Subgroups — C₁₃×#25985 #15712324

Order 3328.

842 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2898	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2898	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2028	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₁₃×#544	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#520	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	1	no	—
23	C₁₃×#479	—	2	1	no	—
24	C₁₃×#478	—	2	1	no	—
25	C₁₃×#478	—	2	1	no	—
26	C₁₃×#477	—	2	1	no	—
27	C₁₃×#476	—	2	1	no	—
28	C₁₃×#475	—	2	1	no	—
29	C₁₃×#474	—	2	1	no	—
30	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
32	C₁₃×#428	C₂²	1	1	yes	characteristic
33	C₁₃×#428	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
36	C₁₃×#424	C₂²	1	1	yes	characteristic
37	C₁₃×#424	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
40	C₁₃×#419	—	2	1	no	—
41	C₁₃×#419	—	2	1	no	—
42	C₁₃×#419	C₂²	1	1	yes	characteristic
43	C₁₃×#419	C₂²	1	1	yes	characteristic
44	C₁₃×#417	—	2	1	no	—
45	C₁₃×#417	—	2	1	no	—
46	C₁₃×#417	C₂²	1	1	yes	characteristic
47	C₁₃×#417	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#416	—	2	1	no	—
51	C₁₃×#416	—	2	1	no	—
52	C₁₃×#416	C₂²	1	1	yes	characteristic
53	C₁₃×#416	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#103	—	2	1	no	—
55	C₂×C₁₃×#103	—	2	1	no	—
56	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
59	C₁₃×#391	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×#343	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#336	C₂²	1	1	yes	characteristic
67	C₁₃×2₋¹⁺⁴	—	2	2	no	—
68	C₁₃×2₋¹⁺⁴	—	2	2	no	—
69	C₁₃×2₋¹⁺⁴	—	4	1	no	—
70	C₁₃×2₋¹⁺⁴	Q₈	1	4	yes	complemented
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	4	1	no	—
74	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	—	2	1	no	—
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#131	—	2	2	no	—
80	C₁₃×#131	—	2	2	no	—
81	C₁₃×#131	—	4	1	no	—
82	C₁₃×#131	—	4	1	no	—
83	C₂×C₁₃×M₁₆	—	2	1	no	—
84	C₂×C₁₃×M₁₆	—	2	1	no	—
85	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	—	2	1	no	—
90	C₂²×C₈×C₁₃	—	2	1	no	—
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	—	2	1	no	—
94	C₁₃×C₄⋊Q₈	—	2	1	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×C₂²⋊Q₈	—	4	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	4	1	no	—
103	C₄×D₄×C₁₃	—	4	1	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	C₂³	1	1	yes	characteristic
107	C₁₃×#117	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#108	—	4	1	no	—
115	C₁₃×#108	—	4	1	no	—
116	C₁₃×#107	—	2	1	no	—
117	C₁₃×#107	—	2	1	no	—
118	C₁₃×#107	—	2	1	no	—
119	C₁₃×#107	—	2	1	no	—
120	C₁₃×#106	—	2	1	no	—
121	C₁₃×#106	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×#104	—	2	2	no	—
129	C₁₃×#104	—	2	2	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	—	2	1	no	—
140	C₁₃×#103	—	2	1	no	—
141	C₁₃×#103	—	2	1	no	—
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×#103	D₄	1	1	yes	characteristic
146	C₁₃×#102	—	2	1	no	—
147	C₁₃×#102	—	2	1	no	—
148	C₁₃×#102	—	2	1	no	—
149	C₁₃×#102	—	2	1	no	—
150	C₁₃×#102	D₄	1	1	yes	characteristic
151	C₁₃×#102	D₄	1	1	yes	characteristic
152	C₁₃×#102	D₄	1	1	yes	characteristic
153	C₁₃×#102	D₄	1	1	yes	characteristic
154	C₁₃×#101	—	4	1	no	—
155	C₁₃×#95	—	4	1	no	—
156	C₁₃×#95	—	4	1	no	—
157	#25985	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₁₃×#41	—	2	1	no	—
159	C₁₃×#41	—	2	1	no	—
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	—	2	1	no	—
162	C₁₃×#41	—	2	4	no	—
163	C₁₃×#41	—	2	4	no	—
164	C₁₃×#41	—	4	4	no	—
165	C₁₃×#41	—	4	2	no	—
166	C₁₃×#41	—	4	2	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₁₃×#41	C₂×Q₈	1	2	yes	—
169	C₁₃×#41	C₂×Q₈	1	2	yes	—
170	C₁₃×#41	#41	1	2	yes	—
171	C₁₃×#41	#41	1	2	yes	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	4	no	—
174	C₂×Q₈×C₁₃	—	2	4	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	—	4	1	no	—
180	C₂×Q₈×C₁₃	—	4	1	no	—
181	C₂×Q₈×C₁₃	—	4	2	no	—
182	C₂×Q₈×C₁₃	—	4	2	no	—
183	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	4	1	no	—
189	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
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	—	4	1	no	—
199	C₂²×C₄×C₁₃	—	4	1	no	—
200	C₂²×C₄×C₁₃	—	4	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₁₃×M₁₆	—	2	1	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	—	2	1	no	—
211	C₁₃×M₁₆	—	4	2	no	—
212	C₁₃×M₁₆	—	4	2	no	—
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	—	4	2	no	—
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	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	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	—	4	1	no	—
237	C₁₃×C₄⋊C₄	—	4	1	no	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
242	C₁₃×C₂²⋊C₄	—	2	1	no	—
243	C₁₃×C₂²⋊C₄	—	2	1	no	—
244	C₁₃×C₂²⋊C₄	—	4	1	no	—
245	C₁₃×C₂²⋊C₄	—	4	1	no	—
246	C₄²×C₁₃	—	2	1	no	—
247	C₄²×C₁₃	—	2	1	no	—
248	C₄²×C₁₃	—	2	1	no	—
249	C₄²×C₁₃	—	2	1	no	—
250	C₄²×C₁₃	—	4	1	no	—
251	C₄²×C₁₃	—	4	1	no	—
252	#3084	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#3083	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2898	C₂×C₁₃	1	1	yes	characteristic
255	#2898	C₂×C₁₃	1	1	yes	characteristic
256	#2097	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#2028	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1866	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1866	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#1816	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#1793	C₂×C₁₃	1	1	yes	characteristic
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
270	Q₈×C₁₃	—	2	1	no	—
271	Q₈×C₁₃	—	2	1	no	—
272	Q₈×C₁₃	—	2	2	no	—
273	Q₈×C₁₃	—	2	2	no	—
274	Q₈×C₁₃	—	4	4	no	—
275	Q₈×C₁₃	—	4	1	no	—
276	Q₈×C₁₃	—	4	1	no	—
277	Q₈×C₁₃	—	16	1	no	—
278	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
279	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
280	D₄×C₁₃	—	2	2	no	—
281	D₄×C₁₃	—	2	2	no	—
282	D₄×C₁₃	—	2	2	no	—
283	D₄×C₁₃	—	2	2	no	—
284	D₄×C₁₃	—	2	1	no	—
285	D₄×C₁₃	—	2	1	no	—
286	D₄×C₁₃	—	4	4	no	—
287	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
288	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	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	1	no	—
300	C₂×C₄×C₁₃	—	4	4	no	—
301	C₂×C₄×C₁₃	—	4	4	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	—	8	1	no	—
311	C₂×C₄×C₁₃	—	8	1	no	—
312	C₂×C₄×C₁₃	—	8	1	no	—
313	C₂×C₄×C₁₃	—	16	1	no	—
314	C₂×C₄×C₁₃	—	16	1	no	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
321	C₈×C₁₃	—	2	1	no	—
322	C₈×C₁₃	—	2	1	no	—
323	C₈×C₁₃	—	2	1	no	—
324	C₈×C₁₃	—	2	1	no	—
325	C₈×C₁₃	—	4	1	no	—
326	C₈×C₁₃	—	4	1	no	—
327	C₈×C₁₃	—	4	1	no	—
328	C₈×C₁₃	—	4	1	no	—
329	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
332	#544	C₂²×C₁₃	1	1	yes	characteristic
333	#520	C₂²×C₁₃	1	1	yes	characteristic
334	#520	C₂²×C₁₃	1	1	yes	characteristic
335	#479	—	2	1	no	—
336	#479	—	2	1	no	—
337	#478	—	2	1	no	—
338	#478	—	2	1	no	—
339	#477	—	2	1	no	—
340	#476	—	2	1	no	—
341	#475	—	2	1	no	—
342	#474	—	2	1	no	—
343	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
345	#428	C₂²×C₁₃	1	1	yes	characteristic
346	#428	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
349	#424	C₂²×C₁₃	1	1	yes	characteristic
350	#424	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
353	#419	—	2	1	no	—
354	#419	—	2	1	no	—
355	#419	C₂²×C₁₃	1	1	yes	characteristic
356	#419	C₂²×C₁₃	1	1	yes	characteristic
357	#417	—	2	1	no	—
358	#417	—	2	1	no	—
359	#417	C₂²×C₁₃	1	1	yes	characteristic
360	#417	C₂²×C₁₃	1	1	yes	characteristic
361	#417	C₂²×C₁₃	1	1	yes	characteristic
362	#417	C₂²×C₁₃	1	1	yes	characteristic
363	#416	—	2	1	no	—
364	#416	—	2	1	no	—
365	#416	C₂²×C₁₃	1	1	yes	characteristic
366	#416	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#103	—	2	1	no	—
368	C₂×#103	—	2	1	no	—
369	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
372	#391	C₂²×C₁₃	1	1	yes	characteristic
373	#382	C₂²×C₁₃	1	1	yes	characteristic
374	#343	C₂²×C₁₃	1	1	yes	characteristic
375	#343	C₂²×C₁₃	1	1	yes	characteristic
376	#343	C₂²×C₁₃	1	1	yes	characteristic
377	#339	C₂²×C₁₃	1	1	yes	characteristic
378	#339	C₂²×C₁₃	1	1	yes	characteristic
379	#336	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×C₁₃	—	2	1	no	—
381	C₂²×C₁₃	—	2	1	no	—
382	C₂²×C₁₃	—	2	2	no	—
383	C₂²×C₁₃	—	2	2	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	#543	1	1	yes	characteristic
389	C₂²×C₁₃	D₄²	1	1	yes	characteristic
390	C₂²×C₁₃	#551	1	1	yes	characteristic
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	2	2	no	—
393	C₄×C₁₃	—	4	2	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	4	1	no	—
396	C₄×C₁₃	—	4	1	no	—
397	C₄×C₁₃	—	4	1	no	—
398	C₄×C₁₃	—	8	1	no	—
399	C₄×C₁₃	—	8	1	no	—
400	C₄×C₁₃	—	8	1	no	—
401	C₄×C₁₃	—	8	1	no	—
402	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
403	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
404	C₄×C₁₃	#546	1	1	yes	characteristic
405	C₄×C₁₃	#546	1	1	yes	characteristic
406	2₋¹⁺⁴	—	2	2	no	—
407	2₋¹⁺⁴	—	2	2	no	—
408	2₋¹⁺⁴	—	4	1	no	—
409	2₋¹⁺⁴	Q₈×C₁₃	1	4	yes	complemented
410	C₂×#41	—	2	1	no	—
411	C₂×#41	—	2	1	no	—
412	C₂×#41	—	4	1	no	—
413	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×Q₈	—	2	1	no	—
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
418	#131	—	2	2	no	—
419	#131	—	2	2	no	—
420	#131	—	4	1	no	—
421	#131	—	4	1	no	—
422	C₂×M₁₆	—	2	1	no	—
423	C₂×M₁₆	—	2	1	no	—
424	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×C₈	—	2	1	no	—
429	C₂²×C₈	—	2	1	no	—
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	#125	—	2	1	no	—
435	#125	—	2	1	no	—
436	C₂²⋊Q₈	—	4	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	4	1	no	—
442	C₄×D₄	—	4	1	no	—
443	#117	—	2	1	no	—
444	#117	—	2	1	no	—
445	#117	C₂³×C₁₃	1	1	yes	characteristic
446	#117	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
453	#108	—	4	1	no	—
454	#108	—	4	1	no	—
455	#107	—	2	1	no	—
456	#107	—	2	1	no	—
457	#107	—	2	1	no	—
458	#107	—	2	1	no	—
459	#106	—	2	1	no	—
460	#106	—	2	1	no	—
461	#106	—	2	1	no	—
462	#106	—	2	1	no	—
463	C₄⋊C₈	—	2	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	2	1	no	—
467	#104	—	2	2	no	—
468	#104	—	2	2	no	—
469	#103	—	2	1	no	—
470	#103	—	2	1	no	—
471	#103	—	2	1	no	—
472	#103	—	2	1	no	—
473	#103	—	2	1	no	—
474	#103	—	2	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	D₄×C₁₃	1	1	yes	characteristic
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	#102	—	2	1	no	—
486	#102	—	2	1	no	—
487	#102	—	2	1	no	—
488	#102	—	2	1	no	—
489	#102	D₄×C₁₃	1	1	yes	characteristic
490	#102	D₄×C₁₃	1	1	yes	characteristic
491	#102	D₄×C₁₃	1	1	yes	characteristic
492	#102	D₄×C₁₃	1	1	yes	characteristic
493	#101	—	4	1	no	—
494	#95	—	4	1	no	—
495	#95	—	4	1	no	—
496	C₂×C₁₃	—	2	1	no	—
497	C₂×C₁₃	—	2	1	no	—
498	C₂×C₁₃	—	4	2	no	—
499	C₂×C₁₃	—	4	2	no	—
500	C₂×C₁₃	#2437	1	1	yes	characteristic
501	C₂×C₁₃	#3289	1	1	yes	characteristic
502	C₂×C₁₃	#3290	1	1	yes	characteristic
503	#41	—	2	1	no	—
504	#41	—	2	1	no	—
505	#41	—	2	1	no	—
506	#41	—	2	1	no	—
507	#41	—	2	4	no	—
508	#41	—	2	4	no	—
509	#41	—	4	4	no	—
510	#41	—	4	2	no	—
511	#41	—	4	2	no	—
512	#41	—	4	4	no	—
513	#41	C₂×Q₈×C₁₃	1	2	yes	—
514	#41	C₂×Q₈×C₁₃	1	2	yes	—
515	#41	C₁₃×#41	1	2	yes	—
516	#41	C₁₃×#41	1	2	yes	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	4	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	—	4	1	no	—
525	C₂×Q₈	—	4	1	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	—	4	2	no	—
528	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	—	4	1	no	—
546	C₂²×C₄	—	4	1	no	—
547	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
548	M₁₆	—	2	1	no	—
549	M₁₆	—	2	1	no	—
550	M₁₆	—	2	1	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	—	4	2	no	—
557	M₁₆	—	4	2	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
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	—	4	2	no	—
567	C₂×C₈	—	4	2	no	—
568	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
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	—	2	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	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	4	1	no	—
596	C₄²	—	4	1	no	—
597	C₁₃	#25985	1	1	yes	characteristic, direct product factor, Sylow
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
601	Q₈	—	2	1	no	—
602	Q₈	—	2	1	no	—
603	Q₈	—	2	2	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	4	4	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	16	1	no	—
609	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
610	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	1	no	—
616	D₄	—	2	1	no	—
617	D₄	—	4	4	no	—
618	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
619	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	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	—	4	4	no	—
632	C₂×C₄	—	4	4	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	—	8	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	1	no	—
644	C₂×C₄	—	16	1	no	—
645	C₂×C₄	—	16	1	no	—
646	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
648	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
650	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
651	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
652	C₈	—	2	1	no	—
653	C₈	—	2	1	no	—
654	C₈	—	2	1	no	—
655	C₈	—	2	1	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	C₁₃×#543	1	1	yes	characteristic
669	C₂²	D₄²×C₁₃	1	1	yes	characteristic
670	C₂²	C₁₃×#551	1	1	yes	characteristic
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	2	no	—
678	C₄	—	8	1	no	—
679	C₄	—	8	1	no	—
680	C₄	—	8	1	no	—
681	C₄	—	8	1	no	—
682	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
683	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
684	C₄	C₁₃×#546	1	1	yes	characteristic
685	C₄	C₁₃×#546	1	1	yes	characteristic
686	C₂	—	2	1	no	—
687	C₂	—	2	1	no	—
688	C₂	—	4	2	no	—
689	C₂	—	4	2	no	—
690	C₂	C₁₃×#2437	1	1	yes	characteristic
691	C₂	C₁₃×#3289	1	1	yes	characteristic
692	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×2₋¹⁺⁴	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
1. C₁₃×#3084	C₂	semidirect
2. C₁₃×#3083	C₂	semidirect
5. C₁₃×#2097	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2028	C₂	semidirect
9. C₁₃×#1866	C₂	semidirect
10. C₁₃×#1866	C₂	semidirect
11. C₁₃×#1860	C₂	semidirect
12. C₁₃×#1860	C₂	semidirect
13. C₁₃×#1816	C₂	semidirect
14. C₁₃×#1815	C₂	semidirect
70. C₁₃×2₋¹⁺⁴	Q₈	semidirect
157. #25985	C₁₃	direct (N × H)
252. #3084	C₂×C₁₃	semidirect
253. #3083	C₂×C₁₃	semidirect
256. #2097	C₂×C₁₃	semidirect
257. #2064	C₂×C₁₃	semidirect
258. #2064	C₂×C₁₃	semidirect
259. #2028	C₂×C₁₃	semidirect
260. #1866	C₂×C₁₃	semidirect
261. #1866	C₂×C₁₃	semidirect
262. #1860	C₂×C₁₃	semidirect
263. #1860	C₂×C₁₃	semidirect
264. #1816	C₂×C₁₃	semidirect
265. #1815	C₂×C₁₃	semidirect
409. 2₋¹⁺⁴	Q₈×C₁₃	semidirect
597. C₁₃	#25985	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×#3084	2
C₁₃×#3083	2
C₁₃×#2898	2
C₁₃×#2097	2
C₁₃×#2064	2
C₁₃×#2028	2
C₁₃×#1866	2
C₁₃×#1860	2
C₁₃×#1816	2
C₁₃×#1815	2
C₁₃×#1793	2
#25985	13

Subgroups — C13×#25985 #15712324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25985 #15712324