Subgroups — #15861375

Order 3328.

1274 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718495	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₃×#97	C₂	1	2	yes	maximal, complemented
4	C₄×#88147	C₂	1	1	yes	maximal, characteristic
5	#13114705	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114691	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114613	C₂	1	2	yes	maximal, complemented
8	#13114611	C₂	1	2	yes	maximal, complemented
9	#13114597	C₂	1	2	yes	maximal, complemented
10	C₄×#88055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
13	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
14	C₂×#88147	C₄	1	2	yes	—
15	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₁₃	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×#88060	C₂²	1	2	yes	—
22	C₂×#88060	C₂²	1	2	yes	—
23	C₂×#88055	C₂²	1	2	yes	—
24	C₂×#88055	C₂²	1	1	yes	characteristic
25	C₂×#88055	C₂²	1	1	yes	characteristic
26	C₂×#88055	C₂²	1	1	yes	characteristic
27	C₂×#88055	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×Dic₁₃	C₄	1	2	yes	—
29	C₄×#6103	C₂²	1	2	yes	—
30	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
32	C₂×#88043	C₂²	1	2	yes	—
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	#11718495	C₄	1	8	yes	complemented
35	D₁₃×#97	—	2	8	no	—
36	C₈×D₅₂	C₄	1	8	yes	complemented
37	#11718327	C₄	1	4	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	#11718142	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂×C₄	1	4	yes	—
43	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×#6103	C₂×C₄	1	4	yes	—
51	C₂×#6103	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
58	C₂²×#1055	C₂³	1	2	yes	—
59	C₂²×#1055	C₂³	1	1	yes	characteristic
60	C₂²×#1055	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₁₃	—	2	4	no	—
62	C₂×C₈×D₁₃	—	2	4	no	—
63	C₂×C₈×D₁₃	—	2	4	no	—
64	C₂×C₈×D₁₃	—	2	4	no	—
65	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	complemented
66	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	complemented
67	#88147	—	2	8	no	—
68	C₄×D₅₂	C₂×C₄	1	4	yes	—
69	C₄×D₅₂	C₂×C₄	1	4	yes	—
70	C₄²×D₁₃	—	2	4	no	—
71	C₄²×D₁₃	—	2	4	no	—
72	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
73	C₁₃×#97	—	2	4	no	—
74	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
75	C₁₃×#95	C₂×C₄	1	2	yes	—
76	#88071	C₂×C₄	1	4	yes	—
77	#88060	C₂×C₄	1	8	yes	complemented
78	#88060	C₂×C₄	1	8	yes	complemented
79	#88055	—	2	2	no	—
80	#88055	—	2	4	no	—
81	#88055	—	2	2	no	—
82	#88055	—	2	2	no	—
83	#88055	D₄	1	4	yes	complemented
84	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
85	#88043	—	2	4	no	—
86	C₄×#1055	C₂×C₄	1	4	yes	complemented
87	D₄×#97	—	13	1	no	maximal, Sylow
88	C₂³×D₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
96	C₂×D₅₂	C₄²	1	4	yes	—
97	C₂×D₅₂	M₁₆	1	8	yes	—
98	C₂×C₄×D₁₃	—	2	2	no	—
99	C₂×C₄×D₁₃	—	2	2	no	—
100	C₂×C₄×D₁₃	—	2	2	no	—
101	C₂×C₄×D₁₃	—	2	2	no	—
102	C₂×C₄×D₁₃	—	2	8	no	—
103	C₂×C₄×D₁₃	—	2	8	no	—
104	C₂×C₄×D₁₃	—	4	4	no	—
105	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
121	#6103	—	2	8	no	—
122	#6103	C₄²	1	8	yes	—
123	C₄⋊Dic₁₃	C₄²	1	4	yes	—
124	C₄×Dic₁₃	—	2	4	no	—
125	C₄×Dic₁₃	—	2	1	no	—
126	C₄×Dic₁₃	—	2	1	no	—
127	C₄×Dic₁₃	—	2	8	no	—
128	C₄×Dic₁₃	—	4	2	no	—
129	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
130	C₄×Dic₁₃	#41	1	2	yes	—
131	C₂×#1055	—	2	2	no	—
132	C₂×#1055	—	2	2	no	—
133	C₂×#1055	—	2	1	no	—
134	C₂×#1055	—	2	1	no	—
135	C₂×#1055	C₂²×C₄	1	4	yes	—
136	C₂×#1055	C₂²×C₄	1	2	yes	—
137	C₂×#1055	C₂²×C₄	1	2	yes	—
138	C₂×#1055	C₂×D₄	1	2	yes	—
139	C₂×#1055	#41	1	2	yes	—
140	C₈×D₁₃	—	2	16	no	—
141	C₈×D₁₃	—	2	16	no	—
142	C₂×C₈×D₄	—	13	1	no	—
143	C₂×C₈×D₄	—	13	1	no	—
144	C₂²×#97	—	13	2	no	—
145	C₄²×D₄	—	13	1	no	—
146	#1770	—	13	1	no	—
147	#1770	D₁₃	1	1	yes	characteristic, complemented
148	#1767	—	13	1	no	—
149	#1752	—	13	2	no	—
150	#1752	—	13	2	no	—
151	#1749	—	13	2	no	—
152	C₄×#97	—	13	1	no	—
153	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
154	C₂²×D₁₃	—	2	2	no	—
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	—	2	4	no	—
157	C₂²×D₁₃	C₂×C₄²	1	4	yes	—
158	C₂²×D₁₃	C₂×M₁₆	1	8	yes	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	2	2	no	—
175	C₂×Dic₁₃	—	2	2	no	—
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
180	C₂×Dic₁₃	C₄×D₄	1	4	yes	—
181	D₅₂	#97	1	16	yes	complemented
182	C₄×D₁₃	—	2	4	no	—
183	C₄×D₁₃	—	2	4	no	—
184	C₄×D₁₃	—	2	4	no	—
185	C₄×D₁₃	—	2	4	no	—
186	C₄×D₁₃	—	4	16	no	—
187	C₈×C₁₃	—	2	4	no	—
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	C₄×D₄	1	4	yes	complemented
190	#1055	—	2	4	no	—
191	#1055	—	2	2	no	—
192	#1055	C₄×D₄	1	4	yes	complemented
193	C₂³×C₈	—	13	2	no	—
194	C₂³×C₈	—	13	2	no	—
195	C₂×C₄×D₄	—	13	2	no	—
196	C₂×C₄×D₄	—	13	1	no	—
197	C₂²×C₄²	—	13	2	no	—
198	C₈×D₄	—	13	8	no	—
199	C₈×D₄	—	13	8	no	—
200	C₂×C₄⋊C₈	—	13	1	no	—
201	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	—	13	2	no	—
203	C₂×C₂²⋊C₈	—	13	2	no	—
204	C₂×#97	—	13	1	no	—
205	C₂×#97	—	13	2	no	—
206	C₂×#97	—	13	1	no	—
207	C₂×#97	—	13	1	no	—
208	C₂×#97	—	13	1	no	—
209	C₂×#97	—	13	2	no	—
210	C₂×#97	—	26	8	no	—
211	C₂×#97	C₂×D₁₃	1	2	yes	—
212	C₂×C₄×C₈	—	13	1	no	—
213	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
214	C₄×C₄⋊C₄	—	13	2	no	—
215	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
216	C₄×C₂²⋊C₄	—	13	2	no	—
217	C₄×C₂²⋊C₄	—	13	4	no	—
218	C₄³	—	13	1	no	—
219	#336	—	13	2	no	—
220	#336	—	13	2	no	—
221	#336	C₂×D₁₃	1	2	yes	—
222	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
223	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
225	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
226	C₂²×C₁₃	#568	1	2	yes	—
227	C₂×D₁₃	—	2	4	no	—
228	C₂×D₁₃	—	2	8	no	—
229	C₂×D₁₃	—	2	8	no	—
230	C₂×D₁₃	—	2	4	no	—
231	C₂×D₁₃	C₂×#97	1	8	yes	complemented
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	4	4	no	—
234	C₄×C₁₃	C₂×#97	1	4	yes	complemented
235	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
237	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
238	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
239	Dic₁₃	—	2	4	no	—
240	Dic₁₃	—	2	4	no	—
241	Dic₁₃	—	4	2	no	—
242	C₂²×D₄	—	13	1	no	—
243	C₂³×C₄	—	13	2	no	—
244	C₂³×C₄	—	13	4	no	—
245	C₂²×C₈	—	13	1	no	—
246	C₂²×C₈	—	13	2	no	—
247	C₂²×C₈	—	13	1	no	—
248	C₂²×C₈	—	13	8	no	—
249	C₂²×C₈	—	13	8	no	—
250	C₂²×C₈	—	26	4	no	—
251	C₂²×C₈	—	26	4	no	—
252	C₂²×C₈	—	26	4	no	—
253	C₂²×C₈	—	26	4	no	—
254	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
255	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
257	C₄×D₄	—	13	4	no	—
258	C₄×D₄	—	13	4	no	—
259	C₄×D₄	—	26	8	no	—
260	C₂×C₄⋊C₄	—	13	1	no	—
261	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	—	13	2	no	—
263	C₂×C₂²⋊C₄	—	13	4	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	2	no	—
266	C₂×C₄²	—	13	4	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	2	no	—
269	C₂×C₄²	—	26	4	no	—
270	C₂×C₄²	—	26	4	no	—
271	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
272	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
273	C₄⋊C₈	—	13	4	no	—
274	C₄⋊C₈	C₄×D₁₃	1	4	yes	complemented
275	C₂²⋊C₈	—	13	8	no	—
276	C₂²⋊C₈	—	13	8	no	—
277	#97	—	2	4	no	—
278	#97	—	13	4	no	—
279	#97	—	26	4	no	—
280	#97	—	26	4	no	—
281	#97	—	26	2	no	—
282	#97	—	26	2	no	—
283	#97	—	26	2	no	—
284	C₄×C₈	—	13	4	no	—
285	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
286	#95	—	13	4	no	—
287	#95	C₄×D₁₃	1	2	yes	—
288	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
289	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
290	C₂×C₁₃	#2875	1	1	yes	characteristic
291	C₂×C₁₃	D₄×M₁₆	1	2	yes	—
292	C₂×C₁₃	#2970	1	2	yes	—
293	D₁₃	—	2	8	no	—
294	C₂⁴	—	13	2	no	—
295	C₂×D₄	—	13	4	no	—
296	C₂×D₄	—	13	8	no	—
297	C₂²×C₄	—	13	2	no	—
298	C₂²×C₄	—	13	2	no	—
299	C₂²×C₄	—	13	4	no	—
300	C₂²×C₄	—	13	4	no	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	26	8	no	—
303	C₂²×C₄	—	26	8	no	—
304	C₂²×C₄	—	26	2	no	—
305	C₂²×C₄	—	26	2	no	—
306	C₂²×C₄	—	26	2	no	—
307	C₂²×C₄	—	26	2	no	—
308	C₂²×C₄	—	52	4	no	—
309	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
310	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	13	2	no	—
318	C₂×C₈	—	13	2	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	4	no	—
322	C₂×C₈	—	26	16	no	—
323	C₂×C₈	—	26	2	no	—
324	C₂×C₈	—	26	1	no	—
325	C₂×C₈	—	26	2	no	—
326	C₂×C₈	—	26	1	no	—
327	C₂×C₈	—	26	16	no	—
328	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
329	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
330	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
331	C₂×C₈	D₄×D₁₃	1	2	yes	—
332	C₂×C₈	#6131	1	2	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	13	4	no	—
335	C₂²⋊C₄	—	13	8	no	—
336	C₂²⋊C₄	—	26	8	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	13	2	no	—
340	C₄²	—	13	2	no	—
341	C₄²	—	26	8	no	—
342	C₄²	—	26	4	no	—
343	C₄²	—	26	1	no	—
344	C₄²	—	26	1	no	—
345	C₄²	—	52	2	no	—
346	C₄²	C₂×C₄×D₁₃	1	2	yes	—
347	C₄²	C₂×C₄×D₁₃	1	2	yes	—
348	C₁₃	D₄×#97	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	13	4	no	—
350	C₂³	—	13	8	no	—
351	C₂³	—	26	4	no	—
352	C₂³	—	26	2	no	—
353	C₂³	—	26	2	no	—
354	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
355	D₄	—	13	16	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	13	4	no	—
361	C₂×C₄	—	13	4	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	4	no	—
367	C₂×C₄	—	26	4	no	—
368	C₂×C₄	—	26	4	no	—
369	C₂×C₄	—	26	4	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	52	16	no	—
374	C₂×C₄	C₄²×D₁₃	1	2	yes	—
375	C₂×C₄	C₄²×D₁₃	1	2	yes	—
376	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
377	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂×#6131	1	1	yes	characteristic
381	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
382	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	4	no	—
385	C₈	—	13	4	no	—
386	C₈	—	26	4	no	—
387	C₈	—	26	2	no	—
388	C₈	#88147	1	4	yes	complemented
389	C₂²	—	13	8	no	—
390	C₂²	—	26	8	no	—
391	C₂²	—	26	4	no	—
392	C₂²	—	26	8	no	—
393	C₂²	—	26	4	no	—
394	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
396	C₂²	C₄×#6131	1	1	yes	characteristic
397	C₂²	C₂×M₁₆×D₁₃	1	2	yes	—
398	C₂²	#11719455	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	4	4	no	—
401	C₄	—	26	4	no	—
402	C₄	—	26	4	no	—
403	C₄	—	52	2	no	—
404	C₄	D₁₃×#97	1	4	yes	complemented
405	C₄	C₂×#88147	1	1	yes	characteristic
406	C₄	#11719227	1	1	yes	characteristic
407	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
408	C₄	C₄×#6131	1	1	yes	characteristic
409	C₂	—	26	8	no	—
410	C₂	C₄×#88147	1	1	yes	characteristic
411	C₂	C₂×D₁₃×#97	1	1	yes	characteristic
412	C₂	#13123263	1	1	yes	characteristic
413	C₂	#13123572	1	2	yes	—
414	C₂	#13123849	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1770	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₅₂	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1770	D₁₃
hypocenter	C₁₃	D₄×#97
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
3. C₂×D₁₃×#97	C₂	semidirect
5. #13114705	C₂	semidirect
6. #13114691	C₂	semidirect
7. #13114613	C₂	semidirect
8. #13114611	C₂	semidirect
9. #13114597	C₂	semidirect
10. C₄×#88055	C₂	semidirect
11. C₁₃×#1770	C₂	semidirect
34. #11718495	C₄	semidirect
36. C₈×D₅₂	C₄	semidirect
65. C₂×C₈×D₁₃	C₂×C₄	semidirect
66. C₂×C₈×D₁₃	C₂×C₄	semidirect
72. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
74. C₄×C₈×C₁₃	C₂×C₄	semidirect
77. #88060	C₂×C₄	semidirect
78. #88060	C₂×C₄	semidirect
83. #88055	D₄	semidirect
84. C₄⋊#1055	C₂×C₄	semidirect
86. C₄×#1055	C₂×C₄	semidirect
147. #1770	D₁₃	semidirect
181. D₅₂	#97	semidirect
189. C₈×C₁₃	C₄×D₄	semidirect
192. #1055	C₄×D₄	semidirect
231. C₂×D₁₃	C₂×#97	semidirect
234. C₄×C₁₃	C₂×#97	semidirect
274. C₄⋊C₈	C₄×D₁₃	semidirect
285. C₄×C₈	C₄×D₁₃	semidirect
348. C₁₃	D₄×#97	semidirect
388. C₈	#88147	semidirect
404. C₄	D₁₃×#97	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅₂	2
C₂×#11718495	2
C₂×D₁₃×#97	2
C₄×#88147	2
#13114705	2
#13114691	2
#13114613	2
#13114611	2
#13114597	2
C₄×#88055	2
C₁₃×#1770	2
D₄×#97	13