Subgroups — C₁₃×#61958 #15748297

Order 3328.

1922 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3305	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3303	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3287	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3284	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3247	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3207	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3102	C₂	1	3	yes	maximal, complemented
14	C₁₃×#3035	C₂	1	3	yes	maximal, complemented
15	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	6	yes	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#557	C₂²	1	1	yes	characteristic
19	C₁₃×#555	—	2	3	no	—
20	C₁₃×#555	C₂²	1	3	yes	—
21	C₁₃×#553	—	2	3	no	—
22	C₁₃×#550	—	2	1	no	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	C₂²	1	3	yes	—
25	C₁₃×#550	C₂²	1	3	yes	—
26	C₁₃×#550	C₂²	1	1	yes	characteristic
27	C₁₃×#550	C₂²	1	1	yes	characteristic
28	C₁₃×#547	C₂²	1	3	yes	—
29	C₁₃×#540	—	2	3	no	—
30	C₁₃×#532	—	2	3	no	—
31	C₁₃×#532	C₂²	1	3	yes	—
32	C₁₃×#532	C₂²	1	3	yes	—
33	C₁₃×#529	C₂²	1	3	yes	—
34	C₁₃×#520	—	2	1	no	—
35	C₄×C₁₃×#41	—	2	1	no	—
36	C₄×C₁₃×#41	C₂²	1	3	yes	—
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₁₃×#493	C₂²	1	3	yes	—
39	C₁₃×#492	C₂²	1	3	yes	—
40	C₁₃×#487	C₂²	1	3	yes	—
41	C₁₃×#486	C₂²	1	3	yes	—
42	C₁₃×#485	C₂²	1	3	yes	—
43	C₁₃×#482	C₂²	1	3	yes	—
44	C₁₃×#479	C₂²	1	1	yes	characteristic
45	C₁₃×#478	C₂²	1	3	yes	—
46	C₁₃×#477	C₂²	1	3	yes	—
47	C₁₃×#476	C₂²	1	3	yes	—
48	C₁₃×#466	C₂²	1	6	yes	—
49	C₁₃×#465	C₂²	1	6	yes	—
50	C₁₃×#464	C₂²	1	3	yes	—
51	C₁₃×#463	C₂²	1	6	yes	—
52	C₁₃×#463	C₂²	1	3	yes	—
53	C₁₃×#462	C₂²	1	3	yes	—
54	C₁₃×#461	C₂²	1	3	yes	—
55	C₁₃×#460	C₂²	1	3	yes	—
56	C₁₃×#460	C₂²	1	3	yes	—
57	C₁₃×#459	C₂²	1	3	yes	—
58	C₁₃×#459	C₂²	1	3	yes	—
59	C₁₃×#452	C₂²	1	3	yes	—
60	C₁₃×#449	C₂²	1	6	yes	—
61	C₁₃×#449	C₂²	1	3	yes	—
62	C₁₃×#449	C₂²	1	6	yes	—
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
66	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
67	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
68	C₄×C₁₃×D₈	C₂²	1	3	yes	—
69	C₈×D₄×C₁₃	C₂²	1	3	yes	—
70	C₈×D₄×C₁₃	C₂²	1	3	yes	—
71	C₁₃×#431	C₂²	1	3	yes	—
72	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
73	C₁₃×#416	C₂²	1	6	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	3	no	—
77	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
78	C₂×C₁₃×#41	C₂³	1	3	yes	—
79	C₂×C₁₃×#41	C₂³	1	6	yes	—
80	C₁₃×#135	—	4	12	no	—
81	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
85	C₂×C₁₃×D₈	C₂³	1	3	yes	—
86	C₂×C₁₃×D₈	C₂³	1	6	yes	—
87	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
88	C₁₃×C₄⋊Q₈	—	2	3	no	—
89	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×#127	—	2	3	no	—
92	C₁₃×#127	—	2	3	no	—
93	C₁₃×#127	C₂³	1	3	yes	—
94	C₁₃×#127	C₂³	1	3	yes	—
95	C₁₃×#126	—	2	3	no	—
96	C₁₃×#125	—	2	3	no	—
97	C₁₃×#125	C₂³	1	1	yes	characteristic
98	C₁₃×#124	—	2	6	no	—
99	C₁₃×#124	—	2	3	no	—
100	C₁₃×#124	C₂³	1	3	yes	—
101	C₁₃×#123	—	2	3	no	—
102	C₁₃×#123	—	2	6	no	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
104	C₁₃×#121	—	2	3	no	—
105	C₁₃×#121	—	2	3	no	—
106	C₁₃×#121	—	2	3	no	—
107	C₁₃×#121	—	2	3	no	—
108	C₁₃×#121	—	2	3	no	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	—	2	6	no	—
112	C₁₃×#121	—	2	6	no	—
113	C₁₃×#121	C₂³	1	6	yes	—
114	C₁₃×#121	C₂³	1	3	yes	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	—	2	1	no	—
117	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
118	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₁₃	—	2	3	no	—
123	C₄×D₄×C₁₃	—	2	3	no	—
124	C₄×D₄×C₁₃	—	2	3	no	—
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	—	2	3	no	—
129	C₄×D₄×C₁₃	—	2	3	no	—
130	C₄×D₄×C₁₃	D₄	1	3	yes	—
131	C₄×D₄×C₁₃	C₂³	1	3	yes	—
132	C₄×D₄×C₁₃	C₂³	1	3	yes	—
133	C₄×D₄×C₁₃	C₂³	1	3	yes	—
134	C₄×D₄×C₁₃	C₂³	1	3	yes	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	—	2	3	no	—
137	C₁₃×#117	—	2	3	no	—
138	C₁₃×#117	D₄	1	3	yes	—
139	C₁₃×#117	C₂³	1	3	yes	—
140	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
141	C₂×C₄²×C₁₃	—	2	3	no	—
142	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
143	C₁₃×#107	C₂³	1	1	yes	characteristic
144	C₁₃×#107	C₂³	1	3	yes	—
145	C₁₃×#106	C₂³	1	1	yes	characteristic
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	6	yes	—
153	C₁₃×#103	C₂³	1	1	yes	characteristic
154	C₁₃×#103	C₂³	1	1	yes	characteristic
155	C₁₃×#103	C₂³	1	3	yes	—
156	C₁₃×#102	C₂³	1	3	yes	—
157	C₁₃×#102	C₂³	1	6	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	3	yes	—
160	C₁₃×#102	C₂³	1	3	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	#61958	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	2	6	no	—
168	C₁₃×#41	—	4	3	no	—
169	C₁₃×#41	—	4	6	no	—
170	C₁₃×#41	—	4	6	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	—	8	6	no	—
174	C₂×Q₈×C₁₃	—	2	3	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₃	—	2	3	no	—
179	C₂×D₄×C₁₃	—	2	3	no	—
180	C₂×D₄×C₁₃	—	2	6	no	—
181	C₂×D₄×C₁₃	—	2	6	no	—
182	C₂×D₄×C₁₃	—	2	3	no	—
183	C₂×D₄×C₁₃	—	2	3	no	—
184	C₂×D₄×C₁₃	—	2	3	no	—
185	C₂×D₄×C₁₃	—	2	3	no	—
186	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
189	C₂²×C₄×C₁₃	—	2	3	no	—
190	C₂²×C₄×C₁₃	—	2	3	no	—
191	C₂²×C₄×C₁₃	—	2	3	no	—
192	C₂²×C₄×C₁₃	—	2	3	no	—
193	C₂²×C₄×C₁₃	—	2	6	no	—
194	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
195	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
197	C₁₃×Q₁₆	—	2	6	no	—
198	C₁₃×SD₁₆	—	2	6	no	—
199	C₁₃×SD₁₆	—	4	3	no	—
200	C₁₃×SD₁₆	—	4	6	no	—
201	C₁₃×D₈	—	4	3	no	—
202	C₁₃×D₈	—	4	6	no	—
203	C₂×C₈×C₁₃	—	4	6	no	—
204	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
207	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
208	C₁₃×C₄⋊C₄	—	2	3	no	—
209	C₁₃×C₄⋊C₄	—	2	3	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	3	no	—
213	C₁₃×C₄⋊C₄	—	2	3	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	3	no	—
216	C₁₃×C₄⋊C₄	—	2	3	no	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
222	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
223	C₁₃×C₂²⋊C₄	—	2	3	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	3	no	—
226	C₁₃×C₂²⋊C₄	—	2	3	no	—
227	C₁₃×C₂²⋊C₄	—	2	6	no	—
228	C₁₃×C₂²⋊C₄	—	2	3	no	—
229	C₁₃×C₂²⋊C₄	—	2	3	no	—
230	C₁₃×C₂²⋊C₄	—	2	3	no	—
231	C₁₃×C₂²⋊C₄	—	2	3	no	—
232	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	3	no	—
235	C₄²×C₁₃	—	2	3	no	—
236	C₄²×C₁₃	—	2	3	no	—
237	C₄²×C₁₃	C₂×D₄	1	3	yes	—
238	C₄²×C₁₃	C₂×D₄	1	3	yes	—
239	C₄²×C₁₃	C₂⁴	1	3	yes	—
240	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
241	#3517	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#3305	C₂×C₁₃	1	3	yes	complemented
248	#3303	C₂×C₁₃	1	3	yes	complemented
249	#3287	C₂×C₁₃	1	3	yes	complemented
250	#3284	C₂×C₁₃	1	3	yes	complemented
251	#3247	C₂×C₁₃	1	3	yes	complemented
252	#3207	C₂×C₁₃	1	3	yes	complemented
253	#3102	C₂×C₁₃	1	3	yes	complemented
254	#3035	C₂×C₁₃	1	3	yes	complemented
255	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₁₃	—	2	3	no	—
257	C₂³×C₁₃	—	2	3	no	—
258	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
259	Q₈×C₁₃	—	2	1	no	—
260	Q₈×C₁₃	—	2	3	no	—
261	Q₈×C₁₃	—	2	3	no	—
262	Q₈×C₁₃	—	8	3	no	—
263	Q₈×C₁₃	#135	1	4	yes	complemented
264	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
265	D₄×C₁₃	—	2	6	no	—
266	D₄×C₁₃	—	2	3	no	—
267	D₄×C₁₃	—	2	3	no	—
268	D₄×C₁₃	—	2	3	no	—
269	D₄×C₁₃	—	2	3	no	—
270	D₄×C₁₃	—	4	6	no	—
271	D₄×C₁₃	—	4	6	no	—
272	D₄×C₁₃	—	4	6	no	—
273	D₄×C₁₃	—	8	3	no	—
274	D₄×C₁₃	—	8	3	no	—
275	D₄×C₁₃	—	8	3	no	—
276	D₄×C₁₃	—	8	6	no	—
277	D₄×C₁₃	—	8	6	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	6	no	—
280	C₂×C₄×C₁₃	—	2	3	no	—
281	C₂×C₄×C₁₃	—	2	3	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	3	no	—
285	C₂×C₄×C₁₃	—	2	3	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	4	3	no	—
288	C₂×C₄×C₁₃	—	4	6	no	—
289	C₂×C₄×C₁₃	—	4	6	no	—
290	C₂×C₄×C₁₃	—	4	6	no	—
291	C₂×C₄×C₁₃	—	4	6	no	—
292	C₂×C₄×C₁₃	—	8	6	no	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
297	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
298	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
299	C₈×C₁₃	—	2	3	no	—
300	C₈×C₁₃	—	2	3	no	—
301	C₈×C₁₃	—	2	1	no	—
302	C₈×C₁₃	—	2	1	no	—
303	C₂×#135	C₂²×C₁₃	1	6	yes	—
304	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
305	#557	C₂²×C₁₃	1	1	yes	characteristic
306	#555	—	2	3	no	—
307	#555	C₂²×C₁₃	1	3	yes	—
308	#553	—	2	3	no	—
309	#550	—	2	1	no	—
310	#550	—	2	1	no	—
311	#550	C₂²×C₁₃	1	3	yes	—
312	#550	C₂²×C₁₃	1	3	yes	—
313	#550	C₂²×C₁₃	1	1	yes	characteristic
314	#550	C₂²×C₁₃	1	1	yes	characteristic
315	#547	C₂²×C₁₃	1	3	yes	—
316	#540	—	2	3	no	—
317	#532	—	2	3	no	—
318	#532	C₂²×C₁₃	1	3	yes	—
319	#532	C₂²×C₁₃	1	3	yes	—
320	#529	C₂²×C₁₃	1	3	yes	—
321	#520	—	2	1	no	—
322	C₄×#41	—	2	1	no	—
323	C₄×#41	C₂²×C₁₃	1	3	yes	—
324	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
325	#493	C₂²×C₁₃	1	3	yes	—
326	#492	C₂²×C₁₃	1	3	yes	—
327	#487	C₂²×C₁₃	1	3	yes	—
328	#486	C₂²×C₁₃	1	3	yes	—
329	#485	C₂²×C₁₃	1	3	yes	—
330	#482	C₂²×C₁₃	1	3	yes	—
331	#479	C₂²×C₁₃	1	1	yes	characteristic
332	#478	C₂²×C₁₃	1	3	yes	—
333	#477	C₂²×C₁₃	1	3	yes	—
334	#476	C₂²×C₁₃	1	3	yes	—
335	#466	C₂²×C₁₃	1	6	yes	—
336	#465	C₂²×C₁₃	1	6	yes	—
337	#464	C₂²×C₁₃	1	3	yes	—
338	#463	C₂²×C₁₃	1	3	yes	—
339	#463	C₂²×C₁₃	1	6	yes	—
340	#462	C₂²×C₁₃	1	3	yes	—
341	#461	C₂²×C₁₃	1	3	yes	—
342	#460	C₂²×C₁₃	1	3	yes	—
343	#460	C₂²×C₁₃	1	3	yes	—
344	#459	C₂²×C₁₃	1	3	yes	—
345	#459	C₂²×C₁₃	1	3	yes	—
346	#452	C₂²×C₁₃	1	3	yes	—
347	#449	C₂²×C₁₃	1	3	yes	—
348	#449	C₂²×C₁₃	1	6	yes	—
349	#449	C₂²×C₁₃	1	6	yes	—
350	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
351	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
352	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
353	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
354	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
355	C₄×D₈	C₂²×C₁₃	1	3	yes	—
356	C₈×D₄	C₂²×C₁₃	1	3	yes	—
357	C₈×D₄	C₂²×C₁₃	1	3	yes	—
358	#431	C₂²×C₁₃	1	3	yes	—
359	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
360	#416	C₂²×C₁₃	1	6	yes	—
361	C₂²×C₁₃	—	2	3	no	—
362	C₂²×C₁₃	—	2	3	no	—
363	C₂²×C₁₃	—	2	3	no	—
364	C₂²×C₁₃	—	4	3	no	—
365	C₂²×C₁₃	—	4	3	no	—
366	C₂²×C₁₃	—	4	3	no	—
367	C₂²×C₁₃	—	4	3	no	—
368	C₂²×C₁₃	—	4	3	no	—
369	C₂²×C₁₃	—	4	3	no	—
370	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₁₃	—	2	1	no	—
372	C₄×C₁₃	—	2	3	no	—
373	C₄×C₁₃	—	2	3	no	—
374	C₄×C₁₃	—	2	2	no	—
375	C₄×C₁₃	—	2	1	no	—
376	C₄×C₁₃	—	4	3	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	3	no	—
379	C₄×C₁₃	—	4	1	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	C₂×#135	1	6	yes	—
382	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₄×C₁₃	#585	1	1	yes	characteristic
384	C₂×#41	—	2	1	no	—
385	C₂×#41	—	2	1	no	—
386	C₂×#41	—	2	3	no	—
387	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
388	C₂×#41	C₂³×C₁₃	1	3	yes	—
389	C₂×#41	C₂³×C₁₃	1	6	yes	—
390	#135	—	4	12	no	—
391	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
392	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
393	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
394	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
395	C₂×D₈	C₂³×C₁₃	1	6	yes	—
396	C₂×D₈	C₂³×C₁₃	1	3	yes	—
397	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
398	C₄⋊Q₈	—	2	3	no	—
399	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
400	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
401	#127	—	2	3	no	—
402	#127	—	2	3	no	—
403	#127	C₂³×C₁₃	1	3	yes	—
404	#127	C₂³×C₁₃	1	3	yes	—
405	#126	—	2	3	no	—
406	#125	—	2	3	no	—
407	#125	C₂³×C₁₃	1	1	yes	characteristic
408	#124	—	2	6	no	—
409	#124	—	2	3	no	—
410	#124	C₂³×C₁₃	1	3	yes	—
411	#123	—	2	3	no	—
412	#123	—	2	6	no	—
413	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
414	#121	—	2	3	no	—
415	#121	—	2	3	no	—
416	#121	—	2	3	no	—
417	#121	—	2	3	no	—
418	#121	—	2	3	no	—
419	#121	—	2	3	no	—
420	#121	—	2	3	no	—
421	#121	—	2	6	no	—
422	#121	—	2	6	no	—
423	#121	C₂³×C₁₃	1	3	yes	—
424	#121	C₂³×C₁₃	1	6	yes	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
428	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
430	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
431	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	—	2	3	no	—
435	C₄×D₄	—	2	3	no	—
436	C₄×D₄	—	2	3	no	—
437	C₄×D₄	—	2	3	no	—
438	C₄×D₄	—	2	3	no	—
439	C₄×D₄	—	2	3	no	—
440	C₄×D₄	D₄×C₁₃	1	3	yes	—
441	C₄×D₄	C₂³×C₁₃	1	3	yes	—
442	C₄×D₄	C₂³×C₁₃	1	3	yes	—
443	C₄×D₄	C₂³×C₁₃	1	3	yes	—
444	C₄×D₄	C₂³×C₁₃	1	3	yes	—
445	#117	—	2	3	no	—
446	#117	—	2	3	no	—
447	#117	—	2	3	no	—
448	#117	D₄×C₁₃	1	3	yes	—
449	#117	C₂³×C₁₃	1	3	yes	—
450	C₂×C₄⋊C₄	—	2	3	no	—
451	C₂×C₄²	—	2	3	no	—
452	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
453	#107	C₂³×C₁₃	1	1	yes	characteristic
454	#107	C₂³×C₁₃	1	3	yes	—
455	#106	C₂³×C₁₃	1	1	yes	characteristic
456	#106	C₂³×C₁₃	1	3	yes	—
457	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
458	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
459	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
460	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
461	#103	C₂³×C₁₃	1	3	yes	—
462	#103	C₂³×C₁₃	1	6	yes	—
463	#103	C₂³×C₁₃	1	1	yes	characteristic
464	#103	C₂³×C₁₃	1	1	yes	characteristic
465	#103	C₂³×C₁₃	1	3	yes	—
466	#102	C₂³×C₁₃	1	3	yes	—
467	#102	C₂³×C₁₃	1	6	yes	—
468	#102	C₂³×C₁₃	1	3	yes	—
469	#102	C₂³×C₁₃	1	3	yes	—
470	#102	C₂³×C₁₃	1	3	yes	—
471	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
472	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
473	C₄×C₈	C₂³×C₁₃	1	3	yes	—
474	C₄×C₈	C₂³×C₁₃	1	3	yes	—
475	C₂×C₁₃	—	4	3	no	—
476	C₂×C₁₃	—	8	3	no	—
477	C₂×C₁₃	—	8	3	no	—
478	C₂×C₁₃	#3488	1	1	yes	characteristic
479	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
480	C₂×C₁₃	#3585	1	1	yes	characteristic
481	#41	—	2	4	no	—
482	#41	—	2	6	no	—
483	#41	—	4	3	no	—
484	#41	—	4	6	no	—
485	#41	—	4	6	no	—
486	#41	—	4	4	no	—
487	#41	—	4	4	no	—
488	#41	—	8	6	no	—
489	C₂×Q₈	—	2	3	no	—
490	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
492	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₂×D₄	—	2	3	no	—
494	C₂×D₄	—	2	3	no	—
495	C₂×D₄	—	2	6	no	—
496	C₂×D₄	—	2	6	no	—
497	C₂×D₄	—	2	3	no	—
498	C₂×D₄	—	2	3	no	—
499	C₂×D₄	—	2	3	no	—
500	C₂×D₄	—	2	3	no	—
501	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
502	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
503	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
504	C₂²×C₄	—	2	3	no	—
505	C₂²×C₄	—	2	3	no	—
506	C₂²×C₄	—	2	3	no	—
507	C₂²×C₄	—	2	3	no	—
508	C₂²×C₄	—	2	6	no	—
509	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
510	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
511	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
512	Q₁₆	—	2	6	no	—
513	SD₁₆	—	2	6	no	—
514	SD₁₆	—	4	6	no	—
515	SD₁₆	—	4	3	no	—
516	D₈	—	4	6	no	—
517	D₈	—	4	3	no	—
518	C₂×C₈	—	4	6	no	—
519	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
520	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
521	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
522	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
523	C₄⋊C₄	—	2	3	no	—
524	C₄⋊C₄	—	2	3	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	3	no	—
528	C₄⋊C₄	—	2	3	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	3	no	—
531	C₄⋊C₄	—	2	3	no	—
532	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
533	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
534	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
536	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
538	C₂²⋊C₄	—	2	3	no	—
539	C₂²⋊C₄	—	2	3	no	—
540	C₂²⋊C₄	—	2	3	no	—
541	C₂²⋊C₄	—	2	3	no	—
542	C₂²⋊C₄	—	2	6	no	—
543	C₂²⋊C₄	—	2	3	no	—
544	C₂²⋊C₄	—	2	3	no	—
545	C₂²⋊C₄	—	2	3	no	—
546	C₂²⋊C₄	—	2	3	no	—
547	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	3	no	—
550	C₄²	—	2	3	no	—
551	C₄²	—	2	3	no	—
552	C₄²	C₂×D₄×C₁₃	1	3	yes	—
553	C₄²	C₂×D₄×C₁₃	1	3	yes	—
554	C₄²	C₂⁴×C₁₃	1	3	yes	—
555	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
556	C₁₃	#61958	1	1	yes	characteristic, direct product factor, Sylow
557	C₂³	—	2	3	no	—
558	C₂³	—	2	3	no	—
559	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
560	Q₈	—	2	1	no	—
561	Q₈	—	2	3	no	—
562	Q₈	—	2	3	no	—
563	Q₈	—	8	3	no	—
564	Q₈	C₁₃×#135	1	4	yes	complemented
565	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
566	D₄	—	2	6	no	—
567	D₄	—	2	3	no	—
568	D₄	—	2	3	no	—
569	D₄	—	2	3	no	—
570	D₄	—	2	3	no	—
571	D₄	—	4	6	no	—
572	D₄	—	4	6	no	—
573	D₄	—	4	6	no	—
574	D₄	—	8	3	no	—
575	D₄	—	8	3	no	—
576	D₄	—	8	3	no	—
577	D₄	—	8	6	no	—
578	D₄	—	8	6	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	6	no	—
581	C₂×C₄	—	2	3	no	—
582	C₂×C₄	—	2	3	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	3	no	—
586	C₂×C₄	—	2	3	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	4	3	no	—
589	C₂×C₄	—	4	6	no	—
590	C₂×C₄	—	4	6	no	—
591	C₂×C₄	—	4	6	no	—
592	C₂×C₄	—	4	6	no	—
593	C₂×C₄	—	8	6	no	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
599	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
600	C₈	—	2	3	no	—
601	C₈	—	2	3	no	—
602	C₈	—	2	1	no	—
603	C₈	—	2	1	no	—
604	C₂²	—	2	3	no	—
605	C₂²	—	2	3	no	—
606	C₂²	—	2	3	no	—
607	C₂²	—	4	3	no	—
608	C₂²	—	4	3	no	—
609	C₂²	—	4	3	no	—
610	C₂²	—	4	3	no	—
611	C₂²	—	4	3	no	—
612	C₂²	—	4	3	no	—
613	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	3	no	—
617	C₄	—	2	3	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	3	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	3	no	—
624	C₄	C₂×C₁₃×#135	1	6	yes	—
625	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
626	C₄	C₁₃×#585	1	1	yes	characteristic
627	C₂	—	4	3	no	—
628	C₂	—	8	3	no	—
629	C₂	—	8	3	no	—
630	C₂	C₁₃×#3488	1	1	yes	characteristic
631	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
632	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3517	C₂	semidirect
2. C₁₃×#3483	C₂	semidirect
3. C₁₃×#3392	C₂	semidirect
4. C₁₃×#3391	C₂	semidirect
5. C₁₃×#3363	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3305	C₂	semidirect
8. C₁₃×#3303	C₂	semidirect
9. C₁₃×#3287	C₂	semidirect
10. C₁₃×#3284	C₂	semidirect
11. C₁₃×#3247	C₂	semidirect
12. C₁₃×#3207	C₂	semidirect
13. C₁₃×#3102	C₂	semidirect
14. C₁₃×#3035	C₂	semidirect
15. C₁₃×#2988	C₂	semidirect
165. #61958	C₁₃	direct (N × H)
241. #3517	C₂×C₁₃	semidirect
242. #3483	C₂×C₁₃	semidirect
243. #3392	C₂×C₁₃	semidirect
244. #3391	C₂×C₁₃	semidirect
245. #3363	C₂×C₁₃	semidirect
246. #3362	C₂×C₁₃	semidirect
247. #3305	C₂×C₁₃	semidirect
248. #3303	C₂×C₁₃	semidirect
249. #3287	C₂×C₁₃	semidirect
250. #3284	C₂×C₁₃	semidirect
251. #3247	C₂×C₁₃	semidirect
252. #3207	C₂×C₁₃	semidirect
253. #3102	C₂×C₁₃	semidirect
254. #3035	C₂×C₁₃	semidirect
255. #2988	C₂×C₁₃	semidirect
263. Q₈×C₁₃	#135	semidirect
556. C₁₃	#61958	direct (N × H)
564. Q₈	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3517	2
C₁₃×#3483	2
C₁₃×#3392	2
C₁₃×#3391	2
C₁₃×#3363	2
C₁₃×#3362	2
C₁₃×#3305	2
C₁₃×#3303	2
C₁₃×#3287	2
C₁₃×#3284	2
C₁₃×#3247	2
C₁₃×#3207	2
C₁₃×#3102	2
C₁₃×#3035	2
C₁₃×#2988	2
#61958	13

Subgroups — C13×#61958 #15748297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61958 #15748297