Subgroups — C₁₃×#62852 #15749191

Order 3328.

11618 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3500	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3498	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3488	C₂	1	16	yes	maximal, complemented
6	C₁₃×#3487	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3484	C₂	1	12	yes	maximal, complemented
8	C₁₃×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₃×#535	C₂	1	6	yes	maximal, complemented
10	C₁₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#585	—	2	16	no	—
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
14	C₂×C₁₃×H(5,𝔽₂)	—	2	16	no	—
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	6	yes	complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
21	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
23	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
24	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
25	C₂³×D₄×C₁₃	C₂²	1	6	yes	complemented
26	C₁₃×#550	C₂²	1	32	yes	complemented
27	C₁₃×#548	C₂²	1	32	yes	complemented
28	C₁₃×#546	C₂²	1	96	yes	complemented
29	D₄²×C₁₃	C₂²	1	96	yes	complemented
30	C₁₃×#537	C₂²	1	24	yes	complemented
31	C₁₃×#536	C₂²	1	4	yes	complemented
32	C₁₃×#536	C₂²	1	12	yes	complemented
33	C₁₃×#535	C₂²	1	12	yes	complemented
34	C₁₃×#535	C₂²	1	24	yes	complemented
35	C₁₃×#535	C₂²	1	24	yes	complemented
36	C₁₃×#535	C₂²	1	24	yes	complemented
37	C₁₃×#535	C₂²	1	12	yes	complemented
38	C₁₃×#534	C₂²	1	24	yes	complemented
39	C₁₃×#532	C₂²	1	24	yes	complemented
40	C₂×C₁₃×#127	C₂²	1	12	yes	complemented
41	C₂×C₁₃×#124	C₂²	1	12	yes	complemented
42	C₁₃×#525	C₂²	1	24	yes	complemented
43	C₁₃×#525	C₂²	1	24	yes	complemented
44	C₂×C₁₃×#121	C₂²	1	24	yes	complemented
45	C₂×C₁₃×#120	C₂²	1	24	yes	complemented
46	C₁₃×#520	C₂²	1	8	yes	complemented
47	C₁₃×#519	C₂²	1	2	yes	complemented
48	C₁₃×#518	C₂²	1	6	yes	complemented
49	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
50	C₂×C₁₃×#117	C₂²	1	6	yes	complemented
51	C₂⁵×C₁₃	C₂³	1	6	yes	—
52	C₁₃×2₋¹⁺⁴	—	2	32	no	—
53	C₁₃×2₋¹⁺⁴	—	2	16	no	—
54	C₁₃×H(5,𝔽₂)	—	2	64	no	—
55	C₁₃×H(5,𝔽₂)	—	2	64	no	—
56	C₁₃×H(5,𝔽₂)	—	2	32	no	—
57	C₁₃×H(5,𝔽₂)	—	2	48	no	—
58	C₂×C₁₃×#41	—	2	64	no	—
59	C₂×C₁₃×#41	—	2	16	no	—
60	C₂×C₁₃×#41	—	2	24	no	—
61	C₂×C₁₃×#41	—	2	48	no	—
62	C₂×C₁₃×#41	D₄	1	16	yes	complemented
63	C₂×C₁₃×#41	C₂³	1	12	yes	—
64	C₂×C₁₃×#41	C₂³	1	12	yes	—
65	C₂×C₁₃×#41	C₂³	1	12	yes	—
66	C₂×C₁₃×#41	C₂³	1	4	yes	—
67	C₂×C₁₃×#41	C₂³	1	16	yes	—
68	C₂×C₁₃×#41	C₂³	1	4	yes	—
69	C₂×C₁₃×#41	C₂³	1	4	yes	—
70	C₂×C₁₃×#41	C₂³	1	12	yes	complemented
71	C₂×C₁₃×#41	C₂³	1	12	yes	complemented
72	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
73	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	C₂³	1	6	yes	complemented
77	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
78	C₂²×D₄×C₁₃	—	2	48	no	—
79	C₂²×D₄×C₁₃	—	2	24	no	—
80	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	48	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	6	yes	complemented
89	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
90	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
91	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
94	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
95	C₁₃×#127	C₂³	1	24	yes	complemented
96	C₁₃×#127	C₂³	1	48	yes	complemented
97	C₁₃×#124	C₂³	1	24	yes	complemented
98	C₁₃×#124	C₂³	1	48	yes	complemented
99	C₁₃×#124	C₂³	1	8	yes	complemented
100	C₁₃×#123	C₂³	1	16	yes	—
101	C₁₃×#123	C₂³	1	48	yes	complemented
102	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
103	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
104	C₁₃×#121	C₂³	1	48	yes	complemented
105	C₁₃×#121	C₂³	1	96	yes	complemented
106	C₁₃×#121	C₂³	1	48	yes	complemented
107	C₁₃×#121	C₂³	1	96	yes	complemented
108	C₁₃×#120	C₂³	1	48	yes	—
109	C₁₃×#120	C₂³	1	96	yes	complemented
110	C₁₃×#120	C₂³	1	48	yes	complemented
111	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
112	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
113	C₄×D₄×C₁₃	C₂³	1	96	yes	complemented
114	C₁₃×#117	C₂³	1	4	yes	—
115	C₁₃×#117	C₂³	1	12	yes	—
116	C₁₃×#117	C₂³	1	12	yes	complemented
117	C₁₃×#117	C₂³	1	12	yes	complemented
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
121	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
122	#62852	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	—	2	24	no	—
124	C₂⁴×C₁₃	—	8	12	no	—
125	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
128	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
129	C₁₃×#41	—	2	64	no	—
130	C₁₃×#41	—	2	32	no	—
131	C₁₃×#41	—	2	96	no	—
132	C₁₃×#41	—	2	16	no	—
133	C₁₃×#41	—	2	48	no	—
134	C₁₃×#41	—	2	48	no	—
135	C₁₃×#41	—	2	48	no	—
136	C₁₃×#41	—	2	48	no	—
137	C₁₃×#41	—	2	48	no	—
138	C₁₃×#41	C₂×D₄	1	32	yes	complemented
139	C₁₃×#41	C₂×D₄	1	32	yes	complemented
140	C₂×Q₈×C₁₃	—	2	32	no	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	—	2	24	no	—
143	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
144	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
145	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
146	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
147	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	—	2	24	no	—
150	C₂×D₄×C₁₃	—	2	48	no	—
151	C₂×D₄×C₁₃	—	2	192	no	—
152	C₂×D₄×C₁₃	—	2	96	no	—
153	C₂×D₄×C₁₃	—	2	24	no	—
154	C₂×D₄×C₁₃	—	2	12	no	—
155	C₂×D₄×C₁₃	—	2	48	no	—
156	C₂×D₄×C₁₃	—	2	48	no	—
157	C₂×D₄×C₁₃	—	2	24	no	—
158	C₂×D₄×C₁₃	—	8	48	no	—
159	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
160	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
161	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂×D₄×C₁₃	C₂⁴	1	96	yes	—
169	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
170	C₂²×C₄×C₁₃	—	2	24	no	—
171	C₂²×C₄×C₁₃	—	2	48	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
173	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
186	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
187	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
188	C₁₃×C₂²⋊C₄	C₂⁴	1	96	yes	—
189	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
190	C₄²×C₁₃	C₂⁴	1	8	yes	—
191	C₄²×C₁₃	C₂⁴	1	24	yes	—
192	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#3500	C₂×C₁₃	1	8	yes	complemented
195	#3498	C₂×C₁₃	1	8	yes	complemented
196	#3488	C₂×C₁₃	1	16	yes	complemented
197	#3487	C₂×C₁₃	1	4	yes	complemented
198	#3484	C₂×C₁₃	1	12	yes	complemented
199	#3449	C₂×C₁₃	1	6	yes	complemented
200	C₂×#535	C₂×C₁₃	1	6	yes	complemented
201	#3428	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂³×C₁₃	—	2	12	no	—
203	C₂³×C₁₃	—	2	24	no	—
204	C₂³×C₁₃	—	2	48	no	—
205	C₂³×C₁₃	—	4	6	no	—
206	C₂³×C₁₃	—	4	12	no	—
207	C₂³×C₁₃	—	4	24	no	—
208	C₂³×C₁₃	—	4	48	no	—
209	C₂³×C₁₃	—	8	48	no	—
210	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
211	C₂³×C₁₃	C₂⁵	1	12	yes	—
212	C₂³×C₁₃	C₂⁵	1	8	yes	—
213	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
214	C₂³×C₁₃	C₂⁵	1	6	yes	—
215	Q₈×C₁₃	—	2	24	no	—
216	Q₈×C₁₃	—	2	8	no	—
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	2	4	no	—
219	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
220	D₄×C₁₃	—	2	48	no	—
221	D₄×C₁₃	—	2	16	no	—
222	D₄×C₁₃	—	2	48	no	—
223	D₄×C₁₃	—	2	12	no	—
224	D₄×C₁₃	—	2	48	no	—
225	D₄×C₁₃	—	2	12	no	—
226	D₄×C₁₃	—	2	24	no	—
227	D₄×C₁₃	—	2	8	no	—
228	D₄×C₁₃	—	4	96	no	—
229	D₄×C₁₃	C₂²×D₄	1	48	yes	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	24	no	—
232	C₂×C₄×C₁₃	—	2	16	no	—
233	C₂×C₄×C₁₃	—	2	48	no	—
234	C₂×C₄×C₁₃	—	2	48	no	—
235	C₂×C₄×C₁₃	—	4	24	no	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
240	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
246	#585	—	2	16	no	—
247	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
248	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
249	C₂×H(5,𝔽₂)	—	2	16	no	—
250	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	8	yes	complemented
251	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	8	yes	complemented
252	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	6	yes	complemented
253	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
254	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
256	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
257	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
258	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
259	C₂³×D₄	C₂²×C₁₃	1	3	yes	complemented
260	C₂³×D₄	C₂²×C₁₃	1	6	yes	complemented
261	#550	C₂²×C₁₃	1	32	yes	complemented
262	#548	C₂²×C₁₃	1	32	yes	complemented
263	#546	C₂²×C₁₃	1	96	yes	complemented
264	D₄²	C₂²×C₁₃	1	96	yes	complemented
265	#537	C₂²×C₁₃	1	24	yes	complemented
266	#536	C₂²×C₁₃	1	4	yes	complemented
267	#536	C₂²×C₁₃	1	12	yes	complemented
268	#535	C₂²×C₁₃	1	12	yes	complemented
269	#535	C₂²×C₁₃	1	24	yes	complemented
270	#535	C₂²×C₁₃	1	24	yes	complemented
271	#535	C₂²×C₁₃	1	24	yes	complemented
272	#535	C₂²×C₁₃	1	12	yes	complemented
273	#534	C₂²×C₁₃	1	24	yes	complemented
274	#532	C₂²×C₁₃	1	24	yes	complemented
275	C₂×#127	C₂²×C₁₃	1	12	yes	complemented
276	C₂×#124	C₂²×C₁₃	1	12	yes	complemented
277	#525	C₂²×C₁₃	1	24	yes	complemented
278	#525	C₂²×C₁₃	1	24	yes	complemented
279	C₂×#121	C₂²×C₁₃	1	24	yes	complemented
280	C₂×#120	C₂²×C₁₃	1	24	yes	complemented
281	#520	C₂²×C₁₃	1	8	yes	complemented
282	#519	C₂²×C₁₃	1	2	yes	complemented
283	#518	C₂²×C₁₃	1	6	yes	complemented
284	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
285	C₂×#117	C₂²×C₁₃	1	6	yes	complemented
286	C₂²×C₁₃	—	2	12	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	8	no	—
289	C₂²×C₁₃	—	2	12	no	—
290	C₂²×C₁₃	—	2	16	no	—
291	C₂²×C₁₃	—	2	24	no	—
292	C₂²×C₁₃	—	4	12	no	—
293	C₂²×C₁₃	—	4	24	no	—
294	C₂²×C₁₃	—	8	24	no	—
295	C₂²×C₁₃	—	8	48	no	—
296	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
297	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
298	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	2	8	no	—
301	C₄×C₁₃	—	2	16	no	—
302	C₄×C₁₃	C₂³×D₄	1	2	yes	—
303	C₄×C₁₃	C₂³×D₄	1	12	yes	—
304	C₄×C₁₃	C₂³×D₄	1	2	yes	—
305	C₂⁵	C₂³×C₁₃	1	6	yes	—
306	2₋¹⁺⁴	—	2	32	no	—
307	2₋¹⁺⁴	—	2	16	no	—
308	H(5,𝔽₂)	—	2	64	no	—
309	H(5,𝔽₂)	—	2	64	no	—
310	H(5,𝔽₂)	—	2	32	no	—
311	H(5,𝔽₂)	—	2	48	no	—
312	C₂×#41	—	2	64	no	—
313	C₂×#41	—	2	16	no	—
314	C₂×#41	—	2	24	no	—
315	C₂×#41	—	2	48	no	—
316	C₂×#41	D₄×C₁₃	1	16	yes	complemented
317	C₂×#41	C₂³×C₁₃	1	12	yes	—
318	C₂×#41	C₂³×C₁₃	1	12	yes	—
319	C₂×#41	C₂³×C₁₃	1	12	yes	—
320	C₂×#41	C₂³×C₁₃	1	4	yes	—
321	C₂×#41	C₂³×C₁₃	1	16	yes	—
322	C₂×#41	C₂³×C₁₃	1	4	yes	—
323	C₂×#41	C₂³×C₁₃	1	4	yes	—
324	C₂×#41	C₂³×C₁₃	1	12	yes	complemented
325	C₂×#41	C₂³×C₁₃	1	12	yes	complemented
326	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
327	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
328	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₁₃	1	6	yes	complemented
331	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
332	C₂²×D₄	—	2	48	no	—
333	C₂²×D₄	—	2	24	no	—
334	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
338	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
339	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
340	C₂²×D₄	C₂³×C₁₃	1	48	yes	—
341	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
342	C₂²×D₄	C₂³×C₁₃	1	6	yes	complemented
343	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
344	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
345	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
347	C₂³×C₄	C₂³×C₁₃	1	12	yes	complemented
348	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
349	#127	C₂³×C₁₃	1	24	yes	complemented
350	#127	C₂³×C₁₃	1	48	yes	complemented
351	#124	C₂³×C₁₃	1	24	yes	complemented
352	#124	C₂³×C₁₃	1	48	yes	complemented
353	#124	C₂³×C₁₃	1	8	yes	complemented
354	#123	C₂³×C₁₃	1	16	yes	—
355	#123	C₂³×C₁₃	1	48	yes	complemented
356	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
357	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
358	#121	C₂³×C₁₃	1	48	yes	complemented
359	#121	C₂³×C₁₃	1	96	yes	complemented
360	#121	C₂³×C₁₃	1	48	yes	complemented
361	#121	C₂³×C₁₃	1	96	yes	complemented
362	#120	C₂³×C₁₃	1	48	yes	—
363	#120	C₂³×C₁₃	1	96	yes	complemented
364	#120	C₂³×C₁₃	1	48	yes	complemented
365	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
366	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
367	C₄×D₄	C₂³×C₁₃	1	96	yes	complemented
368	#117	C₂³×C₁₃	1	4	yes	—
369	#117	C₂³×C₁₃	1	12	yes	—
370	#117	C₂³×C₁₃	1	12	yes	complemented
371	#117	C₂³×C₁₃	1	12	yes	complemented
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	complemented
375	C₂×C₄²	C₂³×C₁₃	1	12	yes	complemented
376	C₂×C₁₃	—	2	2	no	—
377	C₂×C₁₃	—	2	12	no	—
378	C₂×C₁₃	—	4	12	no	—
379	C₂×C₁₃	—	4	8	no	—
380	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
381	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
382	C₂⁴	—	2	24	no	—
383	C₂⁴	—	8	12	no	—
384	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
385	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
386	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
387	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
388	#41	—	2	64	no	—
389	#41	—	2	32	no	—
390	#41	—	2	96	no	—
391	#41	—	2	16	no	—
392	#41	—	2	48	no	—
393	#41	—	2	48	no	—
394	#41	—	2	48	no	—
395	#41	—	2	48	no	—
396	#41	—	2	48	no	—
397	#41	C₂×D₄×C₁₃	1	32	yes	complemented
398	#41	C₂×D₄×C₁₃	1	32	yes	complemented
399	C₂×Q₈	—	2	32	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	24	no	—
402	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	complemented
403	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
404	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
405	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
406	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
407	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
408	C₂×D₄	—	2	24	no	—
409	C₂×D₄	—	2	48	no	—
410	C₂×D₄	—	2	192	no	—
411	C₂×D₄	—	2	96	no	—
412	C₂×D₄	—	2	24	no	—
413	C₂×D₄	—	2	12	no	—
414	C₂×D₄	—	2	48	no	—
415	C₂×D₄	—	2	48	no	—
416	C₂×D₄	—	2	24	no	—
417	C₂×D₄	—	8	48	no	—
418	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	complemented
419	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
420	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
421	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
422	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
423	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
424	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
425	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
426	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	96	yes	—
428	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
429	C₂²×C₄	—	2	24	no	—
430	C₂²×C₄	—	2	48	no	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	complemented
432	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
443	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
444	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
445	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
446	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
447	C₂²⋊C₄	C₂⁴×C₁₃	1	96	yes	—
448	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
449	C₄²	C₂⁴×C₁₃	1	8	yes	—
450	C₄²	C₂⁴×C₁₃	1	24	yes	—
451	C₁₃	#62852	1	1	yes	characteristic, direct product factor, Sylow
452	C₂³	—	2	12	no	—
453	C₂³	—	2	24	no	—
454	C₂³	—	2	48	no	—
455	C₂³	—	4	6	no	—
456	C₂³	—	4	12	no	—
457	C₂³	—	4	24	no	—
458	C₂³	—	4	48	no	—
459	C₂³	—	8	48	no	—
460	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
461	C₂³	C₂⁵×C₁₃	1	12	yes	—
462	C₂³	C₂⁵×C₁₃	1	8	yes	—
463	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
464	C₂³	C₂⁵×C₁₃	1	6	yes	—
465	Q₈	—	2	24	no	—
466	Q₈	—	2	8	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
470	D₄	—	2	48	no	—
471	D₄	—	2	16	no	—
472	D₄	—	2	48	no	—
473	D₄	—	2	12	no	—
474	D₄	—	2	48	no	—
475	D₄	—	2	12	no	—
476	D₄	—	2	24	no	—
477	D₄	—	2	8	no	—
478	D₄	—	4	96	no	—
479	D₄	C₂²×D₄×C₁₃	1	48	yes	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	24	no	—
482	C₂×C₄	—	2	16	no	—
483	C₂×C₄	—	2	48	no	—
484	C₂×C₄	—	2	48	no	—
485	C₂×C₄	—	4	24	no	—
486	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
490	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
491	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
492	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
493	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
494	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
495	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
496	C₂²	—	2	12	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	12	no	—
500	C₂²	—	2	16	no	—
501	C₂²	—	2	24	no	—
502	C₂²	—	4	12	no	—
503	C₂²	—	4	24	no	—
504	C₂²	—	8	24	no	—
505	C₂²	—	8	48	no	—
506	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
507	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
508	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
509	C₄	—	2	4	no	—
510	C₄	—	2	8	no	—
511	C₄	—	2	16	no	—
512	C₄	C₂³×D₄×C₁₃	1	2	yes	—
513	C₄	C₂³×D₄×C₁₃	1	12	yes	—
514	C₄	C₂³×D₄×C₁₃	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	12	no	—
517	C₂	—	4	12	no	—
518	C₂	—	4	8	no	—
519	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
520	C₂	C₁₃×H(7,𝔽₂)	1	2	yes	—

	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. C₂×C₁₃×#585	C₂	semidirect
2. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
3. C₁₃×#3500	C₂	semidirect
4. C₁₃×#3498	C₂	semidirect
5. C₁₃×#3488	C₂	semidirect
6. C₁₃×#3487	C₂	semidirect
7. C₁₃×#3484	C₂	semidirect
8. C₁₃×#3449	C₂	semidirect
9. C₂×C₁₃×#535	C₂	semidirect
10. C₁₃×#3428	C₂	semidirect
12. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
23. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂³×D₄×C₁₃	C₂²	semidirect
25. C₂³×D₄×C₁₃	C₂²	semidirect
26. C₁₃×#550	C₂²	semidirect
27. C₁₃×#548	C₂²	semidirect
28. C₁₃×#546	C₂²	semidirect
29. D₄²×C₁₃	C₂²	semidirect
30. C₁₃×#537	C₂²	semidirect
31. C₁₃×#536	C₂²	semidirect
32. C₁₃×#536	C₂²	semidirect
33. C₁₃×#535	C₂²	semidirect
34. C₁₃×#535	C₂²	semidirect
35. C₁₃×#535	C₂²	semidirect
36. C₁₃×#535	C₂²	semidirect
37. C₁₃×#535	C₂²	semidirect
38. C₁₃×#534	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₂×C₁₃×#127	C₂²	semidirect
41. C₂×C₁₃×#124	C₂²	semidirect
42. C₁₃×#525	C₂²	semidirect
43. C₁₃×#525	C₂²	semidirect
44. C₂×C₁₃×#121	C₂²	semidirect
45. C₂×C₁₃×#120	C₂²	semidirect
46. C₁₃×#520	C₂²	semidirect
47. C₁₃×#519	C₂²	semidirect
48. C₁₃×#518	C₂²	semidirect
49. C₄×C₁₃×#41	C₂²	semidirect
50. C₂×C₁₃×#117	C₂²	semidirect
62. C₂×C₁₃×#41	D₄	semidirect
70. C₂×C₁₃×#41	C₂³	semidirect
71. C₂×C₁₃×#41	C₂³	semidirect
72. C₂×C₁₃×#41	C₂³	semidirect
73. C₂×C₁₃×#41	C₂³	semidirect
76. C₂²×Q₈×C₁₃	C₂³	semidirect
77. C₂²×Q₈×C₁₃	C₂³	semidirect
88. C₂²×D₄×C₁₃	C₂³	semidirect
89. C₂²×D₄×C₁₃	C₂³	semidirect
90. C₂²×D₄×C₁₃	C₂³	semidirect
93. C₂³×C₄×C₁₃	C₂³	semidirect
94. C₁₃×C₄⋊Q₈	C₂³	semidirect
95. C₁₃×#127	C₂³	semidirect
96. C₁₃×#127	C₂³	semidirect
97. C₁₃×#124	C₂³	semidirect
98. C₁₃×#124	C₂³	semidirect
99. C₁₃×#124	C₂³	semidirect
101. C₁₃×#123	C₂³	semidirect
102. C₁₃×C₂²⋊Q₈	C₂³	semidirect
103. C₁₃×C₂²⋊Q₈	C₂³	semidirect
104. C₁₃×#121	C₂³	semidirect
105. C₁₃×#121	C₂³	semidirect
106. C₁₃×#121	C₂³	semidirect
107. C₁₃×#121	C₂³	semidirect
109. C₁₃×#120	C₂³	semidirect
110. C₁₃×#120	C₂³	semidirect
111. C₄×Q₈×C₁₃	C₂³	semidirect
112. C₄×D₄×C₁₃	C₂³	semidirect
113. C₄×D₄×C₁₃	C₂³	semidirect
116. C₁₃×#117	C₂³	semidirect
117. C₁₃×#117	C₂³	semidirect
118. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
120. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
121. C₂×C₄²×C₁₃	C₂³	semidirect
122. #62852	C₁₃	direct (N × H)
138. C₁₃×#41	C₂×D₄	semidirect
139. C₁₃×#41	C₂×D₄	semidirect
143. C₂×Q₈×C₁₃	C₂×D₄	semidirect
159. C₂×D₄×C₁₃	C₂×D₄	semidirect
172. C₂²×C₄×C₁₃	C₂×D₄	semidirect
192. C₂×#585	C₂×C₁₃	semidirect
193. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
194. #3500	C₂×C₁₃	semidirect
195. #3498	C₂×C₁₃	semidirect
196. #3488	C₂×C₁₃	semidirect
197. #3487	C₂×C₁₃	semidirect
198. #3484	C₂×C₁₃	semidirect
199. #3449	C₂×C₁₃	semidirect
200. C₂×#535	C₂×C₁₃	semidirect
201. #3428	C₂×C₁₃	semidirect
247. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
248. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
250. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
251. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
252. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
253. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
255. C₂²×#41	C₂²×C₁₃	semidirect
256. C₂²×#41	C₂²×C₁₃	semidirect
257. C₂²×#41	C₂²×C₁₃	semidirect
258. C₂²×#41	C₂²×C₁₃	semidirect
259. C₂³×D₄	C₂²×C₁₃	semidirect
260. C₂³×D₄	C₂²×C₁₃	semidirect
261. #550	C₂²×C₁₃	semidirect
262. #548	C₂²×C₁₃	semidirect
263. #546	C₂²×C₁₃	semidirect
264. D₄²	C₂²×C₁₃	semidirect
265. #537	C₂²×C₁₃	semidirect
266. #536	C₂²×C₁₃	semidirect
267. #536	C₂²×C₁₃	semidirect
268. #535	C₂²×C₁₃	semidirect
269. #535	C₂²×C₁₃	semidirect
270. #535	C₂²×C₁₃	semidirect
271. #535	C₂²×C₁₃	semidirect
272. #535	C₂²×C₁₃	semidirect
273. #534	C₂²×C₁₃	semidirect
274. #532	C₂²×C₁₃	semidirect
275. C₂×#127	C₂²×C₁₃	semidirect
276. C₂×#124	C₂²×C₁₃	semidirect
277. #525	C₂²×C₁₃	semidirect
278. #525	C₂²×C₁₃	semidirect
279. C₂×#121	C₂²×C₁₃	semidirect
280. C₂×#120	C₂²×C₁₃	semidirect
281. #520	C₂²×C₁₃	semidirect
282. #519	C₂²×C₁₃	semidirect
283. #518	C₂²×C₁₃	semidirect
284. C₄×#41	C₂²×C₁₃	semidirect
285. C₂×#117	C₂²×C₁₃	semidirect
316. C₂×#41	D₄×C₁₃	semidirect
324. C₂×#41	C₂³×C₁₃	semidirect
325. C₂×#41	C₂³×C₁₃	semidirect
326. C₂×#41	C₂³×C₁₃	semidirect
327. C₂×#41	C₂³×C₁₃	semidirect
330. C₂²×Q₈	C₂³×C₁₃	semidirect
331. C₂²×Q₈	C₂³×C₁₃	semidirect
342. C₂²×D₄	C₂³×C₁₃	semidirect
343. C₂²×D₄	C₂³×C₁₃	semidirect
344. C₂²×D₄	C₂³×C₁₃	semidirect
347. C₂³×C₄	C₂³×C₁₃	semidirect
348. C₄⋊Q₈	C₂³×C₁₃	semidirect
349. #127	C₂³×C₁₃	semidirect
350. #127	C₂³×C₁₃	semidirect
351. #124	C₂³×C₁₃	semidirect
352. #124	C₂³×C₁₃	semidirect
353. #124	C₂³×C₁₃	semidirect
355. #123	C₂³×C₁₃	semidirect
356. C₂²⋊Q₈	C₂³×C₁₃	semidirect
357. C₂²⋊Q₈	C₂³×C₁₃	semidirect
358. #121	C₂³×C₁₃	semidirect
359. #121	C₂³×C₁₃	semidirect
360. #121	C₂³×C₁₃	semidirect
361. #121	C₂³×C₁₃	semidirect
363. #120	C₂³×C₁₃	semidirect
364. #120	C₂³×C₁₃	semidirect
365. C₄×Q₈	C₂³×C₁₃	semidirect
366. C₄×D₄	C₂³×C₁₃	semidirect
367. C₄×D₄	C₂³×C₁₃	semidirect
370. #117	C₂³×C₁₃	semidirect
371. #117	C₂³×C₁₃	semidirect
372. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
374. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
375. C₂×C₄²	C₂³×C₁₃	semidirect
397. #41	C₂×D₄×C₁₃	semidirect
398. #41	C₂×D₄×C₁₃	semidirect
402. C₂×Q₈	C₂×D₄×C₁₃	semidirect
418. C₂×D₄	C₂×D₄×C₁₃	semidirect
431. C₂²×C₄	C₂×D₄×C₁₃	semidirect
451. C₁₃	#62852	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#585	2
C₂²×C₁₃×H(5,𝔽₂)	2
C₁₃×#3500	2
C₁₃×#3498	2
C₁₃×#3488	2
C₁₃×#3487	2
C₁₃×#3484	2
C₁₃×#3449	2
C₂×C₁₃×#535	2
C₁₃×#3428	2
#62852	13

Subgroups — C13×#62852 #15749191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62852 #15749191