1	no	—
40	C₂×C₄⋊Dic₁₃	—	2	1	no	—
41	C₂×C₄⋊Dic₁₃	—	2	1	no	—
42	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
44	C₂×#6101	—	2	2	no	—
45	C₂²×#1055	—	2	1	no	—
46	C₄⋊C₄×D₁₃	—	4	2	no	—
47	C₄⋊C₄×D₁₃	—	4	2	no	—
48	C₄×D₅₂	—	2	1	no	—
49	C₄×D₅₂	—	2	1	no	—
50	C₄×D₅₂	—	4	2	no	—
51	C₄×D₅₂	—	4	2	no	—
52	C₄×D₅₂	C₂×C₄	1	2	yes	—
53	C₄×D₅₂	Q₈	1	2	yes	—
54	C₁₃×C₄⋊C₈	—	2	1	no	—
55	C₁₃×C₄⋊C₈	—	2	1	no	—
56	C₄×C₈×C₁₃	—	2	1	no	—
57	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
58	C₁₃×#95	—	2	1	no	—
59	#88071	—	2	2	no	—
60	#88061	—	4	2	no	—
61	#88048	—	4	2	no	—
62	C₄⋊#1055	—	2	1	no	—
63	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
64	#8894	—	13	1	no	maximal, Sylow
65	C₂³×D₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₃	—	2	1	no	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×Dic₁₃	—	2	1	no	—
72	C₂²×Dic₁₃	—	2	2	no	—
73	C₂²×Dic₁₃	—	4	1	no	—
74	C₂×D₅₂	—	2	1	no	—
75	C₂×D₅₂	—	2	1	no	—
76	C₂×D₅₂	—	2	1	no	—
77	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
78	C₂×D₅₂	SD₁₆	1	2	yes	—
79	C₂×D₅₂	SD₁₆	1	2	yes	—
80	C₂×C₄×D₁₃	—	2	2	no	—
81	C₂×C₄×D₁₃	—	2	2	no	—
82	C₂×C₄×D₁₃	—	4	1	no	—
83	C₂×C₄×D₁₃	—	4	1	no	—
84	C₂×C₄×D₁₃	—	4	1	no	—
85	C₂×C₄×D₁₃	—	4	1	no	—
86	C₂×C₄×D₁₃	—	4	4	no	—
87	C₂×C₄×D₁₃	—	4	4	no	—
88	C₂×C₄×D₁₃	—	8	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	4	1	no	—
91	C₂×C₈×C₁₃	—	4	1	no	—
92	C₂×C₈×C₁₃	—	4	1	no	—
93	C₂×C₈×C₁₃	—	4	1	no	—
94	C₂×C₈×C₁₃	—	4	1	no	—
95	C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
99	C₄²×C₁₃	—	4	1	no	—
100	C₄²×C₁₃	—	4	1	no	—
101	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₄²×C₁₃	#41	1	1	yes	characteristic
104	C₄²×C₁₃	#41	1	1	yes	characteristic
105	#6103	—	2	2	no	—
106	#6103	—	2	2	no	—
107	#6103	—	4	4	no	—
108	C₄⋊Dic₁₃	—	2	1	no	—
109	C₄⋊Dic₁₃	—	4	1	no	—
110	C₄⋊Dic₁₃	—	4	1	no	—
111	C₄⋊Dic₁₃	—	4	1	no	—
112	C₄⋊Dic₁₃	—	4	1	no	—
113	C₄⋊Dic₁₃	—	4	2	no	—
114	C₄⋊Dic₁₃	—	4	2	no	—
115	C₄⋊Dic₁₃	—	4	1	no	—
116	C₄⋊Dic₁₃	—	4	1	no	—
117	C₄⋊Dic₁₃	—	4	1	no	—
118	C₄⋊Dic₁₃	—	4	1	no	—
119	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
120	#6101	—	4	4	no	—
121	C₂×#1055	—	2	2	no	—
122	C₂×#1055	—	4	1	no	—
123	C₂×#1055	—	4	1	no	—
124	D₄×C₄⋊C₄	—	13	1	no	—
125	#1948	—	13	1	no	—
126	#1834	—	13	1	no	—
127	#1802	—	13	1	no	—
128	C₂×D₄⋊C₈	—	13	1	no	—
129	#1296	—	13	1	no	—
130	#1279	D₁₃	1	1	yes	characteristic, complemented
131	C₂³×C₁₃	#120	1	1	yes	characteristic
132	C₂²×D₁₃	—	2	2	no	—
133	C₂²×D₁₃	—	2	2	no	—
134	C₂²×D₁₃	—	2	2	no	—
135	C₂²×D₁₃	—	4	1	no	—
136	C₂²×D₁₃	—	4	1	no	—
137	C₂²×D₁₃	—	4	1	no	—
138	C₂²×D₁₃	—	4	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	4	1	no	—
143	C₂×C₄×C₁₃	—	4	1	no	—
144	C₂×C₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
157	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	4	1	no	—
163	C₂×Dic₁₃	—	4	1	no	—
164	C₂×Dic₁₃	—	4	2	no	—
165	C₂×Dic₁₃	—	4	2	no	—
166	C₂×Dic₁₃	—	4	2	no	—
167	C₂×Dic₁₃	—	8	1	no	—
168	C₂×Dic₁₃	—	8	1	no	—
169	C₂×Dic₁₃	—	8	1	no	—
170	D₅₂	—	2	2	no	—
171	D₅₂	—	2	2	no	—
172	D₅₂	—	2	2	no	—
173	D₅₂	#106	1	4	yes	complemented
174	C₄×D₁₃	—	4	2	no	—
175	C₄×D₁₃	—	4	2	no	—
176	C₄×D₁₃	—	4	2	no	—
177	C₄×D₁₃	—	4	2	no	—
178	C₄×D₁₃	—	8	8	no	—
179	C₈×C₁₃	—	4	2	no	—
180	C₈×C₁₃	—	8	1	no	—
181	#1055	—	4	2	no	—
182	C₂×C₄×D₄	—	13	1	no	—
183	C₂×C₄×D₄	—	26	1	no	—
184	C₂²×C₄⋊C₄	—	26	1	no	—
185	C₂×#106	—	26	1	no	—
186	C₂×C₄⋊C₈	—	13	1	no	—
187	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
188	C₂×#102	—	26	1	no	—
189	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
190	#389	—	26	1	no	—
191	#385	—	26	2	no	—
192	#384	—	13	1	no	—
193	#384	—	13	1	no	—
194	#380	—	26	1	no	—
195	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
196	#340	—	26	1	no	—
197	#340	—	26	2	no	—
198	#340	—	26	1	no	—
199	D₄⋊C₈	—	13	4	no	—
200	C₂²×C₁₃	#385	1	1	yes	characteristic
201	C₂²×C₁₃	#447	1	1	yes	characteristic
202	C₂²×C₁₃	#448	1	1	yes	characteristic
203	C₂²×C₁₃	#450	1	1	yes	characteristic
204	C₂²×C₁₃	#452	1	1	yes	characteristic
205	C₂²×C₁₃	#454	1	1	yes	characteristic
206	C₂²×C₁₃	#455	1	1	yes	characteristic
207	C₂×D₁₃	—	2	4	no	—
208	C₂×D₁₃	—	4	2	no	—
209	C₂×D₁₃	—	4	2	no	—
210	C₂×D₁₃	—	4	2	no	—
211	C₂×D₁₃	—	4	2	no	—
212	C₂×D₁₃	—	4	2	no	—
213	C₂×D₁₃	—	4	2	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	8	1	no	—
218	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
219	C₄×C₁₃	#428	1	1	yes	characteristic
220	C₄×C₁₃	C₄×D₈	1	1	yes	characteristic
221	C₄×C₁₃	#440	1	1	yes	characteristic
222	C₄×C₁₃	#474	1	1	yes	characteristic
223	C₄×C₁₃	#478	1	1	yes	characteristic
224	C₄×C₁₃	#481	1	1	yes	characteristic
225	C₄×C₁₃	#483	1	1	yes	characteristic
226	Dic₁₃	—	4	2	no	—
227	Dic₁₃	—	8	2	no	—
228	Dic₁₃	—	16	1	no	—
229	C₂²×D₄	—	13	1	no	—
230	C₂³×C₄	—	26	2	no	—
231	C₂³×C₄	—	26	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	26	1	no	—
235	C₄×D₄	—	13	2	no	—
236	C₄×D₄	—	13	2	no	—
237	C₄×D₄	—	26	1	no	—
238	C₄×D₄	—	26	1	no	—
239	C₄×D₄	—	52	2	no	—
240	C₄×D₄	—	52	2	no	—
241	C₂×C₄⋊C₄	—	13	1	no	—
242	C₂×C₄⋊C₄	—	13	2	no	—
243	C₂×C₄⋊C₄	—	26	2	no	—
244	C₂×C₄⋊C₄	—	26	1	no	—
245	C₂×C₄⋊C₄	—	26	1	no	—
246	C₂×C₄⋊C₄	—	26	1	no	—
247	C₂×C₄⋊C₄	—	26	1	no	—
248	C₂×C₄⋊C₄	—	26	1	no	—
249	C₂×C₄⋊C₄	—	52	2	no	—
250	C₂×C₄⋊C₄	—	52	2	no	—
251	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
252	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	26	1	no	—
254	C₂×C₂²⋊C₄	—	26	2	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
257	#106	—	52	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	13	2	no	—
261	C₄⋊C₈	—	26	1	no	—
262	#102	—	52	2	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	C₄×D₁₃	1	2	yes	complemented
265	#95	—	2	1	no	—
266	#95	—	26	2	no	—
267	C₂×C₁₃	#1627	1	1	yes	characteristic
268	C₂×C₁₃	#1635	1	1	yes	characteristic
269	C₂×C₁₃	#1639	1	1	yes	characteristic
270	C₂×C₁₃	#1643	1	1	yes	characteristic
271	C₂×C₁₃	#1853	1	1	yes	characteristic
272	C₂×C₁₃	#1860	1	1	yes	characteristic
273	C₂×C₁₃	#1862	1	1	yes	characteristic
274	D₁₃	—	4	4	no	—
275	C₂⁴	—	26	1	no	—
276	C₂×D₄	—	13	2	no	—
277	C₂×D₄	—	13	2	no	—
278	C₂×D₄	—	13	2	no	—
279	C₂×D₄	—	26	1	no	—
280	C₂×D₄	—	26	1	no	—
281	C₂×D₄	—	26	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	26	1	no	—
285	C₂²×C₄	—	26	2	no	—
286	C₂²×C₄	—	26	2	no	—
287	C₂²×C₄	—	26	2	no	—
288	C₂²×C₄	—	52	4	no	—
289	C₂²×C₄	—	52	4	no	—
290	C₂²×C₄	—	52	1	no	—
291	C₂²×C₄	—	52	1	no	—
292	C₂²×C₄	—	52	1	no	—
293	C₂²×C₄	—	52	1	no	—
294	C₂²×C₄	—	52	1	no	—
295	C₂²×C₄	—	104	2	no	—
296	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	26	2	no	—
306	C₂×C₈	—	52	1	no	—
307	C₂×C₈	—	52	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	13	2	no	—
312	C₄⋊C₄	—	26	1	no	—
313	C₄⋊C₄	—	52	2	no	—
314	C₄⋊C₄	—	52	4	no	—
315	C₄⋊C₄	—	52	2	no	—
316	C₄⋊C₄	—	52	1	no	—
317	C₄⋊C₄	—	52	1	no	—
318	C₄⋊C₄	—	52	1	no	—
319	C₄⋊C₄	—	52	1	no	—
320	C₄⋊C₄	—	52	1	no	—
321	C₄⋊C₄	—	52	1	no	—
322	C₄⋊C₄	—	52	1	no	—
323	C₄⋊C₄	—	52	1	no	—
324	C₄⋊C₄	D₁₀₄	1	2	yes	—
325	C₂²⋊C₄	—	26	2	no	—
326	C₂²⋊C₄	—	26	2	no	—
327	C₂²⋊C₄	—	52	4	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
331	C₄²	#6127	1	1	yes	characteristic
332	C₄²	#6129	1	1	yes	characteristic
333	C₄²	Q₈×D₁₃	1	1	yes	characteristic
334	C₁₃	#8894	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	26	2	no	—
336	C₂³	—	26	2	no	—
337	C₂³	—	26	2	no	—
338	C₂³	—	52	1	no	—
339	C₂³	—	52	1	no	—
340	C₂³	—	52	1	no	—
341	C₂³	—	52	1	no	—
342	C₂³	#88136	1	1	yes	characteristic
343	D₄	—	13	4	no	—
344	D₄	—	26	2	no	—
345	D₄	—	26	2	no	—
346	D₄	—	26	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	52	1	no	—
357	C₂×C₄	—	52	1	no	—
358	C₂×C₄	—	52	2	no	—
359	C₂×C₄	—	52	2	no	—
360	C₂×C₄	—	52	2	no	—
361	C₂×C₄	—	52	2	no	—
362	C₂×C₄	—	52	2	no	—
363	C₂×C₄	—	52	2	no	—
364	C₂×C₄	—	52	2	no	—
365	C₂×C₄	—	104	8	no	—
366	C₂×C₄	—	104	1	no	—
367	C₂×C₄	—	104	1	no	—
368	C₂×C₄	—	104	1	no	—
369	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
370	C₂×C₄	#88135	1	1	yes	characteristic
371	C₂×C₄	#88137	1	1	yes	characteristic
372	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
373	C₂×C₄	#88150	1	1	yes	characteristic
374	C₂×C₄	#88151	1	1	yes	characteristic
375	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
376	C₂×C₄	#88158	1	1	yes	characteristic
377	C₂×C₄	#88162	1	1	yes	characteristic
378	C₂×C₄	#88163	1	1	yes	characteristic
379	C₂×C₄	#88165	1	1	yes	characteristic
380	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
381	C₂×C₄	SD₁₆×D₁₃	1	1	yes	characteristic
382	C₂×C₄	#88172	1	1	yes	characteristic
383	C₈	—	4	2	no	—
384	C₈	—	8	1	no	—
385	C₈	—	52	2	no	—
386	C₂²	—	26	4	no	—
387	C₂²	—	52	2	no	—
388	C₂²	—	52	2	no	—
389	C₂²	—	52	2	no	—
390	C₂²	—	52	2	no	—
391	C₂²	—	52	2	no	—
392	C₂²	—	52	2	no	—
393	C₂²	#11718329	1	1	yes	characteristic
394	C₂²	#11718393	1	1	yes	characteristic
395	C₂²	#11718394	1	1	yes	characteristic
396	C₂²	#11718437	1	1	yes	characteristic
397	C₂²	#11718467	1	1	yes	characteristic
398	C₂²	#11718486	1	1	yes	characteristic
399	C₂²	#11718488	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	52	2	no	—
405	C₄	—	104	2	no	—
406	C₄	—	208	1	no	—
407	C₄	C₄×D₁₀₄	1	1	yes	characteristic
408	C₄	#11718371	1	1	yes	characteristic
409	C₄	#11718438	1	1	yes	characteristic
410	C₄	#11718466	1	1	yes	characteristic
411	C₄	#11718507	1	1	yes	characteristic
412	C₄	#11718508	1	1	yes	characteristic
413	C₄	D₁₃×#106	1	1	yes	characteristic
414	C₄	#11718542	1	1	yes	characteristic
415	C₂	—	52	4	no	—
416	C₂	#13113941	1	1	yes	characteristic
417	C₂	#13113990	1	1	yes	characteristic
418	C₂	#13114017	1	1	yes	characteristic
419	C₂	#13114046	1	1	yes	characteristic
420	C₂	#13115030	1	1	yes	characteristic
421	C₂	#13115070	1	1	yes	characteristic
422	C₂	#13115086	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88136
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1279	C₂
socle	C₂³×C₁₃	#120
prime radical	C₂²×D₅₂	D₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1279	D₁₃
hypocenter	C₁₃	#8894
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #13115599	C₂	semidirect
3. #13114964	C₂	semidirect
6. #13112720	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
25. #11718051	C₄	semidirect
57. C₄×C₈×C₁₃	C₂×C₄	semidirect
63. C₄⋊#1055	C₂×C₄	semidirect
130. #1279	D₁₃	semidirect
173. D₅₂	#106	semidirect
264. C₄×C₈	C₄×D₁₃	semidirect
334. C₁₃	#8894	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₄×D₅₂	2
#13115599	2
#13114964	2
#13114837	2
C₂×#11718051	2
#13112720	2
C₁₃×#1279	2
#8894	13