Subgroups — D₁₃×#1833 #15863088

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 572 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	1	yes	maximal, characteristic
4	#13114961	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114960	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114959	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114958	C₂	1	2	yes	maximal, complemented
8	#13114957	C₂	1	2	yes	maximal, complemented
9	D₁₃×#344	C₂	1	2	yes	maximal
10	D₁₃×H(3,ℤ/4)	C₂	1	2	yes	maximal
11	C₁₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	D₁₃×#117	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	1	yes	characteristic
20	C₂×#88062	C₂²	1	2	yes	—
21	#11718783	C₂²	1	1	yes	characteristic
22	C₂×#88059	C₂²	1	1	yes	characteristic
23	#11718767	C₂²	1	1	yes	characteristic
24	#11718762	C₂²	1	1	yes	characteristic
25	#11718659	C₂²	1	2	yes	—
26	#11718658	C₂²	1	1	yes	characteristic
27	D₁₃×#108	—	2	1	no	—
28	D₁₃×#108	—	2	1	no	—
29	D₁₃×#108	—	2	1	no	—
30	D₁₃×#108	—	2	1	no	—
31	#11718541	—	2	1	no	—
32	D₁₃×#107	—	2	1	no	—
33	#11718521	—	2	1	no	—
34	D₁₃×#106	—	2	1	no	—
35	#11718369	C₄	1	2	yes	complemented
36	D₁₃×#97	C₄	1	2	yes	complemented
37	#11718350	C₄	1	2	yes	complemented
38	C₄×C₈×D₁₃	C₄	1	2	yes	complemented
39	C₁₃×#344	C₂²	1	2	yes	—
40	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	—
41	#11718151	C₂²	1	2	yes	—
42	#11718149	C₂²	1	2	yes	—
43	#11718148	C₂²	1	2	yes	—
44	#11718125	C₂²	1	2	yes	—
45	#11718123	C₂²	1	2	yes	—
46	#11718123	C₂²	1	2	yes	—
47	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
49	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#117	C₂³	1	2	yes	—
52	C₁₃×#117	C₂³	1	1	yes	characteristic
53	#88180	C₂³	1	2	yes	—
54	#88180	C₂³	1	1	yes	characteristic
55	C₂×#6099	C₂³	1	2	yes	—
56	C₂×#6099	C₂³	1	1	yes	characteristic
57	C₂²×#1055	C₂³	1	1	yes	characteristic
58	M₁₆×D₁₃	—	2	1	no	—
59	M₁₆×D₁₃	—	2	1	no	—
60	M₁₆×D₁₃	—	2	1	no	—
61	M₁₆×D₁₃	—	2	1	no	—
62	M₁₆×D₁₃	—	2	2	no	—
63	M₁₆×D₁₃	—	2	2	no	—
64	M₁₆×D₁₃	—	2	2	no	—
65	M₁₆×D₁₃	—	2	2	no	—
66	C₂×#6094	—	2	2	no	—
67	C₂×#6094	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₁₃	—	2	2	no	—
69	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
70	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
75	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
76	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
77	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
78	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
79	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
80	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
81	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
82	#88146	—	2	1	no	—
83	#88146	—	2	2	no	—
84	C₄⋊C₄×D₁₃	—	2	1	no	—
85	C₄⋊C₄×D₁₃	—	2	2	no	—
86	C₂²⋊C₄×D₁₃	—	2	1	no	—
87	C₂²⋊C₄×D₁₃	—	2	2	no	—
88	#88131	—	2	1	no	—
89	#88131	—	2	2	no	—
90	#88126	—	2	2	no	—
91	#88126	C₂×C₄	1	2	yes	—
92	C₄²×D₁₃	—	2	2	no	—
93	C₄²×D₁₃	C₂×C₄	1	2	yes	—
94	C₁₃×#108	—	2	1	no	—
95	C₁₃×#108	—	2	1	no	—
96	C₁₃×#107	—	2	1	no	—
97	C₁₃×#106	—	2	1	no	—
98	C₁₃×#97	C₂×C₄	1	2	yes	complemented
99	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
100	#88062	—	2	2	no	—
101	#88062	—	2	2	no	—
102	#88059	—	2	1	no	—
103	#88059	—	2	1	no	—
104	#88058	—	2	1	no	—
105	#88057	—	2	1	no	—
106	#88055	C₂×C₄	1	2	yes	complemented
107	#88055	C₂×C₄	1	2	yes	complemented
108	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
109	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
110	#88048	—	2	2	no	—
111	#88047	—	2	2	no	—
112	#88043	C₂×C₄	1	2	yes	complemented
113	C₄×#1055	C₂×C₄	1	2	yes	complemented
114	C₂×#1833	—	13	1	no	maximal, Sylow
115	C₂³×D₁₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²×Dic₁₃	#41	1	1	yes	characteristic
118	C₂×C₄×D₁₃	—	2	2	no	—
119	C₂×C₄×D₁₃	—	4	2	no	—
120	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
126	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
127	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
128	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
129	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
130	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
131	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
132	C₁₃×M₁₆	—	2	1	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂²⋊Dic₁₃	—	2	1	no	—
151	C₂²⋊Dic₁₃	—	2	2	no	—
152	#6103	—	2	2	no	—
153	#6103	—	4	2	no	—
154	C₄⋊Dic₁₃	—	2	1	no	—
155	C₄⋊Dic₁₃	—	2	2	no	—
156	#6101	—	2	2	no	—
157	#6101	—	4	2	no	—
158	C₄×Dic₁₃	—	2	2	no	—
159	C₄×Dic₁₃	—	2	2	no	—
160	C₄×Dic₁₃	—	4	2	no	—
161	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
162	#6099	—	2	1	no	—
163	#6099	—	2	1	no	—
164	#6099	—	2	2	no	—
165	#6099	—	2	2	no	—
166	C₂×#1055	—	2	2	no	—
167	C₂×#1055	C₂²×C₄	1	2	yes	—
168	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
169	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
170	C₂×#1055	C₂×D₄	1	1	yes	characteristic
171	C₂×#1055	C₂×D₄	1	1	yes	characteristic
172	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
173	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
174	#6094	—	2	2	no	—
175	#6094	—	2	2	no	—
176	#6094	—	4	2	no	—
177	#6094	—	4	2	no	—
178	C₈×D₁₃	—	2	2	no	—
179	C₈×D₁₃	—	2	2	no	—
180	C₈×D₁₃	—	4	2	no	—
181	C₈×D₁₃	—	4	2	no	—
182	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
183	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
184	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
185	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
186	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
187	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
188	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
189	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
190	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
191	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
192	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
193	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
194	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
195	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
196	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
197	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
198	C₂²×#108	—	13	1	no	—
199	C₂×#427	—	13	1	no	—
200	C₂×#405	—	13	1	no	—
201	#1833	—	13	1	no	—
202	#1833	—	13	1	no	—
203	#1833	—	13	1	no	—
204	#1833	—	13	2	no	—
205	#1833	—	13	2	no	—
206	#1833	D₁₃	1	1	yes	characteristic, direct product factor
207	C₂×#344	—	13	2	no	—
208	C₂×H(3,ℤ/4)	—	13	2	no	—
209	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂²×D₁₃	—	4	2	no	—
211	C₂²×D₁₃	#117	1	1	yes	characteristic
212	C₂²×D₁₃	#117	1	1	yes	characteristic
213	C₂²×D₁₃	#124	1	1	yes	characteristic
214	C₂²×D₁₃	#124	1	1	yes	characteristic
215	C₂²×D₁₃	#125	1	1	yes	characteristic
216	C₂²×D₁₃	#125	1	1	yes	characteristic
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₂×Dic₁₃	—	2	2	no	—
226	C₂×Dic₁₃	—	4	2	no	—
227	C₂×Dic₁₃	#117	1	1	yes	characteristic
228	C₂×Dic₁₃	#117	1	1	yes	characteristic
229	C₂×Dic₁₃	#124	1	1	yes	characteristic
230	C₂×Dic₁₃	#124	1	1	yes	characteristic
231	C₂×Dic₁₃	#125	1	1	yes	characteristic
232	C₂×Dic₁₃	#125	1	1	yes	characteristic
233	C₄×D₁₃	—	4	4	no	—
234	C₄×D₁₃	—	8	4	no	—
235	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₄×D₁₃	#117	1	1	yes	characteristic
240	C₄×D₁₃	#117	1	1	yes	characteristic
241	C₄×D₁₃	#117	1	1	yes	characteristic
242	C₄×D₁₃	#117	1	1	yes	characteristic
243	C₄×D₁₃	#124	1	1	yes	characteristic
244	C₄×D₁₃	#124	1	1	yes	characteristic
245	C₄×D₁₃	#124	1	1	yes	characteristic
246	C₄×D₁₃	#124	1	1	yes	characteristic
247	C₄×D₁₃	#125	1	1	yes	characteristic
248	C₄×D₁₃	#125	1	1	yes	characteristic
249	C₄×D₁₃	#125	1	1	yes	characteristic
250	C₄×D₁₃	#125	1	1	yes	characteristic
251	C₈×C₁₃	—	2	2	no	—
252	C₈×C₁₃	—	4	2	no	—
253	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
256	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
257	#1055	—	2	2	no	—
258	#1055	—	4	2	no	—
259	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
260	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
261	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
262	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
263	C₂²×M₁₆	—	13	1	no	—
264	C₂²×M₁₆	—	13	2	no	—
265	C₂³×C₈	—	13	1	no	—
266	C₂×#117	—	13	1	no	—
267	C₂×#117	—	13	2	no	—
268	C₂×#108	—	13	2	no	—
269	C₂×#108	—	13	1	no	—
270	C₂×#108	—	26	1	no	—
271	C₂×#108	—	26	1	no	—
272	C₂×#108	—	26	1	no	—
273	C₂×#108	—	26	1	no	—
274	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
275	#427	—	13	1	no	—
276	#427	—	13	2	no	—
277	#427	—	26	1	no	—
278	#427	—	26	1	no	—
279	#427	C₂×D₁₃	1	1	yes	characteristic
280	C₂×#107	—	26	1	no	—
281	C₂×#106	—	26	1	no	—
282	#405	—	13	1	no	—
283	#405	—	13	1	no	—
284	#405	—	13	1	no	—
285	#405	—	13	2	no	—
286	#405	—	13	2	no	—
287	#405	C₂×D₁₃	1	1	yes	characteristic
288	C₂×#97	—	13	2	no	—
289	C₂×C₄×C₈	—	13	2	no	—
290	#344	—	13	2	no	—
291	#344	—	13	2	no	—
292	#344	—	13	2	no	—
293	#344	C₂×D₁₃	1	2	yes	—
294	H(3,ℤ/4)	—	13	2	no	—
295	H(3,ℤ/4)	—	13	2	no	—
296	H(3,ℤ/4)	—	13	2	no	—
297	H(3,ℤ/4)	C₂×D₁₃	1	2	yes	—
298	C₂²×C₁₃	—	4	1	no	—
299	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
300	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
301	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
302	C₂×D₁₃	—	2	2	no	—
303	C₂×D₁₃	—	2	2	no	—
304	C₂×D₁₃	—	2	2	no	—
305	C₂×D₁₃	—	4	1	no	—
306	C₂×D₁₃	—	4	1	no	—
307	C₂×D₁₃	—	4	1	no	—
308	C₂×D₁₃	#382	1	1	yes	characteristic
309	C₂×D₁₃	#382	1	1	yes	characteristic
310	C₂×D₁₃	#382	1	1	yes	characteristic
311	C₂×D₁₃	#382	1	1	yes	characteristic
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
315	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
316	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
317	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
318	Dic₁₃	—	4	2	no	—
319	Dic₁₃	—	8	2	no	—
320	Dic₁₃	#382	1	1	yes	characteristic
321	Dic₁₃	#382	1	1	yes	characteristic
322	Dic₁₃	#382	1	1	yes	characteristic
323	Dic₁₃	#382	1	1	yes	characteristic
324	C₂³×C₄	—	13	1	no	—
325	C₂×M₁₆	—	13	1	no	—
326	C₂×M₁₆	—	13	2	no	—
327	C₂×M₁₆	—	13	2	no	—
328	C₂×M₁₆	—	26	2	no	—
329	C₂×M₁₆	—	26	1	no	—
330	C₂×M₁₆	—	26	1	no	—
331	C₂×M₁₆	—	26	1	no	—
332	C₂×M₁₆	—	26	1	no	—
333	C₂×M₁₆	—	26	2	no	—
334	C₂×M₁₆	—	26	2	no	—
335	C₂×M₁₆	—	26	2	no	—
336	C₂×M₁₆	—	26	2	no	—
337	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
338	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
339	C₂²×C₈	—	13	1	no	—
340	C₂²×C₈	—	13	1	no	—
341	C₂²×C₈	—	13	1	no	—
342	C₂²×C₈	—	13	1	no	—
343	C₂²×C₈	—	13	1	no	—
344	C₂²×C₈	—	13	1	no	—
345	C₂²×C₈	—	13	1	no	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	13	1	no	—
348	C₂²×C₈	—	13	1	no	—
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	—	13	2	no	—
353	C₂²×C₈	—	26	2	no	—
354	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
355	#117	—	13	1	no	—
356	#117	—	13	2	no	—
357	#117	—	13	2	no	—
358	#117	—	26	2	no	—
359	#117	—	26	1	no	—
360	#117	—	26	1	no	—
361	#117	—	26	2	no	—
362	#117	—	26	2	no	—
363	#117	C₂²×D₁₃	1	2	yes	—
364	#117	C₂²×D₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	—	26	1	no	—
366	C₂×C₄⋊C₄	—	26	2	no	—
367	C₂×C₂²⋊C₄	—	26	1	no	—
368	C₂×C₂²⋊C₄	—	26	2	no	—
369	C₂×C₄²	—	13	2	no	—
370	C₂×C₄²	—	26	2	no	—
371	#108	—	2	1	no	—
372	#108	—	2	1	no	—
373	#108	—	26	2	no	—
374	#108	—	26	2	no	—
375	#108	—	26	1	no	—
376	#108	—	26	1	no	—
377	#107	—	2	1	no	—
378	#107	—	26	2	no	—
379	#107	—	26	1	no	—
380	#106	—	2	1	no	—
381	#106	—	26	2	no	—
382	#106	—	26	1	no	—
383	#97	—	13	2	no	—
384	#97	—	13	2	no	—
385	#97	—	13	2	no	—
386	#97	C₄×D₁₃	1	2	yes	complemented
387	C₄×C₈	—	13	2	no	—
388	C₄×C₈	—	13	2	no	—
389	C₄×C₈	—	13	2	no	—
390	C₄×C₈	C₄×D₁₃	1	2	yes	complemented
391	C₂×C₁₃	—	2	1	no	—
392	C₂×C₁₃	—	2	1	no	—
393	C₂×C₁₃	—	2	1	no	—
394	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
395	D₁₃	—	2	1	no	—
396	D₁₃	—	2	1	no	—
397	D₁₃	—	2	1	no	—
398	D₁₃	#1833	1	2	yes	direct product factor
399	C₂⁴	—	13	1	no	—
400	C₂²×C₄	—	13	1	no	—
401	C₂²×C₄	—	13	1	no	—
402	C₂²×C₄	—	13	1	no	—
403	C₂²×C₄	—	13	1	no	—
404	C₂²×C₄	—	13	1	no	—
405	C₂²×C₄	—	13	1	no	—
406	C₂²×C₄	—	13	1	no	—
407	C₂²×C₄	—	13	1	no	—
408	C₂²×C₄	—	13	1	no	—
409	C₂²×C₄	—	13	1	no	—
410	C₂²×C₄	—	13	1	no	—
411	C₂²×C₄	—	13	1	no	—
412	C₂²×C₄	—	13	1	no	—
413	C₂²×C₄	—	26	2	no	—
414	C₂²×C₄	—	52	2	no	—
415	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	26	2	no	—
421	M₁₆	—	26	2	no	—
422	M₁₆	—	26	1	no	—
423	M₁₆	—	26	1	no	—
424	M₁₆	—	26	2	no	—
425	M₁₆	—	26	2	no	—
426	M₁₆	—	52	2	no	—
427	M₁₆	—	52	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	13	1	no	—
430	C₂×C₈	—	13	1	no	—
431	C₂×C₈	—	13	1	no	—
432	C₂×C₈	—	13	1	no	—
433	C₂×C₈	—	13	1	no	—
434	C₂×C₈	—	13	1	no	—
435	C₂×C₈	—	13	1	no	—
436	C₂×C₈	—	13	1	no	—
437	C₂×C₈	—	13	1	no	—
438	C₂×C₈	—	13	1	no	—
439	C₂×C₈	—	13	1	no	—
440	C₂×C₈	—	13	1	no	—
441	C₂×C₈	—	13	1	no	—
442	C₂×C₈	—	13	1	no	—
443	C₂×C₈	—	13	1	no	—
444	C₂×C₈	—	13	1	no	—
445	C₂×C₈	—	13	1	no	—
446	C₂×C₈	—	13	1	no	—
447	C₂×C₈	—	13	1	no	—
448	C₂×C₈	—	13	1	no	—
449	C₂×C₈	—	13	1	no	—
450	C₂×C₈	—	13	1	no	—
451	C₂×C₈	—	13	2	no	—
452	C₂×C₈	—	26	2	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	—	26	2	no	—
455	C₂×C₈	—	52	2	no	—
456	C₂×C₈	—	52	2	no	—
457	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
458	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
459	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
460	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
461	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
462	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
463	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	26	2	no	—
467	C₄⋊C₄	—	26	1	no	—
468	C₄⋊C₄	—	26	2	no	—
469	C₄⋊C₄	—	52	2	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	26	2	no	—
473	C₂²⋊C₄	—	26	1	no	—
474	C₂²⋊C₄	—	26	2	no	—
475	C₂²⋊C₄	—	52	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	13	2	no	—
478	C₄²	—	26	2	no	—
479	C₄²	—	26	2	no	—
480	C₄²	—	52	2	no	—
481	C₄²	C₂×C₄×D₁₃	1	2	yes	—
482	C₁₃	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
483	C₂³	—	13	1	no	—
484	C₂³	—	13	1	no	—
485	C₂³	—	13	1	no	—
486	C₂³	—	13	1	no	—
487	C₂³	—	13	1	no	—
488	C₂³	—	13	1	no	—
489	C₂³	—	52	2	no	—
490	C₂³	#41×D₁₃	1	1	yes	characteristic
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	13	1	no	—
494	C₂×C₄	—	13	1	no	—
495	C₂×C₄	—	13	1	no	—
496	C₂×C₄	—	13	1	no	—
497	C₂×C₄	—	13	1	no	—
498	C₂×C₄	—	13	1	no	—
499	C₂×C₄	—	13	1	no	—
500	C₂×C₄	—	13	1	no	—
501	C₂×C₄	—	13	1	no	—
502	C₂×C₄	—	13	1	no	—
503	C₂×C₄	—	13	1	no	—
504	C₂×C₄	—	13	1	no	—
505	C₂×C₄	—	13	1	no	—
506	C₂×C₄	—	13	1	no	—
507	C₂×C₄	—	13	1	no	—
508	C₂×C₄	—	13	1	no	—
509	C₂×C₄	—	13	1	no	—
510	C₂×C₄	—	13	1	no	—
511	C₂×C₄	—	13	1	no	—
512	C₂×C₄	—	13	1	no	—
513	C₂×C₄	—	13	1	no	—
514	C₂×C₄	—	13	1	no	—
515	C₂×C₄	—	26	2	no	—
516	C₂×C₄	—	52	4	no	—
517	C₂×C₄	—	52	2	no	—
518	C₂×C₄	—	104	4	no	—
519	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
521	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
522	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
523	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
524	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	4	2	no	—
527	C₈	—	13	1	no	—
528	C₈	—	13	1	no	—
529	C₈	—	13	1	no	—
530	C₈	—	13	1	no	—
531	C₈	—	26	2	no	—
532	C₈	—	52	2	no	—
533	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
534	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
535	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
536	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
537	C₂²	—	4	1	no	—
538	C₂²	—	13	1	no	—
539	C₂²	—	13	1	no	—
540	C₂²	—	13	1	no	—
541	C₂²	—	13	1	no	—
542	C₂²	—	26	2	no	—
543	C₂²	—	26	2	no	—
544	C₂²	—	26	2	no	—
545	C₂²	—	52	1	no	—
546	C₂²	—	52	1	no	—
547	C₂²	—	52	1	no	—
548	C₂²	D₁₃×#117	1	1	yes	characteristic
549	C₂²	D₁₃×#124	1	1	yes	characteristic
550	C₂²	D₁₃×#125	1	1	yes	characteristic
551	C₄	—	4	2	no	—
552	C₄	—	8	2	no	—
553	C₄	—	13	1	no	—
554	C₄	—	13	1	no	—
555	C₄	—	13	1	no	—
556	C₄	—	13	1	no	—
557	C₄	—	52	2	no	—
558	C₄	—	104	2	no	—
559	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
560	C₄	D₁₃×#117	1	1	yes	characteristic
561	C₄	D₁₃×#124	1	1	yes	characteristic
562	C₄	D₁₃×#125	1	1	yes	characteristic
563	C₂	—	2	1	no	—
564	C₂	—	2	1	no	—
565	C₂	—	2	1	no	—
566	C₂	—	13	2	no	—
567	C₂	—	26	1	no	—
568	C₂	—	26	1	no	—
569	C₂	—	26	1	no	—
570	C₂	D₁₃×#382	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃×#117
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1833	C₂
socle	C₂×C₁₃	C₂×#382
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1833	D₁₃
hypocenter	C₁₃	C₂×#1833
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. #13114961	C₂	semidirect
5. #13114960	C₂	semidirect
6. #13114959	C₂	semidirect
7. #13114958	C₂	semidirect
8. #13114957	C₂	semidirect
11. C₁₃×#1833	C₂	semidirect
35. #11718369	C₄	semidirect
36. D₁₃×#97	C₄	semidirect
37. #11718350	C₄	semidirect
38. C₄×C₈×D₁₃	C₄	semidirect
98. C₁₃×#97	C₂×C₄	semidirect
99. C₄×C₈×C₁₃	C₂×C₄	semidirect
106. #88055	C₂×C₄	semidirect
107. #88055	C₂×C₄	semidirect
108. C₈×Dic₁₃	C₂×C₄	semidirect
109. C₈×Dic₁₃	C₂×C₄	semidirect
112. #88043	C₂×C₄	semidirect
113. C₄×#1055	C₂×C₄	semidirect
206. #1833	D₁₃	direct (N × H)
386. #97	C₄×D₁₃	semidirect
390. C₄×C₈	C₄×D₁₃	semidirect
398. D₁₃	#1833	direct (N × H)
482. C₁₃	C₂×#1833	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
#13114961	2
#13114960	2
#13114959	2
#13114958	2
#13114957	2
D₁₃×#344	2
D₁₃×H(3,ℤ/4)	2
C₁₃×#1833	2
C₂×#1833	13

Subgroups — D13×#1833 #15863088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1833 #15863088