Subgroups — C₁₃×#61260 #15747599

Order 3328.

1782 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3493	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3349	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3347	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3340	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3337	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3098	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3093	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#556	—	2	2	no	—
20	C₁₃×#556	C₂²	1	4	yes	—
21	C₁₃×#555	—	2	2	no	—
22	C₁₃×#555	C₂²	1	4	yes	—
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#553	C₂²	1	4	yes	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	C₂²	1	4	yes	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#538	—	2	4	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#529	—	2	4	no	—
31	C₁₃×#525	C₂²	1	2	yes	—
32	C₁₃×#525	C₂²	1	1	yes	characteristic
33	C₁₃×#520	C₂²	1	2	yes	—
34	C₁₃×#520	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₁₃×#501	C₂²	1	4	yes	complemented
37	C₁₃×#499	C₂²	1	2	yes	complemented
38	C₁₃×#498	C₂²	1	2	yes	complemented
39	C₁₃×#485	C₂²	1	4	yes	—
40	C₁₃×#485	C₂²	1	4	yes	—
41	C₁₃×#485	C₂²	1	4	yes	complemented
42	C₁₃×#484	C₂²	1	4	yes	complemented
43	C₁₃×#482	C₂²	1	4	yes	—
44	C₁₃×#482	C₂²	1	4	yes	—
45	C₁₃×#482	C₂²	1	4	yes	complemented
46	C₁₃×#480	C₂²	1	4	yes	complemented
47	C₁₃×#479	C₂²	1	4	yes	complemented
48	C₁₃×#478	C₂²	1	4	yes	complemented
49	C₁₃×#477	C₂²	1	4	yes	complemented
50	C₁₃×#474	C₂²	1	4	yes	complemented
51	C₁₃×#470	C₂²	1	2	yes	complemented
52	C₁₃×#469	C₂²	1	2	yes	complemented
53	C₁₃×#467	C₂²	1	2	yes	—
54	C₁₃×#466	C₂²	1	2	yes	—
55	C₁₃×#465	C₂²	1	2	yes	—
56	C₁₃×#465	C₂²	1	2	yes	—
57	C₁₃×#465	C₂²	1	4	yes	complemented
58	C₁₃×#442	C₂²	1	2	yes	complemented
59	C₁₃×#441	C₂²	1	2	yes	complemented
60	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
61	C₁₃×#435	C₂²	1	4	yes	—
62	C₈×D₄×C₁₃	C₂²	1	4	yes	—
63	C₁₃×#428	C₂²	1	2	yes	—
64	C₁₃×#428	C₂²	1	2	yes	—
65	C₁₃×#428	C₂²	1	4	yes	complemented
66	C₁₃×#427	C₂²	1	1	yes	characteristic
67	C₁₃×#427	C₂²	1	4	yes	—
68	C₁₃×#427	C₂²	1	4	yes	—
69	C₁₃×#427	C₂²	1	2	yes	complemented
70	C₂×C₁₃×#107	C₂²	1	2	yes	—
71	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
74	C₁₃×#424	C₂²	1	1	yes	characteristic
75	C₁₃×#417	C₂²	1	2	yes	—
76	C₁₃×#417	C₂²	1	2	yes	—
77	C₁₃×#416	C₂²	1	2	yes	—
78	C₁₃×#408	C₂²	1	1	yes	characteristic
79	C₁₃×#407	C₂²	1	1	yes	characteristic
80	C₁₃×#405	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	2	yes	—
82	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#135	—	2	4	no	—
85	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
87	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
88	C₁₃×#131	—	2	4	no	—
89	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₃	—	2	4	no	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₁₃×#126	—	2	4	no	—
101	C₁₃×#126	—	2	4	no	—
102	C₁₃×#126	—	2	4	no	—
103	C₁₃×#126	—	2	4	no	—
104	C₁₃×#125	—	2	4	no	—
105	C₁₃×#125	—	2	2	no	—
106	C₁₃×#125	C₂³	1	4	yes	—
107	C₁₃×#124	—	2	4	no	—
108	C₁₃×#124	—	2	4	no	—
109	C₁₃×#124	—	2	4	no	—
110	C₁₃×#123	—	2	4	no	—
111	C₁₃×#123	—	2	2	no	—
112	C₁₃×#123	—	2	4	no	—
113	C₁₃×#123	D₄	1	2	yes	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	4	no	—
116	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
117	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
120	C₁₃×#121	—	2	4	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	4	no	—
123	C₁₃×#121	—	2	4	no	—
124	C₁₃×#121	D₄	1	2	yes	—
125	C₁₃×#121	C₂³	1	2	yes	—
126	C₁₃×#121	C₂³	1	2	yes	—
127	C₁₃×#121	C₂³	1	4	yes	—
128	C₁₃×#120	—	2	2	no	—
129	C₁₃×#120	D₄	1	2	yes	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	4	no	—
132	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
133	C₄×D₄×C₁₃	—	2	4	no	—
134	C₄×D₄×C₁₃	—	2	2	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₄×D₄×C₁₃	C₂³	1	4	yes	—
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	—	2	2	no	—
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	4	no	—
145	C₁₃×#117	—	2	4	no	—
146	C₁₃×#117	C₂³	1	2	yes	—
147	C₁₃×#117	C₂³	1	4	yes	—
148	C₁₃×#117	C₂³	1	4	yes	—
149	C₁₃×#117	C₂³	1	4	yes	—
150	C₁₃×#117	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₂×C₄²×C₁₃	—	2	2	no	—
157	C₁₃×#107	C₂³	1	4	yes	—
158	C₁₃×#107	C₂³	1	4	yes	—
159	C₁₃×#107	C₂³	1	2	yes	—
160	C₁₃×#107	C₂³	1	4	yes	—
161	C₁₃×#107	C₂³	1	4	yes	—
162	C₁₃×#106	C₂³	1	2	yes	—
163	C₁₃×#106	C₂³	1	2	yes	—
164	C₁₃×#106	C₂³	1	2	yes	—
165	C₁₃×#106	C₂³	1	2	yes	—
166	C₁₃×#106	C₂³	1	1	yes	characteristic
167	C₁₃×#106	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	1	yes	characteristic
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	2	yes	—
172	C₁₃×#103	C₂³	1	2	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	2	yes	—
176	C₁₃×#102	C₂³	1	2	yes	—
177	C₁₃×#102	C₂³	1	4	yes	—
178	C₁₃×#102	C₂³	1	4	yes	—
179	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#97	C₂³	1	2	yes	—
182	C₄×C₈×C₁₃	C₂³	1	2	yes	—
183	#61260	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×#41	—	2	2	no	—
186	C₁₃×#41	—	2	2	no	—
187	C₁₃×#41	—	2	4	no	—
188	C₁₃×#41	—	2	4	no	—
189	C₂×Q₈×C₁₃	—	2	4	no	—
190	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
199	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₁₃×Q₁₆	—	2	2	no	—
213	C₁₃×SD₁₆	—	2	4	no	—
214	C₁₃×D₈	—	2	2	no	—
215	C₁₃×M₁₆	—	2	2	no	—
216	C₁₃×M₁₆	—	2	2	no	—
217	C₁₃×M₁₆	—	2	4	no	—
218	C₂×C₈×C₁₃	—	2	2	no	—
219	C₂×C₈×C₁₃	—	2	4	no	—
220	C₂×C₈×C₁₃	—	2	4	no	—
221	C₂×C₈×C₁₃	—	2	4	no	—
222	C₂×C₈×C₁₃	#41	1	4	yes	—
223	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
224	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
225	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	2	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	2	no	—
255	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
256	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
257	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
258	C₄²×C₁₃	—	2	4	no	—
259	C₄²×C₁₃	—	2	4	no	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	—	2	2	no	—
263	C₄²×C₁₃	C₂⁴	1	2	yes	—
264	#3493	C₂×C₁₃	1	2	yes	complemented
265	#3349	C₂×C₁₃	1	4	yes	complemented
266	#3347	C₂×C₁₃	1	4	yes	complemented
267	#3340	C₂×C₁₃	1	4	yes	complemented
268	#3337	C₂×C₁₃	1	4	yes	complemented
269	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#3098	C₂×C₁₃	1	2	yes	complemented
271	#3093	C₂×C₁₃	1	2	yes	complemented
272	#3083	C₂×C₁₃	1	2	yes	complemented
273	#3060	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2912	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	4	2	no	—
282	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
283	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₁₃	—	2	2	no	—
286	Q₈×C₁₃	—	2	2	no	—
287	Q₈×C₁₃	—	2	2	no	—
288	Q₈×C₁₃	—	8	4	no	—
289	D₄×C₁₃	—	2	4	no	—
290	D₄×C₁₃	—	2	2	no	—
291	D₄×C₁₃	—	2	2	no	—
292	D₄×C₁₃	—	2	2	no	—
293	D₄×C₁₃	—	4	4	no	—
294	D₄×C₁₃	—	4	4	no	—
295	D₄×C₁₃	—	8	2	no	—
296	D₄×C₁₃	—	8	4	no	—
297	D₄×C₁₃	—	8	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	4	4	no	—
310	C₂×C₄×C₁₃	—	8	4	no	—
311	C₂×C₄×C₁₃	—	8	2	no	—
312	C₂×C₄×C₁₃	—	8	4	no	—
313	C₂×C₄×C₁₃	—	8	2	no	—
314	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
319	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
320	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
321	C₈×C₁₃	—	2	2	no	—
322	C₈×C₁₃	—	2	2	no	—
323	C₈×C₁₃	—	2	2	no	—
324	C₈×C₁₃	C₂×#41	1	2	yes	—
325	C₈×C₁₃	C₂×#41	1	2	yes	—
326	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
328	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
329	#556	—	2	2	no	—
330	#556	C₂²×C₁₃	1	4	yes	—
331	#555	—	2	2	no	—
332	#555	C₂²×C₁₃	1	4	yes	—
333	#553	—	2	2	no	—
334	#553	C₂²×C₁₃	1	4	yes	—
335	#552	—	2	2	no	—
336	#552	C₂²×C₁₃	1	4	yes	—
337	#544	C₂²×C₁₃	1	2	yes	—
338	#538	—	2	4	no	—
339	#537	C₂²×C₁₃	1	2	yes	—
340	#529	—	2	4	no	—
341	#525	C₂²×C₁₃	1	2	yes	—
342	#525	C₂²×C₁₃	1	1	yes	characteristic
343	#520	C₂²×C₁₃	1	2	yes	—
344	#520	C₂²×C₁₃	1	2	yes	—
345	C₂×#117	C₂²×C₁₃	1	2	yes	—
346	#501	C₂²×C₁₃	1	4	yes	complemented
347	#499	C₂²×C₁₃	1	2	yes	complemented
348	#498	C₂²×C₁₃	1	2	yes	complemented
349	#485	C₂²×C₁₃	1	4	yes	—
350	#485	C₂²×C₁₃	1	4	yes	—
351	#485	C₂²×C₁₃	1	4	yes	complemented
352	#484	C₂²×C₁₃	1	4	yes	complemented
353	#482	C₂²×C₁₃	1	4	yes	—
354	#482	C₂²×C₁₃	1	4	yes	—
355	#482	C₂²×C₁₃	1	4	yes	complemented
356	#480	C₂²×C₁₃	1	4	yes	complemented
357	#479	C₂²×C₁₃	1	4	yes	complemented
358	#478	C₂²×C₁₃	1	4	yes	complemented
359	#477	C₂²×C₁₃	1	4	yes	complemented
360	#474	C₂²×C₁₃	1	4	yes	complemented
361	#470	C₂²×C₁₃	1	2	yes	complemented
362	#469	C₂²×C₁₃	1	2	yes	complemented
363	#467	C₂²×C₁₃	1	2	yes	—
364	#466	C₂²×C₁₃	1	2	yes	—
365	#465	C₂²×C₁₃	1	2	yes	—
366	#465	C₂²×C₁₃	1	2	yes	—
367	#465	C₂²×C₁₃	1	4	yes	complemented
368	#442	C₂²×C₁₃	1	2	yes	complemented
369	#441	C₂²×C₁₃	1	2	yes	complemented
370	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
371	#435	C₂²×C₁₃	1	4	yes	—
372	C₈×D₄	C₂²×C₁₃	1	4	yes	—
373	#428	C₂²×C₁₃	1	2	yes	—
374	#428	C₂²×C₁₃	1	2	yes	—
375	#428	C₂²×C₁₃	1	4	yes	complemented
376	#427	C₂²×C₁₃	1	4	yes	—
377	#427	C₂²×C₁₃	1	4	yes	—
378	#427	C₂²×C₁₃	1	1	yes	characteristic
379	#427	C₂²×C₁₃	1	2	yes	complemented
380	C₂×#107	C₂²×C₁₃	1	2	yes	—
381	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
384	#424	C₂²×C₁₃	1	1	yes	characteristic
385	#417	C₂²×C₁₃	1	2	yes	—
386	#417	C₂²×C₁₃	1	2	yes	—
387	#416	C₂²×C₁₃	1	2	yes	—
388	#408	C₂²×C₁₃	1	1	yes	characteristic
389	#407	C₂²×C₁₃	1	1	yes	characteristic
390	#405	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×C₁₃	—	2	2	no	—
392	C₂²×C₁₃	—	2	4	no	—
393	C₂²×C₁₃	—	2	2	no	—
394	C₂²×C₁₃	—	2	2	no	—
395	C₂²×C₁₃	—	2	2	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	—	4	2	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	#547	1	2	yes	—
402	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
403	C₄×C₁₃	—	2	4	no	—
404	C₄×C₁₃	—	2	2	no	—
405	C₄×C₁₃	—	2	2	no	—
406	C₄×C₁₃	—	4	4	no	—
407	C₄×C₁₃	—	4	2	no	—
408	C₄×C₁₃	—	4	4	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	2	no	—
411	C₄×C₁₃	#547	1	2	yes	—
412	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
413	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
414	C₂×#41	C₂³×C₁₃	1	2	yes	—
415	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
417	#135	—	2	4	no	—
418	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
420	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
421	#131	—	2	4	no	—
422	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
424	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
425	C₂²×C₈	—	2	4	no	—
426	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
428	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
429	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₄⋊Q₈	—	2	2	no	—
432	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
433	#126	—	2	4	no	—
434	#126	—	2	4	no	—
435	#126	—	2	4	no	—
436	#126	—	2	4	no	—
437	#125	—	2	4	no	—
438	#125	—	2	2	no	—
439	#125	C₂³×C₁₃	1	4	yes	—
440	#124	—	2	4	no	—
441	#124	—	2	4	no	—
442	#124	—	2	4	no	—
443	#123	—	2	4	no	—
444	#123	—	2	2	no	—
445	#123	—	2	4	no	—
446	#123	D₄×C₁₃	1	2	yes	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
450	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
451	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
452	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
453	#121	—	2	4	no	—
454	#121	—	2	2	no	—
455	#121	—	2	4	no	—
456	#121	—	2	4	no	—
457	#121	D₄×C₁₃	1	2	yes	—
458	#121	C₂³×C₁₃	1	2	yes	—
459	#121	C₂³×C₁₃	1	2	yes	—
460	#121	C₂³×C₁₃	1	4	yes	—
461	#120	—	2	2	no	—
462	#120	D₄×C₁₃	1	2	yes	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	4	no	—
465	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	4	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	C₂³×C₁₃	1	4	yes	—
473	C₄×D₄	C₂³×C₁₃	1	4	yes	—
474	#117	—	2	2	no	—
475	#117	—	2	2	no	—
476	#117	—	2	2	no	—
477	#117	—	2	4	no	—
478	#117	—	2	4	no	—
479	#117	C₂³×C₁₃	1	4	yes	—
480	#117	C₂³×C₁₃	1	4	yes	—
481	#117	C₂³×C₁₃	1	2	yes	—
482	#117	C₂³×C₁₃	1	4	yes	—
483	#117	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	—	2	2	no	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
488	C₂×C₂²⋊C₄	—	2	2	no	—
489	C₂×C₄²	—	2	2	no	—
490	#107	C₂³×C₁₃	1	4	yes	—
491	#107	C₂³×C₁₃	1	4	yes	—
492	#107	C₂³×C₁₃	1	2	yes	—
493	#107	C₂³×C₁₃	1	4	yes	—
494	#107	C₂³×C₁₃	1	4	yes	—
495	#106	C₂³×C₁₃	1	2	yes	—
496	#106	C₂³×C₁₃	1	2	yes	—
497	#106	C₂³×C₁₃	1	2	yes	—
498	#106	C₂³×C₁₃	1	2	yes	—
499	#106	C₂³×C₁₃	1	1	yes	characteristic
500	#106	C₂³×C₁₃	1	4	yes	—
501	#106	C₂³×C₁₃	1	1	yes	characteristic
502	#106	C₂³×C₁₃	1	4	yes	—
503	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
504	#103	C₂³×C₁₃	1	2	yes	—
505	#103	C₂³×C₁₃	1	2	yes	—
506	#103	C₂³×C₁₃	1	4	yes	—
507	#103	C₂³×C₁₃	1	4	yes	—
508	#102	C₂³×C₁₃	1	2	yes	—
509	#102	C₂³×C₁₃	1	2	yes	—
510	#102	C₂³×C₁₃	1	4	yes	—
511	#102	C₂³×C₁₃	1	4	yes	—
512	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
513	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
514	#97	C₂³×C₁₃	1	2	yes	—
515	C₄×C₈	C₂³×C₁₃	1	2	yes	—
516	C₂×C₁₃	—	2	2	no	—
517	C₂×C₁₃	—	4	2	no	—
518	C₂×C₁₃	—	4	2	no	—
519	C₂×C₁₃	—	8	2	no	—
520	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
521	C₂×C₁₃	#3584	1	2	yes	—
522	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	4	no	—
526	#41	—	2	4	no	—
527	C₂×Q₈	—	2	4	no	—
528	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
535	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
537	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	Q₁₆	—	2	2	no	—
551	SD₁₆	—	2	4	no	—
552	D₈	—	2	2	no	—
553	M₁₆	—	2	2	no	—
554	M₁₆	—	2	2	no	—
555	M₁₆	—	2	4	no	—
556	C₂×C₈	—	2	2	no	—
557	C₂×C₈	—	2	4	no	—
558	C₂×C₈	—	2	4	no	—
559	C₂×C₈	—	2	4	no	—
560	C₂×C₈	C₁₃×#41	1	4	yes	—
561	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
562	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
563	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
564	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
565	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
577	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
578	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
580	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
581	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
594	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
596	C₄²	—	2	4	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	2	no	—
601	C₄²	C₂⁴×C₁₃	1	2	yes	—
602	C₁₃	#61260	1	1	yes	characteristic, direct product factor, Sylow
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	4	2	no	—
606	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
607	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
608	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	2	2	no	—
612	Q₈	—	8	4	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	4	4	no	—
618	D₄	—	4	4	no	—
619	D₄	—	8	2	no	—
620	D₄	—	8	4	no	—
621	D₄	—	8	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	8	4	no	—
635	C₂×C₄	—	8	2	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	—	8	2	no	—
638	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
641	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
642	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
643	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
644	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	C₂×C₁₃×#41	1	2	yes	—
649	C₈	C₂×C₁₃×#41	1	2	yes	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	C₁₃×#547	1	2	yes	—
661	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
662	C₄	—	2	4	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	C₁₃×#547	1	2	yes	—
671	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
672	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂	—	2	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	4	2	no	—
676	C₂	—	8	2	no	—
677	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
678	C₂	C₁₃×#3584	1	2	yes	—

	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 ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3493	C₂	semidirect
2. C₁₃×#3349	C₂	semidirect
3. C₁₃×#3347	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#3337	C₂	semidirect
6. C₁₃×#3163	C₂	semidirect
7. C₁₃×#3098	C₂	semidirect
8. C₁₃×#3093	C₂	semidirect
9. C₁₃×#3083	C₂	semidirect
10. C₁₃×#3060	C₂	semidirect
11. C₁₃×#3050	C₂	semidirect
12. C₁₃×#2952	C₂	semidirect
13. C₁₃×#2929	C₂	semidirect
14. C₁₃×#2912	C₂	semidirect
15. C₂×C₁₃×#427	C₂	semidirect
36. C₁₃×#501	C₂²	semidirect
37. C₁₃×#499	C₂²	semidirect
38. C₁₃×#498	C₂²	semidirect
41. C₁₃×#485	C₂²	semidirect
42. C₁₃×#484	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
46. C₁₃×#480	C₂²	semidirect
47. C₁₃×#479	C₂²	semidirect
48. C₁₃×#478	C₂²	semidirect
49. C₁₃×#477	C₂²	semidirect
50. C₁₃×#474	C₂²	semidirect
51. C₁₃×#470	C₂²	semidirect
52. C₁₃×#469	C₂²	semidirect
57. C₁₃×#465	C₂²	semidirect
58. C₁₃×#442	C₂²	semidirect
59. C₁₃×#441	C₂²	semidirect
60. C₄×C₁₃×SD₁₆	C₂²	semidirect
65. C₁₃×#428	C₂²	semidirect
69. C₁₃×#427	C₂²	semidirect
73. C₂×C₁₃×#106	C₂²	semidirect
183. #61260	C₁₃	direct (N × H)
264. #3493	C₂×C₁₃	semidirect
265. #3349	C₂×C₁₃	semidirect
266. #3347	C₂×C₁₃	semidirect
267. #3340	C₂×C₁₃	semidirect
268. #3337	C₂×C₁₃	semidirect
269. #3163	C₂×C₁₃	semidirect
270. #3098	C₂×C₁₃	semidirect
271. #3093	C₂×C₁₃	semidirect
272. #3083	C₂×C₁₃	semidirect
273. #3060	C₂×C₁₃	semidirect
274. #3050	C₂×C₁₃	semidirect
275. #2952	C₂×C₁₃	semidirect
276. #2929	C₂×C₁₃	semidirect
277. #2912	C₂×C₁₃	semidirect
278. C₂×#427	C₂×C₁₃	semidirect
346. #501	C₂²×C₁₃	semidirect
347. #499	C₂²×C₁₃	semidirect
348. #498	C₂²×C₁₃	semidirect
351. #485	C₂²×C₁₃	semidirect
352. #484	C₂²×C₁₃	semidirect
355. #482	C₂²×C₁₃	semidirect
356. #480	C₂²×C₁₃	semidirect
357. #479	C₂²×C₁₃	semidirect
358. #478	C₂²×C₁₃	semidirect
359. #477	C₂²×C₁₃	semidirect
360. #474	C₂²×C₁₃	semidirect
361. #470	C₂²×C₁₃	semidirect
362. #469	C₂²×C₁₃	semidirect
367. #465	C₂²×C₁₃	semidirect
368. #442	C₂²×C₁₃	semidirect
369. #441	C₂²×C₁₃	semidirect
370. C₄×SD₁₆	C₂²×C₁₃	semidirect
375. #428	C₂²×C₁₃	semidirect
379. #427	C₂²×C₁₃	semidirect
383. C₂×#106	C₂²×C₁₃	semidirect
602. C₁₃	#61260	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×#3493	2
C₁₃×#3349	2
C₁₃×#3347	2
C₁₃×#3340	2
C₁₃×#3337	2
C₁₃×#3163	2
C₁₃×#3098	2
C₁₃×#3093	2
C₁₃×#3083	2
C₁₃×#3060	2
C₁₃×#3050	2
C₁₃×#2952	2
C₁₃×#2929	2
C₁₃×#2912	2
C₂×C₁₃×#427	2
#61260	13

Subgroups — C13×#61260 #15747599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61260 #15747599