Subgroups — C₁₃×#26995 #15713334

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2007	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1938	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₁₃×#537	C₂²	1	1	yes	characteristic
22	C₁₃×#536	C₂²	1	1	yes	characteristic
23	C₁₃×#520	C₂²	1	1	yes	characteristic
24	C₁₃×#519	C₂²	1	1	yes	characteristic
25	C₁₃×#485	—	2	1	no	—
26	C₁₃×#483	—	2	1	no	—
27	C₁₃×#482	—	2	1	no	—
28	C₁₃×#481	—	2	1	no	—
29	C₁₃×#470	—	2	1	no	—
30	C₁₃×#468	—	2	1	no	—
31	C₁₃×#467	—	2	1	no	—
32	C₁₃×#465	—	2	1	no	—
33	C₁₃×#464	—	2	1	no	—
34	C₁₃×#464	—	2	1	no	—
35	C₁₃×#462	—	2	1	no	—
36	C₁₃×#462	—	2	1	no	—
37	C₁₃×#441	—	2	1	no	—
38	C₁₃×#440	—	2	1	no	—
39	C₄×C₁₃×Q₁₆	—	2	1	no	—
40	C₄×C₁₃×SD₁₆	—	2	1	no	—
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#428	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
45	C₁₃×#424	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#416	C₂²	1	1	yes	characteristic
51	C₁₃×#416	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₁₃×#408	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
59	C₁₃×#391	C₂²	1	1	yes	characteristic
60	C₁₃×#391	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#341	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#137	—	2	2	no	—
72	C₁₃×#137	—	2	2	no	—
73	C₁₃×#137	—	2	2	no	—
74	C₁₃×#137	—	2	2	no	—
75	C₁₃×#137	—	4	1	no	—
76	C₁₃×#137	—	4	1	no	—
77	C₂×C₁₃×Q₁₆	—	2	1	no	—
78	C₂×C₁₃×Q₁₆	—	2	1	no	—
79	C₂×C₁₃×Q₁₆	—	2	1	no	—
80	C₂×C₁₃×Q₁₆	—	2	2	no	—
81	C₂×C₁₃×Q₁₆	—	2	1	no	—
82	C₂×C₁₃×Q₁₆	—	2	1	no	—
83	C₂×C₁₃×Q₁₆	—	4	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	2	1	no	—
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₁₃×#131	—	2	2	no	—
88	C₁₃×#131	—	4	1	no	—
89	C₂×C₁₃×M₁₆	—	2	1	no	—
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	—	2	1	no	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#123	—	4	1	no	—
100	C₁₃×C₂²⋊Q₈	—	2	1	no	—
101	C₁₃×C₂²⋊Q₈	—	2	1	no	—
102	C₁₃×C₂²⋊Q₈	—	2	1	no	—
103	C₁₃×C₂²⋊Q₈	—	2	1	no	—
104	C₁₃×#121	—	2	1	no	—
105	C₁₃×#121	—	2	1	no	—
106	C₁₃×#121	—	4	1	no	—
107	C₄×Q₈×C₁₃	—	2	1	no	—
108	C₄×Q₈×C₁₃	—	2	1	no	—
109	C₄×Q₈×C₁₃	—	2	1	no	—
110	C₄×Q₈×C₁₃	—	2	1	no	—
111	C₄×Q₈×C₁₃	—	2	1	no	—
112	C₄×D₄×C₁₃	—	2	1	no	—
113	C₄×D₄×C₁₃	—	4	1	no	—
114	C₁₃×#117	—	2	1	no	—
115	C₁₃×#117	—	4	1	no	—
116	C₁₃×#117	C₂³	1	1	yes	characteristic
117	C₁₃×#117	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#107	—	2	1	no	—
123	C₁₃×#107	—	2	1	no	—
124	C₁₃×#107	—	2	1	no	—
125	C₁₃×#106	—	2	1	no	—
126	C₁₃×#106	—	2	1	no	—
127	C₁₃×#106	—	2	1	no	—
128	C₁₃×#106	—	2	1	no	—
129	C₁₃×#106	—	2	1	no	—
130	C₁₃×C₄⋊C₈	—	2	1	no	—
131	C₁₃×C₄⋊C₈	—	2	1	no	—
132	C₁₃×#104	—	2	2	no	—
133	C₁₃×#104	—	4	1	no	—
134	C₁₃×#103	—	2	1	no	—
135	C₁₃×#103	—	2	1	no	—
136	C₁₃×#103	—	2	1	no	—
137	C₁₃×#103	—	2	1	no	—
138	C₁₃×#103	—	2	1	no	—
139	C₁₃×#103	—	2	1	no	—
140	C₁₃×#103	—	2	1	no	—
141	C₁₃×#103	D₄	1	1	yes	characteristic
142	C₁₃×#103	D₄	1	1	yes	characteristic
143	C₁₃×#103	D₄	1	1	yes	characteristic
144	C₁₃×#103	D₄	1	1	yes	characteristic
145	C₁₃×#102	—	2	1	no	—
146	C₁₃×#102	D₄	1	1	yes	characteristic
147	C₁₃×#102	D₄	1	1	yes	characteristic
148	C₁₃×#102	D₄	1	1	yes	characteristic
149	C₁₃×#102	D₄	1	1	yes	characteristic
150	C₁₃×#101	—	2	2	no	—
151	C₁₃×#101	—	2	2	no	—
152	C₁₃×C₂²⋊C₈	—	2	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	1	no	—
154	C₁₃×#97	—	2	1	no	—
155	C₁₃×#97	—	4	1	no	—
156	C₄×C₈×C₁₃	—	2	1	no	—
157	C₁₃×#95	—	4	1	no	—
158	C₁₃×#95	—	4	1	no	—
159	#26995	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	—	2	1	no	—
162	C₁₃×#41	—	2	1	no	—
163	C₁₃×#41	—	2	1	no	—
164	C₁₃×#41	—	2	1	no	—
165	C₁₃×#41	—	2	1	no	—
166	C₁₃×#41	—	2	1	no	—
167	C₁₃×#41	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×Q₈×C₁₃	#41	1	2	yes	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	4	1	no	—
185	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	—	2	1	no	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	4	1	no	—
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₁₃×Q₁₆	—	2	4	no	—
197	C₁₃×Q₁₆	—	4	2	no	—
198	C₁₃×Q₁₆	—	4	2	no	—
199	C₁₃×Q₁₆	—	4	2	no	—
200	C₁₃×Q₁₆	—	4	2	no	—
201	C₁₃×SD₁₆	—	2	4	no	—
202	C₁₃×SD₁₆	—	4	2	no	—
203	C₁₃×SD₁₆	—	4	2	no	—
204	C₁₃×M₁₆	—	2	1	no	—
205	C₁₃×M₁₆	—	2	1	no	—
206	C₁₃×M₁₆	—	2	1	no	—
207	C₁₃×M₁₆	—	2	1	no	—
208	C₁₃×M₁₆	—	2	1	no	—
209	C₁₃×M₁₆	—	2	1	no	—
210	C₁₃×M₁₆	—	4	2	no	—
211	C₁₃×M₁₆	#41	1	2	yes	—
212	C₁₃×M₁₆	#41	1	2	yes	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	4	2	no	—
222	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	4	1	no	—
231	C₁₃×C₄⋊C₄	—	4	1	no	—
232	C₁₃×C₄⋊C₄	—	4	1	no	—
233	C₁₃×C₄⋊C₄	—	4	1	no	—
234	C₁₃×C₄⋊C₄	—	4	1	no	—
235	C₁₃×C₄⋊C₄	—	4	1	no	—
236	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₂²⋊C₄	—	2	1	no	—
241	C₁₃×C₂²⋊C₄	—	2	1	no	—
242	C₁₃×C₂²⋊C₄	—	4	1	no	—
243	C₁₃×C₂²⋊C₄	—	4	1	no	—
244	C₁₃×C₂²⋊C₄	—	4	1	no	—
245	C₁₃×C₂²⋊C₄	—	4	1	no	—
246	C₁₃×C₂²⋊C₄	—	4	1	no	—
247	C₄²×C₁₃	—	2	1	no	—
248	C₄²×C₁₃	—	2	1	no	—
249	C₄²×C₁₃	—	2	1	no	—
250	C₄²×C₁₃	—	2	1	no	—
251	C₄²×C₁₃	—	4	1	no	—
252	C₄²×C₁₃	—	4	1	no	—
253	C₄²×C₁₃	—	4	1	no	—
254	#3099	C₂×C₁₃	1	1	yes	characteristic
255	#3063	C₂×C₁₃	1	1	yes	characteristic
256	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2947	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#2020	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#2007	C₂×C₁₃	1	1	yes	characteristic
262	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#1938	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1765	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
272	Q₈×C₁₃	—	2	2	no	—
273	Q₈×C₁₃	—	2	1	no	—
274	Q₈×C₁₃	—	2	1	no	—
275	Q₈×C₁₃	—	2	2	no	—
276	Q₈×C₁₃	—	2	1	no	—
277	Q₈×C₁₃	—	2	1	no	—
278	Q₈×C₁₃	—	4	1	no	—
279	Q₈×C₁₃	—	4	1	no	—
280	Q₈×C₁₃	—	4	1	no	—
281	Q₈×C₁₃	—	4	1	no	—
282	Q₈×C₁₃	—	4	1	no	—
283	Q₈×C₁₃	—	4	1	no	—
284	D₄×C₁₃	—	2	1	no	—
285	D₄×C₁₃	—	2	1	no	—
286	D₄×C₁₃	—	2	1	no	—
287	D₄×C₁₃	—	2	1	no	—
288	D₄×C₁₃	—	4	1	no	—
289	D₄×C₁₃	—	4	1	no	—
290	D₄×C₁₃	—	4	1	no	—
291	D₄×C₁₃	—	4	1	no	—
292	D₄×C₁₃	—	16	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	8	1	no	—
315	C₂×C₄×C₁₃	—	8	1	no	—
316	C₂×C₄×C₁₃	—	16	1	no	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
323	C₈×C₁₃	—	2	2	no	—
324	C₈×C₁₃	—	2	1	no	—
325	C₈×C₁₃	—	2	1	no	—
326	C₈×C₁₃	—	2	1	no	—
327	C₈×C₁₃	—	2	1	no	—
328	C₈×C₁₃	—	2	2	no	—
329	C₈×C₁₃	—	4	1	no	—
330	C₈×C₁₃	—	4	1	no	—
331	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
334	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
336	#537	C₂²×C₁₃	1	1	yes	characteristic
337	#536	C₂²×C₁₃	1	1	yes	characteristic
338	#520	C₂²×C₁₃	1	1	yes	characteristic
339	#519	C₂²×C₁₃	1	1	yes	characteristic
340	#485	—	2	1	no	—
341	#483	—	2	1	no	—
342	#482	—	2	1	no	—
343	#481	—	2	1	no	—
344	#470	—	2	1	no	—
345	#468	—	2	1	no	—
346	#467	—	2	1	no	—
347	#465	—	2	1	no	—
348	#464	—	2	1	no	—
349	#464	—	2	1	no	—
350	#462	—	2	1	no	—
351	#462	—	2	1	no	—
352	#441	—	2	1	no	—
353	#440	—	2	1	no	—
354	C₄×Q₁₆	—	2	1	no	—
355	C₄×SD₁₆	—	2	1	no	—
356	#428	C₂²×C₁₃	1	1	yes	characteristic
357	#428	C₂²×C₁₃	1	1	yes	characteristic
358	#428	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
360	#424	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
363	#419	C₂²×C₁₃	1	1	yes	characteristic
364	#417	C₂²×C₁₃	1	1	yes	characteristic
365	#416	C₂²×C₁₃	1	1	yes	characteristic
366	#416	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
371	#408	C₂²×C₁₃	1	1	yes	characteristic
372	#405	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
374	#391	C₂²×C₁₃	1	1	yes	characteristic
375	#391	C₂²×C₁₃	1	1	yes	characteristic
376	#343	C₂²×C₁₃	1	1	yes	characteristic
377	#343	C₂²×C₁₃	1	1	yes	characteristic
378	#341	C₂²×C₁₃	1	1	yes	characteristic
379	#341	C₂²×C₁₃	1	1	yes	characteristic
380	#339	C₂²×C₁₃	1	1	yes	characteristic
381	#339	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×C₁₃	—	2	1	no	—
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	4	1	no	—
385	C₂²×C₁₃	—	4	1	no	—
386	C₂²×C₁₃	—	4	1	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	—	4	1	no	—
389	C₂²×C₁₃	—	4	1	no	—
390	C₂²×C₁₃	#540	1	1	yes	characteristic
391	C₂²×C₁₃	D₄²	1	1	yes	characteristic
392	C₂²×C₁₃	#553	1	1	yes	characteristic
393	C₄×C₁₃	—	4	1	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	4	2	no	—
396	C₄×C₁₃	—	4	1	no	—
397	C₄×C₁₃	—	4	1	no	—
398	C₄×C₁₃	—	4	1	no	—
399	C₄×C₁₃	—	4	1	no	—
400	C₄×C₁₃	—	8	1	no	—
401	C₄×C₁₃	—	8	1	no	—
402	C₄×C₁₃	—	8	1	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	#525	1	1	yes	characteristic
405	C₄×C₁₃	#532	1	1	yes	characteristic
406	C₄×C₁₃	#546	1	1	yes	characteristic
407	C₄×C₁₃	#546	1	1	yes	characteristic
408	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
412	#137	—	2	2	no	—
413	#137	—	2	2	no	—
414	#137	—	2	2	no	—
415	#137	—	2	2	no	—
416	#137	—	4	1	no	—
417	#137	—	4	1	no	—
418	C₂×Q₁₆	—	2	1	no	—
419	C₂×Q₁₆	—	2	1	no	—
420	C₂×Q₁₆	—	2	1	no	—
421	C₂×Q₁₆	—	2	2	no	—
422	C₂×Q₁₆	—	2	1	no	—
423	C₂×Q₁₆	—	2	1	no	—
424	C₂×Q₁₆	—	4	1	no	—
425	C₂×SD₁₆	—	2	1	no	—
426	C₂×SD₁₆	—	2	1	no	—
427	C₂×SD₁₆	—	2	1	no	—
428	#131	—	2	2	no	—
429	#131	—	4	1	no	—
430	C₂×M₁₆	—	2	1	no	—
431	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
435	C₂²×C₈	—	2	1	no	—
436	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄⋊Q₈	—	2	1	no	—
439	#124	—	2	1	no	—
440	#123	—	4	1	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	—	2	1	no	—
444	C₂²⋊Q₈	—	2	1	no	—
445	#121	—	2	1	no	—
446	#121	—	2	1	no	—
447	#121	—	4	1	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	4	1	no	—
455	#117	—	2	1	no	—
456	#117	—	4	1	no	—
457	#117	C₂³×C₁₃	1	1	yes	characteristic
458	#117	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
463	#107	—	2	1	no	—
464	#107	—	2	1	no	—
465	#107	—	2	1	no	—
466	#106	—	2	1	no	—
467	#106	—	2	1	no	—
468	#106	—	2	1	no	—
469	#106	—	2	1	no	—
470	#106	—	2	1	no	—
471	C₄⋊C₈	—	2	1	no	—
472	C₄⋊C₈	—	2	1	no	—
473	#104	—	2	2	no	—
474	#104	—	4	1	no	—
475	#103	—	2	1	no	—
476	#103	—	2	1	no	—
477	#103	—	2	1	no	—
478	#103	—	2	1	no	—
479	#103	—	2	1	no	—
480	#103	—	2	1	no	—
481	#103	—	2	1	no	—
482	#103	D₄×C₁₃	1	1	yes	characteristic
483	#103	D₄×C₁₃	1	1	yes	characteristic
484	#103	D₄×C₁₃	1	1	yes	characteristic
485	#103	D₄×C₁₃	1	1	yes	characteristic
486	#102	—	2	1	no	—
487	#102	D₄×C₁₃	1	1	yes	characteristic
488	#102	D₄×C₁₃	1	1	yes	characteristic
489	#102	D₄×C₁₃	1	1	yes	characteristic
490	#102	D₄×C₁₃	1	1	yes	characteristic
491	#101	—	2	2	no	—
492	#101	—	2	2	no	—
493	C₂²⋊C₈	—	2	1	no	—
494	C₂²⋊C₈	—	2	1	no	—
495	#97	—	2	1	no	—
496	#97	—	4	1	no	—
497	C₄×C₈	—	2	1	no	—
498	#95	—	4	1	no	—
499	#95	—	4	1	no	—
500	C₂×C₁₃	—	2	1	no	—
501	C₂×C₁₃	—	2	1	no	—
502	C₂×C₁₃	—	8	1	no	—
503	C₂×C₁₃	—	8	1	no	—
504	C₂×C₁₃	#2464	1	1	yes	characteristic
505	C₂×C₁₃	#3289	1	1	yes	characteristic
506	C₂×C₁₃	#3289	1	1	yes	characteristic
507	#41	—	2	1	no	—
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	#41	—	2	1	no	—
511	#41	—	2	1	no	—
512	#41	—	2	1	no	—
513	#41	—	2	1	no	—
514	#41	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂×Q₈	C₁₃×#41	1	2	yes	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	4	1	no	—
542	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
543	Q₁₆	—	2	4	no	—
544	Q₁₆	—	4	2	no	—
545	Q₁₆	—	4	2	no	—
546	Q₁₆	—	4	2	no	—
547	Q₁₆	—	4	2	no	—
548	SD₁₆	—	2	4	no	—
549	SD₁₆	—	4	2	no	—
550	SD₁₆	—	4	2	no	—
551	M₁₆	—	2	1	no	—
552	M₁₆	—	2	1	no	—
553	M₁₆	—	2	1	no	—
554	M₁₆	—	2	1	no	—
555	M₁₆	—	2	1	no	—
556	M₁₆	—	2	1	no	—
557	M₁₆	—	4	2	no	—
558	M₁₆	C₁₃×#41	1	2	yes	—
559	M₁₆	C₁₃×#41	1	2	yes	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	4	2	no	—
569	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
571	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
572	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	4	1	no	—
578	C₄⋊C₄	—	4	1	no	—
579	C₄⋊C₄	—	4	1	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
584	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	4	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	4	1	no	—
599	C₄²	—	4	1	no	—
600	C₄²	—	4	1	no	—
601	C₁₃	#26995	1	1	yes	characteristic, direct product factor, Sylow
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	2	1	no	—
607	Q₈	—	2	1	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	2	1	no	—
610	Q₈	—	2	1	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	D₄	—	2	1	no	—
618	D₄	—	2	1	no	—
619	D₄	—	2	1	no	—
620	D₄	—	2	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	16	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	8	1	no	—
648	C₂×C₄	—	8	1	no	—
649	C₂×C₄	—	16	1	no	—
650	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
652	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
653	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
654	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
655	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	2	1	no	—
658	C₈	—	2	1	no	—
659	C₈	—	2	1	no	—
660	C₈	—	2	1	no	—
661	C₈	—	2	2	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	C₁₃×#540	1	1	yes	characteristic
673	C₂²	D₄²×C₁₃	1	1	yes	characteristic
674	C₂²	C₁₃×#553	1	1	yes	characteristic
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₁₃×#525	1	1	yes	characteristic
687	C₄	C₁₃×#532	1	1	yes	characteristic
688	C₄	C₁₃×#546	1	1	yes	characteristic
689	C₄	C₁₃×#546	1	1	yes	characteristic
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	8	1	no	—
693	C₂	—	8	1	no	—
694	C₂	C₁₃×#2464	1	1	yes	characteristic
695	C₂	C₁₃×#3289	1	1	yes	characteristic
696	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#537	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#3044	C₂	semidirect
4. C₁₃×#2947	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2038	C₂	semidirect
7. C₁₃×#2020	C₂	semidirect
9. C₁₃×#1971	C₂	semidirect
10. C₁₃×#1938	C₂	semidirect
11. C₁₃×#1930	C₂	semidirect
12. C₁₃×#1908	C₂	semidirect
13. C₁₃×#1882	C₂	semidirect
14. C₁₃×#1857	C₂	semidirect
15. C₁₃×#1765	C₂	semidirect
159. #26995	C₁₃	direct (N × H)
256. #3044	C₂×C₁₃	semidirect
257. #2947	C₂×C₁₃	semidirect
258. #2090	C₂×C₁₃	semidirect
259. #2038	C₂×C₁₃	semidirect
260. #2020	C₂×C₁₃	semidirect
262. #1971	C₂×C₁₃	semidirect
263. #1938	C₂×C₁₃	semidirect
264. #1930	C₂×C₁₃	semidirect
265. #1908	C₂×C₁₃	semidirect
266. #1882	C₂×C₁₃	semidirect
267. #1857	C₂×C₁₃	semidirect
268. #1765	C₂×C₁₃	semidirect
601. C₁₃	#26995	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3099	2
C₁₃×#3063	2
C₁₃×#3044	2
C₁₃×#2947	2
C₁₃×#2090	2
C₁₃×#2038	2
C₁₃×#2020	2
C₁₃×#2007	2
C₁₃×#1971	2
C₁₃×#1938	2
C₁₃×#1930	2
C₁₃×#1908	2
C₁₃×#1882	2
C₁₃×#1857	2
C₁₃×#1765	2
#26995	13

Subgroups — C13×#26995 #15713334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26995 #15713334