Subgroups — C₁₃×#62916 #15749255

Order 3328.

7938 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3546	C₂	1	12	yes	maximal, complemented
2	C₁₃×#3543	C₂	1	12	yes	maximal, complemented
3	C₁₃×#3537	C₂	1	12	yes	maximal, complemented
4	C₁₃×#3517	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3498	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3498	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3496	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3480	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3460	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	6	yes	complemented
14	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
15	C₁₃×#560	C₂²	1	48	yes	complemented
16	C₁₃×#559	C₂²	1	6	yes	complemented
17	C₁₃×#557	C₂²	1	2	yes	complemented
18	C₁₃×#556	C₂²	1	6	yes	complemented
19	C₁₃×#553	C₂²	1	12	yes	complemented
20	C₁₃×#553	C₂²	1	24	yes	complemented
21	C₁₃×#550	C₂²	1	12	yes	complemented
22	C₁₃×#550	C₂²	1	12	yes	complemented
23	C₁₃×#550	C₂²	1	12	yes	complemented
24	C₁₃×#550	C₂²	1	4	yes	complemented
25	C₁₃×#550	C₂²	1	2	yes	complemented
26	C₁₃×#550	C₂²	1	8	yes	complemented
27	C₁₃×#548	C₂²	1	4	yes	complemented
28	C₁₃×#547	C₂²	1	12	yes	complemented
29	C₁₃×#546	C₂²	1	24	yes	complemented
30	C₁₃×#546	C₂²	1	24	yes	complemented
31	D₄²×C₁₃	C₂²	1	24	yes	complemented
32	D₄²×C₁₃	C₂²	1	24	yes	complemented
33	D₄²×C₁₃	C₂²	1	24	yes	complemented
34	D₄²×C₁₃	C₂²	1	12	yes	complemented
35	D₄²×C₁₃	C₂²	1	12	yes	complemented
36	D₄²×C₁₃	C₂²	1	12	yes	complemented
37	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#542	C₂²	1	12	yes	complemented
39	C₁₃×#540	C₂²	1	24	yes	complemented
40	C₁₃×#540	C₂²	1	12	yes	complemented
41	C₁₃×#538	C₂²	1	12	yes	complemented
42	C₁₃×#538	C₂²	1	24	yes	complemented
43	C₁₃×#537	C₂²	1	12	yes	complemented
44	C₁₃×#537	C₂²	1	3	yes	complemented
45	C₁₃×#535	C₂²	1	24	yes	complemented
46	C₁₃×#535	C₂²	1	12	yes	complemented
47	C₁₃×#535	C₂²	1	24	yes	complemented
48	C₁₃×#535	C₂²	1	6	yes	complemented
49	C₁₃×#534	C₂²	1	12	yes	complemented
50	C₁₃×#534	C₂²	1	24	yes	complemented
51	C₁₃×#532	C₂²	1	12	yes	complemented
52	C₁₃×#532	C₂²	1	12	yes	complemented
53	C₁₃×#532	C₂²	1	6	yes	complemented
54	C₂×C₁₃×#127	C₂²	1	12	yes	complemented
55	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
56	C₁₃×#529	C₂²	1	12	yes	complemented
57	C₁₃×#529	C₂²	1	12	yes	complemented
58	C₁₃×#525	C₂²	1	12	yes	complemented
59	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
60	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
61	C₁₃×#520	C₂²	1	4	yes	complemented
62	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
63	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
64	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
66	C₁₃×H(5,𝔽₂)	—	4	24	no	—
67	C₁₃×H(5,𝔽₂)	—	4	16	no	—
68	C₂×C₁₃×#41	—	4	8	no	—
69	C₂×C₁₃×#41	C₂³	1	6	yes	—
70	C₂×C₁₃×#41	C₂³	1	4	yes	—
71	C₂×C₁₃×#41	C₂³	1	4	yes	—
72	C₂×C₁₃×#41	C₂³	1	12	yes	—
73	C₂×C₁₃×#41	C₂³	1	24	yes	—
74	C₂×C₁₃×#41	C₂³	1	12	yes	—
75	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
87	C₁₃×#127	C₂³	1	12	yes	—
88	C₁₃×#127	C₂³	1	6	yes	—
89	C₁₃×#127	C₂³	1	12	yes	—
90	C₁₃×#127	C₂³	1	12	yes	—
91	C₁₃×#127	C₂³	1	24	yes	—
92	C₁₃×#127	C₂³	1	24	yes	—
93	C₁₃×#126	C₂³	1	24	yes	—
94	C₁₃×#126	C₂³	1	24	yes	—
95	C₁₃×#125	C₂³	1	4	yes	—
96	C₁₃×#125	C₂³	1	12	yes	—
97	C₁₃×#124	C₂³	1	12	yes	—
98	C₁₃×#124	C₂³	1	12	yes	—
99	C₁₃×#124	C₂³	1	24	yes	—
100	C₁₃×#124	C₂³	1	12	yes	—
101	C₁₃×#123	C₂³	1	24	yes	—
102	C₁₃×#123	C₂³	1	24	yes	—
103	C₁₃×#123	C₂³	1	24	yes	—
104	C₁₃×#123	C₂³	1	48	yes	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
109	C₁₃×#121	C₂³	1	12	yes	—
110	C₁₃×#121	C₂³	1	12	yes	—
111	C₁₃×#121	C₂³	1	24	yes	—
112	C₁₃×#121	C₂³	1	24	yes	—
113	C₁₃×#121	C₂³	1	24	yes	—
114	C₁₃×#121	C₂³	1	24	yes	—
115	C₁₃×#121	C₂³	1	12	yes	—
116	C₁₃×#121	C₂³	1	12	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	12	yes	—
121	C₁₃×#121	C₂³	1	12	yes	—
122	C₁₃×#121	C₂³	1	24	yes	—
123	C₁₃×#121	C₂³	1	24	yes	—
124	C₁₃×#121	C₂³	1	48	yes	—
125	C₁₃×#121	C₂³	1	48	yes	—
126	C₁₃×#120	C₂³	1	24	yes	—
127	C₁₃×#120	C₂³	1	48	yes	—
128	C₁₃×#120	C₂³	1	48	yes	—
129	C₁₃×#120	C₂³	1	48	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
132	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
135	C₄×D₄×C₁₃	C₂³	1	12	yes	—
136	C₄×D₄×C₁₃	C₂³	1	12	yes	—
137	C₄×D₄×C₁₃	C₂³	1	12	yes	—
138	C₄×D₄×C₁₃	C₂³	1	12	yes	—
139	C₄×D₄×C₁₃	C₂³	1	6	yes	—
140	C₄×D₄×C₁₃	C₂³	1	12	yes	—
141	C₄×D₄×C₁₃	C₂³	1	12	yes	—
142	C₄×D₄×C₁₃	C₂³	1	6	yes	—
143	C₄×D₄×C₁₃	C₂³	1	24	yes	—
144	C₄×D₄×C₁₃	C₂³	1	24	yes	—
145	C₄×D₄×C₁₃	C₂³	1	12	yes	—
146	C₄×D₄×C₁₃	C₂³	1	24	yes	—
147	C₁₃×#117	C₂³	1	2	yes	—
148	C₁₃×#117	C₂³	1	12	yes	—
149	C₁₃×#117	C₂³	1	12	yes	—
150	C₁₃×#117	C₂³	1	12	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
158	#62916	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
160	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
161	C₁₃×#41	—	2	16	no	—
162	C₁₃×#41	—	2	16	no	—
163	C₁₃×#41	—	2	24	no	—
164	C₁₃×#41	—	4	24	no	—
165	C₁₃×#41	—	4	24	no	—
166	C₁₃×#41	—	4	48	no	—
167	C₂×Q₈×C₁₃	—	2	4	no	—
168	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
169	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
170	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
171	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×D₄×C₁₃	—	2	12	no	—
173	C₂×D₄×C₁₃	—	4	12	no	—
174	C₂×D₄×C₁₃	—	4	24	no	—
175	C₂×D₄×C₁₃	—	4	48	no	—
176	C₂×D₄×C₁₃	—	4	48	no	—
177	C₂×D₄×C₁₃	—	4	48	no	—
178	C₂×D₄×C₁₃	—	8	6	no	—
179	C₂×D₄×C₁₃	—	8	24	no	—
180	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
186	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
189	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
190	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
191	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
192	C₂²×C₄×C₁₃	—	4	12	no	—
193	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
206	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
212	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
213	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
215	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
216	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
217	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
218	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
219	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
220	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
221	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
222	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
223	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
224	C₄²×C₁₃	C₂⁴	1	4	yes	—
225	C₄²×C₁₃	C₂⁴	1	6	yes	—
226	C₄²×C₁₃	C₂⁴	1	12	yes	—
227	C₄²×C₁₃	C₂⁴	1	6	yes	—
228	C₄²×C₁₃	C₂⁴	1	12	yes	—
229	#3546	C₂×C₁₃	1	12	yes	complemented
230	#3543	C₂×C₁₃	1	12	yes	complemented
231	#3537	C₂×C₁₃	1	12	yes	complemented
232	#3517	C₂×C₁₃	1	4	yes	complemented
233	#3498	C₂×C₁₃	1	6	yes	complemented
234	#3498	C₂×C₁₃	1	4	yes	complemented
235	#3496	C₂×C₁₃	1	3	yes	complemented
236	#3488	C₂×C₁₃	1	4	yes	complemented
237	#3480	C₂×C₁₃	1	2	yes	complemented
238	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#3460	C₂×C₁₃	1	3	yes	complemented
240	C₂³×C₁₃	—	2	12	no	—
241	C₂³×C₁₃	—	4	6	no	—
242	C₂³×C₁₃	—	4	6	no	—
243	C₂³×C₁₃	—	4	24	no	—
244	C₂³×C₁₃	—	4	24	no	—
245	C₂³×C₁₃	—	4	24	no	—
246	C₂³×C₁₃	C₂⁵	1	12	yes	—
247	C₂³×C₁₃	C₂⁵	1	12	yes	—
248	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃	—	2	6	no	—
250	Q₈×C₁₃	—	2	12	no	—
251	Q₈×C₁₃	—	4	4	no	—
252	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
253	D₄×C₁₃	—	2	24	no	—
254	D₄×C₁₃	—	2	24	no	—
255	D₄×C₁₃	—	2	24	no	—
256	D₄×C₁₃	—	2	12	no	—
257	D₄×C₁₃	—	2	24	no	—
258	D₄×C₁₃	—	4	12	no	—
259	D₄×C₁₃	—	4	24	no	—
260	D₄×C₁₃	—	4	48	no	—
261	D₄×C₁₃	—	4	12	no	—
262	D₄×C₁₃	—	4	12	no	—
263	D₄×C₁₃	—	4	24	no	—
264	D₄×C₁₃	—	4	24	no	—
265	C₂×C₄×C₁₃	—	2	6	no	—
266	C₂×C₄×C₁₃	—	2	24	no	—
267	C₂×C₄×C₁₃	—	2	24	no	—
268	C₂×C₄×C₁₃	—	2	24	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	12	no	—
271	C₂×C₄×C₁₃	—	4	24	no	—
272	C₂×C₄×C₁₃	—	4	3	no	—
273	C₂×C₄×C₁₃	—	4	12	no	—
274	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
275	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
278	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
279	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
280	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
283	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
284	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	6	yes	complemented
285	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
286	#560	C₂²×C₁₃	1	48	yes	complemented
287	#559	C₂²×C₁₃	1	6	yes	complemented
288	#557	C₂²×C₁₃	1	2	yes	complemented
289	#556	C₂²×C₁₃	1	6	yes	complemented
290	#553	C₂²×C₁₃	1	12	yes	complemented
291	#553	C₂²×C₁₃	1	24	yes	complemented
292	#550	C₂²×C₁₃	1	4	yes	complemented
293	#550	C₂²×C₁₃	1	12	yes	complemented
294	#550	C₂²×C₁₃	1	2	yes	complemented
295	#550	C₂²×C₁₃	1	8	yes	complemented
296	#550	C₂²×C₁₃	1	12	yes	complemented
297	#550	C₂²×C₁₃	1	12	yes	complemented
298	#548	C₂²×C₁₃	1	4	yes	complemented
299	#547	C₂²×C₁₃	1	12	yes	complemented
300	#546	C₂²×C₁₃	1	24	yes	complemented
301	#546	C₂²×C₁₃	1	24	yes	complemented
302	D₄²	C₂²×C₁₃	1	24	yes	complemented
303	D₄²	C₂²×C₁₃	1	12	yes	complemented
304	D₄²	C₂²×C₁₃	1	12	yes	complemented
305	D₄²	C₂²×C₁₃	1	24	yes	complemented
306	D₄²	C₂²×C₁₃	1	24	yes	complemented
307	D₄²	C₂²×C₁₃	1	12	yes	complemented
308	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	#542	C₂²×C₁₃	1	12	yes	complemented
310	#540	C₂²×C₁₃	1	12	yes	complemented
311	#540	C₂²×C₁₃	1	24	yes	complemented
312	#538	C₂²×C₁₃	1	12	yes	complemented
313	#538	C₂²×C₁₃	1	24	yes	complemented
314	#537	C₂²×C₁₃	1	3	yes	complemented
315	#537	C₂²×C₁₃	1	12	yes	complemented
316	#535	C₂²×C₁₃	1	6	yes	complemented
317	#535	C₂²×C₁₃	1	12	yes	complemented
318	#535	C₂²×C₁₃	1	24	yes	complemented
319	#535	C₂²×C₁₃	1	24	yes	complemented
320	#534	C₂²×C₁₃	1	12	yes	complemented
321	#534	C₂²×C₁₃	1	24	yes	complemented
322	#532	C₂²×C₁₃	1	12	yes	complemented
323	#532	C₂²×C₁₃	1	6	yes	complemented
324	#532	C₂²×C₁₃	1	12	yes	complemented
325	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
326	C₂×#127	C₂²×C₁₃	1	12	yes	complemented
327	#529	C₂²×C₁₃	1	12	yes	complemented
328	#529	C₂²×C₁₃	1	12	yes	complemented
329	#525	C₂²×C₁₃	1	12	yes	complemented
330	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
331	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
332	#520	C₂²×C₁₃	1	4	yes	complemented
333	C₄×#41	C₂²×C₁₃	1	6	yes	complemented
334	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
335	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	12	no	—
340	C₂²×C₁₃	—	2	12	no	—
341	C₂²×C₁₃	—	2	12	no	—
342	C₂²×C₁₃	—	2	12	no	—
343	C₂²×C₁₃	—	2	12	no	—
344	C₂²×C₁₃	—	2	12	no	—
345	C₂²×C₁₃	—	8	12	no	—
346	C₂²×C₁₃	—	16	24	no	—
347	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
348	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
349	C₄×C₁₃	—	2	4	no	—
350	C₄×C₁₃	—	2	4	no	—
351	C₄×C₁₃	—	2	12	no	—
352	C₄×C₁₃	—	2	3	no	—
353	C₄×C₁₃	—	2	6	no	—
354	C₄×C₁₃	—	2	4	no	—
355	C₄×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
356	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
357	H(5,𝔽₂)	—	4	24	no	—
358	H(5,𝔽₂)	—	4	16	no	—
359	C₂×#41	—	4	8	no	—
360	C₂×#41	C₂³×C₁₃	1	6	yes	—
361	C₂×#41	C₂³×C₁₃	1	4	yes	—
362	C₂×#41	C₂³×C₁₃	1	4	yes	—
363	C₂×#41	C₂³×C₁₃	1	12	yes	—
364	C₂×#41	C₂³×C₁₃	1	24	yes	—
365	C₂×#41	C₂³×C₁₃	1	12	yes	—
366	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
368	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
369	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
370	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
371	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
372	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
373	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
374	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
375	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
376	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
377	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
378	#127	C₂³×C₁₃	1	12	yes	—
379	#127	C₂³×C₁₃	1	6	yes	—
380	#127	C₂³×C₁₃	1	12	yes	—
381	#127	C₂³×C₁₃	1	12	yes	—
382	#127	C₂³×C₁₃	1	24	yes	—
383	#127	C₂³×C₁₃	1	24	yes	—
384	#126	C₂³×C₁₃	1	24	yes	—
385	#126	C₂³×C₁₃	1	24	yes	—
386	#125	C₂³×C₁₃	1	4	yes	—
387	#125	C₂³×C₁₃	1	12	yes	—
388	#124	C₂³×C₁₃	1	12	yes	—
389	#124	C₂³×C₁₃	1	12	yes	—
390	#124	C₂³×C₁₃	1	24	yes	—
391	#124	C₂³×C₁₃	1	12	yes	—
392	#123	C₂³×C₁₃	1	24	yes	—
393	#123	C₂³×C₁₃	1	24	yes	—
394	#123	C₂³×C₁₃	1	24	yes	—
395	#123	C₂³×C₁₃	1	48	yes	—
396	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
397	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
398	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
399	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
400	#121	C₂³×C₁₃	1	12	yes	—
401	#121	C₂³×C₁₃	1	12	yes	—
402	#121	C₂³×C₁₃	1	24	yes	—
403	#121	C₂³×C₁₃	1	24	yes	—
404	#121	C₂³×C₁₃	1	24	yes	—
405	#121	C₂³×C₁₃	1	24	yes	—
406	#121	C₂³×C₁₃	1	12	yes	—
407	#121	C₂³×C₁₃	1	12	yes	—
408	#121	C₂³×C₁₃	1	12	yes	—
409	#121	C₂³×C₁₃	1	12	yes	—
410	#121	C₂³×C₁₃	1	24	yes	—
411	#121	C₂³×C₁₃	1	12	yes	—
412	#121	C₂³×C₁₃	1	12	yes	—
413	#121	C₂³×C₁₃	1	24	yes	—
414	#121	C₂³×C₁₃	1	24	yes	—
415	#121	C₂³×C₁₃	1	48	yes	—
416	#121	C₂³×C₁₃	1	48	yes	—
417	#120	C₂³×C₁₃	1	24	yes	—
418	#120	C₂³×C₁₃	1	48	yes	—
419	#120	C₂³×C₁₃	1	48	yes	—
420	#120	C₂³×C₁₃	1	48	yes	—
421	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
422	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
426	C₄×D₄	C₂³×C₁₃	1	12	yes	—
427	C₄×D₄	C₂³×C₁₃	1	12	yes	—
428	C₄×D₄	C₂³×C₁₃	1	12	yes	—
429	C₄×D₄	C₂³×C₁₃	1	12	yes	—
430	C₄×D₄	C₂³×C₁₃	1	6	yes	—
431	C₄×D₄	C₂³×C₁₃	1	12	yes	—
432	C₄×D₄	C₂³×C₁₃	1	12	yes	—
433	C₄×D₄	C₂³×C₁₃	1	6	yes	—
434	C₄×D₄	C₂³×C₁₃	1	24	yes	—
435	C₄×D₄	C₂³×C₁₃	1	24	yes	—
436	C₄×D₄	C₂³×C₁₃	1	12	yes	—
437	C₄×D₄	C₂³×C₁₃	1	24	yes	—
438	#117	C₂³×C₁₃	1	2	yes	—
439	#117	C₂³×C₁₃	1	12	yes	—
440	#117	C₂³×C₁₃	1	12	yes	—
441	#117	C₂³×C₁₃	1	12	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
447	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
448	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
449	C₂×C₁₃	—	2	2	no	—
450	C₂×C₁₃	—	4	12	no	—
451	C₂×C₁₃	—	4	12	no	—
452	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
455	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
457	#41	—	2	16	no	—
458	#41	—	2	16	no	—
459	#41	—	2	24	no	—
460	#41	—	4	24	no	—
461	#41	—	4	24	no	—
462	#41	—	4	48	no	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
465	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
466	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
467	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
468	C₂×D₄	—	2	12	no	—
469	C₂×D₄	—	4	12	no	—
470	C₂×D₄	—	4	24	no	—
471	C₂×D₄	—	4	48	no	—
472	C₂×D₄	—	4	48	no	—
473	C₂×D₄	—	4	48	no	—
474	C₂×D₄	—	8	6	no	—
475	C₂×D₄	—	8	24	no	—
476	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
477	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
478	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
479	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
480	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
481	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
482	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
483	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
484	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
485	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
486	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
487	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
488	C₂²×C₄	—	4	12	no	—
489	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
500	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
505	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
506	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
507	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
508	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
509	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
510	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
511	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
512	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
513	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
514	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
515	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
516	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
517	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
518	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
519	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
520	C₄²	C₂⁴×C₁₃	1	4	yes	—
521	C₄²	C₂⁴×C₁₃	1	6	yes	—
522	C₄²	C₂⁴×C₁₃	1	12	yes	—
523	C₄²	C₂⁴×C₁₃	1	6	yes	—
524	C₄²	C₂⁴×C₁₃	1	12	yes	—
525	C₁₃	#62916	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	2	12	no	—
527	C₂³	—	4	6	no	—
528	C₂³	—	4	6	no	—
529	C₂³	—	4	24	no	—
530	C₂³	—	4	24	no	—
531	C₂³	—	4	24	no	—
532	C₂³	C₂⁵×C₁₃	1	12	yes	—
533	C₂³	C₂⁵×C₁₃	1	12	yes	—
534	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
535	Q₈	—	2	6	no	—
536	Q₈	—	2	12	no	—
537	Q₈	—	4	4	no	—
538	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
539	D₄	—	2	24	no	—
540	D₄	—	2	24	no	—
541	D₄	—	2	24	no	—
542	D₄	—	2	12	no	—
543	D₄	—	2	24	no	—
544	D₄	—	4	12	no	—
545	D₄	—	4	24	no	—
546	D₄	—	4	48	no	—
547	D₄	—	4	12	no	—
548	D₄	—	4	12	no	—
549	D₄	—	4	24	no	—
550	D₄	—	4	24	no	—
551	C₂×C₄	—	2	6	no	—
552	C₂×C₄	—	2	24	no	—
553	C₂×C₄	—	2	24	no	—
554	C₂×C₄	—	2	24	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	12	no	—
557	C₂×C₄	—	4	24	no	—
558	C₂×C₄	—	4	3	no	—
559	C₂×C₄	—	4	12	no	—
560	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
561	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
562	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
563	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
564	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
565	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
566	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
567	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
568	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	12	no	—
572	C₂²	—	2	12	no	—
573	C₂²	—	2	12	no	—
574	C₂²	—	2	12	no	—
575	C₂²	—	2	12	no	—
576	C₂²	—	2	12	no	—
577	C₂²	—	8	12	no	—
578	C₂²	—	16	24	no	—
579	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
580	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
581	C₄	—	2	4	no	—
582	C₄	—	2	4	no	—
583	C₄	—	2	12	no	—
584	C₄	—	2	3	no	—
585	C₄	—	2	6	no	—
586	C₄	—	2	4	no	—
587	C₄	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
588	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
589	C₂	—	2	2	no	—
590	C₂	—	4	12	no	—
591	C₂	—	4	12	no	—
592	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂	C₁₃×H(7,𝔽₂)	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×#3546	C₂	semidirect
2. C₁₃×#3543	C₂	semidirect
3. C₁₃×#3537	C₂	semidirect
4. C₁₃×#3517	C₂	semidirect
5. C₁₃×#3498	C₂	semidirect
6. C₁₃×#3498	C₂	semidirect
7. C₁₃×#3496	C₂	semidirect
8. C₁₃×#3488	C₂	semidirect
9. C₁₃×#3480	C₂	semidirect
10. C₂×C₁₃×#550	C₂	semidirect
11. C₁₃×#3460	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
13. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂²×C₁₃×#41	C₂²	semidirect
15. C₁₃×#560	C₂²	semidirect
16. C₁₃×#559	C₂²	semidirect
17. C₁₃×#557	C₂²	semidirect
18. C₁₃×#556	C₂²	semidirect
19. C₁₃×#553	C₂²	semidirect
20. C₁₃×#553	C₂²	semidirect
21. C₁₃×#550	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
23. C₁₃×#550	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
25. C₁₃×#550	C₂²	semidirect
26. C₁₃×#550	C₂²	semidirect
27. C₁₃×#548	C₂²	semidirect
28. C₁₃×#547	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
31. D₄²×C₁₃	C₂²	semidirect
32. D₄²×C₁₃	C₂²	semidirect
33. D₄²×C₁₃	C₂²	semidirect
34. D₄²×C₁₃	C₂²	semidirect
35. D₄²×C₁₃	C₂²	semidirect
36. D₄²×C₁₃	C₂²	semidirect
37. C₁₃×#544	C₂²	semidirect
38. C₁₃×#542	C₂²	semidirect
39. C₁₃×#540	C₂²	semidirect
40. C₁₃×#540	C₂²	semidirect
41. C₁₃×#538	C₂²	semidirect
42. C₁₃×#538	C₂²	semidirect
43. C₁₃×#537	C₂²	semidirect
44. C₁₃×#537	C₂²	semidirect
45. C₁₃×#535	C₂²	semidirect
46. C₁₃×#535	C₂²	semidirect
47. C₁₃×#535	C₂²	semidirect
48. C₁₃×#535	C₂²	semidirect
49. C₁₃×#534	C₂²	semidirect
50. C₁₃×#534	C₂²	semidirect
51. C₁₃×#532	C₂²	semidirect
52. C₁₃×#532	C₂²	semidirect
53. C₁₃×#532	C₂²	semidirect
54. C₂×C₁₃×#127	C₂²	semidirect
55. C₂×C₁₃×#127	C₂²	semidirect
56. C₁₃×#529	C₂²	semidirect
57. C₁₃×#529	C₂²	semidirect
58. C₁₃×#525	C₂²	semidirect
59. C₂×C₁₃×#121	C₂²	semidirect
60. C₂×C₁₃×#121	C₂²	semidirect
61. C₁₃×#520	C₂²	semidirect
62. C₄×C₁₃×#41	C₂²	semidirect
63. C₄×C₁₃×#41	C₂²	semidirect
64. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
65. C₂×C₄×D₄×C₁₃	C₂²	semidirect
158. #62916	C₁₃	direct (N × H)
229. #3546	C₂×C₁₃	semidirect
230. #3543	C₂×C₁₃	semidirect
231. #3537	C₂×C₁₃	semidirect
232. #3517	C₂×C₁₃	semidirect
233. #3498	C₂×C₁₃	semidirect
234. #3498	C₂×C₁₃	semidirect
235. #3496	C₂×C₁₃	semidirect
236. #3488	C₂×C₁₃	semidirect
237. #3480	C₂×C₁₃	semidirect
238. C₂×#550	C₂×C₁₃	semidirect
239. #3460	C₂×C₁₃	semidirect
252. Q₈×C₁₃	H(5,𝔽₂)	semidirect
274. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
283. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
284. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
285. C₂²×#41	C₂²×C₁₃	semidirect
286. #560	C₂²×C₁₃	semidirect
287. #559	C₂²×C₁₃	semidirect
288. #557	C₂²×C₁₃	semidirect
289. #556	C₂²×C₁₃	semidirect
290. #553	C₂²×C₁₃	semidirect
291. #553	C₂²×C₁₃	semidirect
292. #550	C₂²×C₁₃	semidirect
293. #550	C₂²×C₁₃	semidirect
294. #550	C₂²×C₁₃	semidirect
295. #550	C₂²×C₁₃	semidirect
296. #550	C₂²×C₁₃	semidirect
297. #550	C₂²×C₁₃	semidirect
298. #548	C₂²×C₁₃	semidirect
299. #547	C₂²×C₁₃	semidirect
300. #546	C₂²×C₁₃	semidirect
301. #546	C₂²×C₁₃	semidirect
302. D₄²	C₂²×C₁₃	semidirect
303. D₄²	C₂²×C₁₃	semidirect
304. D₄²	C₂²×C₁₃	semidirect
305. D₄²	C₂²×C₁₃	semidirect
306. D₄²	C₂²×C₁₃	semidirect
307. D₄²	C₂²×C₁₃	semidirect
308. #544	C₂²×C₁₃	semidirect
309. #542	C₂²×C₁₃	semidirect
310. #540	C₂²×C₁₃	semidirect
311. #540	C₂²×C₁₃	semidirect
312. #538	C₂²×C₁₃	semidirect
313. #538	C₂²×C₁₃	semidirect
314. #537	C₂²×C₁₃	semidirect
315. #537	C₂²×C₁₃	semidirect
316. #535	C₂²×C₁₃	semidirect
317. #535	C₂²×C₁₃	semidirect
318. #535	C₂²×C₁₃	semidirect
319. #535	C₂²×C₁₃	semidirect
320. #534	C₂²×C₁₃	semidirect
321. #534	C₂²×C₁₃	semidirect
322. #532	C₂²×C₁₃	semidirect
323. #532	C₂²×C₁₃	semidirect
324. #532	C₂²×C₁₃	semidirect
325. C₂×#127	C₂²×C₁₃	semidirect
326. C₂×#127	C₂²×C₁₃	semidirect
327. #529	C₂²×C₁₃	semidirect
328. #529	C₂²×C₁₃	semidirect
329. #525	C₂²×C₁₃	semidirect
330. C₂×#121	C₂²×C₁₃	semidirect
331. C₂×#121	C₂²×C₁₃	semidirect
332. #520	C₂²×C₁₃	semidirect
333. C₄×#41	C₂²×C₁₃	semidirect
334. C₄×#41	C₂²×C₁₃	semidirect
335. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
336. C₂×C₄×D₄	C₂²×C₁₃	semidirect
525. C₁₃	#62916	direct (N × H)
538. Q₈	C₁₃×H(5,𝔽₂)	semidirect
560. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3546	2
C₁₃×#3543	2
C₁₃×#3537	2
C₁₃×#3517	2
C₁₃×#3498	2
C₁₃×#3496	2
C₁₃×#3488	2
C₁₃×#3480	2
C₂×C₁₃×#550	2
C₁₃×#3460	2
#62916	13

Subgroups — C13×#62916 #15749255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62916 #15749255