Subgroups — C₁₃×#26852 #15713191

Order 3328.

698 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2061	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2005	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1938	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1886	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₁₃×#544	C₂²	1	1	yes	characteristic
18	C₁₃×#536	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#519	C₂²	1	1	yes	characteristic
22	C₁₃×#491	—	2	1	no	—
23	C₁₃×#489	—	2	1	no	—
24	C₁₃×#488	—	2	1	no	—
25	C₁₃×#487	—	2	1	no	—
26	C₁₃×#485	—	2	1	no	—
27	C₁₃×#485	—	2	1	no	—
28	C₁₃×#484	—	2	1	no	—
29	C₁₃×#483	—	2	1	no	—
30	C₁₃×#479	—	2	1	no	—
31	C₁₃×#479	—	2	1	no	—
32	C₁₃×#477	—	2	1	no	—
33	C₁₃×#475	—	2	1	no	—
34	C₁₃×#441	—	2	1	no	—
35	C₁₃×#440	—	2	1	no	—
36	C₄×C₁₃×Q₁₆	—	2	1	no	—
37	C₄×C₁₃×SD₁₆	—	2	1	no	—
38	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	C₂²	1	1	yes	characteristic
43	C₁₃×#424	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
45	C₁₃×#419	C₂²	1	1	yes	characteristic
46	C₁₃×#419	C₂²	1	1	yes	characteristic
47	C₁₃×#419	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#416	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	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	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
60	C₁₃×#382	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×#339	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#137	—	2	2	no	—
71	C₁₃×#137	—	2	2	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×#125	—	2	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#124	—	2	1	no	—
88	C₁₃×#123	—	4	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	1	no	—
90	C₁₃×C₂²⋊Q₈	—	2	1	no	—
91	C₁₃×C₂²⋊Q₈	—	4	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	4	1	no	—
99	C₁₃×#117	—	2	1	no	—
100	C₁₃×#117	—	4	1	no	—
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₁₃×#117	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#108	—	2	2	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	D₄	1	1	yes	characteristic
114	C₁₃×#107	D₄	1	1	yes	characteristic
115	C₁₃×#106	—	2	1	no	—
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#106	—	2	1	no	—
118	C₁₃×#106	D₄	1	1	yes	characteristic
119	C₁₃×#106	D₄	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	—	2	1	no	—
121	C₁₃×C₄⋊C₈	—	2	1	no	—
122	C₁₃×#104	—	2	2	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#103	—	2	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	D₄	1	1	yes	characteristic
139	C₁₃×#103	D₄	1	1	yes	characteristic
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	D₄	1	1	yes	characteristic
142	C₁₃×#102	D₄	1	1	yes	characteristic
143	C₁₃×#101	—	2	2	no	—
144	C₁₃×#101	—	2	2	no	—
145	C₁₃×C₂²⋊C₈	—	2	1	no	—
146	C₁₃×C₂²⋊C₈	—	2	1	no	—
147	C₁₃×#97	—	2	1	no	—
148	C₁₃×#97	—	2	1	no	—
149	C₁₃×#97	—	2	2	no	—
150	C₄×C₈×C₁₃	—	2	1	no	—
151	C₄×C₈×C₁₃	—	2	1	no	—
152	C₁₃×#95	—	4	1	no	—
153	#26852	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₁₃×#41	—	2	1	no	—
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	4	1	no	—
170	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂×Q₈×C₁₃	#41	1	2	yes	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	4	1	no	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×Q₁₆	—	2	4	no	—
183	C₁₃×SD₁₆	—	2	4	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	—	2	1	no	—
189	C₁₃×M₁₆	—	2	1	no	—
190	C₁₃×M₁₆	—	2	1	no	—
191	C₁₃×M₁₆	#41	1	2	yes	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	4	1	no	—
209	C₁₃×C₄⋊C₄	—	4	4	no	—
210	C₁₃×C₄⋊C₄	—	4	1	no	—
211	C₁₃×C₄⋊C₄	—	4	1	no	—
212	C₁₃×C₄⋊C₄	—	4	1	no	—
213	C₁₃×C₄⋊C₄	—	4	1	no	—
214	C₁₃×C₄⋊C₄	—	4	1	no	—
215	C₁₃×C₄⋊C₄	—	4	1	no	—
216	C₁₃×C₄⋊C₄	—	4	1	no	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₁₃×C₂²⋊C₄	—	2	1	no	—
224	C₁₃×C₂²⋊C₄	—	2	1	no	—
225	C₁₃×C₂²⋊C₄	—	2	1	no	—
226	C₁₃×C₂²⋊C₄	—	4	1	no	—
227	C₁₃×C₂²⋊C₄	—	4	1	no	—
228	C₁₃×C₂²⋊C₄	—	4	1	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	4	1	no	—
234	C₄²×C₁₃	—	4	1	no	—
235	C₄²×C₁₃	—	4	1	no	—
236	C₄²×C₁₃	#41	1	2	yes	—
237	#3137	C₂×C₁₃	1	1	yes	characteristic
238	#3097	C₂×C₁₃	1	1	yes	characteristic
239	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2947	C₂×C₁₃	1	1	yes	characteristic
241	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2061	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2052	C₂×C₁₃	1	1	yes	characteristic
244	#2005	C₂×C₁₃	1	1	yes	characteristic
245	#1960	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1938	C₂×C₁₃	1	1	yes	characteristic
247	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1886	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1860	C₂×C₁₃	1	1	yes	characteristic
251	#1773	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
254	Q₈×C₁₃	—	2	2	no	—
255	Q₈×C₁₃	—	2	1	no	—
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	2	2	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	Q₈×C₁₃	—	4	1	no	—
260	Q₈×C₁₃	—	4	1	no	—
261	Q₈×C₁₃	—	4	1	no	—
262	Q₈×C₁₃	—	4	1	no	—
263	Q₈×C₁₃	—	4	1	no	—
264	Q₈×C₁₃	—	16	1	no	—
265	D₄×C₁₃	—	2	1	no	—
266	D₄×C₁₃	—	2	1	no	—
267	D₄×C₁₃	—	4	1	no	—
268	D₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	8	1	no	—
290	C₂×C₄×C₁₃	—	8	1	no	—
291	C₂×C₄×C₁₃	—	16	1	no	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₃	—	2	2	no	—
299	C₈×C₁₃	—	2	1	no	—
300	C₈×C₁₃	—	2	1	no	—
301	C₈×C₁₃	—	2	1	no	—
302	C₈×C₁₃	—	2	1	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
307	#544	C₂²×C₁₃	1	1	yes	characteristic
308	#536	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	#520	C₂²×C₁₃	1	1	yes	characteristic
311	#519	C₂²×C₁₃	1	1	yes	characteristic
312	#491	—	2	1	no	—
313	#489	—	2	1	no	—
314	#488	—	2	1	no	—
315	#487	—	2	1	no	—
316	#485	—	2	1	no	—
317	#485	—	2	1	no	—
318	#484	—	2	1	no	—
319	#483	—	2	1	no	—
320	#479	—	2	1	no	—
321	#479	—	2	1	no	—
322	#477	—	2	1	no	—
323	#475	—	2	1	no	—
324	#441	—	2	1	no	—
325	#440	—	2	1	no	—
326	C₄×Q₁₆	—	2	1	no	—
327	C₄×SD₁₆	—	2	1	no	—
328	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
329	#428	C₂²×C₁₃	1	1	yes	characteristic
330	#428	C₂²×C₁₃	1	1	yes	characteristic
331	#428	C₂²×C₁₃	1	1	yes	characteristic
332	#427	C₂²×C₁₃	1	1	yes	characteristic
333	#424	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
335	#419	C₂²×C₁₃	1	1	yes	characteristic
336	#419	C₂²×C₁₃	1	1	yes	characteristic
337	#419	C₂²×C₁₃	1	1	yes	characteristic
338	#417	C₂²×C₁₃	1	1	yes	characteristic
339	#416	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
346	#408	C₂²×C₁₃	1	1	yes	characteristic
347	#405	C₂²×C₁₃	1	1	yes	characteristic
348	#405	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
350	#382	C₂²×C₁₃	1	1	yes	characteristic
351	#343	C₂²×C₁₃	1	1	yes	characteristic
352	#343	C₂²×C₁₃	1	1	yes	characteristic
353	#341	C₂²×C₁₃	1	1	yes	characteristic
354	#339	C₂²×C₁₃	1	1	yes	characteristic
355	#339	C₂²×C₁₃	1	1	yes	characteristic
356	#339	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₁₃	—	2	1	no	—
358	C₂²×C₁₃	—	2	1	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	#542	1	1	yes	characteristic
363	C₂²×C₁₃	D₄²	1	1	yes	characteristic
364	C₂²×C₁₃	#551	1	1	yes	characteristic
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	1	no	—
374	C₄×C₁₃	—	8	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	#525	1	1	yes	characteristic
378	C₄×C₁₃	#532	1	1	yes	characteristic
379	C₄×C₁₃	#547	1	1	yes	characteristic
380	C₄×C₁₃	#548	1	1	yes	characteristic
381	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	#137	—	2	2	no	—
385	#137	—	2	2	no	—
386	C₂×Q₁₆	—	2	1	no	—
387	C₂×SD₁₆	—	2	1	no	—
388	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄⋊Q₈	—	2	1	no	—
395	C₄⋊Q₈	—	2	1	no	—
396	C₄⋊Q₈	—	2	1	no	—
397	C₄⋊Q₈	—	2	2	no	—
398	C₄⋊Q₈	—	2	2	no	—
399	#125	—	2	1	no	—
400	#125	—	2	1	no	—
401	#124	—	2	1	no	—
402	#123	—	4	1	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	4	1	no	—
406	C₄×Q₈	—	2	1	no	—
407	C₄×Q₈	—	2	1	no	—
408	C₄×Q₈	—	2	1	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	4	1	no	—
413	#117	—	2	1	no	—
414	#117	—	4	1	no	—
415	#117	C₂³×C₁₃	1	1	yes	characteristic
416	#117	C₂³×C₁₃	1	1	yes	characteristic
417	#117	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	4	1	no	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	#108	—	2	2	no	—
424	#107	—	2	1	no	—
425	#107	—	2	1	no	—
426	#107	—	2	1	no	—
427	#107	D₄×C₁₃	1	1	yes	characteristic
428	#107	D₄×C₁₃	1	1	yes	characteristic
429	#106	—	2	1	no	—
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	D₄×C₁₃	1	1	yes	characteristic
433	#106	D₄×C₁₃	1	1	yes	characteristic
434	C₄⋊C₈	—	2	1	no	—
435	C₄⋊C₈	—	2	1	no	—
436	#104	—	2	2	no	—
437	#103	—	2	1	no	—
438	#103	—	2	1	no	—
439	#103	—	2	1	no	—
440	#103	—	2	1	no	—
441	#103	—	2	1	no	—
442	#103	—	2	1	no	—
443	#103	—	2	1	no	—
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	—	2	1	no	—
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#103	—	2	1	no	—
450	#103	—	2	1	no	—
451	#103	—	2	1	no	—
452	#103	D₄×C₁₃	1	1	yes	characteristic
453	#103	D₄×C₁₃	1	1	yes	characteristic
454	#102	—	2	1	no	—
455	#102	D₄×C₁₃	1	1	yes	characteristic
456	#102	D₄×C₁₃	1	1	yes	characteristic
457	#101	—	2	2	no	—
458	#101	—	2	2	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	#97	—	2	1	no	—
462	#97	—	2	1	no	—
463	#97	—	2	2	no	—
464	C₄×C₈	—	2	1	no	—
465	C₄×C₈	—	2	1	no	—
466	#95	—	4	1	no	—
467	C₂×C₁₃	—	2	1	no	—
468	C₂×C₁₃	—	2	1	no	—
469	C₂×C₁₃	—	8	1	no	—
470	C₂×C₁₃	#2461	1	1	yes	characteristic
471	C₂×C₁₃	#3289	1	1	yes	characteristic
472	C₂×C₁₃	#3289	1	1	yes	characteristic
473	#41	—	2	1	no	—
474	#41	—	2	1	no	—
475	#41	—	2	1	no	—
476	#41	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	4	1	no	—
489	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×Q₈	C₁₃×#41	1	2	yes	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	Q₁₆	—	2	4	no	—
502	SD₁₆	—	2	4	no	—
503	M₁₆	—	2	1	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	2	1	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	C₁₃×#41	1	2	yes	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	4	1	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	4	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	—	4	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	4	1	no	—
553	C₄²	—	4	1	no	—
554	C₄²	—	4	1	no	—
555	C₄²	C₁₃×#41	1	2	yes	—
556	C₁₃	#26852	1	1	yes	characteristic, direct product factor, Sylow
557	C₂³	—	2	1	no	—
558	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
559	Q₈	—	2	2	no	—
560	Q₈	—	2	1	no	—
561	Q₈	—	2	1	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	16	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	8	1	no	—
595	C₂×C₄	—	8	1	no	—
596	C₂×C₄	—	16	1	no	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
600	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
601	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
602	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
603	C₈	—	2	2	no	—
604	C₈	—	2	1	no	—
605	C₈	—	2	1	no	—
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	4	1	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	C₁₃×#542	1	1	yes	characteristic
617	C₂²	D₄²×C₁₃	1	1	yes	characteristic
618	C₂²	C₁₃×#551	1	1	yes	characteristic
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	C₁₃×#525	1	1	yes	characteristic
632	C₄	C₁₃×#532	1	1	yes	characteristic
633	C₄	C₁₃×#547	1	1	yes	characteristic
634	C₄	C₁₃×#548	1	1	yes	characteristic
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	1	no	—
638	C₂	C₁₃×#2461	1	1	yes	characteristic
639	C₂	C₁₃×#3289	1	1	yes	characteristic
640	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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×#3082	C₂	semidirect
5. C₁₃×#2064	C₂	semidirect
6. C₁₃×#2061	C₂	semidirect
9. C₁₃×#1960	C₂	semidirect
11. C₁₃×#1930	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1886	C₂	semidirect
15. C₁₃×#1773	C₂	semidirect
153. #26852	C₁₃	direct (N × H)
239. #3082	C₂×C₁₃	semidirect
241. #2064	C₂×C₁₃	semidirect
242. #2061	C₂×C₁₃	semidirect
245. #1960	C₂×C₁₃	semidirect
247. #1930	C₂×C₁₃	semidirect
248. #1930	C₂×C₁₃	semidirect
249. #1886	C₂×C₁₃	semidirect
251. #1773	C₂×C₁₃	semidirect
556. C₁₃	#26852	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×#3137	2
C₁₃×#3097	2
C₁₃×#3082	2
C₁₃×#2947	2
C₁₃×#2064	2
C₁₃×#2061	2
C₁₃×#2052	2
C₁₃×#2005	2
C₁₃×#1960	2
C₁₃×#1938	2
C₁₃×#1930	2
C₁₃×#1886	2
C₁₃×#1860	2
C₁₃×#1773	2
#26852	13

Subgroups — C13×#26852 #15713191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26852 #15713191