Subgroups — C₁₃×#26849 #15713188

Order 3328.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 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×#2060	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×#1956	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1937	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×#1859	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1772	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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
60	C₁₃×#384	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	—	4	1	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#108	—	2	2	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	D₄	1	1	yes	characteristic
115	C₁₃×#107	D₄	1	1	yes	characteristic
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#106	—	2	1	no	—
118	C₁₃×#106	—	2	1	no	—
119	C₁₃×#106	D₄	1	1	yes	characteristic
120	C₁₃×#106	D₄	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	—	2	1	no	—
122	C₁₃×C₄⋊C₈	—	2	1	no	—
123	C₁₃×#104	—	2	2	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	—	2	1	no	—
139	C₁₃×#103	D₄	1	1	yes	characteristic
140	C₁₃×#103	D₄	1	1	yes	characteristic
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	D₄	1	1	yes	characteristic
143	C₁₃×#102	D₄	1	1	yes	characteristic
144	C₁₃×#101	—	2	2	no	—
145	C₁₃×#101	—	2	2	no	—
146	C₁₃×C₂²⋊C₈	—	2	1	no	—
147	C₁₃×C₂²⋊C₈	—	2	1	no	—
148	C₁₃×#97	—	2	1	no	—
149	C₁₃×#97	—	2	1	no	—
150	C₄×C₈×C₁₃	—	2	1	no	—
151	C₄×C₈×C₁₃	—	2	1	no	—
152	C₄×C₈×C₁₃	—	2	2	no	—
153	#26849	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	—	8	2	no	—
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×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₁₃×C₂²⋊C₄	—	2	1	no	—
225	C₁₃×C₂²⋊C₄	—	2	1	no	—
226	C₁₃×C₂²⋊C₄	—	2	1	no	—
227	C₁₃×C₂²⋊C₄	—	4	1	no	—
228	C₁₃×C₂²⋊C₄	—	4	1	no	—
229	C₁₃×C₂²⋊C₄	—	4	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	4	1	no	—
235	C₄²×C₁₃	—	4	1	no	—
236	C₄²×C₁₃	—	4	1	no	—
237	C₄²×C₁₃	#41	1	2	yes	—
238	#3137	C₂×C₁₃	1	1	yes	characteristic
239	#3097	C₂×C₁₃	1	1	yes	characteristic
240	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2947	C₂×C₁₃	1	1	yes	characteristic
242	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2060	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2052	C₂×C₁₃	1	1	yes	characteristic
245	#2005	C₂×C₁₃	1	1	yes	characteristic
246	#1956	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#1937	C₂×C₁₃	1	1	yes	characteristic
248	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1886	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1859	C₂×C₁₃	1	1	yes	characteristic
252	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
255	Q₈×C₁₃	—	2	2	no	—
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	2	1	no	—
258	Q₈×C₁₃	—	2	2	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	—	4	1	no	—
265	Q₈×C₁₃	—	16	1	no	—
266	D₄×C₁₃	—	2	1	no	—
267	D₄×C₁₃	—	2	1	no	—
268	D₄×C₁₃	—	4	1	no	—
269	D₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	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	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
290	C₂×C₄×C₁₃	—	8	1	no	—
291	C₂×C₄×C₁₃	—	8	1	no	—
292	C₂×C₄×C₁₃	—	16	1	no	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
299	C₈×C₁₃	—	2	2	no	—
300	C₈×C₁₃	—	2	1	no	—
301	C₈×C₁₃	—	2	1	no	—
302	C₈×C₁₃	—	2	1	no	—
303	C₈×C₁₃	—	2	1	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₈×C₁₃	—	4	1	no	—
306	C₈×C₁₃	—	4	1	no	—
307	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
308	#544	C₂²×C₁₃	1	1	yes	characteristic
309	#536	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
311	#520	C₂²×C₁₃	1	1	yes	characteristic
312	#519	C₂²×C₁₃	1	1	yes	characteristic
313	#491	—	2	1	no	—
314	#489	—	2	1	no	—
315	#488	—	2	1	no	—
316	#487	—	2	1	no	—
317	#485	—	2	1	no	—
318	#485	—	2	1	no	—
319	#484	—	2	1	no	—
320	#483	—	2	1	no	—
321	#479	—	2	1	no	—
322	#479	—	2	1	no	—
323	#477	—	2	1	no	—
324	#475	—	2	1	no	—
325	#441	—	2	1	no	—
326	#440	—	2	1	no	—
327	C₄×Q₁₆	—	2	1	no	—
328	C₄×SD₁₆	—	2	1	no	—
329	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
330	#428	C₂²×C₁₃	1	1	yes	characteristic
331	#428	C₂²×C₁₃	1	1	yes	characteristic
332	#428	C₂²×C₁₃	1	1	yes	characteristic
333	#427	C₂²×C₁₃	1	1	yes	characteristic
334	#424	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
336	#419	C₂²×C₁₃	1	1	yes	characteristic
337	#419	C₂²×C₁₃	1	1	yes	characteristic
338	#419	C₂²×C₁₃	1	1	yes	characteristic
339	#417	C₂²×C₁₃	1	1	yes	characteristic
340	#416	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×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
347	#408	C₂²×C₁₃	1	1	yes	characteristic
348	#405	C₂²×C₁₃	1	1	yes	characteristic
349	#405	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
351	#384	C₂²×C₁₃	1	1	yes	characteristic
352	#343	C₂²×C₁₃	1	1	yes	characteristic
353	#343	C₂²×C₁₃	1	1	yes	characteristic
354	#341	C₂²×C₁₃	1	1	yes	characteristic
355	#339	C₂²×C₁₃	1	1	yes	characteristic
356	#339	C₂²×C₁₃	1	1	yes	characteristic
357	#339	C₂²×C₁₃	1	1	yes	characteristic
358	C₂²×C₁₃	—	2	1	no	—
359	C₂²×C₁₃	—	2	1	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	#542	1	1	yes	characteristic
364	C₂²×C₁₃	D₄²	1	1	yes	characteristic
365	C₂²×C₁₃	#551	1	1	yes	characteristic
366	C₄×C₁₃	—	2	4	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	2	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	—	4	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	—	8	1	no	—
378	C₄×C₁₃	#525	1	1	yes	characteristic
379	C₄×C₁₃	#532	1	1	yes	characteristic
380	C₄×C₁₃	#547	1	1	yes	characteristic
381	C₄×C₁₃	#548	1	1	yes	characteristic
382	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	#137	—	2	2	no	—
386	#137	—	2	2	no	—
387	C₂×Q₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
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	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄⋊Q₈	—	2	1	no	—
396	C₄⋊Q₈	—	2	1	no	—
397	C₄⋊Q₈	—	2	1	no	—
398	C₄⋊Q₈	—	2	2	no	—
399	C₄⋊Q₈	—	2	2	no	—
400	#125	—	2	1	no	—
401	#125	—	2	1	no	—
402	#124	—	2	1	no	—
403	#123	—	4	1	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	—	4	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×Q₈	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	4	1	no	—
414	#117	—	2	1	no	—
415	#117	—	4	1	no	—
416	#117	C₂³×C₁₃	1	1	yes	characteristic
417	#117	C₂³×C₁₃	1	1	yes	characteristic
418	#117	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	4	1	no	—
421	C₂×C₄⋊C₄	—	4	1	no	—
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	#108	—	2	2	no	—
426	#107	—	2	1	no	—
427	#107	—	2	1	no	—
428	#107	—	2	1	no	—
429	#107	D₄×C₁₃	1	1	yes	characteristic
430	#107	D₄×C₁₃	1	1	yes	characteristic
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	—	2	1	no	—
434	#106	D₄×C₁₃	1	1	yes	characteristic
435	#106	D₄×C₁₃	1	1	yes	characteristic
436	C₄⋊C₈	—	2	1	no	—
437	C₄⋊C₈	—	2	1	no	—
438	#104	—	2	2	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	—	2	1	no	—
453	#103	—	2	1	no	—
454	#103	D₄×C₁₃	1	1	yes	characteristic
455	#103	D₄×C₁₃	1	1	yes	characteristic
456	#102	—	2	1	no	—
457	#102	D₄×C₁₃	1	1	yes	characteristic
458	#102	D₄×C₁₃	1	1	yes	characteristic
459	#101	—	2	2	no	—
460	#101	—	2	2	no	—
461	C₂²⋊C₈	—	2	1	no	—
462	C₂²⋊C₈	—	2	1	no	—
463	#97	—	2	1	no	—
464	#97	—	2	1	no	—
465	C₄×C₈	—	2	1	no	—
466	C₄×C₈	—	2	1	no	—
467	C₄×C₈	—	2	2	no	—
468	C₂×C₁₃	—	2	1	no	—
469	C₂×C₁₃	—	2	1	no	—
470	C₂×C₁₃	—	8	1	no	—
471	C₂×C₁₃	#2461	1	1	yes	characteristic
472	C₂×C₁₃	#3291	1	1	yes	characteristic
473	C₂×C₁₃	#3293	1	1	yes	characteristic
474	#41	—	2	1	no	—
475	#41	—	2	1	no	—
476	#41	—	2	1	no	—
477	#41	—	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	—	2	1	no	—
489	C₂×Q₈	—	4	1	no	—
490	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂×Q₈	C₁₃×#41	1	2	yes	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
502	Q₁₆	—	2	4	no	—
503	SD₁₆	—	2	4	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	—	2	1	no	—
511	M₁₆	C₁₃×#41	1	2	yes	—
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	—	2	1	no	—
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	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	4	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	—	4	1	no	—
537	C₄⋊C₄	—	8	2	no	—
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	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	4	1	no	—
555	C₄²	—	4	1	no	—
556	C₄²	—	4	1	no	—
557	C₄²	C₁₃×#41	1	2	yes	—
558	C₁₃	#26849	1	1	yes	characteristic, direct product factor, Sylow
559	C₂³	—	2	1	no	—
560	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
561	Q₈	—	2	2	no	—
562	Q₈	—	2	1	no	—
563	Q₈	—	2	1	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	4	1	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	16	1	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	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	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	8	1	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	—	16	1	no	—
599	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
602	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
604	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
605	C₈	—	2	2	no	—
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	2	1	no	—
609	C₈	—	2	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	C₁₃×#542	1	1	yes	characteristic
619	C₂²	D₄²×C₁₃	1	1	yes	characteristic
620	C₂²	C₁₃×#551	1	1	yes	characteristic
621	C₄	—	2	4	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	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₁₃×#525	1	1	yes	characteristic
634	C₄	C₁₃×#532	1	1	yes	characteristic
635	C₄	C₁₃×#547	1	1	yes	characteristic
636	C₄	C₁₃×#548	1	1	yes	characteristic
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	8	1	no	—
640	C₂	C₁₃×#2461	1	1	yes	characteristic
641	C₂	C₁₃×#3291	1	1	yes	characteristic
642	C₂	C₁₃×#3293	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×#2060	C₂	semidirect
9. C₁₃×#1956	C₂	semidirect
11. C₁₃×#1930	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1886	C₂	semidirect
15. C₁₃×#1772	C₂	semidirect
153. #26849	C₁₃	direct (N × H)
240. #3082	C₂×C₁₃	semidirect
242. #2064	C₂×C₁₃	semidirect
243. #2060	C₂×C₁₃	semidirect
246. #1956	C₂×C₁₃	semidirect
248. #1930	C₂×C₁₃	semidirect
249. #1930	C₂×C₁₃	semidirect
250. #1886	C₂×C₁₃	semidirect
252. #1772	C₂×C₁₃	semidirect
558. C₁₃	#26849	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×#2060	2
C₁₃×#2052	2
C₁₃×#2005	2
C₁₃×#1956	2
C₁₃×#1937	2
C₁₃×#1930	2
C₁₃×#1886	2
C₁₃×#1859	2
C₁₃×#1772	2
#26849	13

Subgroups — C13×#26849 #15713188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26849 #15713188