Subgroups — C₁₃×#61882 #15748221

Order 3328.

1750 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×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3394	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3393	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3364	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3360	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3108	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	C₂²	1	2	yes	complemented
15	C₁₃×#557	C₂²	1	2	yes	complemented
16	C₁₃×#556	—	2	2	no	—
17	C₁₃×#556	—	2	2	no	—
18	C₁₃×#556	—	2	2	no	—
19	C₁₃×#556	C₂²	1	4	yes	—
20	C₁₃×#556	C₂²	1	4	yes	—
21	C₁₃×#556	C₂²	1	2	yes	complemented
22	C₁₃×#554	C₂²	1	2	yes	complemented
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#539	—	2	2	no	—
25	C₁₃×#536	—	2	1	no	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₃×#529	C₂²	1	4	yes	—
30	C₂×C₁₃×#126	—	2	2	no	—
31	C₂×C₁₃×#124	C₂²	1	2	yes	—
32	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
33	C₁₃×#520	—	2	1	no	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	—	2	1	no	—
38	C₁₃×#495	C₂²	1	8	yes	—
39	C₁₃×#494	C₂²	1	2	yes	complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#488	C₂²	1	8	yes	—
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#487	C₂²	1	2	yes	complemented
44	C₁₃×#483	C₂²	1	2	yes	—
45	C₁₃×#480	C₂²	1	2	yes	—
46	C₁₃×#479	C₂²	1	8	yes	complemented
47	C₁₃×#476	C₂²	1	2	yes	—
48	C₁₃×#474	C₂²	1	2	yes	—
49	C₁₃×#464	C₂²	1	8	yes	—
50	C₁₃×#464	C₂²	1	8	yes	complemented
51	C₁₃×#463	C₂²	1	8	yes	—
52	C₁₃×#462	C₂²	1	4	yes	complemented
53	C₁₃×#461	C₂²	1	2	yes	—
54	C₁₃×#461	C₂²	1	4	yes	complemented
55	C₁₃×#459	C₂²	1	2	yes	—
56	C₁₃×#451	C₂²	1	4	yes	—
57	C₁₃×#450	C₂²	1	2	yes	—
58	C₁₃×#448	C₂²	1	4	yes	—
59	C₁₃×#447	C₂²	1	2	yes	—
60	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
61	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
62	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
63	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
64	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
65	C₄×C₁₃×D₈	C₂²	1	4	yes	—
66	C₁₃×#431	C₂²	1	1	yes	characteristic
67	C₁₃×#431	C₂²	1	1	yes	characteristic
68	C₁₃×#431	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	—	2	1	no	—
74	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
77	C₂×C₁₃×D₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×#127	C₂³	1	1	yes	characteristic
87	C₁₃×#126	—	2	8	no	—
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#126	—	2	4	no	—
90	C₁₃×#126	—	2	4	no	—
91	C₁₃×#125	—	2	4	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₁₃×#125	C₂³	1	4	yes	—
94	C₁₃×#124	—	2	2	no	—
95	C₁₃×#124	—	2	4	no	—
96	C₁₃×#124	—	2	1	no	—
97	C₁₃×#124	C₂³	1	8	yes	—
98	C₁₃×#124	C₂³	1	4	yes	—
99	C₁₃×#123	—	2	4	no	—
100	C₁₃×#123	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	—	2	4	no	—
102	C₁₃×C₂²⋊Q₈	—	2	4	no	—
103	C₁₃×C₂²⋊Q₈	—	2	2	no	—
104	C₁₃×C₂²⋊Q₈	—	2	2	no	—
105	C₁₃×C₂²⋊Q₈	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	4	no	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
108	C₁₃×#121	—	2	1	no	—
109	C₁₃×#121	C₂³	1	2	yes	—
110	C₄×Q₈×C₁₃	—	2	2	no	—
111	C₄×Q₈×C₁₃	—	2	4	no	—
112	C₄×Q₈×C₁₃	—	2	1	no	—
113	C₄×Q₈×C₁₃	D₄	1	2	yes	—
114	C₄×Q₈×C₁₃	D₄	1	2	yes	—
115	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
117	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
120	C₄×D₄×C₁₃	—	2	4	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	—	2	1	no	—
123	C₄×D₄×C₁₃	—	2	1	no	—
124	C₄×D₄×C₁₃	—	2	1	no	—
125	C₄×D₄×C₁₃	C₂³	1	2	yes	—
126	C₄×D₄×C₁₃	C₂³	1	2	yes	—
127	C₄×D₄×C₁₃	C₂³	1	2	yes	—
128	C₄×D₄×C₁₃	C₂³	1	4	yes	—
129	C₁₃×#117	—	2	1	no	—
130	C₁₃×#117	—	2	4	no	—
131	C₁₃×#117	—	2	4	no	—
132	C₁₃×#117	—	2	2	no	—
133	C₁₃×#117	—	2	4	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
144	C₂×C₄²×C₁₃	—	2	2	no	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
147	C₁₃×#107	C₂³	1	4	yes	—
148	C₁₃×#106	C₂³	1	4	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	8	yes	—
154	C₁₃×#103	C₂³	1	8	yes	—
155	C₁₃×#102	C₂³	1	4	yes	—
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
160	C₄×C₈×C₁₃	C₂³	1	2	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	8	yes	—
163	#61882	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₁₃×#41	—	4	4	no	—
166	C₂×Q₈×C₁₃	—	2	4	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	4	4	no	—
171	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
172	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	4	2	no	—
180	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×Q₁₆	—	4	8	no	—
195	C₁₃×SD₁₆	—	4	8	no	—
196	C₁₃×SD₁₆	—	4	4	no	—
197	C₁₃×D₈	—	4	4	no	—
198	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
199	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	8	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	2	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	4	no	—
215	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
222	C₁₃×C₂²⋊C₄	—	2	2	no	—
223	C₁₃×C₂²⋊C₄	—	2	8	no	—
224	C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₁₃×C₂²⋊C₄	—	2	2	no	—
226	C₁₃×C₂²⋊C₄	—	2	8	no	—
227	C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	2	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₄²×C₁₃	—	2	8	no	—
233	C₄²×C₁₃	—	2	4	no	—
234	C₄²×C₁₃	—	2	2	no	—
235	C₄²×C₁₃	C₂×D₄	1	4	yes	—
236	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₄²×C₁₃	C₂⁴	1	4	yes	—
241	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
242	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3394	C₂×C₁₃	1	4	yes	complemented
244	#3393	C₂×C₁₃	1	4	yes	complemented
245	#3364	C₂×C₁₃	1	4	yes	complemented
246	#3360	C₂×C₁₃	1	4	yes	complemented
247	#3211	C₂×C₁₃	1	4	yes	complemented
248	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#3108	C₂×C₁₃	1	4	yes	complemented
251	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3100	C₂×C₁₃	1	1	yes	characteristic
253	#2982	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	4	2	no	—
257	C₂³×C₁₃	—	4	2	no	—
258	C₂³×C₁₃	—	4	2	no	—
259	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₁₃	—	2	4	no	—
261	Q₈×C₁₃	—	2	4	no	—
262	Q₈×C₁₃	—	2	4	no	—
263	Q₈×C₁₃	—	2	8	no	—
264	Q₈×C₁₃	—	4	4	no	—
265	Q₈×C₁₃	—	4	2	no	—
266	Q₈×C₁₃	—	8	1	no	—
267	D₄×C₁₃	—	2	2	no	—
268	D₄×C₁₃	—	2	4	no	—
269	D₄×C₁₃	—	2	2	no	—
270	D₄×C₁₃	—	4	2	no	—
271	D₄×C₁₃	—	4	4	no	—
272	D₄×C₁₃	—	4	2	no	—
273	D₄×C₁₃	—	8	1	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	4	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	4	no	—
286	C₂×C₄×C₁₃	—	4	4	no	—
287	C₂×C₄×C₁₃	—	4	4	no	—
288	C₂×C₄×C₁₃	—	8	4	no	—
289	C₂×C₄×C₁₃	#135	1	4	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
298	C₈×C₁₃	—	2	4	no	—
299	C₈×C₁₃	—	2	4	no	—
300	#559	C₂²×C₁₃	1	2	yes	complemented
301	#557	C₂²×C₁₃	1	2	yes	complemented
302	#556	—	2	2	no	—
303	#556	—	2	2	no	—
304	#556	—	2	2	no	—
305	#556	C₂²×C₁₃	1	4	yes	—
306	#556	C₂²×C₁₃	1	4	yes	—
307	#556	C₂²×C₁₃	1	2	yes	complemented
308	#554	C₂²×C₁₃	1	2	yes	complemented
309	#552	—	2	2	no	—
310	#539	—	2	2	no	—
311	#536	—	2	1	no	—
312	#533	C₂²×C₁₃	1	1	yes	characteristic
313	#532	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
315	#529	C₂²×C₁₃	1	4	yes	—
316	C₂×#126	—	2	2	no	—
317	C₂×#124	C₂²×C₁₃	1	2	yes	—
318	C₂×C₂²⋊Q₈	—	2	1	no	—
319	#520	—	2	1	no	—
320	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
321	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#117	—	2	1	no	—
324	#495	C₂²×C₁₃	1	8	yes	—
325	#494	C₂²×C₁₃	1	2	yes	complemented
326	#492	C₂²×C₁₃	1	2	yes	complemented
327	#488	C₂²×C₁₃	1	8	yes	—
328	#487	C₂²×C₁₃	1	2	yes	complemented
329	#487	C₂²×C₁₃	1	2	yes	complemented
330	#483	C₂²×C₁₃	1	2	yes	—
331	#480	C₂²×C₁₃	1	2	yes	—
332	#479	C₂²×C₁₃	1	8	yes	complemented
333	#476	C₂²×C₁₃	1	2	yes	—
334	#474	C₂²×C₁₃	1	2	yes	—
335	#464	C₂²×C₁₃	1	8	yes	—
336	#464	C₂²×C₁₃	1	8	yes	complemented
337	#463	C₂²×C₁₃	1	8	yes	—
338	#462	C₂²×C₁₃	1	4	yes	complemented
339	#461	C₂²×C₁₃	1	2	yes	—
340	#461	C₂²×C₁₃	1	4	yes	complemented
341	#459	C₂²×C₁₃	1	2	yes	—
342	#451	C₂²×C₁₃	1	4	yes	—
343	#450	C₂²×C₁₃	1	2	yes	—
344	#448	C₂²×C₁₃	1	4	yes	—
345	#447	C₂²×C₁₃	1	2	yes	—
346	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
347	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
348	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
349	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
350	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
351	C₄×D₈	C₂²×C₁₃	1	4	yes	—
352	#431	C₂²×C₁₃	1	1	yes	characteristic
353	#431	C₂²×C₁₃	1	1	yes	characteristic
354	#431	C₂²×C₁₃	1	4	yes	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	1	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	4	2	no	—
361	C₂²×C₁₃	—	4	2	no	—
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	8	4	no	—
364	C₂²×C₁₃	C₂×#135	1	2	yes	—
365	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₁₃	—	2	4	no	—
367	C₄×C₁₃	—	2	1	no	—
368	C₄×C₁₃	—	2	1	no	—
369	C₄×C₁₃	—	2	1	no	—
370	C₄×C₁₃	—	2	4	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	4	4	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	C₂×#135	1	2	yes	—
377	C₄×C₁₃	C₂×#135	1	2	yes	—
378	C₄×C₁₃	#585	1	2	yes	—
379	C₂×#41	—	2	1	no	—
380	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
382	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
385	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
386	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
387	C₂×D₈	C₂³×C₁₃	1	4	yes	—
388	C₄⋊Q₈	—	2	2	no	—
389	C₄⋊Q₈	—	2	1	no	—
390	C₄⋊Q₈	—	2	1	no	—
391	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
392	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
393	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
396	#127	C₂³×C₁₃	1	1	yes	characteristic
397	#126	—	2	8	no	—
398	#126	—	2	8	no	—
399	#126	—	2	4	no	—
400	#126	—	2	4	no	—
401	#125	—	2	4	no	—
402	#125	—	2	1	no	—
403	#125	C₂³×C₁₃	1	4	yes	—
404	#124	—	2	2	no	—
405	#124	—	2	4	no	—
406	#124	—	2	1	no	—
407	#124	C₂³×C₁₃	1	8	yes	—
408	#124	C₂³×C₁₃	1	4	yes	—
409	#123	—	2	4	no	—
410	#123	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	—	2	1	no	—
416	C₂²⋊Q₈	—	2	4	no	—
417	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
418	#121	—	2	1	no	—
419	#121	C₂³×C₁₃	1	2	yes	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	4	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	D₄×C₁₃	1	2	yes	—
424	C₄×Q₈	D₄×C₁₃	1	2	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
427	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
428	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
429	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
430	C₄×D₄	—	2	4	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	C₂³×C₁₃	1	2	yes	—
436	C₄×D₄	C₂³×C₁₃	1	2	yes	—
437	C₄×D₄	C₂³×C₁₃	1	4	yes	—
438	C₄×D₄	C₂³×C₁₃	1	2	yes	—
439	#117	—	2	1	no	—
440	#117	—	2	4	no	—
441	#117	—	2	4	no	—
442	#117	—	2	2	no	—
443	#117	—	2	4	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	2	no	—
448	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	2	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₄²	—	2	2	no	—
455	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
457	#107	C₂³×C₁₃	1	4	yes	—
458	#106	C₂³×C₁₃	1	4	yes	—
459	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
460	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
461	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
462	#103	C₂³×C₁₃	1	4	yes	—
463	#103	C₂³×C₁₃	1	8	yes	—
464	#103	C₂³×C₁₃	1	8	yes	—
465	#102	C₂³×C₁₃	1	4	yes	—
466	#102	C₂³×C₁₃	1	4	yes	—
467	#102	C₂³×C₁₃	1	4	yes	—
468	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
469	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
470	C₄×C₈	C₂³×C₁₃	1	2	yes	—
471	C₄×C₈	C₂³×C₁₃	1	2	yes	—
472	C₄×C₈	C₂³×C₁₃	1	8	yes	—
473	C₂×C₁₃	—	2	2	no	—
474	C₂×C₁₃	—	8	2	no	—
475	C₂×C₁₃	—	8	2	no	—
476	C₂×C₁₃	#3487	1	1	yes	characteristic
477	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
478	C₂×C₁₃	#3586	1	1	yes	characteristic
479	C₂⁴	—	2	1	no	—
480	#41	—	4	4	no	—
481	C₂×Q₈	—	2	4	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	4	4	no	—
486	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
487	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
488	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
489	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	4	4	no	—
504	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
506	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
509	Q₁₆	—	4	8	no	—
510	SD₁₆	—	4	8	no	—
511	SD₁₆	—	4	4	no	—
512	D₈	—	4	4	no	—
513	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
514	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	8	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
531	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
532	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
533	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
534	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
535	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	8	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	8	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₄²	—	2	8	no	—
548	C₄²	—	2	4	no	—
549	C₄²	—	2	2	no	—
550	C₄²	C₂×D₄×C₁₃	1	4	yes	—
551	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
553	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
554	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₄²	C₂⁴×C₁₃	1	4	yes	—
556	C₁₃	#61882	1	1	yes	characteristic, direct product factor, Sylow
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	Q₈	—	2	4	no	—
564	Q₈	—	2	4	no	—
565	Q₈	—	2	4	no	—
566	Q₈	—	2	8	no	—
567	Q₈	—	4	4	no	—
568	Q₈	—	4	2	no	—
569	Q₈	—	8	1	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	4	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	4	no	—
575	D₄	—	4	2	no	—
576	D₄	—	8	1	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	8	4	no	—
592	C₂×C₄	C₁₃×#135	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
601	C₈	—	2	4	no	—
602	C₈	—	2	4	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	4	no	—
612	C₂²	C₂×C₁₃×#135	1	2	yes	—
613	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
614	C₄	—	2	4	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	4	no	—
623	C₄	—	4	2	no	—
624	C₄	C₂×C₁₃×#135	1	2	yes	—
625	C₄	C₂×C₁₃×#135	1	2	yes	—
626	C₄	C₁₃×#585	1	2	yes	—
627	C₂	—	2	2	no	—
628	C₂	—	8	2	no	—
629	C₂	—	8	2	no	—
630	C₂	C₁₃×#3487	1	1	yes	characteristic
631	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
632	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3394	C₂	semidirect
4. C₁₃×#3393	C₂	semidirect
5. C₁₃×#3364	C₂	semidirect
6. C₁₃×#3360	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3209	C₂	semidirect
9. C₁₃×#3206	C₂	semidirect
10. C₁₃×#3108	C₂	semidirect
11. C₁₃×#3101	C₂	semidirect
13. C₁₃×#2982	C₂	semidirect
14. C₁₃×#559	C₂²	semidirect
15. C₁₃×#557	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
39. C₁₃×#494	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#487	C₂²	semidirect
46. C₁₃×#479	C₂²	semidirect
50. C₁₃×#464	C₂²	semidirect
52. C₁₃×#462	C₂²	semidirect
54. C₁₃×#461	C₂²	semidirect
60. C₈×Q₈×C₁₃	C₂²	semidirect
61. C₈×Q₈×C₁₃	C₂²	semidirect
62. C₄×C₁₃×Q₁₆	C₂²	semidirect
64. C₄×C₁₃×SD₁₆	C₂²	semidirect
163. #61882	C₁₃	direct (N × H)
241. #3507	C₂×C₁₃	semidirect
242. C₂×#556	C₂×C₁₃	semidirect
243. #3394	C₂×C₁₃	semidirect
244. #3393	C₂×C₁₃	semidirect
245. #3364	C₂×C₁₃	semidirect
246. #3360	C₂×C₁₃	semidirect
247. #3211	C₂×C₁₃	semidirect
248. #3209	C₂×C₁₃	semidirect
249. #3206	C₂×C₁₃	semidirect
250. #3108	C₂×C₁₃	semidirect
251. #3101	C₂×C₁₃	semidirect
253. #2982	C₂×C₁₃	semidirect
300. #559	C₂²×C₁₃	semidirect
301. #557	C₂²×C₁₃	semidirect
307. #556	C₂²×C₁₃	semidirect
308. #554	C₂²×C₁₃	semidirect
325. #494	C₂²×C₁₃	semidirect
326. #492	C₂²×C₁₃	semidirect
328. #487	C₂²×C₁₃	semidirect
329. #487	C₂²×C₁₃	semidirect
332. #479	C₂²×C₁₃	semidirect
336. #464	C₂²×C₁₃	semidirect
338. #462	C₂²×C₁₃	semidirect
340. #461	C₂²×C₁₃	semidirect
346. C₈×Q₈	C₂²×C₁₃	semidirect
347. C₈×Q₈	C₂²×C₁₃	semidirect
348. C₄×Q₁₆	C₂²×C₁₃	semidirect
350. C₄×SD₁₆	C₂²×C₁₃	semidirect
556. C₁₃	#61882	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×#3507	2
C₂×C₁₃×#556	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3364	2
C₁₃×#3360	2
C₁₃×#3211	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3108	2
C₁₃×#3101	2
C₁₃×#3100	2
C₁₃×#2982	2
#61882	13

Subgroups — C13×#61882 #15748221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61882 #15748221