Subgroups — D₁₃×#1772 #15860923

Order 3328.

1102 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	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#405	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	#13114718	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114717	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114716	C₂	1	2	yes	maximal, complemented
8	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114714	C₂	1	2	yes	maximal, complemented
10	D₁₃×#339	C₂	1	2	yes	maximal
11	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
18	C₁₃×#427	C₂²	1	1	yes	characteristic
19	C₁₃×#405	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×#88062	C₂²	1	2	yes	—
22	#11718783	C₂²	1	2	yes	—
23	C₂×#88059	C₂²	1	1	yes	characteristic
24	#11718767	C₂²	1	1	yes	characteristic
25	#11718762	C₂²	1	2	yes	—
26	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	#11718659	C₂²	1	2	yes	—
29	#11718658	C₂²	1	2	yes	—
30	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
31	D₁₃×#108	C₄	1	8	yes	complemented
32	#11718541	C₄	1	2	yes	complemented
33	D₁₃×#107	C₄	1	2	yes	complemented
34	#11718521	C₄	1	2	yes	complemented
35	D₁₃×#106	C₄	1	2	yes	complemented
36	#11718369	—	2	2	no	—
37	D₁₃×#97	—	2	2	no	—
38	#11718350	—	2	2	no	—
39	C₄×C₈×D₁₃	—	2	2	no	—
40	C₄×C₈×D₁₃	C₄	1	8	yes	complemented
41	C₁₃×#339	C₂²	1	2	yes	—
42	#11718147	C₂²	1	2	yes	—
43	#11718124	C₂²	1	2	yes	—
44	#11718115	C₂²	1	2	yes	—
45	C₂²×C₄×D₁₃	—	2	1	no	—
46	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#117	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	#88180	C₂³	1	2	yes	—
53	C₂×C₄×Dic₁₃	—	2	1	no	—
54	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
55	C₂×#6099	C₂³	1	2	yes	—
56	C₂²×#1055	C₂³	1	1	yes	characteristic
57	C₂²×#1055	C₂³	1	1	yes	characteristic
58	M₁₆×D₁₃	—	2	4	no	—
59	M₁₆×D₁₃	C₂×C₄	1	8	yes	—
60	C₂×#6094	—	2	2	no	—
61	C₂×C₈×D₁₃	—	2	2	no	—
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
67	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
68	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
69	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
71	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
72	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
73	C₂×C₈×D₁₃	Q₈	1	4	yes	—
74	#88146	C₂×C₄	1	4	yes	—
75	C₄⋊C₄×D₁₃	C₂×C₄	1	4	yes	—
76	C₂²⋊C₄×D₁₃	—	2	2	no	—
77	#88131	—	2	2	no	—
78	#88126	—	2	2	no	—
79	C₄²×D₁₃	—	2	2	no	—
80	C₄²×D₁₃	—	2	2	no	—
81	C₄²×D₁₃	C₂×C₄	1	4	yes	—
82	C₁₃×#108	C₂×C₄	1	4	yes	complemented
83	C₁₃×#107	C₂×C₄	1	2	yes	complemented
84	C₁₃×#106	C₂×C₄	1	2	yes	complemented
85	C₁₃×#97	—	2	2	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
88	#88062	C₂×C₄	1	8	yes	complemented
89	#88059	C₂×C₄	1	4	yes	complemented
90	#88058	C₂×C₄	1	2	yes	complemented
91	#88057	C₂×C₄	1	2	yes	complemented
92	#88055	—	2	2	no	—
93	#88055	—	2	2	no	—
94	C₈×Dic₁₃	—	2	2	no	—
95	C₈×Dic₁₃	—	2	2	no	—
96	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
97	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
98	#88048	C₂×C₄	1	4	yes	complemented
99	#88047	C₂×C₄	1	4	yes	complemented
100	#88043	—	2	2	no	—
101	C₄×#1055	—	2	2	no	—
102	C₄×#1055	C₂×C₄	1	4	yes	complemented
103	C₂×#1772	—	13	1	no	maximal, Sylow
104	C₂³×D₁₃	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₁₃	—	2	1	no	—
108	C₂²×Dic₁₃	#41	1	1	yes	characteristic
109	C₂×C₄×D₁₃	—	2	8	no	—
110	C₂×C₄×D₁₃	—	2	4	no	—
111	C₂×C₄×D₁₃	—	2	4	no	—
112	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
119	C₂×C₄×D₁₃	#41	1	2	yes	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂²⋊Dic₁₃	—	2	2	no	—
137	#6103	—	2	4	no	—
138	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
139	#6101	—	2	4	no	—
140	C₄×Dic₁₃	—	2	2	no	—
141	C₄×Dic₁₃	—	2	1	no	—
142	C₄×Dic₁₃	—	2	4	no	—
143	C₄×Dic₁₃	—	2	4	no	—
144	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
145	#6099	—	2	2	no	—
146	#6099	C₂²×C₄	1	4	yes	—
147	C₂×#1055	—	2	2	no	—
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
150	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
151	C₂×#1055	C₂²×C₄	1	2	yes	—
152	C₂×#1055	C₂²×C₄	1	2	yes	—
153	C₂×#1055	C₂×D₄	1	1	yes	characteristic
154	C₂×#1055	C₂×D₄	1	1	yes	characteristic
155	C₂×#1055	C₂×Q₈	1	2	yes	—
156	#6094	—	2	8	no	—
157	C₈×D₁₃	—	2	8	no	—
158	C₈×D₁₃	C₄²	1	4	yes	—
159	C₈×D₁₃	C₄²	1	4	yes	—
160	C₈×D₁₃	C₄²	1	4	yes	—
161	C₈×D₁₃	C₄²	1	4	yes	—
162	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
163	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
164	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
165	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
166	C₂²×#108	—	13	1	no	—
167	C₂×#427	—	13	1	no	—
168	C₂×#405	—	13	2	no	—
169	C₂²×C₄×C₈	—	13	1	no	—
170	#1772	—	13	1	no	—
171	#1772	—	13	1	no	—
172	#1772	—	13	2	no	—
173	#1772	—	13	1	no	—
174	#1772	—	13	2	no	—
175	#1772	D₁₃	1	1	yes	characteristic, direct product factor
176	C₂×#339	—	13	2	no	—
177	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₂²×D₁₃	—	2	4	no	—
179	C₂²×D₁₃	#117	1	2	yes	—
180	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
181	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
182	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×Dic₁₃	—	2	4	no	—
193	C₂×Dic₁₃	—	2	2	no	—
194	C₂×Dic₁₃	—	2	4	no	—
195	C₂×Dic₁₃	#117	1	2	yes	—
196	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
199	C₄×D₁₃	—	2	16	no	—
200	C₄×D₁₃	—	4	8	no	—
201	C₄×D₁₃	C₂×C₄²	1	2	yes	—
202	C₄×D₁₃	C₂×C₄²	1	2	yes	—
203	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₄×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
205	C₄×D₁₃	C₄×D₄	1	2	yes	—
206	C₄×D₁₃	C₄×D₄	1	2	yes	—
207	C₄×D₁₃	C₄×Q₈	1	2	yes	—
208	C₄×D₁₃	C₄×Q₈	1	2	yes	—
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	C₂×C₄²	1	2	yes	—
211	C₈×C₁₃	C₂×C₄²	1	2	yes	—
212	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
213	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
214	#1055	—	2	4	no	—
215	#1055	C₂×C₄²	1	2	yes	—
216	#1055	C₂×C₄²	1	2	yes	—
217	#1055	C₂×C₄⋊C₄	1	2	yes	—
218	#1055	C₂×C₄⋊C₄	1	2	yes	—
219	C₂²×M₁₆	—	13	2	no	—
220	C₂³×C₈	—	13	1	no	—
221	C₂³×C₈	—	13	1	no	—
222	C₂×#117	—	13	2	no	—
223	C₂²×C₄²	—	13	1	no	—
224	C₂×#108	—	13	2	no	—
225	C₂×#108	—	13	1	no	—
226	C₂×#108	—	13	8	no	—
227	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
228	#427	—	13	1	no	—
229	#427	—	13	2	no	—
230	#427	—	13	2	no	—
231	#427	—	13	2	no	—
232	#427	C₂×D₁₃	1	1	yes	characteristic
233	C₂×#107	—	13	2	no	—
234	C₂×#106	—	13	2	no	—
235	#405	—	13	2	no	—
236	#405	—	13	2	no	—
237	#405	—	13	2	no	—
238	#405	—	26	2	no	—
239	#405	—	26	2	no	—
240	#405	C₂×D₁₃	1	2	yes	—
241	C₂×#97	—	26	2	no	—
242	C₂×C₄×C₈	—	13	1	no	—
243	C₂×C₄×C₈	—	13	1	no	—
244	C₂×C₄×C₈	—	13	1	no	—
245	C₂×C₄×C₈	—	13	8	no	—
246	C₂×C₄×C₈	—	26	2	no	—
247	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
248	#339	—	13	2	no	—
249	#339	—	13	2	no	—
250	#339	—	13	2	no	—
251	#339	C₂×D₁₃	1	2	yes	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
256	C₂×D₁₃	—	2	2	no	—
257	C₂×D₁₃	—	2	4	no	—
258	C₂×D₁₃	—	2	4	no	—
259	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
260	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
261	C₂×D₁₃	#443	1	4	yes	—
262	C₄×C₁₃	—	2	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
265	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
268	Dic₁₃	—	2	4	no	—
269	Dic₁₃	—	4	4	no	—
270	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
271	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
272	C₂³×C₄	—	13	1	no	—
273	C₂³×C₄	—	26	1	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	13	8	no	—
276	C₂×M₁₆	—	26	2	no	—
277	C₂×M₁₆	—	26	4	no	—
278	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	13	1	no	—
281	C₂²×C₈	—	13	4	no	—
282	C₂²×C₈	—	13	4	no	—
283	C₂²×C₈	—	13	1	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	13	1	no	—
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	4	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	13	1	no	—
291	C₂²×C₈	—	13	1	no	—
292	C₂²×C₈	—	13	4	no	—
293	C₂²×C₈	—	26	2	no	—
294	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
296	#117	—	13	2	no	—
297	#117	—	13	4	no	—
298	#117	—	26	2	no	—
299	#117	—	26	2	no	—
300	#117	C₂²×D₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	—	13	4	no	—
302	C₂×C₂²⋊C₄	—	26	2	no	—
303	C₂×C₄²	—	13	1	no	—
304	C₂×C₄²	—	13	4	no	—
305	C₂×C₄²	—	26	2	no	—
306	C₂×C₄²	—	26	2	no	—
307	C₂×C₄²	—	26	1	no	—
308	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
309	#108	—	13	8	no	—
310	#108	—	13	4	no	—
311	#108	C₄×D₁₃	1	4	yes	complemented
312	#107	—	13	2	no	—
313	#107	—	13	4	no	—
314	#107	C₄×D₁₃	1	2	yes	complemented
315	#106	—	13	2	no	—
316	#106	—	13	4	no	—
317	#106	C₄×D₁₃	1	2	yes	complemented
318	#97	—	2	2	no	—
319	#97	—	26	2	no	—
320	#97	—	26	2	no	—
321	#97	—	26	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	13	4	no	—
324	C₄×C₈	—	13	4	no	—
325	C₄×C₈	—	13	4	no	—
326	C₄×C₈	—	26	2	no	—
327	C₄×C₈	—	26	2	no	—
328	C₄×C₈	—	26	2	no	—
329	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
330	C₂×C₁₃	—	2	1	no	—
331	C₂×C₁₃	—	2	1	no	—
332	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₁₃	C₂×#443	1	2	yes	—
334	D₁₃	—	2	2	no	—
335	D₁₃	#1772	1	4	yes	direct product factor
336	C₂⁴	—	13	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	2	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	2	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	1	no	—
345	C₂²×C₄	—	13	2	no	—
346	C₂²×C₄	—	13	2	no	—
347	C₂²×C₄	—	26	4	no	—
348	C₂²×C₄	—	26	8	no	—
349	C₂²×C₄	—	26	4	no	—
350	C₂²×C₄	—	26	1	no	—
351	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
352	M₁₆	—	2	2	no	—
353	M₁₆	—	13	4	no	—
354	M₁₆	—	26	8	no	—
355	M₁₆	—	26	2	no	—
356	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	13	2	no	—
360	C₂×C₈	—	13	1	no	—
361	C₂×C₈	—	13	1	no	—
362	C₂×C₈	—	13	2	no	—
363	C₂×C₈	—	13	1	no	—
364	C₂×C₈	—	13	1	no	—
365	C₂×C₈	—	13	2	no	—
366	C₂×C₈	—	13	4	no	—
367	C₂×C₈	—	13	4	no	—
368	C₂×C₈	—	13	4	no	—
369	C₂×C₈	—	13	4	no	—
370	C₂×C₈	—	13	4	no	—
371	C₂×C₈	—	13	4	no	—
372	C₂×C₈	—	13	4	no	—
373	C₂×C₈	—	13	4	no	—
374	C₂×C₈	—	26	8	no	—
375	C₂×C₈	—	26	2	no	—
376	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
377	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
380	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
381	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
382	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
383	C₂×C₈	Q₈×D₁₃	1	2	yes	—
384	C₄⋊C₄	—	13	4	no	—
385	C₄⋊C₄	—	26	4	no	—
386	C₄⋊C₄	C₂×C₄×D₁₃	1	4	yes	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	26	4	no	—
389	C₂²⋊C₄	—	26	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	13	2	no	—
393	C₄²	—	26	4	no	—
394	C₄²	—	26	4	no	—
395	C₄²	—	26	2	no	—
396	C₄²	—	26	1	no	—
397	C₄²	C₂×C₄×D₁₃	1	2	yes	—
398	C₁₃	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
399	C₂³	—	13	1	no	—
400	C₂³	—	13	2	no	—
401	C₂³	—	13	1	no	—
402	C₂³	—	13	2	no	—
403	C₂³	—	26	4	no	—
404	C₂³	#41×D₁₃	1	1	yes	characteristic
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	13	2	no	—
409	C₂×C₄	—	13	1	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	13	2	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	2	no	—
414	C₂×C₄	—	13	2	no	—
415	C₂×C₄	—	13	2	no	—
416	C₂×C₄	—	13	2	no	—
417	C₂×C₄	—	13	2	no	—
418	C₂×C₄	—	13	2	no	—
419	C₂×C₄	—	13	2	no	—
420	C₂×C₄	—	26	16	no	—
421	C₂×C₄	—	26	4	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	4	no	—
424	C₂×C₄	—	52	8	no	—
425	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
430	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	—	13	2	no	—
433	C₈	—	13	2	no	—
434	C₈	—	13	2	no	—
435	C₈	—	13	2	no	—
436	C₈	—	26	4	no	—
437	C₈	C₄²×D₁₃	1	2	yes	—
438	C₈	C₄²×D₁₃	1	2	yes	—
439	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
440	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
441	C₂²	—	2	2	no	—
442	C₂²	—	13	4	no	—
443	C₂²	—	13	2	no	—
444	C₂²	—	13	2	no	—
445	C₂²	—	26	4	no	—
446	C₂²	—	26	4	no	—
447	C₂²	—	26	2	no	—
448	C₂²	D₁₃×#117	1	1	yes	characteristic
449	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
450	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	4	4	no	—
453	C₄	—	13	2	no	—
454	C₄	—	13	2	no	—
455	C₄	—	26	4	no	—
456	C₄	—	52	4	no	—
457	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
458	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
459	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
460	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	13	4	no	—
464	C₂	—	26	2	no	—
465	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
466	C₂	D₁₃×#443	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1772	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1772	D₁₃
hypocenter	C₁₃	C₂×#1772
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #13114718	C₂	semidirect
6. #13114717	C₂	semidirect
7. #13114716	C₂	semidirect
8. #13114715	C₂	semidirect
9. #13114714	C₂	semidirect
11. C₁₃×#1772	C₂	semidirect
31. D₁₃×#108	C₄	semidirect
32. #11718541	C₄	semidirect
33. D₁₃×#107	C₄	semidirect
34. #11718521	C₄	semidirect
35. D₁₃×#106	C₄	semidirect
40. C₄×C₈×D₁₃	C₄	semidirect
82. C₁₃×#108	C₂×C₄	semidirect
83. C₁₃×#107	C₂×C₄	semidirect
84. C₁₃×#106	C₂×C₄	semidirect
87. C₄×C₈×C₁₃	C₂×C₄	semidirect
88. #88062	C₂×C₄	semidirect
89. #88059	C₂×C₄	semidirect
90. #88058	C₂×C₄	semidirect
91. #88057	C₂×C₄	semidirect
96. C₈×Dic₁₃	C₂×C₄	semidirect
97. C₈×Dic₁₃	C₂×C₄	semidirect
98. #88048	C₂×C₄	semidirect
99. #88047	C₂×C₄	semidirect
102. C₄×#1055	C₂×C₄	semidirect
175. #1772	D₁₃	direct (N × H)
311. #108	C₄×D₁₃	semidirect
314. #107	C₄×D₁₃	semidirect
317. #106	C₄×D₁₃	semidirect
329. C₄×C₈	C₄×D₁₃	semidirect
335. D₁₃	#1772	direct (N × H)
398. C₁₃	C₂×#1772	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×#108	2
D₁₃×#427	2
D₁₃×#405	2
C₂×C₄×C₈×D₁₃	2
#13114718	2
#13114717	2
#13114716	2
#13114715	2
#13114714	2
D₁₃×#339	2
C₁₃×#1772	2
C₂×#1772	13

Subgroups — D13×#1772 #15860923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1772 #15860923