Subgroups — C₁₃×#62851 #15749190

Order 3328.

7066 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3524	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3522	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3517	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3516	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3506	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3492	C₂	1	6	yes	maximal, complemented
9	C₁₃×#3487	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3460	C₂	1	6	yes	maximal, complemented
11	C₁₃×#3455	C₂	1	6	yes	maximal, complemented
12	C₄×C₁₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₁₃×#559	C₂²	1	24	yes	complemented
17	Q₈²×C₁₃	C₂²	1	4	yes	complemented
18	C₁₃×#557	C₂²	1	4	yes	complemented
19	C₁₃×#557	C₂²	1	8	yes	complemented
20	C₁₃×#556	C₂²	1	12	yes	complemented
21	C₁₃×#555	C₂²	1	12	yes	complemented
22	C₁₃×#554	C₂²	1	24	yes	complemented
23	C₁₃×#553	C₂²	1	24	yes	complemented
24	C₁₃×#553	C₂²	1	24	yes	complemented
25	C₁₃×#552	C₂²	1	24	yes	complemented
26	C₁₃×#550	C₂²	1	8	yes	—
27	C₁₃×#550	C₂²	1	8	yes	—
28	C₁₃×#550	C₂²	1	4	yes	complemented
29	C₁₃×#550	C₂²	1	12	yes	complemented
30	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
31	C₁₃×#548	C₂²	1	8	yes	—
32	C₁₃×#548	C₂²	1	8	yes	—
33	C₁₃×#548	C₂²	1	8	yes	complemented
34	C₁₃×#547	C₂²	1	12	yes	complemented
35	C₁₃×#547	C₂²	1	24	yes	complemented
36	C₁₃×#544	C₂²	1	6	yes	—
37	C₁₃×#542	C₂²	1	12	yes	complemented
38	C₁₃×#542	C₂²	1	24	yes	complemented
39	C₁₃×#542	C₂²	1	12	yes	complemented
40	C₁₃×#541	C₂²	1	12	yes	complemented
41	C₁₃×#540	C₂²	1	24	yes	complemented
42	C₁₃×#540	C₂²	1	12	yes	complemented
43	C₁₃×#539	C₂²	1	4	yes	—
44	C₁₃×#539	C₂²	1	12	yes	—
45	C₁₃×#538	C₂²	1	12	yes	—
46	C₁₃×#538	C₂²	1	12	yes	—
47	C₁₃×#537	C₂²	1	6	yes	—
48	C₁₃×#535	C₂²	1	12	yes	—
49	C₁₃×#533	C₂²	1	6	yes	—
50	C₁₃×#532	C₂²	1	6	yes	—
51	C₁₃×#532	C₂²	1	24	yes	complemented
52	C₁₃×#529	C₂²	1	24	yes	complemented
53	C₁₃×#529	C₂²	1	24	yes	complemented
54	C₁₃×#529	C₂²	1	24	yes	complemented
55	C₁₃×#525	C₂²	1	12	yes	—
56	C₁₃×#525	C₂²	1	24	yes	—
57	C₁₃×#520	C₂²	1	8	yes	—
58	C₁₃×#520	C₂²	1	8	yes	—
59	C₁₃×#520	C₂²	1	12	yes	—
60	C₁₃×#520	C₂²	1	8	yes	complemented
61	C₁₃×#519	C₂²	1	2	yes	—
62	C₁₃×#519	C₂²	1	8	yes	complemented
63	C₄×C₁₃×#41	C₂²	1	12	yes	—
64	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
65	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
68	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
69	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
70	C₂×C₁₃×#117	C₂²	1	3	yes	—
71	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
72	C₁₃×2₋¹⁺⁴	—	2	16	no	—
73	C₂×C₁₃×#41	—	2	8	no	—
74	C₂×C₁₃×#41	C₂³	1	12	yes	—
75	C₂×C₁₃×#41	C₂³	1	8	yes	—
76	C₂×C₁₃×#41	C₂³	1	8	yes	—
77	C₂×C₁₃×#41	C₂³	1	24	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
84	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
87	C₁₃×#127	C₂³	1	6	yes	—
88	C₁₃×#127	C₂³	1	24	yes	—
89	C₁₃×#126	C₂³	1	24	yes	—
90	C₁₃×#126	C₂³	1	8	yes	—
91	C₁₃×#126	C₂³	1	24	yes	—
92	C₁₃×#126	C₂³	1	24	yes	—
93	C₁₃×#125	C₂³	1	8	yes	—
94	C₁₃×#125	C₂³	1	24	yes	—
95	C₁₃×#125	C₂³	1	24	yes	—
96	C₁₃×#125	C₂³	1	12	yes	—
97	C₁₃×#124	C₂³	1	24	yes	—
98	C₁₃×#124	C₂³	1	24	yes	—
99	C₁₃×#124	C₂³	1	24	yes	—
100	C₁₃×#124	C₂³	1	12	yes	—
101	C₁₃×#123	C₂³	1	8	yes	—
102	C₁₃×#123	C₂³	1	48	yes	—
103	C₁₃×#123	C₂³	1	24	yes	—
104	C₁₃×#123	C₂³	1	8	yes	—
105	C₁₃×#123	C₂³	1	24	yes	—
106	C₁₃×#123	C₂³	1	24	yes	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
112	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
113	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
114	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×#121	C₂³	1	12	yes	—
116	C₁₃×#121	C₂³	1	24	yes	—
117	C₁₃×#121	C₂³	1	12	yes	—
118	C₁₃×#121	C₂³	1	12	yes	—
119	C₁₃×#121	C₂³	1	24	yes	—
120	C₁₃×#121	C₂³	1	24	yes	—
121	C₁₃×#121	C₂³	1	24	yes	—
122	C₁₃×#121	C₂³	1	4	yes	—
123	C₁₃×#121	C₂³	1	24	yes	—
124	C₁₃×#121	C₂³	1	24	yes	—
125	C₁₃×#120	C₂³	1	24	yes	—
126	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
127	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
128	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
132	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
136	C₄×D₄×C₁₃	C₂³	1	24	yes	—
137	C₄×D₄×C₁₃	C₂³	1	12	yes	—
138	C₄×D₄×C₁₃	C₂³	1	12	yes	—
139	C₄×D₄×C₁₃	C₂³	1	8	yes	—
140	C₄×D₄×C₁₃	C₂³	1	12	yes	—
141	C₄×D₄×C₁₃	C₂³	1	24	yes	—
142	C₄×D₄×C₁₃	C₂³	1	12	yes	—
143	C₄×D₄×C₁₃	C₂³	1	24	yes	—
144	C₄×D₄×C₁₃	C₂³	1	24	yes	—
145	C₄×D₄×C₁₃	C₂³	1	24	yes	—
146	C₄×D₄×C₁₃	C₂³	1	48	yes	—
147	C₄×D₄×C₁₃	C₂³	1	12	yes	—
148	C₄×D₄×C₁₃	C₂³	1	12	yes	—
149	C₁₃×#117	C₂³	1	12	yes	—
150	C₁₃×#117	C₂³	1	12	yes	—
151	C₁₃×#117	C₂³	1	12	yes	—
152	C₁₃×#117	C₂³	1	24	yes	—
153	C₁₃×#117	C₂³	1	24	yes	—
154	C₁₃×#117	C₂³	1	24	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
166	#62851	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
168	C₁₃×#41	—	2	32	no	—
169	C₁₃×#41	—	2	32	no	—
170	C₁₃×#41	—	2	48	no	—
171	C₁₃×#41	—	8	24	no	—
172	C₂×Q₈×C₁₃	—	2	32	no	—
173	C₂×Q₈×C₁₃	#41	1	8	yes	complemented
174	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
175	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₃	—	2	12	no	—
179	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
186	C₂²×C₄×C₁₃	—	2	12	no	—
187	C₂²×C₄×C₁₃	—	8	6	no	—
188	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
206	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
211	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
212	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
213	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
216	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
217	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
218	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
219	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
220	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
221	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
222	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
223	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
224	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
225	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
226	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
227	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
228	C₄²×C₁₃	C₂⁴	1	12	yes	—
229	C₄²×C₁₃	C₂⁴	1	8	yes	—
230	C₄²×C₁₃	C₂⁴	1	24	yes	—
231	C₄²×C₁₃	C₂⁴	1	6	yes	—
232	C₄²×C₁₃	C₂⁴	1	6	yes	—
233	C₄²×C₁₃	C₂⁴	1	24	yes	—
234	#3524	C₂×C₁₃	1	8	yes	complemented
235	#3522	C₂×C₁₃	1	8	yes	complemented
236	#3517	C₂×C₁₃	1	8	yes	complemented
237	#3516	C₂×C₁₃	1	8	yes	complemented
238	#3506	C₂×C₁₃	1	6	yes	complemented
239	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3492	C₂×C₁₃	1	6	yes	complemented
242	#3487	C₂×C₁₃	1	2	yes	complemented
243	#3460	C₂×C₁₃	1	6	yes	complemented
244	#3455	C₂×C₁₃	1	6	yes	complemented
245	C₄×2₋¹⁺⁴	C₂×C₁₃	1	2	yes	complemented
246	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	2	6	no	—
248	C₂³×C₁₃	—	4	3	no	—
249	C₂³×C₁₃	—	4	3	no	—
250	C₂³×C₁₃	C₂⁵	1	6	yes	—
251	C₂³×C₁₃	C₂⁵	1	8	yes	—
252	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
253	Q₈×C₁₃	—	2	24	no	—
254	Q₈×C₁₃	—	4	4	no	—
255	Q₈×C₁₃	—	4	12	no	—
256	Q₈×C₁₃	C₂×#41	1	16	yes	—
257	D₄×C₁₃	—	2	16	no	—
258	D₄×C₁₃	—	2	24	no	—
259	D₄×C₁₃	—	2	24	no	—
260	D₄×C₁₃	—	4	4	no	—
261	D₄×C₁₃	—	4	24	no	—
262	D₄×C₁₃	—	4	12	no	—
263	D₄×C₁₃	—	4	24	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	24	no	—
266	C₂×C₄×C₁₃	—	2	48	no	—
267	C₂×C₄×C₁₃	—	4	3	no	—
268	C₂×C₄×C₁₃	—	4	3	no	—
269	C₂×C₄×C₁₃	—	4	24	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	8	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	24	no	—
274	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
275	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
278	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
280	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
283	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
284	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
285	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
286	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
287	#559	C₂²×C₁₃	1	24	yes	complemented
288	Q₈²	C₂²×C₁₃	1	4	yes	complemented
289	#557	C₂²×C₁₃	1	8	yes	complemented
290	#557	C₂²×C₁₃	1	4	yes	complemented
291	#556	C₂²×C₁₃	1	12	yes	complemented
292	#555	C₂²×C₁₃	1	12	yes	complemented
293	#554	C₂²×C₁₃	1	24	yes	complemented
294	#553	C₂²×C₁₃	1	24	yes	complemented
295	#553	C₂²×C₁₃	1	24	yes	complemented
296	#552	C₂²×C₁₃	1	24	yes	complemented
297	#550	C₂²×C₁₃	1	8	yes	—
298	#550	C₂²×C₁₃	1	8	yes	—
299	#550	C₂²×C₁₃	1	4	yes	complemented
300	#550	C₂²×C₁₃	1	12	yes	complemented
301	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
302	#548	C₂²×C₁₃	1	8	yes	—
303	#548	C₂²×C₁₃	1	8	yes	—
304	#548	C₂²×C₁₃	1	8	yes	complemented
305	#547	C₂²×C₁₃	1	24	yes	complemented
306	#547	C₂²×C₁₃	1	12	yes	complemented
307	#544	C₂²×C₁₃	1	6	yes	—
308	#542	C₂²×C₁₃	1	12	yes	complemented
309	#542	C₂²×C₁₃	1	12	yes	complemented
310	#542	C₂²×C₁₃	1	24	yes	complemented
311	#541	C₂²×C₁₃	1	12	yes	complemented
312	#540	C₂²×C₁₃	1	12	yes	complemented
313	#540	C₂²×C₁₃	1	24	yes	complemented
314	#539	C₂²×C₁₃	1	4	yes	—
315	#539	C₂²×C₁₃	1	12	yes	—
316	#538	C₂²×C₁₃	1	12	yes	—
317	#538	C₂²×C₁₃	1	12	yes	—
318	#537	C₂²×C₁₃	1	6	yes	—
319	#535	C₂²×C₁₃	1	12	yes	—
320	#533	C₂²×C₁₃	1	6	yes	—
321	#532	C₂²×C₁₃	1	6	yes	—
322	#532	C₂²×C₁₃	1	24	yes	complemented
323	#529	C₂²×C₁₃	1	24	yes	complemented
324	#529	C₂²×C₁₃	1	24	yes	complemented
325	#529	C₂²×C₁₃	1	24	yes	complemented
326	#525	C₂²×C₁₃	1	12	yes	—
327	#525	C₂²×C₁₃	1	24	yes	—
328	#520	C₂²×C₁₃	1	8	yes	—
329	#520	C₂²×C₁₃	1	8	yes	—
330	#520	C₂²×C₁₃	1	12	yes	—
331	#520	C₂²×C₁₃	1	8	yes	complemented
332	#519	C₂²×C₁₃	1	2	yes	—
333	#519	C₂²×C₁₃	1	8	yes	complemented
334	C₄×#41	C₂²×C₁₃	1	12	yes	—
335	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
336	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
339	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
340	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
341	C₂×#117	C₂²×C₁₃	1	3	yes	—
342	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
343	C₂²×C₁₃	—	2	1	no	—
344	C₂²×C₁₃	—	2	1	no	—
345	C₂²×C₁₃	—	2	8	no	—
346	C₂²×C₁₃	—	2	6	no	—
347	C₂²×C₁₃	—	2	6	no	—
348	C₂²×C₁₃	—	2	8	no	—
349	C₂²×C₁₃	—	2	8	no	—
350	C₂²×C₁₃	—	2	6	no	—
351	C₂²×C₁₃	—	4	12	no	—
352	C₂²×C₁₃	C₂²×#41	1	2	yes	—
353	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	8	no	—
356	C₄×C₁₃	—	2	6	no	—
357	C₄×C₁₃	—	2	6	no	—
358	C₄×C₁₃	—	2	8	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	8	no	—
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	C₂²×#41	1	12	yes	—
364	2₋¹⁺⁴	—	2	16	no	—
365	C₂×#41	—	2	8	no	—
366	C₂×#41	C₂³×C₁₃	1	12	yes	—
367	C₂×#41	C₂³×C₁₃	1	8	yes	—
368	C₂×#41	C₂³×C₁₃	1	8	yes	—
369	C₂×#41	C₂³×C₁₃	1	24	yes	—
370	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
371	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
375	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
376	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
377	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
378	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
379	#127	C₂³×C₁₃	1	6	yes	—
380	#127	C₂³×C₁₃	1	24	yes	—
381	#126	C₂³×C₁₃	1	24	yes	—
382	#126	C₂³×C₁₃	1	8	yes	—
383	#126	C₂³×C₁₃	1	24	yes	—
384	#126	C₂³×C₁₃	1	24	yes	—
385	#125	C₂³×C₁₃	1	8	yes	—
386	#125	C₂³×C₁₃	1	24	yes	—
387	#125	C₂³×C₁₃	1	24	yes	—
388	#125	C₂³×C₁₃	1	12	yes	—
389	#124	C₂³×C₁₃	1	24	yes	—
390	#124	C₂³×C₁₃	1	24	yes	—
391	#124	C₂³×C₁₃	1	24	yes	—
392	#124	C₂³×C₁₃	1	12	yes	—
393	#123	C₂³×C₁₃	1	8	yes	—
394	#123	C₂³×C₁₃	1	48	yes	—
395	#123	C₂³×C₁₃	1	24	yes	—
396	#123	C₂³×C₁₃	1	8	yes	—
397	#123	C₂³×C₁₃	1	24	yes	—
398	#123	C₂³×C₁₃	1	24	yes	—
399	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
400	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
401	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
402	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
403	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
404	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
405	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
406	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
407	#121	C₂³×C₁₃	1	12	yes	—
408	#121	C₂³×C₁₃	1	24	yes	—
409	#121	C₂³×C₁₃	1	12	yes	—
410	#121	C₂³×C₁₃	1	12	yes	—
411	#121	C₂³×C₁₃	1	24	yes	—
412	#121	C₂³×C₁₃	1	24	yes	—
413	#121	C₂³×C₁₃	1	24	yes	—
414	#121	C₂³×C₁₃	1	4	yes	—
415	#121	C₂³×C₁₃	1	24	yes	—
416	#121	C₂³×C₁₃	1	24	yes	—
417	#120	C₂³×C₁₃	1	24	yes	—
418	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
419	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
420	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
421	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
422	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
427	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
428	C₄×D₄	C₂³×C₁₃	1	24	yes	—
429	C₄×D₄	C₂³×C₁₃	1	12	yes	—
430	C₄×D₄	C₂³×C₁₃	1	12	yes	—
431	C₄×D₄	C₂³×C₁₃	1	8	yes	—
432	C₄×D₄	C₂³×C₁₃	1	12	yes	—
433	C₄×D₄	C₂³×C₁₃	1	24	yes	—
434	C₄×D₄	C₂³×C₁₃	1	12	yes	—
435	C₄×D₄	C₂³×C₁₃	1	24	yes	—
436	C₄×D₄	C₂³×C₁₃	1	24	yes	—
437	C₄×D₄	C₂³×C₁₃	1	24	yes	—
438	C₄×D₄	C₂³×C₁₃	1	48	yes	—
439	C₄×D₄	C₂³×C₁₃	1	12	yes	—
440	C₄×D₄	C₂³×C₁₃	1	12	yes	—
441	#117	C₂³×C₁₃	1	12	yes	—
442	#117	C₂³×C₁₃	1	12	yes	—
443	#117	C₂³×C₁₃	1	12	yes	—
444	#117	C₂³×C₁₃	1	24	yes	—
445	#117	C₂³×C₁₃	1	24	yes	—
446	#117	C₂³×C₁₃	1	24	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
455	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
456	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
457	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
458	C₂×C₁₃	—	2	2	no	—
459	C₂×C₁₃	—	4	8	no	—
460	C₂×C₁₃	—	4	6	no	—
461	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
462	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
463	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
464	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
465	#41	—	2	32	no	—
466	#41	—	2	32	no	—
467	#41	—	2	48	no	—
468	#41	—	8	24	no	—
469	C₂×Q₈	—	2	32	no	—
470	C₂×Q₈	C₁₃×#41	1	8	yes	complemented
471	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
472	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
473	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
474	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
475	C₂×D₄	—	2	12	no	—
476	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
477	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
478	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
479	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
480	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
481	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
482	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
483	C₂²×C₄	—	2	12	no	—
484	C₂²×C₄	—	8	6	no	—
485	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
496	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
497	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
498	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
499	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
500	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
505	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
506	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
507	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
508	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
509	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
510	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
511	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
512	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
514	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
515	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
516	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
517	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
518	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
519	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
520	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
521	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
522	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
523	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
524	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
525	C₄²	C₂⁴×C₁₃	1	12	yes	—
526	C₄²	C₂⁴×C₁₃	1	8	yes	—
527	C₄²	C₂⁴×C₁₃	1	24	yes	—
528	C₄²	C₂⁴×C₁₃	1	6	yes	—
529	C₄²	C₂⁴×C₁₃	1	6	yes	—
530	C₄²	C₂⁴×C₁₃	1	24	yes	—
531	C₁₃	#62851	1	1	yes	characteristic, direct product factor, Sylow
532	C₂³	—	2	6	no	—
533	C₂³	—	4	3	no	—
534	C₂³	—	4	3	no	—
535	C₂³	C₂⁵×C₁₃	1	6	yes	—
536	C₂³	C₂⁵×C₁₃	1	8	yes	—
537	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
538	Q₈	—	2	24	no	—
539	Q₈	—	4	12	no	—
540	Q₈	—	4	4	no	—
541	Q₈	C₂×C₁₃×#41	1	16	yes	—
542	D₄	—	2	16	no	—
543	D₄	—	2	24	no	—
544	D₄	—	2	24	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	24	no	—
547	D₄	—	4	12	no	—
548	D₄	—	4	24	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	24	no	—
551	C₂×C₄	—	2	48	no	—
552	C₂×C₄	—	4	3	no	—
553	C₂×C₄	—	4	3	no	—
554	C₂×C₄	—	4	24	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	8	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	24	no	—
559	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
560	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
561	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
563	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
565	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
566	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
567	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
568	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
569	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	6	no	—
574	C₂²	—	2	6	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	6	no	—
578	C₂²	—	4	12	no	—
579	C₂²	C₂²×C₁₃×#41	1	2	yes	—
580	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	6	no	—
584	C₄	—	2	6	no	—
585	C₄	—	2	8	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	8	no	—
589	C₄	—	2	1	no	—
590	C₄	C₂²×C₁₃×#41	1	12	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	4	6	no	—
593	C₂	—	4	8	no	—
594	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
595	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic
596	C₂	C₁₃×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3524	C₂	semidirect
2. C₁₃×#3522	C₂	semidirect
3. C₁₃×#3517	C₂	semidirect
4. C₁₃×#3516	C₂	semidirect
5. C₁₃×#3506	C₂	semidirect
6. C₁₃×#3502	C₂	semidirect
7. C₁₃×#3497	C₂	semidirect
8. C₁₃×#3492	C₂	semidirect
9. C₁₃×#3487	C₂	semidirect
10. C₁₃×#3460	C₂	semidirect
11. C₁₃×#3455	C₂	semidirect
12. C₄×C₁₃×2₋¹⁺⁴	C₂	semidirect
13. C₂×C₁₃×#520	C₂	semidirect
16. C₁₃×#559	C₂²	semidirect
17. Q₈²×C₁₃	C₂²	semidirect
18. C₁₃×#557	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#555	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
24. C₁₃×#553	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
28. C₁₃×#550	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
30. D₄×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#548	C₂²	semidirect
34. C₁₃×#547	C₂²	semidirect
35. C₁₃×#547	C₂²	semidirect
37. C₁₃×#542	C₂²	semidirect
38. C₁₃×#542	C₂²	semidirect
39. C₁₃×#542	C₂²	semidirect
40. C₁₃×#541	C₂²	semidirect
41. C₁₃×#540	C₂²	semidirect
42. C₁₃×#540	C₂²	semidirect
51. C₁₃×#532	C₂²	semidirect
52. C₁₃×#529	C₂²	semidirect
53. C₁₃×#529	C₂²	semidirect
54. C₁₃×#529	C₂²	semidirect
60. C₁₃×#520	C₂²	semidirect
62. C₁₃×#519	C₂²	semidirect
64. C₄×C₁₃×#41	C₂²	semidirect
67. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
166. #62851	C₁₃	direct (N × H)
173. C₂×Q₈×C₁₃	#41	semidirect
234. #3524	C₂×C₁₃	semidirect
235. #3522	C₂×C₁₃	semidirect
236. #3517	C₂×C₁₃	semidirect
237. #3516	C₂×C₁₃	semidirect
238. #3506	C₂×C₁₃	semidirect
239. #3502	C₂×C₁₃	semidirect
240. #3497	C₂×C₁₃	semidirect
241. #3492	C₂×C₁₃	semidirect
242. #3487	C₂×C₁₃	semidirect
243. #3460	C₂×C₁₃	semidirect
244. #3455	C₂×C₁₃	semidirect
245. C₄×2₋¹⁺⁴	C₂×C₁₃	semidirect
246. C₂×#520	C₂×C₁₃	semidirect
287. #559	C₂²×C₁₃	semidirect
288. Q₈²	C₂²×C₁₃	semidirect
289. #557	C₂²×C₁₃	semidirect
290. #557	C₂²×C₁₃	semidirect
291. #556	C₂²×C₁₃	semidirect
292. #555	C₂²×C₁₃	semidirect
293. #554	C₂²×C₁₃	semidirect
294. #553	C₂²×C₁₃	semidirect
295. #553	C₂²×C₁₃	semidirect
296. #552	C₂²×C₁₃	semidirect
299. #550	C₂²×C₁₃	semidirect
300. #550	C₂²×C₁₃	semidirect
301. D₄×Q₈	C₂²×C₁₃	semidirect
304. #548	C₂²×C₁₃	semidirect
305. #547	C₂²×C₁₃	semidirect
306. #547	C₂²×C₁₃	semidirect
308. #542	C₂²×C₁₃	semidirect
309. #542	C₂²×C₁₃	semidirect
310. #542	C₂²×C₁₃	semidirect
311. #541	C₂²×C₁₃	semidirect
312. #540	C₂²×C₁₃	semidirect
313. #540	C₂²×C₁₃	semidirect
322. #532	C₂²×C₁₃	semidirect
323. #529	C₂²×C₁₃	semidirect
324. #529	C₂²×C₁₃	semidirect
325. #529	C₂²×C₁₃	semidirect
331. #520	C₂²×C₁₃	semidirect
333. #519	C₂²×C₁₃	semidirect
335. C₄×#41	C₂²×C₁₃	semidirect
338. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
470. C₂×Q₈	C₁₃×#41	semidirect
531. C₁₃	#62851	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×#3524	2
C₁₃×#3522	2
C₁₃×#3517	2
C₁₃×#3516	2
C₁₃×#3506	2
C₁₃×#3502	2
C₁₃×#3497	2
C₁₃×#3492	2
C₁₃×#3487	2
C₁₃×#3460	2
C₁₃×#3455	2
C₄×C₁₃×2₋¹⁺⁴	2
C₂×C₁₃×#520	2
#62851	13

Subgroups — C13×#62851 #15749190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62851 #15749190