Subgroups — D₁₃×#3177 #16732755

Order 3328.

1842 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#541	C₂	1	2	yes	maximal
2	#13125496	C₂	1	1	yes	maximal, characteristic, complemented
3	#13125495	C₂	1	1	yes	maximal, characteristic, complemented
4	#13125494	C₂	1	2	yes	maximal, complemented
5	#13125493	C₂	1	2	yes	maximal, complemented
6	#13125492	C₂	1	1	yes	maximal, characteristic, complemented
7	#13125491	C₂	1	2	yes	maximal, complemented
8	#13125490	C₂	1	2	yes	maximal, complemented
9	#13125489	C₂	1	2	yes	maximal, complemented
10	#13125488	C₂	1	2	yes	maximal, complemented
11	D₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×#491	C₂	1	2	yes	maximal, complemented
14	D₁₃×#470	C₂	1	2	yes	maximal
15	D₁₃×#467	C₂	1	2	yes	maximal
16	D₁₃×#441	C₂	1	2	yes	maximal, complemented
17	C₄×Q₁₆×D₁₃	C₂	1	2	yes	maximal, complemented
18	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#3177	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#541	C₂²	1	2	yes	—
21	C₂×Q₁₆×D₁₃	C₂²	1	2	yes	—
22	C₂×Q₁₆×D₁₃	C₂²	1	2	yes	—
23	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	#11719436	C₂²	1	2	yes	—
26	D₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	D₁₃×#126	—	2	4	no	—
28	#11719406	—	2	4	no	—
29	#11719402	C₂²	1	2	yes	—
30	#11719401	—	2	4	no	—
31	D₁₃×#125	—	2	4	no	—
32	D₁₃×#125	C₂²	1	2	yes	—
33	D₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
34	#11719330	C₂²	1	4	yes	—
35	#11719288	C₂²	1	4	yes	—
36	C₄×Q₈×D₁₃	C₂²	1	4	yes	—
37	D₁₃×#117	C₂²	1	1	yes	characteristic
38	#11719223	C₂²	1	2	yes	—
39	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#491	C₂²	1	2	yes	complemented
42	C₁₃×#470	C₂²	1	2	yes	—
43	C₁₃×#467	C₂²	1	2	yes	—
44	C₁₃×#441	C₂²	1	2	yes	complemented
45	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
46	C₁₃×#405	C₂²	1	1	yes	characteristic
47	#11718850	C₂²	1	2	yes	—
48	#11718849	C₂²	1	2	yes	—
49	#11718845	C₂²	1	2	yes	complemented
50	Q₁₆×Dic₁₃	C₂²	1	2	yes	complemented
51	#11718842	C₂²	1	2	yes	complemented
52	#11718842	C₂²	1	2	yes	complemented
53	#11718798	C₂²	1	2	yes	—
54	#11718783	C₂²	1	1	yes	characteristic
55	#11718777	C₂²	1	2	yes	—
56	#11718762	C₂²	1	1	yes	characteristic
57	#11718753	C₂²	1	2	yes	complemented
58	#11718743	C₂²	1	2	yes	complemented
59	#11718730	C₂²	1	2	yes	complemented
60	#11718725	C₂²	1	2	yes	complemented
61	#11718713	C₂²	1	4	yes	—
62	#11718712	C₂²	1	4	yes	—
63	#11718691	C₂²	1	4	yes	complemented
64	C₄×#6107	C₂²	1	4	yes	complemented
65	#11718658	C₂²	1	1	yes	characteristic
66	#11718548	C₂²	1	2	yes	—
67	D₁₃×#107	C₂²	1	2	yes	—
68	#11718539	C₂²	1	2	yes	complemented
69	#11718534	C₂²	1	2	yes	complemented
70	#11718529	C₂²	1	2	yes	—
71	D₁₃×#106	C₂²	1	2	yes	—
72	#11718519	C₂²	1	2	yes	complemented
73	#11718514	C₂²	1	2	yes	complemented
74	#11718477	C₂²	1	4	yes	—
75	#11718474	C₂²	1	4	yes	—
76	D₁₃×#103	C₂²	1	4	yes	—
77	D₁₃×#103	C₂²	1	4	yes	—
78	#11718458	C₂²	1	4	yes	complemented
79	#11718458	C₂²	1	4	yes	complemented
80	#11718451	C₂²	1	4	yes	complemented
81	#11718450	C₂²	1	4	yes	complemented
82	#11718377	C₂²	1	2	yes	complemented
83	#11718369	C₂²	1	1	yes	characteristic
84	#11718369	C₂²	1	1	yes	characteristic
85	D₁₃×#97	C₂²	1	1	yes	characteristic
86	D₁₃×#97	C₂²	1	1	yes	characteristic
87	#11718364	C₂²	1	2	yes	complemented
88	#11718360	C₂²	1	1	yes	characteristic, complemented
89	C₄×Dic₅₂	C₂²	1	2	yes	complemented
90	#11718350	C₂²	1	1	yes	characteristic
91	#11718350	C₂²	1	1	yes	characteristic
92	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
93	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
94	#11718344	C₂²	1	1	yes	characteristic, complemented
95	C₂×Q₈×D₁₃	C₂³	1	4	yes	—
96	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₁₃×#126	—	2	4	no	—
103	C₁₃×#125	—	2	4	no	—
104	C₁₃×#125	C₂³	1	2	yes	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
106	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
107	C₁₃×#117	C₂³	1	1	yes	characteristic
108	#88200	C₂³	1	4	yes	—
109	Q₈×Dic₁₃	C₂³	1	4	yes	—
110	#88198	C₂³	1	4	yes	—
111	C₂×#6107	C₂³	1	4	yes	—
112	C₂×#6107	C₂³	1	4	yes	—
113	#88180	C₂³	1	1	yes	characteristic
114	#88178	C₂³	1	4	yes	—
115	C₂×#6099	C₂³	1	1	yes	characteristic
116	C₂²×#1055	C₂³	1	1	yes	characteristic
117	Q₁₆×D₁₃	—	2	8	no	—
118	Q₁₆×D₁₃	—	2	8	no	—
119	M₁₆×D₁₃	—	2	4	no	—
120	C₂×Dic₅₂	C₂³	1	2	yes	—
121	C₂×Dic₅₂	C₂³	1	2	yes	—
122	C₂×#6094	C₂³	1	1	yes	characteristic
123	C₂×#6094	C₂³	1	1	yes	characteristic
124	C₂×C₈×D₁₃	—	2	4	no	—
125	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
131	#88152	—	2	4	no	—
132	#88152	—	2	4	no	—
133	#88152	—	2	4	no	—
134	#88151	C₂³	1	4	yes	—
135	#88150	—	2	4	no	—
136	#88146	D₄	1	2	yes	—
137	C₄⋊C₄×D₁₃	—	2	4	no	—
138	C₄⋊C₄×D₁₃	—	2	4	no	—
139	C₄⋊C₄×D₁₃	—	2	4	no	—
140	C₄⋊C₄×D₁₃	—	2	4	no	—
141	C₄⋊C₄×D₁₃	D₄	1	2	yes	—
142	C₄⋊C₄×D₁₃	C₂³	1	4	yes	—
143	#88144	—	2	4	no	—
144	#88144	—	2	4	no	—
145	#88144	C₂³	1	4	yes	—
146	#88143	—	2	4	no	—
147	#88143	—	2	4	no	—
148	#88143	—	2	4	no	—
149	#88143	—	2	4	no	—
150	#88143	—	2	4	no	—
151	#88142	—	2	4	no	—
152	#88141	—	2	4	no	—
153	#88141	C₂³	1	4	yes	—
154	C₂²⋊C₄×D₁₃	—	2	4	no	—
155	C₂²⋊C₄×D₁₃	D₄	1	2	yes	—
156	#88133	—	2	4	no	—
157	#88133	—	2	4	no	—
158	#88133	—	2	4	no	—
159	#88132	—	2	4	no	—
160	#88131	D₄	1	2	yes	—
161	#88130	—	2	4	no	—
162	#88126	C₂³	1	1	yes	characteristic
163	#88126	C₂³	1	1	yes	characteristic
164	C₄²×D₁₃	—	2	4	no	—
165	C₄²×D₁₃	C₂³	1	1	yes	characteristic
166	C₄²×D₁₃	C₂³	1	1	yes	characteristic
167	#88124	—	2	4	no	—
168	#88124	C₂³	1	2	yes	—
169	#88123	C₂³	1	2	yes	—
170	C₄×Dic₂₆	—	2	4	no	—
171	C₄×Dic₂₆	C₂³	1	4	yes	—
172	C₁₃×#107	C₂³	1	2	yes	—
173	C₁₃×#106	C₂³	1	2	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	1	yes	characteristic
177	C₁₃×#97	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
180	#88075	C₂³	1	4	yes	—
181	#88075	C₂³	1	4	yes	—
182	#88058	C₂³	1	2	yes	—
183	#88057	C₂³	1	2	yes	—
184	#88056	C₂³	1	4	yes	—
185	#88056	C₂³	1	4	yes	—
186	#88055	C₂³	1	1	yes	characteristic
187	#88055	C₂³	1	1	yes	characteristic
188	#88055	C₂³	1	1	yes	characteristic
189	#88055	C₂³	1	1	yes	characteristic
190	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
191	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
192	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
193	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
194	#88050	C₂³	1	4	yes	—
195	#88050	C₂³	1	4	yes	—
196	#88048	C₂³	1	4	yes	—
197	#88047	C₂³	1	4	yes	—
198	#88043	C₂³	1	1	yes	characteristic
199	#88043	C₂³	1	1	yes	characteristic
200	C₄×#1055	C₂³	1	1	yes	characteristic
201	C₄×#1055	C₂³	1	1	yes	characteristic
202	C₂×#3177	—	13	1	no	maximal, Sylow
203	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
207	Q₈×D₁₃	—	2	8	no	—
208	Q₈×D₁₃	—	2	8	no	—
209	C₂×C₄×D₁₃	—	2	2	no	—
210	C₂×C₄×D₁₃	—	2	2	no	—
211	C₂×C₄×D₁₃	—	2	4	no	—
212	C₂×C₄×D₁₃	—	2	4	no	—
213	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
214	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
215	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
219	C₂×Dic₂₆	—	2	4	no	—
220	C₂×Dic₂₆	C₂⁴	1	4	yes	—
221	C₁₃×Q₁₆	—	2	4	no	—
222	C₁₃×Q₁₆	—	2	4	no	—
223	C₁₃×M₁₆	—	2	2	no	—
224	C₂×C₈×C₁₃	—	2	2	no	—
225	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²⋊Dic₁₃	—	2	4	no	—
241	C₂²⋊Dic₁₃	C₂×D₄	1	2	yes	—
242	#6107	—	2	8	no	—
243	#6107	—	2	8	no	—
244	#6103	—	2	4	no	—
245	#6103	—	2	4	no	—
246	#6103	C₂×D₄	1	2	yes	—
247	#6103	C₂×D₄	1	2	yes	—
248	C₄⋊Dic₁₃	—	2	4	no	—
249	C₄⋊Dic₁₃	—	2	4	no	—
250	C₄⋊Dic₁₃	—	2	4	no	—
251	C₄⋊Dic₁₃	—	2	4	no	—
252	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
253	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
254	#6101	—	2	4	no	—
255	#6101	—	2	4	no	—
256	#6101	—	2	4	no	—
257	#6101	—	2	4	no	—
258	#6101	—	2	4	no	—
259	#6101	—	2	4	no	—
260	#6101	—	2	4	no	—
261	#6101	—	2	4	no	—
262	#6101	—	2	4	no	—
263	#6101	C₂×D₄	1	2	yes	—
264	#6101	C₂×D₄	1	2	yes	—
265	C₄×Dic₁₃	—	2	4	no	—
266	C₄×Dic₁₃	—	2	4	no	—
267	C₄×Dic₁₃	—	2	4	no	—
268	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
269	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
270	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	#6099	—	2	2	no	—
273	C₂×#1055	—	2	2	no	—
274	C₂×#1055	C₂⁴	1	1	yes	characteristic
275	C₂×#1055	C₂⁴	1	1	yes	characteristic
276	C₂×#1055	C₂⁴	1	1	yes	characteristic
277	C₂×#1055	C₂⁴	1	1	yes	characteristic
278	Dic₅₂	—	2	4	no	—
279	Dic₅₂	—	2	4	no	—
280	#6094	—	2	2	no	—
281	#6094	—	2	2	no	—
282	C₈×D₁₃	—	2	2	no	—
283	C₈×D₁₃	—	2	2	no	—
284	C₈×D₁₃	—	2	2	no	—
285	C₈×D₁₃	—	2	2	no	—
286	C₈×D₁₃	#41	1	4	yes	—
287	C₈×D₁₃	#41	1	4	yes	—
288	C₂×#541	—	13	2	no	—
289	#3177	—	13	1	no	—
290	#3177	—	13	1	no	—
291	#3177	—	13	2	no	—
292	#3177	—	13	2	no	—
293	#3177	—	13	2	no	—
294	#3177	—	13	2	no	—
295	#3177	—	13	2	no	—
296	#3177	—	13	1	no	—
297	#3177	—	13	2	no	—
298	#3177	D₁₃	1	1	yes	characteristic, direct product factor
299	C₂×#499	—	13	1	no	—
300	C₂×#494	—	13	1	no	—
301	C₂×#491	—	13	2	no	—
302	C₂×#470	—	13	2	no	—
303	C₂×#467	—	13	2	no	—
304	C₂×#441	—	13	2	no	—
305	C₂×C₄×Q₁₆	—	13	2	no	—
306	C₂×#405	—	13	1	no	—
307	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
308	C₂²×D₁₃	—	2	2	no	—
309	C₂²×D₁₃	—	2	4	no	—
310	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
311	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₁₃	—	2	4	no	—
313	Q₈×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	2	4	no	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
322	C₂×Dic₁₃	—	2	2	no	—
323	C₂×Dic₁₃	—	2	4	no	—
324	C₂×Dic₁₃	—	2	4	no	—
325	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
326	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
327	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₄×D₁₃	—	2	2	no	—
330	C₄×D₁₃	—	2	4	no	—
331	C₄×D₁₃	—	2	4	no	—
332	C₄×D₁₃	—	2	1	no	—
333	C₄×D₁₃	—	2	1	no	—
334	C₄×D₁₃	—	2	2	no	—
335	C₄×D₁₃	—	4	8	no	—
336	C₄×D₁₃	—	4	8	no	—
337	C₄×D₁₃	C₂×#41	1	2	yes	—
338	C₄×D₁₃	C₂×#41	1	2	yes	—
339	Dic₂₆	—	2	4	no	—
340	Dic₂₆	—	2	4	no	—
341	Dic₂₆	—	4	8	no	—
342	C₈×C₁₃	—	2	1	no	—
343	C₈×C₁₃	—	2	1	no	—
344	C₈×C₁₃	C₂×#41	1	2	yes	—
345	C₈×C₁₃	C₂×#41	1	2	yes	—
346	#1055	—	2	1	no	—
347	#1055	—	2	1	no	—
348	#1055	C₂×#41	1	2	yes	—
349	#1055	C₂×#41	1	2	yes	—
350	C₂²×Q₁₆	—	13	2	no	—
351	C₂²×Q₁₆	—	13	2	no	—
352	C₂²×M₁₆	—	13	1	no	—
353	C₂³×C₈	—	13	1	no	—
354	#541	—	13	2	no	—
355	#541	—	13	2	no	—
356	#541	—	13	4	no	—
357	#541	—	13	4	no	—
358	#541	—	13	2	no	—
359	#541	—	26	4	no	—
360	#541	—	26	4	no	—
361	#541	C₂×D₁₃	1	2	yes	—
362	C₂×C₄⋊Q₈	—	13	2	no	—
363	C₂×#126	—	26	4	no	—
364	C₂×#125	—	13	2	no	—
365	C₂×#125	—	26	4	no	—
366	C₂×C₂²⋊Q₈	—	13	4	no	—
367	C₂×C₄×Q₈	—	13	4	no	—
368	C₂×#117	—	13	1	no	—
369	#499	—	13	2	no	—
370	#499	—	13	2	no	—
371	#499	—	13	2	no	—
372	#499	—	13	1	no	—
373	#499	C₂×D₁₃	1	1	yes	characteristic, complemented
374	#494	—	13	2	no	—
375	#494	—	13	2	no	—
376	#494	—	13	2	no	—
377	#494	—	13	1	no	—
378	#494	C₂×D₁₃	1	1	yes	characteristic, complemented
379	#491	—	13	2	no	—
380	#491	—	13	2	no	—
381	#491	—	13	4	no	—
382	#491	—	13	4	no	—
383	#491	—	13	2	no	—
384	#491	C₂×D₁₃	1	2	yes	complemented
385	#470	—	13	2	no	—
386	#470	—	13	2	no	—
387	#470	—	13	4	no	—
388	#470	—	13	2	no	—
389	#470	—	13	4	no	—
390	#470	C₂×D₁₃	1	2	yes	—
391	#467	—	13	2	no	—
392	#467	—	13	2	no	—
393	#467	—	13	4	no	—
394	#467	—	13	2	no	—
395	#467	—	13	4	no	—
396	#467	C₂×D₁₃	1	2	yes	—
397	#441	—	13	2	no	—
398	#441	—	13	4	no	—
399	#441	—	13	2	no	—
400	#441	—	13	4	no	—
401	#441	—	13	2	no	—
402	#441	C₂×D₁₃	1	2	yes	complemented
403	C₄×Q₁₆	—	13	2	no	—
404	C₄×Q₁₆	—	13	4	no	—
405	C₄×Q₁₆	—	13	2	no	—
406	C₄×Q₁₆	—	13	4	no	—
407	C₄×Q₁₆	—	13	2	no	—
408	C₄×Q₁₆	C₂×D₁₃	1	2	yes	complemented
409	C₂×#107	—	13	2	no	—
410	C₂×#106	—	13	2	no	—
411	C₂×#103	—	13	4	no	—
412	C₂×#103	—	13	4	no	—
413	#405	—	13	1	no	—
414	#405	—	13	1	no	—
415	#405	—	13	1	no	—
416	#405	—	13	1	no	—
417	#405	—	13	1	no	—
418	#405	—	13	1	no	—
419	#405	—	13	1	no	—
420	#405	C₂×D₁₃	1	1	yes	characteristic
421	C₂×#97	—	13	1	no	—
422	C₂×#97	—	13	1	no	—
423	C₂×C₄×C₈	—	13	1	no	—
424	C₂×C₄×C₈	—	13	1	no	—
425	C₂²×C₁₃	—	2	1	no	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
428	C₂×D₁₃	—	2	1	no	—
429	C₂×D₁₃	—	2	2	no	—
430	C₂×D₁₃	—	4	4	no	—
431	C₂×D₁₃	#532	1	2	yes	—
432	C₂×D₁₃	#578	1	4	yes	—
433	C₄×C₁₃	—	2	1	no	—
434	C₄×C₁₃	—	2	2	no	—
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	4	4	no	—
437	C₄×C₁₃	—	4	4	no	—
438	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
439	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
440	Dic₁₃	—	2	1	no	—
441	Dic₁₃	—	2	2	no	—
442	Dic₁₃	—	2	2	no	—
443	Dic₁₃	—	4	4	no	—
444	Dic₁₃	—	4	4	no	—
445	Dic₁₃	#532	1	2	yes	—
446	C₂²×Q₈	—	13	4	no	—
447	C₂³×C₄	—	13	1	no	—
448	C₂×Q₁₆	—	13	4	no	—
449	C₂×Q₁₆	—	13	4	no	—
450	C₂×Q₁₆	—	13	2	no	—
451	C₂×Q₁₆	—	13	2	no	—
452	C₂×Q₁₆	—	26	8	no	—
453	C₂×Q₁₆	—	26	8	no	—
454	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
455	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
456	C₂×M₁₆	—	13	1	no	—
457	C₂×M₁₆	—	13	1	no	—
458	C₂×M₁₆	—	13	1	no	—
459	C₂×M₁₆	—	26	4	no	—
460	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
461	C₂²×C₈	—	13	1	no	—
462	C₂²×C₈	—	13	1	no	—
463	C₂²×C₈	—	13	1	no	—
464	C₂²×C₈	—	13	1	no	—
465	C₂²×C₈	—	13	1	no	—
466	C₂²×C₈	—	13	1	no	—
467	C₂²×C₈	—	13	1	no	—
468	C₂²×C₈	—	26	4	no	—
469	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
470	C₄⋊Q₈	—	13	4	no	—
471	C₄⋊Q₈	—	13	2	no	—
472	C₄⋊Q₈	—	26	4	no	—
473	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
474	#126	—	2	4	no	—
475	#126	—	26	4	no	—
476	#126	—	26	4	no	—
477	#126	—	26	4	no	—
478	#126	—	26	4	no	—
479	#126	—	26	4	no	—
480	#126	—	26	4	no	—
481	#126	—	26	4	no	—
482	#125	—	2	4	no	—
483	#125	—	13	4	no	—
484	#125	—	13	2	no	—
485	#125	—	26	4	no	—
486	#125	—	26	4	no	—
487	#125	—	26	4	no	—
488	#125	—	26	4	no	—
489	#125	—	26	4	no	—
490	#125	—	26	4	no	—
491	#125	—	26	4	no	—
492	#125	—	26	4	no	—
493	#125	C₂²×D₁₃	1	2	yes	—
494	C₂²⋊Q₈	—	13	4	no	—
495	C₂²⋊Q₈	—	13	4	no	—
496	C₂²⋊Q₈	—	13	4	no	—
497	C₂²⋊Q₈	—	26	4	no	—
498	C₂²⋊Q₈	—	26	4	no	—
499	C₂²⋊Q₈	C₂²×D₁₃	1	4	yes	—
500	C₄×Q₈	—	13	4	no	—
501	C₄×Q₈	—	13	4	no	—
502	C₄×Q₈	—	13	4	no	—
503	C₄×Q₈	—	26	4	no	—
504	C₄×Q₈	—	26	4	no	—
505	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
506	#117	—	13	1	no	—
507	#117	—	13	2	no	—
508	#117	—	13	2	no	—
509	#117	—	13	1	no	—
510	#117	—	13	1	no	—
511	#117	C₂²×D₁₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	—	13	2	no	—
513	C₂×C₄⋊C₄	—	13	4	no	—
514	C₂×C₄⋊C₄	—	26	4	no	—
515	C₂×C₄⋊C₄	—	26	4	no	—
516	C₂×C₄⋊C₄	—	26	4	no	—
517	C₂×C₄⋊C₄	—	26	4	no	—
518	C₂×C₂²⋊C₄	—	13	2	no	—
519	C₂×C₂²⋊C₄	—	26	4	no	—
520	C₂×C₄²	—	13	1	no	—
521	C₂×C₄²	—	13	1	no	—
522	C₂×C₄²	—	26	4	no	—
523	#107	—	13	2	no	—
524	#107	—	13	4	no	—
525	#107	C₂²×D₁₃	1	2	yes	—
526	#106	—	13	2	no	—
527	#106	—	13	4	no	—
528	#106	C₂²×D₁₃	1	2	yes	—
529	#103	—	13	4	no	—
530	#103	—	13	4	no	—
531	#103	—	13	4	no	—
532	#103	—	13	4	no	—
533	#103	—	13	4	no	—
534	#103	—	13	4	no	—
535	#103	C₂²×D₁₃	1	4	yes	—
536	#103	C₂²×D₁₃	1	4	yes	—
537	#97	—	13	1	no	—
538	#97	—	13	1	no	—
539	#97	—	13	1	no	—
540	#97	—	13	1	no	—
541	#97	—	13	1	no	—
542	#97	—	13	1	no	—
543	#97	C₂²×D₁₃	1	1	yes	characteristic
544	#97	C₂²×D₁₃	1	1	yes	characteristic
545	C₄×C₈	—	13	1	no	—
546	C₄×C₈	—	13	1	no	—
547	C₄×C₈	—	13	1	no	—
548	C₄×C₈	—	13	1	no	—
549	C₄×C₈	—	13	1	no	—
550	C₄×C₈	—	13	1	no	—
551	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
552	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
553	C₂×C₁₃	—	4	1	no	—
554	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
555	C₂×C₁₃	C₂×#578	1	2	yes	—
556	D₁₃	—	4	1	no	—
557	D₁₃	#3177	1	4	yes	direct product factor
558	C₂⁴	—	13	1	no	—
559	C₂×Q₈	—	13	4	no	—
560	C₂×Q₈	—	26	4	no	—
561	C₂×Q₈	—	26	8	no	—
562	C₂×Q₈	—	26	8	no	—
563	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
564	C₂²×C₄	—	13	1	no	—
565	C₂²×C₄	—	13	1	no	—
566	C₂²×C₄	—	13	2	no	—
567	C₂²×C₄	—	13	2	no	—
568	C₂²×C₄	—	13	1	no	—
569	C₂²×C₄	—	13	1	no	—
570	C₂²×C₄	—	13	1	no	—
571	C₂²×C₄	—	26	2	no	—
572	C₂²×C₄	—	26	2	no	—
573	C₂²×C₄	—	26	4	no	—
574	C₂²×C₄	—	26	4	no	—
575	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
576	Q₁₆	—	2	4	no	—
577	Q₁₆	—	2	4	no	—
578	Q₁₆	—	26	8	no	—
579	Q₁₆	—	26	8	no	—
580	Q₁₆	—	26	4	no	—
581	Q₁₆	—	26	4	no	—
582	M₁₆	—	2	2	no	—
583	M₁₆	—	26	2	no	—
584	M₁₆	—	26	2	no	—
585	M₁₆	—	26	2	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	13	1	no	—
588	C₂×C₈	—	13	1	no	—
589	C₂×C₈	—	13	4	no	—
590	C₂×C₈	—	13	4	no	—
591	C₂×C₈	—	13	1	no	—
592	C₂×C₈	—	13	1	no	—
593	C₂×C₈	—	26	2	no	—
594	C₂×C₈	—	26	2	no	—
595	C₂×C₈	—	26	2	no	—
596	C₂×C₈	—	26	2	no	—
597	C₂×C₈	—	26	2	no	—
598	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
599	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
600	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
601	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	13	2	no	—
607	C₄⋊C₄	—	13	2	no	—
608	C₄⋊C₄	—	13	2	no	—
609	C₄⋊C₄	—	13	4	no	—
610	C₄⋊C₄	—	26	4	no	—
611	C₄⋊C₄	—	26	4	no	—
612	C₄⋊C₄	—	26	4	no	—
613	C₄⋊C₄	—	26	4	no	—
614	C₄⋊C₄	—	26	4	no	—
615	C₄⋊C₄	—	26	4	no	—
616	C₄⋊C₄	—	26	4	no	—
617	C₄⋊C₄	—	26	4	no	—
618	C₄⋊C₄	—	26	4	no	—
619	C₄⋊C₄	—	26	4	no	—
620	C₄⋊C₄	—	26	4	no	—
621	C₄⋊C₄	—	26	4	no	—
622	C₄⋊C₄	—	26	4	no	—
623	C₄⋊C₄	D₄×D₁₃	1	2	yes	—
624	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	13	2	no	—
627	C₂²⋊C₄	—	13	2	no	—
628	C₂²⋊C₄	—	13	2	no	—
629	C₂²⋊C₄	—	26	4	no	—
630	C₂²⋊C₄	—	26	4	no	—
631	C₂²⋊C₄	—	26	4	no	—
632	C₂²⋊C₄	D₄×D₁₃	1	2	yes	—
633	C₄²	—	2	4	no	—
634	C₄²	—	13	2	no	—
635	C₄²	—	13	2	no	—
636	C₄²	—	13	1	no	—
637	C₄²	—	13	1	no	—
638	C₄²	—	26	4	no	—
639	C₄²	—	26	4	no	—
640	C₄²	—	26	4	no	—
641	C₄²	C₂³×D₁₃	1	1	yes	characteristic
642	C₄²	C₂³×D₁₃	1	1	yes	characteristic
643	C₁₃	C₂×#3177	1	1	yes	characteristic, complemented, Sylow
644	C₂³	—	13	1	no	—
645	C₂³	—	13	1	no	—
646	C₂³	—	26	2	no	—
647	C₂³	—	26	4	no	—
648	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
649	Q₈	—	2	4	no	—
650	Q₈	—	2	4	no	—
651	Q₈	—	26	4	no	—
652	Q₈	—	26	4	no	—
653	Q₈	—	52	8	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	13	1	no	—
659	C₂×C₄	—	13	2	no	—
660	C₂×C₄	—	13	2	no	—
661	C₂×C₄	—	13	2	no	—
662	C₂×C₄	—	13	2	no	—
663	C₂×C₄	—	13	1	no	—
664	C₂×C₄	—	26	2	no	—
665	C₂×C₄	—	26	4	no	—
666	C₂×C₄	—	26	4	no	—
667	C₂×C₄	—	26	2	no	—
668	C₂×C₄	—	26	2	no	—
669	C₂×C₄	—	26	1	no	—
670	C₂×C₄	—	26	1	no	—
671	C₂×C₄	—	26	4	no	—
672	C₂×C₄	—	26	4	no	—
673	C₂×C₄	—	52	8	no	—
674	C₂×C₄	—	52	8	no	—
675	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
676	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
677	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
678	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
679	C₈	—	2	1	no	—
680	C₈	—	2	1	no	—
681	C₈	—	13	2	no	—
682	C₈	—	13	2	no	—
683	C₈	—	26	1	no	—
684	C₈	—	26	1	no	—
685	C₈	#41×D₁₃	1	2	yes	—
686	C₈	#41×D₁₃	1	2	yes	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	13	4	no	—
690	C₂²	—	13	2	no	—
691	C₂²	—	26	2	no	—
692	C₂²	—	26	1	no	—
693	C₂²	—	52	4	no	—
694	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	4	no	—
700	C₄	—	13	2	no	—
701	C₄	—	26	2	no	—
702	C₄	—	26	2	no	—
703	C₄	—	26	1	no	—
704	C₄	—	52	4	no	—
705	C₄	—	52	4	no	—
706	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
707	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
708	C₂	—	4	1	no	—
709	C₂	—	13	4	no	—
710	C₂	—	52	1	no	—
711	C₂	D₁₃×#532	1	1	yes	characteristic
712	C₂	D₁₃×#578	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₁₃×#3177	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂³×D₁₃	C₂×D₄
hypercenter	#3177	D₁₃
hypocenter	C₁₃	C₂×#3177
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3177

Complements

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

N	H ≅ G/N	type
2. #13125496	C₂	semidirect
3. #13125495	C₂	semidirect
4. #13125494	C₂	semidirect
5. #13125493	C₂	semidirect
6. #13125492	C₂	semidirect
7. #13125491	C₂	semidirect
8. #13125490	C₂	semidirect
9. #13125489	C₂	semidirect
10. #13125488	C₂	semidirect
11. D₁₃×#499	C₂	semidirect
12. D₁₃×#494	C₂	semidirect
13. D₁₃×#491	C₂	semidirect
16. D₁₃×#441	C₂	semidirect
17. C₄×Q₁₆×D₁₃	C₂	semidirect
19. C₁₃×#3177	C₂	semidirect
39. C₁₃×#499	C₂²	semidirect
40. C₁₃×#494	C₂²	semidirect
41. C₁₃×#491	C₂²	semidirect
44. C₁₃×#441	C₂²	semidirect
45. C₄×C₁₃×Q₁₆	C₂²	semidirect
49. #11718845	C₂²	semidirect
50. Q₁₆×Dic₁₃	C₂²	semidirect
51. #11718842	C₂²	semidirect
52. #11718842	C₂²	semidirect
57. #11718753	C₂²	semidirect
58. #11718743	C₂²	semidirect
59. #11718730	C₂²	semidirect
60. #11718725	C₂²	semidirect
63. #11718691	C₂²	semidirect
64. C₄×#6107	C₂²	semidirect
68. #11718539	C₂²	semidirect
69. #11718534	C₂²	semidirect
72. #11718519	C₂²	semidirect
73. #11718514	C₂²	semidirect
78. #11718458	C₂²	semidirect
79. #11718458	C₂²	semidirect
80. #11718451	C₂²	semidirect
81. #11718450	C₂²	semidirect
82. #11718377	C₂²	semidirect
87. #11718364	C₂²	semidirect
88. #11718360	C₂²	semidirect
89. C₄×Dic₅₂	C₂²	semidirect
94. #11718344	C₂²	semidirect
298. #3177	D₁₃	direct (N × H)
373. #499	C₂×D₁₃	semidirect
378. #494	C₂×D₁₃	semidirect
384. #491	C₂×D₁₃	semidirect
402. #441	C₂×D₁₃	semidirect
408. C₄×Q₁₆	C₂×D₁₃	semidirect
557. D₁₃	#3177	direct (N × H)
643. C₁₃	C₂×#3177	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#541	2
#13125496	2
#13125495	2
#13125494	2
#13125493	2
#13125492	2
#13125491	2
#13125490	2
#13125489	2
#13125488	2
D₁₃×#499	2
D₁₃×#494	2
D₁₃×#491	2
D₁₃×#470	2
D₁₃×#467	2
D₁₃×#441	2
C₄×Q₁₆×D₁₃	2
D₁₃×#405	2
C₁₃×#3177	2
C₂×#3177	13

Subgroups — D13×#3177 #16732755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#3177 #16732755