Subgroups — C₁₃×#32863 #15719202

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2863	C₂	1	2	yes	maximal
2	C₁₃×#2088	C₂	1	2	yes	maximal
3	C₁₃×#2086	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2068	C₂	1	2	yes	maximal
5	C₁₃×#2066	C₂	1	2	yes	maximal
6	C₁₃×#2066	C₂	1	2	yes	maximal
7	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2056	C₂	1	2	yes	maximal
9	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#106	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₁₃×#391	C₂²	1	2	yes	—
21	C₁₃×#391	C₂²	1	2	yes	—
22	C₁₃×#391	C₂²	1	2	yes	—
23	C₁₃×#389	C₂²	1	2	yes	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#387	—	2	2	no	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#387	—	2	2	no	—
29	C₁₃×#383	—	2	2	no	—
30	C₄³×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#340	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	1	yes	characteristic
33	C₁₃×#340	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
36	C₂×C₁₃×Q₁₆	—	4	2	no	—
37	C₂×C₁₃×Q₁₆	—	4	1	no	—
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
45	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
47	C₂×C₄²×C₁₃	D₄	1	2	yes	—
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
52	C₁₃×#107	—	4	1	no	—
53	C₁₃×#106	—	4	2	no	—
54	C₁₃×C₄⋊C₈	—	4	1	no	—
55	C₁₃×C₄⋊C₈	—	4	2	no	—
56	C₁₃×C₄⋊C₈	—	4	2	no	—
57	C₁₃×C₄⋊C₈	—	4	1	no	—
58	C₁₃×#103	—	4	2	no	—
59	C₁₃×#103	—	4	2	no	—
60	C₁₃×#103	—	4	2	no	—
61	C₁₃×#95	—	2	2	no	—
62	C₁₃×#95	—	2	2	no	—
63	C₁₃×#95	—	2	2	no	—
64	C₁₃×#95	—	2	2	no	—
65	C₁₃×#95	—	2	2	no	—
66	C₁₃×#95	—	2	2	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	#32863	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂×Q₈×C₁₃	—	2	2	no	—
72	C₂×Q₈×C₁₃	—	2	2	no	—
73	C₂×Q₈×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₁₃×Q₁₆	—	4	4	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	2	1	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	—	4	4	no	—
101	C₁₃×C₄⋊C₄	—	4	4	no	—
102	C₁₃×C₄⋊C₄	—	4	4	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	—	2	4	no	—
105	C₄²×C₁₃	—	2	2	no	—
106	C₄²×C₁₃	—	2	1	no	—
107	C₄²×C₁₃	—	2	2	no	—
108	C₄²×C₁₃	—	2	1	no	—
109	C₄²×C₁₃	—	4	1	no	—
110	#2863	C₂×C₁₃	1	2	yes	—
111	#2088	C₂×C₁₃	1	2	yes	—
112	#2086	C₂×C₁₃	1	1	yes	characteristic
113	#2068	C₂×C₁₃	1	2	yes	—
114	#2066	C₂×C₁₃	1	2	yes	—
115	#2066	C₂×C₁₃	1	2	yes	—
116	#2056	C₂×C₁₃	1	2	yes	—
117	#2056	C₂×C₁₃	1	1	yes	characteristic
118	#1842	C₂×C₁₃	1	1	yes	characteristic
119	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₁₃	—	4	2	no	—
121	Q₈×C₁₃	—	4	2	no	—
122	Q₈×C₁₃	—	4	2	no	—
123	Q₈×C₁₃	—	4	2	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	1	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	—	4	2	no	—
135	C₂×C₄×C₁₃	—	4	2	no	—
136	C₂×C₄×C₁₃	—	4	2	no	—
137	C₂×C₄×C₁₃	—	4	2	no	—
138	C₂×C₄×C₁₃	—	4	2	no	—
139	C₂×C₄×C₁₃	—	4	2	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	2	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	#135	1	2	yes	—
146	C₂×C₄×C₁₃	#137	1	4	yes	—
147	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
148	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
150	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
151	C₈×C₁₃	—	4	2	no	—
152	C₈×C₁₃	—	4	1	no	—
153	C₈×C₁₃	—	4	1	no	—
154	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
155	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
156	C₂×#106	C₂²×C₁₃	1	2	yes	—
157	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
158	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
159	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
160	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
161	C₂×#103	C₂²×C₁₃	1	2	yes	—
162	C₂×#103	C₂²×C₁₃	1	2	yes	—
163	C₂×#103	C₂²×C₁₃	1	2	yes	—
164	#391	C₂²×C₁₃	1	2	yes	—
165	#391	C₂²×C₁₃	1	2	yes	—
166	#391	C₂²×C₁₃	1	2	yes	—
167	#389	C₂²×C₁₃	1	2	yes	—
168	#389	C₂²×C₁₃	1	2	yes	—
169	#389	C₂²×C₁₃	1	2	yes	—
170	#387	—	2	2	no	—
171	#387	—	2	2	no	—
172	#387	—	2	2	no	—
173	#383	—	2	2	no	—
174	C₄³	C₂²×C₁₃	1	1	yes	characteristic
175	#340	C₂²×C₁₃	1	2	yes	—
176	#340	C₂²×C₁₃	1	1	yes	characteristic
177	#340	C₂²×C₁₃	1	1	yes	characteristic
178	#340	C₂²×C₁₃	1	2	yes	—
179	C₂²×C₁₃	#537	1	2	yes	—
180	C₂²×C₁₃	#537	1	1	yes	characteristic
181	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
182	C₂²×C₁₃	C₂×#137	1	2	yes	—
183	C₂²×C₁₃	#575	1	1	yes	characteristic
184	C₄×C₁₃	—	2	4	no	—
185	C₄×C₁₃	—	2	2	no	—
186	C₄×C₁₃	—	4	2	no	—
187	C₄×C₁₃	—	4	1	no	—
188	C₄×C₁₃	—	8	2	no	—
189	C₄×C₁₃	—	8	2	no	—
190	C₄×C₁₃	—	8	2	no	—
191	C₄×C₁₃	—	8	2	no	—
192	C₄×C₁₃	#560	1	1	yes	characteristic
193	C₄×C₁₃	#563	1	2	yes	—
194	C₄×C₁₃	#563	1	1	yes	characteristic
195	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
196	C₂×Q₁₆	—	4	2	no	—
197	C₂×Q₁₆	—	4	1	no	—
198	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
199	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
200	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	—	2	2	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
205	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
206	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
207	C₂×C₄²	D₄×C₁₃	1	2	yes	—
208	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
209	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
210	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
212	#107	—	4	1	no	—
213	#106	—	4	2	no	—
214	C₄⋊C₈	—	4	1	no	—
215	C₄⋊C₈	—	4	2	no	—
216	C₄⋊C₈	—	4	2	no	—
217	C₄⋊C₈	—	4	1	no	—
218	#103	—	4	2	no	—
219	#103	—	4	2	no	—
220	#103	—	4	2	no	—
221	#95	—	2	2	no	—
222	#95	—	2	2	no	—
223	#95	—	2	2	no	—
224	#95	—	2	2	no	—
225	#95	—	2	2	no	—
226	#95	—	2	2	no	—
227	#95	—	2	2	no	—
228	#95	—	2	2	no	—
229	#95	—	2	2	no	—
230	C₂×C₁₃	#2823	1	1	yes	characteristic
231	C₂×C₁₃	#3248	1	2	yes	—
232	C₂×C₁₃	#3250	1	1	yes	characteristic
233	C₂×C₁₃	#3252	1	2	yes	—
234	C₂×C₁₃	#3255	1	1	yes	characteristic
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	—	2	2	no	—
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
247	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
249	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
250	Q₁₆	—	4	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	1	no	—
258	C₄⋊C₄	—	2	2	no	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₄⋊C₄	—	4	4	no	—
266	C₄⋊C₄	—	4	4	no	—
267	C₄²	—	2	2	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	1	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	2	1	no	—
273	C₄²	—	4	1	no	—
274	C₁₃	#32863	1	1	yes	characteristic, direct product factor, Sylow
275	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
276	Q₈	—	4	2	no	—
277	Q₈	—	4	2	no	—
278	Q₈	—	4	2	no	—
279	Q₈	—	4	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	—	4	2	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	C₁₃×#135	1	2	yes	—
302	C₂×C₄	C₁₃×#137	1	4	yes	—
303	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
304	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
306	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
307	C₈	—	4	2	no	—
308	C₈	—	4	1	no	—
309	C₈	—	4	1	no	—
310	C₂²	C₁₃×#537	1	2	yes	—
311	C₂²	C₁₃×#537	1	1	yes	characteristic
312	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
313	C₂²	C₂×C₁₃×#137	1	2	yes	—
314	C₂²	C₁₃×#575	1	1	yes	characteristic
315	C₄	—	2	4	no	—
316	C₄	—	2	2	no	—
317	C₄	—	4	2	no	—
318	C₄	—	4	1	no	—
319	C₄	—	8	2	no	—
320	C₄	—	8	2	no	—
321	C₄	—	8	2	no	—
322	C₄	—	8	2	no	—
323	C₄	C₁₃×#560	1	1	yes	characteristic
324	C₄	C₁₃×#563	1	2	yes	—
325	C₄	C₁₃×#563	1	1	yes	characteristic
326	C₂	C₁₃×#2823	1	1	yes	characteristic
327	C₂	C₁₃×#3248	1	2	yes	—
328	C₂	C₁₃×#3250	1	1	yes	characteristic
329	C₂	C₁₃×#3252	1	2	yes	—
330	C₂	C₁₃×#3255	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
70. #32863	C₁₃	direct (N × H)
274. C₁₃	#32863	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×#2863	2
C₁₃×#2088	2
C₁₃×#2086	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#2056	2
C₁₃×#1842	2
#32863	13

Subgroups — C13×#32863 #15719202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32863 #15719202