Subgroups — C₁₃×#62859 #15749198

Order 3328.

10986 conjugacy classes of subgroups.

The subgroup lattice has 512 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×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3500	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3499	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3489	C₂	1	16	yes	maximal, complemented
6	C₁₃×#3486	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3485	C₂	1	12	yes	maximal, complemented
8	C₁₃×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₃×#536	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	—	2	16	no	—
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	8	yes	complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	8	yes	complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	6	yes	—
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	6	yes	—
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
22	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
23	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
24	C₂³×Q₈×C₁₃	C₂²	1	3	yes	complemented
25	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	D₄×Q₈×C₁₃	C₂²	1	32	yes	complemented
27	C₁₃×#548	C₂²	1	32	yes	complemented
28	C₁₃×#547	C₂²	1	96	yes	complemented
29	C₁₃×#546	C₂²	1	96	yes	complemented
30	C₁₃×#537	C₂²	1	24	yes	complemented
31	C₁₃×#536	C₂²	1	12	yes	complemented
32	C₁₃×#536	C₂²	1	24	yes	complemented
33	C₁₃×#536	C₂²	1	24	yes	complemented
34	C₁₃×#536	C₂²	1	24	yes	complemented
35	C₁₃×#536	C₂²	1	12	yes	complemented
36	C₁₃×#535	C₂²	1	4	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×C₄⋊Q₈	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×#123	C₂²	1	24	yes	complemented
45	C₂×C₁₃×C₂²⋊Q₈	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	C₁₃×2₋¹⁺⁴	—	2	64	no	—
52	C₁₃×2₋¹⁺⁴	—	2	64	no	—
53	C₁₃×2₋¹⁺⁴	—	2	32	no	—
54	C₁₃×2₋¹⁺⁴	—	2	16	no	—
55	C₁₃×H(5,𝔽₂)	—	2	32	no	—
56	C₁₃×H(5,𝔽₂)	—	2	48	no	—
57	C₂×C₁₃×#41	—	2	64	no	—
58	C₂×C₁₃×#41	—	2	48	no	—
59	C₂×C₁₃×#41	—	2	48	no	—
60	C₂×C₁₃×#41	—	2	24	no	—
61	C₂×C₁₃×#41	D₄	1	16	yes	complemented
62	C₂×C₁₃×#41	C₂³	1	12	yes	—
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	12	yes	—
68	C₂×C₁₃×#41	C₂³	1	48	yes	—
69	C₂×C₁₃×#41	C₂³	1	24	yes	—
70	C₂×C₁₃×#41	C₂³	1	8	yes	—
71	C₂×C₁₃×#41	C₂³	1	4	yes	—
72	C₂×C₁₃×#41	C₂³	1	4	yes	—
73	C₂²×Q₈×C₁₃	—	2	16	no	—
74	C₂²×Q₈×C₁₃	—	2	24	no	—
75	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
80	C₂²×Q₈×C₁₃	C₂³	1	16	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	48	yes	—
95	C₁₃×#127	C₂³	1	8	yes	—
96	C₁₃×#124	C₂³	1	24	yes	—
97	C₁₃×#124	C₂³	1	48	yes	—
98	C₁₃×#124	C₂³	1	8	yes	—
99	C₁₃×#123	C₂³	1	48	yes	—
100	C₁₃×#123	C₂³	1	96	yes	—
101	C₁₃×#123	C₂³	1	48	yes	—
102	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	96	yes	—
104	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	—
105	C₁₃×#121	C₂³	1	16	yes	—
106	C₁₃×#121	C₂³	1	48	yes	—
107	C₁₃×#121	C₂³	1	96	yes	—
108	C₁₃×#120	C₂³	1	16	yes	—
109	C₁₃×#120	C₂³	1	48	yes	—
110	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
111	C₄×D₄×C₁₃	C₂³	1	48	yes	—
112	C₄×D₄×C₁₃	C₂³	1	96	yes	—
113	C₁₃×#117	C₂³	1	4	yes	—
114	C₁₃×#117	C₂³	1	12	yes	—
115	C₁₃×#117	C₂³	1	12	yes	—
116	C₁₃×#117	C₂³	1	12	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
122	#62859	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
126	C₁₃×#41	—	2	32	no	—
127	C₁₃×#41	—	2	96	no	—
128	C₁₃×#41	—	2	192	no	—
129	C₁₃×#41	—	2	48	no	—
130	C₁₃×#41	—	2	16	no	—
131	C₁₃×#41	—	2	48	no	—
132	C₁₃×#41	—	2	48	no	—
133	C₁₃×#41	—	2	48	no	—
134	C₁₃×#41	—	2	48	no	—
135	C₁₃×#41	C₂×D₄	1	32	yes	—
136	C₁₃×#41	C₂×D₄	1	32	yes	—
137	C₂×Q₈×C₁₃	—	2	64	no	—
138	C₂×Q₈×C₁₃	—	2	32	no	—
139	C₂×Q₈×C₁₃	—	2	24	no	—
140	C₂×Q₈×C₁₃	—	2	12	no	—
141	C₂×Q₈×C₁₃	—	2	48	no	—
142	C₂×Q₈×C₁₃	—	2	48	no	—
143	C₂×Q₈×C₁₃	—	2	24	no	—
144	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
145	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
146	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
147	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
149	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
150	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
151	C₂×D₄×C₁₃	—	2	24	no	—
152	C₂×D₄×C₁₃	—	2	48	no	—
153	C₂×D₄×C₁₃	—	2	96	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	24	no	—
156	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
161	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
166	C₂²×C₄×C₁₃	—	2	24	no	—
167	C₂²×C₄×C₁₃	—	2	24	no	—
168	C₂²×C₄×C₁₃	—	2	48	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	96	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
184	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
185	C₁₃×C₂²⋊C₄	C₂⁴	1	96	yes	—
186	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
187	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
188	C₄²×C₁₃	C₂⁴	1	8	yes	—
189	C₄²×C₁₃	C₂⁴	1	24	yes	—
190	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#3500	C₂×C₁₃	1	8	yes	complemented
193	#3499	C₂×C₁₃	1	8	yes	complemented
194	#3489	C₂×C₁₃	1	16	yes	complemented
195	#3486	C₂×C₁₃	1	4	yes	complemented
196	#3485	C₂×C₁₃	1	12	yes	complemented
197	#3449	C₂×C₁₃	1	6	yes	complemented
198	C₂×#536	C₂×C₁₃	1	6	yes	complemented
199	#3428	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂³×C₁₃	—	2	4	no	—
201	C₂³×C₁₃	—	2	24	no	—
202	C₂³×C₁₃	—	4	6	no	—
203	C₂³×C₁₃	—	4	4	no	—
204	C₂³×C₁₃	—	4	24	no	—
205	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
206	C₂³×C₁₃	C₂⁵	1	8	yes	—
207	C₂³×C₁₃	C₂⁵	1	4	yes	—
208	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
209	C₂³×C₁₃	C₂⁵	1	6	yes	—
210	Q₈×C₁₃	—	2	12	no	—
211	Q₈×C₁₃	—	2	48	no	—
212	Q₈×C₁₃	—	2	12	no	—
213	Q₈×C₁₃	—	2	24	no	—
214	Q₈×C₁₃	—	2	8	no	—
215	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
216	D₄×C₁₃	—	2	16	no	—
217	D₄×C₁₃	—	2	48	no	—
218	D₄×C₁₃	—	2	48	no	—
219	D₄×C₁₃	—	2	24	no	—
220	D₄×C₁₃	—	2	8	no	—
221	D₄×C₁₃	—	2	4	no	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	4	32	no	—
224	D₄×C₁₃	C₂²×D₄	1	48	yes	—
225	C₂×C₄×C₁₃	—	2	12	no	—
226	C₂×C₄×C₁₃	—	2	24	no	—
227	C₂×C₄×C₁₃	—	2	48	no	—
228	C₂×C₄×C₁₃	—	2	16	no	—
229	C₂×C₄×C₁₃	—	2	48	no	—
230	C₂×C₄×C₁₃	—	2	48	no	—
231	C₂×C₄×C₁₃	—	4	24	no	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
239	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
242	#585	—	2	16	no	—
243	C₂×2₋¹⁺⁴	—	2	16	no	—
244	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
245	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	8	yes	complemented
246	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	8	yes	complemented
247	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
248	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	6	yes	—
249	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
250	C₂²×#41	C₂²×C₁₃	1	6	yes	—
251	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
253	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
254	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
255	C₂³×Q₈	C₂²×C₁₃	1	3	yes	complemented
256	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
257	D₄×Q₈	C₂²×C₁₃	1	32	yes	complemented
258	#548	C₂²×C₁₃	1	32	yes	complemented
259	#547	C₂²×C₁₃	1	96	yes	complemented
260	#546	C₂²×C₁₃	1	96	yes	complemented
261	#537	C₂²×C₁₃	1	24	yes	complemented
262	#536	C₂²×C₁₃	1	12	yes	complemented
263	#536	C₂²×C₁₃	1	24	yes	complemented
264	#536	C₂²×C₁₃	1	24	yes	complemented
265	#536	C₂²×C₁₃	1	24	yes	complemented
266	#536	C₂²×C₁₃	1	12	yes	complemented
267	#535	C₂²×C₁₃	1	4	yes	complemented
268	#535	C₂²×C₁₃	1	12	yes	complemented
269	#534	C₂²×C₁₃	1	24	yes	complemented
270	#532	C₂²×C₁₃	1	24	yes	complemented
271	C₂×C₄⋊Q₈	C₂²×C₁₃	1	12	yes	complemented
272	C₂×#124	C₂²×C₁₃	1	12	yes	complemented
273	#525	C₂²×C₁₃	1	24	yes	complemented
274	#525	C₂²×C₁₃	1	24	yes	complemented
275	C₂×#123	C₂²×C₁₃	1	24	yes	complemented
276	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
277	#520	C₂²×C₁₃	1	8	yes	complemented
278	#519	C₂²×C₁₃	1	2	yes	complemented
279	#518	C₂²×C₁₃	1	6	yes	complemented
280	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
281	C₂×#117	C₂²×C₁₃	1	6	yes	complemented
282	C₂²×C₁₃	—	2	12	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	2	8	no	—
286	C₂²×C₁₃	—	2	8	no	—
287	C₂²×C₁₃	—	2	16	no	—
288	C₂²×C₁₃	—	4	12	no	—
289	C₂²×C₁₃	—	4	8	no	—
290	C₂²×C₁₃	—	8	24	no	—
291	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
292	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
293	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
294	C₄×C₁₃	—	2	8	no	—
295	C₄×C₁₃	—	2	12	no	—
296	C₄×C₁₃	—	2	16	no	—
297	C₄×C₁₃	C₂³×D₄	1	2	yes	—
298	C₄×C₁₃	C₂³×D₄	1	12	yes	—
299	C₄×C₁₃	C₂³×D₄	1	2	yes	—
300	2₋¹⁺⁴	—	2	64	no	—
301	2₋¹⁺⁴	—	2	64	no	—
302	2₋¹⁺⁴	—	2	32	no	—
303	2₋¹⁺⁴	—	2	16	no	—
304	H(5,𝔽₂)	—	2	32	no	—
305	H(5,𝔽₂)	—	2	48	no	—
306	C₂×#41	—	2	64	no	—
307	C₂×#41	—	2	48	no	—
308	C₂×#41	—	2	48	no	—
309	C₂×#41	—	2	24	no	—
310	C₂×#41	D₄×C₁₃	1	16	yes	complemented
311	C₂×#41	C₂³×C₁₃	1	12	yes	—
312	C₂×#41	C₂³×C₁₃	1	12	yes	—
313	C₂×#41	C₂³×C₁₃	1	12	yes	—
314	C₂×#41	C₂³×C₁₃	1	12	yes	—
315	C₂×#41	C₂³×C₁₃	1	4	yes	—
316	C₂×#41	C₂³×C₁₃	1	12	yes	—
317	C₂×#41	C₂³×C₁₃	1	48	yes	—
318	C₂×#41	C₂³×C₁₃	1	24	yes	—
319	C₂×#41	C₂³×C₁₃	1	8	yes	—
320	C₂×#41	C₂³×C₁₃	1	4	yes	—
321	C₂×#41	C₂³×C₁₃	1	4	yes	—
322	C₂²×Q₈	—	2	16	no	—
323	C₂²×Q₈	—	2	24	no	—
324	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
325	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
326	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
327	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
328	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
329	C₂²×Q₈	C₂³×C₁₃	1	16	yes	—
330	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
331	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
342	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
343	C₄⋊Q₈	C₂³×C₁₃	1	48	yes	—
344	#127	C₂³×C₁₃	1	8	yes	—
345	#124	C₂³×C₁₃	1	24	yes	—
346	#124	C₂³×C₁₃	1	48	yes	—
347	#124	C₂³×C₁₃	1	8	yes	—
348	#123	C₂³×C₁₃	1	48	yes	—
349	#123	C₂³×C₁₃	1	96	yes	—
350	#123	C₂³×C₁₃	1	48	yes	—
351	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	—
352	C₂²⋊Q₈	C₂³×C₁₃	1	96	yes	—
353	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	—
354	#121	C₂³×C₁₃	1	16	yes	—
355	#121	C₂³×C₁₃	1	48	yes	—
356	#121	C₂³×C₁₃	1	96	yes	—
357	#120	C₂³×C₁₃	1	16	yes	—
358	#120	C₂³×C₁₃	1	48	yes	—
359	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
360	C₄×D₄	C₂³×C₁₃	1	48	yes	—
361	C₄×D₄	C₂³×C₁₃	1	96	yes	—
362	#117	C₂³×C₁₃	1	4	yes	—
363	#117	C₂³×C₁₃	1	12	yes	—
364	#117	C₂³×C₁₃	1	12	yes	—
365	#117	C₂³×C₁₃	1	12	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
370	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
371	C₂×C₁₃	—	2	2	no	—
372	C₂×C₁₃	—	2	12	no	—
373	C₂×C₁₃	—	4	4	no	—
374	C₂×C₁₃	—	4	8	no	—
375	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
376	C₂×C₁₃	2₋¹⁺⁶	1	2	yes	—
377	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
378	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
379	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
380	#41	—	2	32	no	—
381	#41	—	2	96	no	—
382	#41	—	2	192	no	—
383	#41	—	2	48	no	—
384	#41	—	2	16	no	—
385	#41	—	2	48	no	—
386	#41	—	2	48	no	—
387	#41	—	2	48	no	—
388	#41	—	2	48	no	—
389	#41	C₂×D₄×C₁₃	1	32	yes	—
390	#41	C₂×D₄×C₁₃	1	32	yes	—
391	C₂×Q₈	—	2	64	no	—
392	C₂×Q₈	—	2	32	no	—
393	C₂×Q₈	—	2	24	no	—
394	C₂×Q₈	—	2	12	no	—
395	C₂×Q₈	—	2	48	no	—
396	C₂×Q₈	—	2	48	no	—
397	C₂×Q₈	—	2	24	no	—
398	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
399	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
400	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
401	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
402	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
403	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
404	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
405	C₂×D₄	—	2	24	no	—
406	C₂×D₄	—	2	48	no	—
407	C₂×D₄	—	2	96	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	24	no	—
410	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	—
411	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
412	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
413	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
414	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
415	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
416	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
418	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
419	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
420	C₂²×C₄	—	2	24	no	—
421	C₂²×C₄	—	2	24	no	—
422	C₂²×C₄	—	2	48	no	—
423	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
428	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
431	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
436	C₄⋊C₄	C₂⁴×C₁₃	1	96	yes	—
437	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
438	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
439	C₂²⋊C₄	C₂⁴×C₁₃	1	96	yes	—
440	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
441	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
442	C₄²	C₂⁴×C₁₃	1	8	yes	—
443	C₄²	C₂⁴×C₁₃	1	24	yes	—
444	C₁₃	#62859	1	1	yes	characteristic, direct product factor, Sylow
445	C₂³	—	2	4	no	—
446	C₂³	—	2	24	no	—
447	C₂³	—	4	6	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	24	no	—
450	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
451	C₂³	C₂⁵×C₁₃	1	8	yes	—
452	C₂³	C₂⁵×C₁₃	1	4	yes	—
453	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
454	C₂³	C₂⁵×C₁₃	1	6	yes	—
455	Q₈	—	2	12	no	—
456	Q₈	—	2	48	no	—
457	Q₈	—	2	12	no	—
458	Q₈	—	2	24	no	—
459	Q₈	—	2	8	no	—
460	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
461	D₄	—	2	16	no	—
462	D₄	—	2	48	no	—
463	D₄	—	2	48	no	—
464	D₄	—	2	24	no	—
465	D₄	—	2	8	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	32	no	—
469	D₄	C₂²×D₄×C₁₃	1	48	yes	—
470	C₂×C₄	—	2	12	no	—
471	C₂×C₄	—	2	24	no	—
472	C₂×C₄	—	2	48	no	—
473	C₂×C₄	—	2	16	no	—
474	C₂×C₄	—	2	48	no	—
475	C₂×C₄	—	2	48	no	—
476	C₂×C₄	—	4	24	no	—
477	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
481	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
482	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
483	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
484	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
486	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
487	C₂²	—	2	12	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	16	no	—
493	C₂²	—	4	12	no	—
494	C₂²	—	4	8	no	—
495	C₂²	—	8	24	no	—
496	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
498	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
499	C₄	—	2	8	no	—
500	C₄	—	2	12	no	—
501	C₄	—	2	16	no	—
502	C₄	C₂³×D₄×C₁₃	1	2	yes	—
503	C₄	C₂³×D₄×C₁₃	1	12	yes	—
504	C₄	C₂³×D₄×C₁₃	1	2	yes	—
505	C₂	—	2	2	no	—
506	C₂	—	2	12	no	—
507	C₂	—	4	4	no	—
508	C₂	—	4	8	no	—
509	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
510	C₂	C₁₃×2₋¹⁺⁶	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×C₁₃×2₋¹⁺⁴	C₂	semidirect
3. C₁₃×#3500	C₂	semidirect
4. C₁₃×#3499	C₂	semidirect
5. C₁₃×#3489	C₂	semidirect
6. C₁₃×#3486	C₂	semidirect
7. C₁₃×#3485	C₂	semidirect
8. C₁₃×#3449	C₂	semidirect
9. C₂×C₁₃×#536	C₂	semidirect
10. C₁₃×#3428	C₂	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
23. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂³×Q₈×C₁₃	C₂²	semidirect
25. C₂³×Q₈×C₁₃	C₂²	semidirect
26. D₄×Q₈×C₁₃	C₂²	semidirect
27. C₁₃×#548	C₂²	semidirect
28. C₁₃×#547	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#537	C₂²	semidirect
31. C₁₃×#536	C₂²	semidirect
32. C₁₃×#536	C₂²	semidirect
33. C₁₃×#536	C₂²	semidirect
34. C₁₃×#536	C₂²	semidirect
35. C₁₃×#536	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×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×#124	C₂²	semidirect
42. C₁₃×#525	C₂²	semidirect
43. C₁₃×#525	C₂²	semidirect
44. C₂×C₁₃×#123	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊Q₈	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
61. C₂×C₁₃×#41	D₄	semidirect
122. #62859	C₁₃	direct (N × H)
190. C₂×#585	C₂×C₁₃	semidirect
191. C₂²×2₋¹⁺⁴	C₂×C₁₃	semidirect
192. #3500	C₂×C₁₃	semidirect
193. #3499	C₂×C₁₃	semidirect
194. #3489	C₂×C₁₃	semidirect
195. #3486	C₂×C₁₃	semidirect
196. #3485	C₂×C₁₃	semidirect
197. #3449	C₂×C₁₃	semidirect
198. C₂×#536	C₂×C₁₃	semidirect
199. #3428	C₂×C₁₃	semidirect
245. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
246. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
247. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
249. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
252. C₂²×#41	C₂²×C₁₃	semidirect
253. C₂²×#41	C₂²×C₁₃	semidirect
254. C₂²×#41	C₂²×C₁₃	semidirect
255. C₂³×Q₈	C₂²×C₁₃	semidirect
256. C₂³×Q₈	C₂²×C₁₃	semidirect
257. D₄×Q₈	C₂²×C₁₃	semidirect
258. #548	C₂²×C₁₃	semidirect
259. #547	C₂²×C₁₃	semidirect
260. #546	C₂²×C₁₃	semidirect
261. #537	C₂²×C₁₃	semidirect
262. #536	C₂²×C₁₃	semidirect
263. #536	C₂²×C₁₃	semidirect
264. #536	C₂²×C₁₃	semidirect
265. #536	C₂²×C₁₃	semidirect
266. #536	C₂²×C₁₃	semidirect
267. #535	C₂²×C₁₃	semidirect
268. #535	C₂²×C₁₃	semidirect
269. #534	C₂²×C₁₃	semidirect
270. #532	C₂²×C₁₃	semidirect
271. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
272. C₂×#124	C₂²×C₁₃	semidirect
273. #525	C₂²×C₁₃	semidirect
274. #525	C₂²×C₁₃	semidirect
275. C₂×#123	C₂²×C₁₃	semidirect
276. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
277. #520	C₂²×C₁₃	semidirect
278. #519	C₂²×C₁₃	semidirect
279. #518	C₂²×C₁₃	semidirect
280. C₄×#41	C₂²×C₁₃	semidirect
281. C₂×#117	C₂²×C₁₃	semidirect
310. C₂×#41	D₄×C₁₃	semidirect
444. C₁₃	#62859	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×C₁₃×2₋¹⁺⁴	2
C₁₃×#3500	2
C₁₃×#3499	2
C₁₃×#3489	2
C₁₃×#3486	2
C₁₃×#3485	2
C₁₃×#3449	2
C₂×C₁₃×#536	2
C₁₃×#3428	2
#62859	13

Subgroups — C13×#62859 #15749198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62859 #15749198