Subgroups — C₁₃×#24801 #15711140

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3045	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₁₃×#536	C₂²	1	1	yes	characteristic
23	C₁₃×#535	C₂²	1	1	yes	characteristic
24	C₁₃×#520	C₂²	1	1	yes	characteristic
25	C₁₃×#520	C₂²	1	1	yes	characteristic
26	C₁₃×#471	—	2	4	no	—
27	C₁₃×#468	—	2	1	no	—
28	C₁₃×#468	—	2	1	no	—
29	C₁₃×#465	—	2	1	no	—
30	C₁₃×#465	—	2	1	no	—
31	C₁₃×#464	—	2	1	no	—
32	C₁₃×#464	—	2	1	no	—
33	C₁₃×#463	—	2	1	no	—
34	C₁₃×#463	—	2	1	no	—
35	C₁₃×#462	—	2	1	no	—
36	C₁₃×#461	—	2	1	no	—
37	C₁₃×#460	—	2	1	no	—
38	C₁₃×#459	—	2	1	no	—
39	C₁₃×#444	—	2	4	no	—
40	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
42	C₁₃×#428	—	2	1	no	—
43	C₁₃×#428	—	2	1	no	—
44	C₁₃×#428	C₂²	1	1	yes	characteristic
45	C₁₃×#428	C₂²	1	1	yes	characteristic
46	C₁₃×#427	—	2	1	no	—
47	C₁₃×#427	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#107	—	2	1	no	—
49	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
50	C₁₃×#424	C₂²	1	1	yes	characteristic
51	C₁₃×#424	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
54	C₁₃×#419	C₂²	1	1	yes	characteristic
55	C₁₃×#418	C₂²	1	1	yes	characteristic
56	C₁₃×#417	C₂²	1	1	yes	characteristic
57	C₁₃×#417	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
63	C₁₃×#391	C₂²	1	1	yes	characteristic
64	C₁₃×#390	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#339	C₂²	1	1	yes	characteristic
68	C₁₃×#339	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#137	—	2	2	no	—
74	C₁₃×#137	—	2	2	no	—
75	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
76	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
77	C₁₃×#135	—	2	2	no	—
78	C₁₃×#135	—	2	2	no	—
79	C₂×C₁₃×Q₁₆	—	2	1	no	—
80	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
81	C₂×C₁₃×SD₁₆	—	2	1	no	—
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	2	2	no	—
86	C₂×C₁₃×SD₁₆	—	2	2	no	—
87	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
88	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
89	C₂×C₁₃×D₈	—	2	1	no	—
90	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
91	C₁₃×#131	—	2	2	no	—
92	C₁₃×#131	—	2	2	no	—
93	C₁₃×#131	—	2	2	no	—
94	C₁₃×#131	D₄	1	4	yes	complemented
95	C₂×C₁₃×M₁₆	—	2	1	no	—
96	C₂×C₁₃×M₁₆	—	2	1	no	—
97	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₃	—	2	1	no	—
102	C₂²×C₈×C₁₃	—	2	1	no	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	—	2	1	no	—
106	C₁₃×#127	—	2	1	no	—
107	C₁₃×#124	—	2	1	no	—
108	C₁₃×#124	—	2	1	no	—
109	C₁₃×#123	—	4	1	no	—
110	C₁₃×C₂²⋊Q₈	—	2	1	no	—
111	C₁₃×C₂²⋊Q₈	—	2	1	no	—
112	C₁₃×#121	—	2	1	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#120	—	4	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	—	2	1	no	—
117	C₄×D₄×C₁₃	—	2	1	no	—
118	C₄×D₄×C₁₃	—	2	1	no	—
119	C₄×D₄×C₁₃	—	4	1	no	—
120	C₄×D₄×C₁₃	—	4	1	no	—
121	C₁₃×#117	—	2	1	no	—
122	C₁₃×#117	—	2	1	no	—
123	C₁₃×#117	C₂³	1	1	yes	characteristic
124	C₁₃×#117	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₁₃×#108	—	2	2	no	—
132	C₁₃×#108	—	2	2	no	—
133	C₁₃×#107	—	2	1	no	—
134	C₁₃×#107	—	2	1	no	—
135	C₁₃×#107	—	2	1	no	—
136	C₁₃×#107	—	2	1	no	—
137	C₁₃×#107	D₄	1	1	yes	characteristic
138	C₁₃×#107	D₄	1	1	yes	characteristic
139	C₁₃×#106	—	2	1	no	—
140	C₁₃×#106	—	2	1	no	—
141	C₁₃×#106	D₄	1	1	yes	characteristic
142	C₁₃×#106	D₄	1	1	yes	characteristic
143	C₁₃×C₄⋊C₈	—	2	1	no	—
144	C₁₃×C₄⋊C₈	—	2	1	no	—
145	C₁₃×C₄⋊C₈	—	2	1	no	—
146	C₁₃×C₄⋊C₈	—	2	1	no	—
147	C₁₃×#104	—	2	2	no	—
148	C₁₃×#104	—	2	2	no	—
149	C₁₃×#103	—	2	1	no	—
150	C₁₃×#103	—	2	1	no	—
151	C₁₃×#103	—	2	1	no	—
152	C₁₃×#103	—	2	1	no	—
153	C₁₃×#103	—	2	1	no	—
154	C₁₃×#103	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#102	—	2	1	no	—
159	C₁₃×#102	—	2	1	no	—
160	C₁₃×#102	—	2	1	no	—
161	C₁₃×#101	—	2	2	no	—
162	C₁₃×#100	—	2	2	no	—
163	C₁₃×#97	—	2	2	no	—
164	C₁₃×#95	—	4	1	no	—
165	#24801	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	—	2	1	no	—
167	C₁₃×#41	—	2	1	no	—
168	C₁₃×#41	—	2	1	no	—
169	C₁₃×#41	—	2	1	no	—
170	C₁₃×#41	—	2	1	no	—
171	C₁₃×#41	—	2	1	no	—
172	C₁₃×#41	—	2	1	no	—
173	C₁₃×#41	C₂×D₄	1	2	yes	—
174	C₁₃×#41	#41	1	2	yes	—
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	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	4	1	no	—
192	C₂×D₄×C₁₃	—	4	1	no	—
193	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	—	4	1	no	—
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₁₃×Q₁₆	—	2	2	no	—
205	C₁₃×Q₁₆	—	4	2	no	—
206	C₁₃×SD₁₆	—	2	2	no	—
207	C₁₃×SD₁₆	—	2	2	no	—
208	C₁₃×SD₁₆	—	4	2	no	—
209	C₁₃×SD₁₆	—	4	2	no	—
210	C₁₃×SD₁₆	—	4	2	no	—
211	C₁₃×SD₁₆	—	4	2	no	—
212	C₁₃×D₈	—	2	2	no	—
213	C₁₃×D₈	—	4	2	no	—
214	C₁₃×M₁₆	—	2	1	no	—
215	C₁₃×M₁₆	—	2	4	no	—
216	C₁₃×M₁₆	—	2	1	no	—
217	C₁₃×M₁₆	—	2	1	no	—
218	C₁₃×M₁₆	—	2	1	no	—
219	C₁₃×M₁₆	—	2	1	no	—
220	C₁₃×M₁₆	—	2	1	no	—
221	C₁₃×M₁₆	—	2	1	no	—
222	C₁₃×M₁₆	—	4	2	no	—
223	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	4	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	2	1	no	—
231	C₂×C₈×C₁₃	—	4	2	no	—
232	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂×C₈×C₁₃	#41	1	2	yes	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	4	1	no	—
243	C₁₃×C₄⋊C₄	—	4	1	no	—
244	C₁₃×C₄⋊C₄	—	4	1	no	—
245	C₁₃×C₄⋊C₄	—	4	1	no	—
246	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₁₃×C₂²⋊C₄	—	2	1	no	—
251	C₁₃×C₂²⋊C₄	—	2	1	no	—
252	C₁₃×C₂²⋊C₄	—	4	1	no	—
253	C₁₃×C₂²⋊C₄	—	4	1	no	—
254	C₁₃×C₂²⋊C₄	—	4	1	no	—
255	C₁₃×C₂²⋊C₄	—	4	1	no	—
256	C₁₃×C₂²⋊C₄	—	4	1	no	—
257	C₁₃×C₂²⋊C₄	—	4	1	no	—
258	C₁₃×C₂²⋊C₄	—	8	2	no	—
259	C₄²×C₁₃	—	2	1	no	—
260	C₄²×C₁₃	—	2	1	no	—
261	C₄²×C₁₃	—	2	1	no	—
262	C₄²×C₁₃	—	2	1	no	—
263	C₄²×C₁₃	—	4	1	no	—
264	C₄²×C₁₃	—	4	1	no	—
265	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#3057	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#3046	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#3045	C₂×C₁₃	1	1	yes	characteristic
269	C₂×#444	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1973	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1946	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1883	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	—	2	1	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	8	1	no	—
286	C₂³×C₁₃	—	8	1	no	—
287	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
288	Q₈×C₁₃	—	2	1	no	—
289	Q₈×C₁₃	—	2	1	no	—
290	Q₈×C₁₃	—	2	1	no	—
291	Q₈×C₁₃	—	4	1	no	—
292	Q₈×C₁₃	—	4	1	no	—
293	Q₈×C₁₃	—	4	1	no	—
294	Q₈×C₁₃	—	4	1	no	—
295	Q₈×C₁₃	#121	1	2	yes	—
296	D₄×C₁₃	—	2	2	no	—
297	D₄×C₁₃	—	2	2	no	—
298	D₄×C₁₃	—	2	1	no	—
299	D₄×C₁₃	—	2	1	no	—
300	D₄×C₁₃	—	2	1	no	—
301	D₄×C₁₃	—	4	1	no	—
302	D₄×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	4	1	no	—
304	D₄×C₁₃	—	4	1	no	—
305	D₄×C₁₃	—	4	1	no	—
306	D₄×C₁₃	—	4	1	no	—
307	D₄×C₁₃	—	16	1	no	—
308	D₄×C₁₃	—	16	1	no	—
309	D₄×C₁₃	#121	1	2	yes	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	8	1	no	—
329	C₂×C₄×C₁₃	—	8	1	no	—
330	C₂×C₄×C₁₃	—	16	1	no	—
331	C₂×C₄×C₁₃	—	16	1	no	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
338	C₈×C₁₃	—	2	2	no	—
339	C₈×C₁₃	—	2	1	no	—
340	C₈×C₁₃	—	2	1	no	—
341	C₈×C₁₃	—	4	1	no	—
342	C₈×C₁₃	—	4	1	no	—
343	C₈×C₁₃	—	4	1	no	—
344	C₈×C₁₃	#121	1	2	yes	—
345	C₈×C₁₃	#121	1	2	yes	—
346	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
349	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
352	#536	C₂²×C₁₃	1	1	yes	characteristic
353	#535	C₂²×C₁₃	1	1	yes	characteristic
354	#520	C₂²×C₁₃	1	1	yes	characteristic
355	#520	C₂²×C₁₃	1	1	yes	characteristic
356	#471	—	2	4	no	—
357	#468	—	2	1	no	—
358	#468	—	2	1	no	—
359	#465	—	2	1	no	—
360	#465	—	2	1	no	—
361	#464	—	2	1	no	—
362	#464	—	2	1	no	—
363	#463	—	2	1	no	—
364	#463	—	2	1	no	—
365	#462	—	2	1	no	—
366	#461	—	2	1	no	—
367	#460	—	2	1	no	—
368	#459	—	2	1	no	—
369	#444	—	2	4	no	—
370	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
372	#428	—	2	1	no	—
373	#428	—	2	1	no	—
374	#428	C₂²×C₁₃	1	1	yes	characteristic
375	#428	C₂²×C₁₃	1	1	yes	characteristic
376	#427	—	2	1	no	—
377	#427	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#107	—	2	1	no	—
379	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
380	#424	C₂²×C₁₃	1	1	yes	characteristic
381	#424	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
384	#419	C₂²×C₁₃	1	1	yes	characteristic
385	#418	C₂²×C₁₃	1	1	yes	characteristic
386	#417	C₂²×C₁₃	1	1	yes	characteristic
387	#417	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
393	#391	C₂²×C₁₃	1	1	yes	characteristic
394	#390	C₂²×C₁₃	1	1	yes	characteristic
395	#343	C₂²×C₁₃	1	1	yes	characteristic
396	#343	C₂²×C₁₃	1	1	yes	characteristic
397	#339	C₂²×C₁₃	1	1	yes	characteristic
398	#339	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×C₁₃	—	2	1	no	—
400	C₂²×C₁₃	—	2	1	no	—
401	C₂²×C₁₃	—	2	2	no	—
402	C₂²×C₁₃	—	4	1	no	—
403	C₂²×C₁₃	—	4	1	no	—
404	C₂²×C₁₃	—	4	1	no	—
405	C₂²×C₁₃	—	4	1	no	—
406	C₂²×C₁₃	—	4	1	no	—
407	C₂²×C₁₃	—	8	2	no	—
408	C₂²×C₁₃	—	8	1	no	—
409	C₂²×C₁₃	—	8	1	no	—
410	C₂²×C₁₃	—	8	1	no	—
411	C₂²×C₁₃	—	16	1	no	—
412	C₂²×C₁₃	#537	1	1	yes	characteristic
413	C₂²×C₁₃	D₄²	1	1	yes	characteristic
414	C₂²×C₁₃	#553	1	1	yes	characteristic
415	C₄×C₁₃	—	2	2	no	—
416	C₄×C₁₃	—	4	1	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	4	1	no	—
420	C₄×C₁₃	—	4	1	no	—
421	C₄×C₁₃	—	8	1	no	—
422	C₄×C₁₃	—	8	1	no	—
423	C₄×C₁₃	—	8	1	no	—
424	C₄×C₁₃	—	8	1	no	—
425	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
426	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
427	C₄×C₁₃	#547	1	1	yes	characteristic
428	C₄×C₁₃	#548	1	1	yes	characteristic
429	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
433	#137	—	2	2	no	—
434	#137	—	2	2	no	—
435	AGL(1,ℤ/8)	—	2	2	no	—
436	AGL(1,ℤ/8)	—	2	2	no	—
437	#135	—	2	2	no	—
438	#135	—	2	2	no	—
439	C₂×Q₁₆	—	2	1	no	—
440	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
441	C₂×SD₁₆	—	2	1	no	—
442	C₂×SD₁₆	—	2	1	no	—
443	C₂×SD₁₆	—	2	1	no	—
444	C₂×SD₁₆	—	2	1	no	—
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	2	no	—
447	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
448	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
449	C₂×D₈	—	2	1	no	—
450	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
451	#131	—	2	2	no	—
452	#131	—	2	2	no	—
453	#131	—	2	2	no	—
454	#131	D₄×C₁₃	1	4	yes	complemented
455	C₂×M₁₆	—	2	1	no	—
456	C₂×M₁₆	—	2	1	no	—
457	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×C₈	—	2	1	no	—
462	C₂²×C₈	—	2	1	no	—
463	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
465	C₄⋊Q₈	—	2	1	no	—
466	#127	—	2	1	no	—
467	#124	—	2	1	no	—
468	#124	—	2	1	no	—
469	#123	—	4	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	#121	—	2	1	no	—
473	#121	—	2	1	no	—
474	#120	—	4	1	no	—
475	C₄×Q₈	—	2	1	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×D₄	—	2	1	no	—
478	C₄×D₄	—	2	1	no	—
479	C₄×D₄	—	4	1	no	—
480	C₄×D₄	—	4	1	no	—
481	#117	—	2	1	no	—
482	#117	—	2	1	no	—
483	#117	C₂³×C₁₃	1	1	yes	characteristic
484	#117	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	—	4	1	no	—
490	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
491	#108	—	2	2	no	—
492	#108	—	2	2	no	—
493	#107	—	2	1	no	—
494	#107	—	2	1	no	—
495	#107	—	2	1	no	—
496	#107	—	2	1	no	—
497	#107	D₄×C₁₃	1	1	yes	characteristic
498	#107	D₄×C₁₃	1	1	yes	characteristic
499	#106	—	2	1	no	—
500	#106	—	2	1	no	—
501	#106	D₄×C₁₃	1	1	yes	characteristic
502	#106	D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₈	—	2	1	no	—
504	C₄⋊C₈	—	2	1	no	—
505	C₄⋊C₈	—	2	1	no	—
506	C₄⋊C₈	—	2	1	no	—
507	#104	—	2	2	no	—
508	#104	—	2	2	no	—
509	#103	—	2	1	no	—
510	#103	—	2	1	no	—
511	#103	—	2	1	no	—
512	#103	—	2	1	no	—
513	#103	—	2	1	no	—
514	#103	—	2	1	no	—
515	#102	—	2	1	no	—
516	#102	—	2	1	no	—
517	#102	—	2	1	no	—
518	#102	—	2	1	no	—
519	#102	—	2	1	no	—
520	#102	—	2	1	no	—
521	#101	—	2	2	no	—
522	#100	—	2	2	no	—
523	#97	—	2	2	no	—
524	#95	—	4	1	no	—
525	C₂×C₁₃	—	2	1	no	—
526	C₂×C₁₃	—	2	1	no	—
527	C₂×C₁₃	—	4	2	no	—
528	C₂×C₁₃	—	8	1	no	—
529	C₂×C₁₃	—	16	1	no	—
530	C₂×C₁₃	#2416	1	1	yes	characteristic
531	C₂×C₁₃	#3288	1	1	yes	characteristic
532	C₂×C₁₃	#3289	1	1	yes	characteristic
533	C₂⁴	—	2	1	no	—
534	#41	—	2	1	no	—
535	#41	—	2	1	no	—
536	#41	—	2	1	no	—
537	#41	—	2	1	no	—
538	#41	—	2	1	no	—
539	#41	—	2	1	no	—
540	#41	C₂×D₄×C₁₃	1	2	yes	—
541	#41	C₁₃×#41	1	2	yes	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	4	1	no	—
559	C₂×D₄	—	4	1	no	—
560	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
561	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	4	1	no	—
569	C₂²×C₄	—	4	1	no	—
570	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
571	Q₁₆	—	2	2	no	—
572	Q₁₆	—	4	2	no	—
573	SD₁₆	—	2	2	no	—
574	SD₁₆	—	2	2	no	—
575	SD₁₆	—	4	2	no	—
576	SD₁₆	—	4	2	no	—
577	SD₁₆	—	4	2	no	—
578	SD₁₆	—	4	2	no	—
579	D₈	—	2	2	no	—
580	D₈	—	4	2	no	—
581	M₁₆	—	2	1	no	—
582	M₁₆	—	2	4	no	—
583	M₁₆	—	2	1	no	—
584	M₁₆	—	2	1	no	—
585	M₁₆	—	2	1	no	—
586	M₁₆	—	2	1	no	—
587	M₁₆	—	2	1	no	—
588	M₁₆	—	2	1	no	—
589	M₁₆	—	4	2	no	—
590	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	4	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	4	2	no	—
599	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
602	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₂×C₈	C₁₃×#41	1	2	yes	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	4	1	no	—
610	C₄⋊C₄	—	4	1	no	—
611	C₄⋊C₄	—	4	1	no	—
612	C₄⋊C₄	—	4	1	no	—
613	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
614	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	4	1	no	—
620	C₂²⋊C₄	—	4	1	no	—
621	C₂²⋊C₄	—	4	1	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	1	no	—
624	C₂²⋊C₄	—	4	1	no	—
625	C₂²⋊C₄	—	8	2	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₄²	—	2	1	no	—
629	C₄²	—	2	1	no	—
630	C₄²	—	4	1	no	—
631	C₄²	—	4	1	no	—
632	C₁₃	#24801	1	1	yes	characteristic, direct product factor, Sylow
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	8	1	no	—
639	C₂³	—	8	1	no	—
640	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
641	Q₈	—	2	1	no	—
642	Q₈	—	2	1	no	—
643	Q₈	—	2	1	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	C₁₃×#121	1	2	yes	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	2	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	D₄	—	4	1	no	—
657	D₄	—	4	1	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	16	1	no	—
661	D₄	—	16	1	no	—
662	D₄	C₁₃×#121	1	2	yes	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	8	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	16	1	no	—
684	C₂×C₄	—	16	1	no	—
685	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
689	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
690	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	1	no	—
693	C₈	—	2	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₈	—	4	1	no	—
697	C₈	C₁₃×#121	1	2	yes	—
698	C₈	C₁₃×#121	1	2	yes	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	8	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	16	1	no	—
712	C₂²	C₁₃×#537	1	1	yes	characteristic
713	C₂²	D₄²×C₁₃	1	1	yes	characteristic
714	C₂²	C₁₃×#553	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
726	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
727	C₄	C₁₃×#547	1	1	yes	characteristic
728	C₄	C₁₃×#548	1	1	yes	characteristic
729	C₂	—	2	1	no	—
730	C₂	—	2	1	no	—
731	C₂	—	4	2	no	—
732	C₂	—	8	1	no	—
733	C₂	—	16	1	no	—
734	C₂	C₁₃×#2416	1	1	yes	characteristic
735	C₂	C₁₃×#3288	1	1	yes	characteristic
736	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×#3045	C₂
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
1. C₂×C₁₃×#471	C₂	semidirect
2. C₁₃×#3057	C₂	semidirect
3. C₁₃×#3046	C₂	semidirect
5. C₂×C₁₃×#444	C₂	semidirect
6. C₁₃×#2913	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#2038	C₂	semidirect
10. C₁₃×#2037	C₂	semidirect
11. C₁₃×#1973	C₂	semidirect
12. C₁₃×#1946	C₂	semidirect
13. C₁₃×#1883	C₂	semidirect
14. C₁₃×#1882	C₂	semidirect
15. C₁₃×#1816	C₂	semidirect
94. C₁₃×#131	D₄	semidirect
165. #24801	C₁₃	direct (N × H)
265. C₂×#471	C₂×C₁₃	semidirect
266. #3057	C₂×C₁₃	semidirect
267. #3046	C₂×C₁₃	semidirect
269. C₂×#444	C₂×C₁₃	semidirect
270. #2913	C₂×C₁₃	semidirect
271. #2064	C₂×C₁₃	semidirect
272. #2063	C₂×C₁₃	semidirect
273. #2038	C₂×C₁₃	semidirect
274. #2037	C₂×C₁₃	semidirect
275. #1973	C₂×C₁₃	semidirect
276. #1946	C₂×C₁₃	semidirect
277. #1883	C₂×C₁₃	semidirect
278. #1882	C₂×C₁₃	semidirect
279. #1816	C₂×C₁₃	semidirect
454. #131	D₄×C₁₃	semidirect
632. C₁₃	#24801	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#471	2
C₁₃×#3057	2
C₁₃×#3046	2
C₁₃×#3045	2
C₂×C₁₃×#444	2
C₁₃×#2913	2
C₁₃×#2064	2
C₁₃×#2063	2
C₁₃×#2038	2
C₁₃×#2037	2
C₁₃×#1973	2
C₁₃×#1946	2
C₁₃×#1883	2
C₁₃×#1882	2
C₁₃×#1816	2
#24801	13

Subgroups — C13×#24801 #15711140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24801 #15711140