Subgroups — C₁₃×#61469 #15747808

Order 3328.

1866 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×Q₁₆	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×#3357	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3333	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3329	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3278	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3182	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3116	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3112	C₂	1	3	yes	maximal, complemented
14	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#137	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₃×#137	C₂²	1	3	yes	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	1	yes	characteristic
21	C₁₃×#555	—	2	3	no	—
22	C₁₃×#555	C₂²	1	3	yes	—
23	C₁₃×#554	—	2	3	no	—
24	C₁₃×#554	C₂²	1	3	yes	—
25	C₁₃×#550	—	2	1	no	—
26	C₁₃×#550	C₂²	1	3	yes	—
27	C₁₃×#550	C₂²	1	1	yes	characteristic
28	D₄×Q₈×C₁₃	C₂²	1	3	yes	—
29	C₁₃×#533	—	2	3	no	—
30	C₁₃×#533	C₂²	1	3	yes	—
31	C₁₃×#532	—	2	3	no	—
32	C₁₃×#532	C₂²	1	3	yes	—
33	C₄×C₁₃×#41	—	2	1	no	—
34	C₄×C₁₃×#41	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	3	yes	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
38	C₁₃×#500	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	6	yes	—
43	C₁₃×#480	C₂²	1	6	yes	—
44	C₁₃×#477	C₂²	1	3	yes	—
45	C₁₃×#477	C₂²	1	3	yes	—
46	C₁₃×#477	C₂²	1	3	yes	—
47	C₁₃×#476	C₂²	1	3	yes	—
48	C₁₃×#468	C₂²	1	6	yes	—
49	C₁₃×#468	C₂²	1	6	yes	—
50	C₁₃×#462	C₂²	1	3	yes	—
51	C₁₃×#461	C₂²	1	3	yes	—
52	C₁₃×#460	C₂²	1	3	yes	—
53	C₁₃×#460	C₂²	1	3	yes	—
54	C₁₃×#452	C₂²	1	6	yes	—
55	C₁₃×#448	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₁₃×#441	C₂²	1	3	yes	—
59	C₁₃×#441	C₂²	1	1	yes	characteristic
60	C₁₃×#440	C₂²	1	3	yes	—
61	C₁₃×#440	C₂²	1	6	yes	—
62	C₁₃×#440	C₂²	1	3	yes	—
63	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
64	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
65	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
66	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
67	C₁₃×#436	C₂²	1	3	yes	—
68	C₁₃×#436	C₂²	1	3	yes	—
69	C₁₃×#432	C₂²	1	3	yes	—
70	C₁₃×#428	C₂²	1	3	yes	—
71	C₁₃×#419	C₂²	1	3	yes	—
72	C₁₃×#417	C₂²	1	3	yes	—
73	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	3	no	—
76	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
77	C₂×C₁₃×#41	C₂³	1	3	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
79	C₁₃×#137	—	2	12	no	—
80	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
81	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
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×M₁₆	C₂³	1	3	yes	—
86	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
87	C₁₃×C₄⋊Q₈	—	2	3	no	—
88	C₁₃×C₄⋊Q₈	—	2	3	no	—
89	C₁₃×C₄⋊Q₈	—	2	3	no	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₁₃×#127	—	2	3	no	—
94	C₁₃×#127	C₂³	1	3	yes	—
95	C₁₃×#125	—	2	3	no	—
96	C₁₃×#125	—	2	3	no	—
97	C₁₃×#125	—	2	3	no	—
98	C₁₃×#124	—	2	6	no	—
99	C₁₃×#124	—	2	3	no	—
100	C₁₃×C₂²⋊Q₈	—	2	3	no	—
101	C₁₃×C₂²⋊Q₈	—	2	6	no	—
102	C₁₃×C₂²⋊Q₈	—	2	6	no	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
104	C₁₃×#121	—	2	3	no	—
105	C₁₃×#121	—	2	3	no	—
106	C₁₃×#121	—	2	3	no	—
107	C₁₃×#121	—	2	6	no	—
108	C₁₃×#121	C₂³	1	6	yes	—
109	C₄×Q₈×C₁₃	—	2	1	no	—
110	C₄×Q₈×C₁₃	—	2	1	no	—
111	C₄×Q₈×C₁₃	—	2	1	no	—
112	C₄×Q₈×C₁₃	—	2	3	no	—
113	C₄×Q₈×C₁₃	—	2	3	no	—
114	C₄×Q₈×C₁₃	—	2	3	no	—
115	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
116	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
117	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	D₄	1	3	yes	—
130	C₄×D₄×C₁₃	C₂³	1	3	yes	—
131	C₄×D₄×C₁₃	C₂³	1	3	yes	—
132	C₄×D₄×C₁₃	C₂³	1	3	yes	—
133	C₁₃×#117	—	2	3	no	—
134	C₁₃×#117	—	2	3	no	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	D₄	1	3	yes	—
137	C₁₃×#117	C₂³	1	3	yes	—
138	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
140	C₂×C₄²×C₁₃	—	2	3	no	—
141	C₂×C₄²×C₁₃	—	2	3	no	—
142	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
143	C₁₃×#107	C₂³	1	3	yes	—
144	C₁₃×#107	C₂³	1	3	yes	—
145	C₁₃×#107	C₂³	1	6	yes	—
146	C₁₃×#106	C₂³	1	1	yes	characteristic
147	C₁₃×#106	C₂³	1	3	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×#103	C₂³	1	1	yes	characteristic
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	1	yes	characteristic
153	C₁₃×#103	C₂³	1	3	yes	—
154	C₁₃×#103	C₂³	1	3	yes	—
155	C₁₃×#103	C₂³	1	3	yes	—
156	C₁₃×#103	C₂³	1	6	yes	—
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	6	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
161	C₁₃×#97	C₂³	1	1	yes	characteristic
162	C₁₃×#97	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	#61469	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	4	no	—
170	C₁₃×#41	—	8	6	no	—
171	C₂×Q₈×C₁₃	—	2	3	no	—
172	C₂×Q₈×C₁₃	—	2	3	no	—
173	C₂×Q₈×C₁₃	—	2	3	no	—
174	C₂×Q₈×C₁₃	—	2	6	no	—
175	C₂×Q₈×C₁₃	—	4	3	no	—
176	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×D₄×C₁₃	—	2	3	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	C₂×D₄	1	3	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
186	C₂²×C₄×C₁₃	—	2	3	no	—
187	C₂²×C₄×C₁₃	—	2	3	no	—
188	C₂²×C₄×C₁₃	—	2	3	no	—
189	C₂²×C₄×C₁₃	—	2	3	no	—
190	C₂²×C₄×C₁₃	—	2	3	no	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
192	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
194	C₁₃×Q₁₆	—	2	6	no	—
195	C₁₃×Q₁₆	#41	1	4	yes	complemented
196	C₁₃×SD₁₆	—	2	6	no	—
197	C₁₃×SD₁₆	—	2	6	no	—
198	C₁₃×SD₁₆	—	4	6	no	—
199	C₁₃×M₁₆	—	2	6	no	—
200	C₁₃×M₁₆	—	4	3	no	—
201	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
203	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
204	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	3	no	—
207	C₁₃×C₄⋊C₄	—	2	3	no	—
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	3	no	—
212	C₁₃×C₄⋊C₄	—	2	3	no	—
213	C₁₃×C₄⋊C₄	—	2	3	no	—
214	C₁₃×C₄⋊C₄	—	2	3	no	—
215	C₁₃×C₄⋊C₄	—	2	3	no	—
216	C₁₃×C₄⋊C₄	—	2	6	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	3	yes	—
223	C₁₃×C₂²⋊C₄	—	2	6	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	6	no	—
226	C₁₃×C₂²⋊C₄	—	2	3	no	—
227	C₁₃×C₂²⋊C₄	—	2	3	no	—
228	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	3	no	—
232	C₄²×C₁₃	—	2	3	no	—
233	C₄²×C₁₃	—	2	3	no	—
234	C₄²×C₁₃	—	2	3	no	—
235	C₄²×C₁₃	—	2	3	no	—
236	C₄²×C₁₃	C₂×D₄	1	3	yes	—
237	C₄²×C₁₃	C₂×D₄	1	3	yes	—
238	C₄²×C₁₃	C₂⁴	1	3	yes	—
239	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
240	#3483	C₂×C₁₃	1	1	yes	characteristic
241	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
243	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#3357	C₂×C₁₃	1	3	yes	complemented
247	#3333	C₂×C₁₃	1	3	yes	complemented
248	#3329	C₂×C₁₃	1	3	yes	complemented
249	#3278	C₂×C₁₃	1	3	yes	complemented
250	#3182	C₂×C₁₃	1	3	yes	complemented
251	#3116	C₂×C₁₃	1	3	yes	complemented
252	#3112	C₂×C₁₃	1	3	yes	complemented
253	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₄×#137	C₂×C₁₃	1	3	yes	complemented
255	C₂³×C₁₃	—	2	3	no	—
256	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
257	Q₈×C₁₃	—	2	1	no	—
258	Q₈×C₁₃	—	2	1	no	—
259	Q₈×C₁₃	—	2	3	no	—
260	Q₈×C₁₃	—	2	3	no	—
261	Q₈×C₁₃	—	4	6	no	—
262	Q₈×C₁₃	—	8	3	no	—
263	Q₈×C₁₃	—	8	3	no	—
264	Q₈×C₁₃	#137	1	4	yes	complemented
265	Q₈×C₁₃	C₂×#41	1	2	yes	—
266	Q₈×C₁₃	C₂×#41	1	2	yes	—
267	D₄×C₁₃	—	2	6	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	—	8	3	no	—
273	D₄×C₁₃	—	8	6	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	6	no	—
277	C₂×C₄×C₁₃	—	2	3	no	—
278	C₂×C₄×C₁₃	—	2	3	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	3	no	—
282	C₂×C₄×C₁₃	—	2	3	no	—
283	C₂×C₄×C₁₃	—	2	3	no	—
284	C₂×C₄×C₁₃	—	4	3	no	—
285	C₂×C₄×C₁₃	—	4	6	no	—
286	C₂×C₄×C₁₃	—	4	6	no	—
287	C₂×C₄×C₁₃	—	4	6	no	—
288	C₂×C₄×C₁₃	—	4	6	no	—
289	C₂×C₄×C₁₃	—	8	3	no	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
295	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
296	C₈×C₁₃	—	2	3	no	—
297	C₈×C₁₃	—	2	1	no	—
298	C₈×C₁₃	—	2	3	no	—
299	C₈×C₁₃	C₂×#41	1	2	yes	—
300	C₂×#137	C₂²×C₁₃	1	3	yes	—
301	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
302	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
303	#557	—	2	1	no	—
304	#557	C₂²×C₁₃	1	1	yes	characteristic
305	#555	—	2	3	no	—
306	#555	C₂²×C₁₃	1	3	yes	—
307	#554	—	2	3	no	—
308	#554	C₂²×C₁₃	1	3	yes	—
309	#550	—	2	1	no	—
310	#550	C₂²×C₁₃	1	3	yes	—
311	#550	C₂²×C₁₃	1	1	yes	characteristic
312	D₄×Q₈	C₂²×C₁₃	1	3	yes	—
313	#533	—	2	3	no	—
314	#533	C₂²×C₁₃	1	3	yes	—
315	#532	—	2	3	no	—
316	#532	C₂²×C₁₃	1	3	yes	—
317	C₄×#41	—	2	1	no	—
318	C₄×#41	—	2	1	no	—
319	C₄×#41	C₂²×C₁₃	1	3	yes	—
320	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
322	#500	C₂²×C₁₃	1	3	yes	—
323	#492	C₂²×C₁₃	1	3	yes	—
324	#487	C₂²×C₁₃	1	3	yes	—
325	#486	C₂²×C₁₃	1	3	yes	—
326	#485	C₂²×C₁₃	1	6	yes	—
327	#480	C₂²×C₁₃	1	6	yes	—
328	#477	C₂²×C₁₃	1	3	yes	—
329	#477	C₂²×C₁₃	1	3	yes	—
330	#477	C₂²×C₁₃	1	3	yes	—
331	#476	C₂²×C₁₃	1	3	yes	—
332	#468	C₂²×C₁₃	1	6	yes	—
333	#468	C₂²×C₁₃	1	6	yes	—
334	#462	C₂²×C₁₃	1	3	yes	—
335	#461	C₂²×C₁₃	1	3	yes	—
336	#460	C₂²×C₁₃	1	3	yes	—
337	#460	C₂²×C₁₃	1	3	yes	—
338	#452	C₂²×C₁₃	1	6	yes	—
339	#448	C₂²×C₁₃	1	6	yes	—
340	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
342	#441	C₂²×C₁₃	1	3	yes	—
343	#441	C₂²×C₁₃	1	1	yes	characteristic
344	#440	C₂²×C₁₃	1	3	yes	—
345	#440	C₂²×C₁₃	1	6	yes	—
346	#440	C₂²×C₁₃	1	3	yes	—
347	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
348	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
349	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
350	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
351	#436	C₂²×C₁₃	1	3	yes	—
352	#436	C₂²×C₁₃	1	3	yes	—
353	#432	C₂²×C₁₃	1	3	yes	—
354	#428	C₂²×C₁₃	1	3	yes	—
355	#419	C₂²×C₁₃	1	3	yes	—
356	#417	C₂²×C₁₃	1	3	yes	—
357	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
358	C₂²×C₁₃	—	2	3	no	—
359	C₂²×C₁₃	—	2	3	no	—
360	C₂²×C₁₃	—	2	3	no	—
361	C₂²×C₁₃	—	4	3	no	—
362	C₂²×C₁₃	—	4	3	no	—
363	C₂²×C₁₃	—	4	3	no	—
364	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	2	3	no	—
367	C₄×C₁₃	—	2	3	no	—
368	C₄×C₁₃	—	2	2	no	—
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	1	no	—
371	C₄×C₁₃	—	4	3	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	3	no	—
374	C₄×C₁₃	—	4	3	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	C₂×#137	1	6	yes	—
377	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
378	C₄×C₁₃	#585	1	1	yes	characteristic
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	3	no	—
381	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
382	C₂×#41	C₂³×C₁₃	1	3	yes	—
383	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
384	#137	—	2	12	no	—
385	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
386	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
388	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
389	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
390	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
391	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
392	C₄⋊Q₈	—	2	3	no	—
393	C₄⋊Q₈	—	2	3	no	—
394	C₄⋊Q₈	—	2	3	no	—
395	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
396	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
397	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
398	#127	—	2	3	no	—
399	#127	C₂³×C₁₃	1	3	yes	—
400	#125	—	2	3	no	—
401	#125	—	2	3	no	—
402	#125	—	2	3	no	—
403	#124	—	2	6	no	—
404	#124	—	2	3	no	—
405	C₂²⋊Q₈	—	2	3	no	—
406	C₂²⋊Q₈	—	2	6	no	—
407	C₂²⋊Q₈	—	2	6	no	—
408	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
409	#121	—	2	3	no	—
410	#121	—	2	3	no	—
411	#121	—	2	3	no	—
412	#121	—	2	6	no	—
413	#121	C₂³×C₁₃	1	6	yes	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	3	no	—
418	C₄×Q₈	—	2	3	no	—
419	C₄×Q₈	—	2	3	no	—
420	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
421	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
427	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×D₄	—	2	3	no	—
429	C₄×D₄	—	2	3	no	—
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	D₄×C₁₃	1	3	yes	—
435	C₄×D₄	C₂³×C₁₃	1	3	yes	—
436	C₄×D₄	C₂³×C₁₃	1	3	yes	—
437	C₄×D₄	C₂³×C₁₃	1	3	yes	—
438	#117	—	2	3	no	—
439	#117	—	2	3	no	—
440	#117	—	2	3	no	—
441	#117	D₄×C₁₃	1	3	yes	—
442	#117	C₂³×C₁₃	1	3	yes	—
443	C₂×C₄⋊C₄	—	2	3	no	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
445	C₂×C₄²	—	2	3	no	—
446	C₂×C₄²	—	2	3	no	—
447	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
448	#107	C₂³×C₁₃	1	3	yes	—
449	#107	C₂³×C₁₃	1	3	yes	—
450	#107	C₂³×C₁₃	1	6	yes	—
451	#106	C₂³×C₁₃	1	1	yes	characteristic
452	#106	C₂³×C₁₃	1	3	yes	—
453	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
454	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
455	#103	C₂³×C₁₃	1	1	yes	characteristic
456	#103	C₂³×C₁₃	1	3	yes	—
457	#103	C₂³×C₁₃	1	1	yes	characteristic
458	#103	C₂³×C₁₃	1	3	yes	—
459	#103	C₂³×C₁₃	1	3	yes	—
460	#103	C₂³×C₁₃	1	3	yes	—
461	#103	C₂³×C₁₃	1	6	yes	—
462	#102	C₂³×C₁₃	1	3	yes	—
463	#102	C₂³×C₁₃	1	3	yes	—
464	#102	C₂³×C₁₃	1	6	yes	—
465	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
466	#97	C₂³×C₁₃	1	1	yes	characteristic
467	#97	C₂³×C₁₃	1	3	yes	—
468	C₄×C₈	C₂³×C₁₃	1	3	yes	—
469	C₄×C₈	C₂³×C₁₃	1	3	yes	—
470	C₂×C₁₃	—	4	3	no	—
471	C₂×C₁₃	—	8	3	no	—
472	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
473	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
474	C₂×C₁₃	#3585	1	1	yes	characteristic
475	#41	—	2	4	no	—
476	#41	—	2	6	no	—
477	#41	—	4	3	no	—
478	#41	—	4	4	no	—
479	#41	—	8	6	no	—
480	C₂×Q₈	—	2	3	no	—
481	C₂×Q₈	—	2	3	no	—
482	C₂×Q₈	—	2	3	no	—
483	C₂×Q₈	—	2	6	no	—
484	C₂×Q₈	—	4	3	no	—
485	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
487	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
488	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₂×D₄	—	2	3	no	—
490	C₂×D₄	—	2	6	no	—
491	C₂×D₄	—	2	3	no	—
492	C₂×D₄	—	2	3	no	—
493	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
494	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
495	C₂²×C₄	—	2	3	no	—
496	C₂²×C₄	—	2	3	no	—
497	C₂²×C₄	—	2	3	no	—
498	C₂²×C₄	—	2	3	no	—
499	C₂²×C₄	—	2	3	no	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
503	Q₁₆	—	2	6	no	—
504	Q₁₆	C₁₃×#41	1	4	yes	complemented
505	SD₁₆	—	2	6	no	—
506	SD₁₆	—	2	6	no	—
507	SD₁₆	—	4	6	no	—
508	M₁₆	—	2	6	no	—
509	M₁₆	—	4	3	no	—
510	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
511	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
512	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
513	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	3	no	—
521	C₄⋊C₄	—	2	3	no	—
522	C₄⋊C₄	—	2	3	no	—
523	C₄⋊C₄	—	2	3	no	—
524	C₄⋊C₄	—	2	3	no	—
525	C₄⋊C₄	—	2	6	no	—
526	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
527	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
528	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
530	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
532	C₂²⋊C₄	—	2	6	no	—
533	C₂²⋊C₄	—	2	3	no	—
534	C₂²⋊C₄	—	2	6	no	—
535	C₂²⋊C₄	—	2	3	no	—
536	C₂²⋊C₄	—	2	3	no	—
537	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	3	no	—
541	C₄²	—	2	3	no	—
542	C₄²	—	2	3	no	—
543	C₄²	—	2	3	no	—
544	C₄²	—	2	3	no	—
545	C₄²	C₂×D₄×C₁₃	1	3	yes	—
546	C₄²	C₂×D₄×C₁₃	1	3	yes	—
547	C₄²	C₂⁴×C₁₃	1	3	yes	—
548	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
549	C₁₃	#61469	1	1	yes	characteristic, direct product factor, Sylow
550	C₂³	—	2	3	no	—
551	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
552	Q₈	—	2	1	no	—
553	Q₈	—	2	1	no	—
554	Q₈	—	2	3	no	—
555	Q₈	—	2	3	no	—
556	Q₈	—	4	6	no	—
557	Q₈	—	8	3	no	—
558	Q₈	—	8	3	no	—
559	Q₈	C₁₃×#137	1	4	yes	complemented
560	Q₈	C₂×C₁₃×#41	1	2	yes	—
561	Q₈	C₂×C₁₃×#41	1	2	yes	—
562	D₄	—	2	6	no	—
563	D₄	—	2	3	no	—
564	D₄	—	2	3	no	—
565	D₄	—	4	6	no	—
566	D₄	—	4	6	no	—
567	D₄	—	8	3	no	—
568	D₄	—	8	6	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	6	no	—
572	C₂×C₄	—	2	3	no	—
573	C₂×C₄	—	2	3	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	3	no	—
577	C₂×C₄	—	2	3	no	—
578	C₂×C₄	—	2	3	no	—
579	C₂×C₄	—	4	3	no	—
580	C₂×C₄	—	4	6	no	—
581	C₂×C₄	—	4	6	no	—
582	C₂×C₄	—	4	6	no	—
583	C₂×C₄	—	4	6	no	—
584	C₂×C₄	—	8	3	no	—
585	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
588	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
589	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
590	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
591	C₈	—	2	3	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	3	no	—
594	C₈	C₂×C₁₃×#41	1	2	yes	—
595	C₂²	—	2	3	no	—
596	C₂²	—	2	3	no	—
597	C₂²	—	2	3	no	—
598	C₂²	—	4	3	no	—
599	C₂²	—	4	3	no	—
600	C₂²	—	4	3	no	—
601	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	3	no	—
605	C₄	—	2	3	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	3	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	3	no	—
612	C₄	—	4	3	no	—
613	C₄	C₂×C₁₃×#137	1	6	yes	—
614	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
615	C₄	C₁₃×#585	1	1	yes	characteristic
616	C₂	—	4	3	no	—
617	C₂	—	8	3	no	—
618	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
619	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
620	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3483	C₂
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
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3392	C₂	semidirect
4. Q₈×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#3363	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3357	C₂	semidirect
8. C₁₃×#3333	C₂	semidirect
9. C₁₃×#3329	C₂	semidirect
10. C₁₃×#3278	C₂	semidirect
11. C₁₃×#3182	C₂	semidirect
12. C₁₃×#3116	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#2971	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
165. #61469	C₁₃	direct (N × H)
195. C₁₃×Q₁₆	#41	semidirect
241. Q₈×#41	C₂×C₁₃	semidirect
242. #3392	C₂×C₁₃	semidirect
243. Q₈×Q₁₆	C₂×C₁₃	semidirect
244. #3363	C₂×C₁₃	semidirect
245. #3362	C₂×C₁₃	semidirect
246. #3357	C₂×C₁₃	semidirect
247. #3333	C₂×C₁₃	semidirect
248. #3329	C₂×C₁₃	semidirect
249. #3278	C₂×C₁₃	semidirect
250. #3182	C₂×C₁₃	semidirect
251. #3116	C₂×C₁₃	semidirect
252. #3112	C₂×C₁₃	semidirect
253. #2971	C₂×C₁₃	semidirect
254. C₄×#137	C₂×C₁₃	semidirect
264. Q₈×C₁₃	#137	semidirect
504. Q₁₆	C₁₃×#41	semidirect
549. C₁₃	#61469	direct (N × H)
559. Q₈	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3483	2
Q₈×C₁₃×#41	2
C₁₃×#3392	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3363	2
C₁₃×#3362	2
C₁₃×#3357	2
C₁₃×#3333	2
C₁₃×#3329	2
C₁₃×#3278	2
C₁₃×#3182	2
C₁₃×#3116	2
C₁₃×#3112	2
C₁₃×#2971	2
C₄×C₁₃×#137	2
#61469	13

Subgroups — C13×#61469 #15747808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61469 #15747808