Subgroups — C₁₃×#24217 #15710556

Order 3328.

1558 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1983	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂×C₁₃×#124	—	2	8	no	—
17	C₂×C₁₃×#124	—	2	1	no	—
18	C₂×C₁₃×#124	—	2	1	no	—
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
24	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#464	—	2	8	no	—
27	C₁₃×#451	—	2	4	no	—
28	C₁₃×#450	—	2	4	no	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#387	—	2	1	no	—
41	C₁₃×#385	—	2	1	no	—
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
46	C₁₃×#336	C₂²	1	2	yes	complemented
47	C₂⁵×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	4	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	—	2	2	no	—
51	C₂²×Q₈×C₁₃	—	2	2	no	—
52	C₂²×Q₈×C₁₃	—	4	2	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	—	2	2	no	—
58	C₂²×D₄×C₁₃	—	2	2	no	—
59	C₂²×D₄×C₁₃	—	4	2	no	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×Q₁₆	—	2	4	no	—
66	C₂×C₁₃×Q₁₆	—	2	4	no	—
67	C₂×C₁₃×Q₁₆	—	4	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	4	no	—
69	C₂×C₁₃×SD₁₆	—	2	4	no	—
70	C₂×C₁₃×SD₁₆	—	4	2	no	—
71	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×#124	—	2	8	no	—
74	C₁₃×#124	—	2	8	no	—
75	C₁₃×#124	—	2	4	no	—
76	C₁₃×#124	—	2	4	no	—
77	C₁₃×#124	—	2	4	no	—
78	C₁₃×#124	D₄	1	8	yes	—
79	C₁₃×C₂²⋊Q₈	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
81	C₄×Q₈×C₁₃	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	4	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	—	2	4	no	—
104	C₁₃×#103	—	2	4	no	—
105	C₁₃×#103	—	2	4	no	—
106	C₁₃×#103	—	4	2	no	—
107	C₁₃×#102	—	2	4	no	—
108	C₁₃×#102	—	2	4	no	—
109	C₁₃×#102	—	4	2	no	—
110	C₁₃×C₂²⋊C₈	—	2	2	no	—
111	C₁₃×C₂²⋊C₈	—	2	2	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	#24217	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂⁴×C₁₃	—	2	4	no	—
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	4	2	no	—
121	C₂⁴×C₁₃	—	4	2	no	—
122	C₂⁴×C₁₃	—	4	2	no	—
123	C₂⁴×C₁₃	—	4	2	no	—
124	C₂⁴×C₁₃	—	4	2	no	—
125	C₂⁴×C₁₃	—	4	2	no	—
126	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	4	8	no	—
137	C₂×Q₈×C₁₃	—	4	8	no	—
138	C₂×Q₈×C₁₃	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	4	2	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	4	8	no	—
149	C₂×D₄×C₁₃	—	4	8	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	4	2	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	#41	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×Q₁₆	—	4	8	no	—
178	C₁₃×SD₁₆	—	4	8	no	—
179	C₂×C₈×C₁₃	—	2	2	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	4	2	no	—
190	C₁₃×C₄⋊C₄	—	4	2	no	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	8	no	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₁₃×C₂²⋊C₄	—	4	2	no	—
198	C₄²×C₁₃	—	2	2	no	—
199	C₄²×C₁₃	—	2	2	no	—
200	C₄²×C₁₃	—	2	2	no	—
201	C₄²×C₁₃	—	4	2	no	—
202	C₄²×C₁₃	—	4	2	no	—
203	C₄²×C₁₃	C₂×D₄	1	4	yes	—
204	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
205	C₂×#464	C₂×C₁₃	1	2	yes	complemented
206	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
208	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2042	C₂×C₁₃	1	2	yes	complemented
210	#2015	C₂×C₁₃	1	2	yes	complemented
211	#1983	C₂×C₁₃	1	2	yes	complemented
212	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1786	C₂×C₁₃	1	1	yes	characteristic
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	1	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	4	8	no	—
221	C₂³×C₁₃	—	4	8	no	—
222	C₂³×C₁₃	—	4	8	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	4	2	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	—	8	4	no	—
230	C₂³×C₁₃	—	8	4	no	—
231	C₂³×C₁₃	—	8	4	no	—
232	C₂³×C₁₃	—	8	4	no	—
233	C₂³×C₁₃	#121	1	2	yes	—
234	C₂³×C₁₃	#135	1	2	yes	—
235	C₂³×C₁₃	#137	1	2	yes	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	4	no	—
238	Q₈×C₁₃	—	2	4	no	—
239	Q₈×C₁₃	—	2	4	no	—
240	Q₈×C₁₃	—	4	8	no	—
241	Q₈×C₁₃	—	4	2	no	—
242	Q₈×C₁₃	—	4	2	no	—
243	Q₈×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	4	8	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	8	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	#120	1	2	yes	—
282	C₂×C₄×C₁₃	#120	1	2	yes	—
283	C₂×C₄×C₁₃	#121	1	2	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
288	C₈×C₁₃	—	4	2	no	—
289	C₈×C₁₃	—	4	2	no	—
290	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
293	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
294	C₂×#124	—	2	8	no	—
295	C₂×#124	—	2	1	no	—
296	C₂×#124	—	2	1	no	—
297	C₂×#124	C₂²×C₁₃	1	2	yes	—
298	C₂×#124	C₂²×C₁₃	1	2	yes	—
299	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
301	C₂²×C₂²⋊C₄	—	2	1	no	—
302	C₂²×C₂²⋊C₄	—	2	1	no	—
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#464	—	2	8	no	—
305	#451	—	2	4	no	—
306	#450	—	2	4	no	—
307	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
308	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
309	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
310	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
311	C₂×#102	C₂²×C₁₃	1	2	yes	—
312	C₂×#102	C₂²×C₁₃	1	2	yes	—
313	C₂×#102	C₂²×C₁₃	1	2	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	#387	—	2	1	no	—
319	#385	—	2	1	no	—
320	#380	C₂²×C₁₃	1	1	yes	characteristic
321	C₄×C₄⋊C₄	—	2	1	no	—
322	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
323	C₄×C₂²⋊C₄	—	2	1	no	—
324	#336	C₂²×C₁₃	1	2	yes	complemented
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	4	4	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	8	16	no	—
335	C₂²×C₁₃	—	8	2	no	—
336	C₂²×C₁₃	—	8	2	no	—
337	C₂²×C₁₃	—	8	2	no	—
338	C₂²×C₁₃	—	8	2	no	—
339	C₂²×C₁₃	#464	1	4	yes	complemented
340	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
341	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
342	C₂²×C₁₃	#535	1	1	yes	characteristic
343	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
344	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
345	C₂²×C₁₃	#575	1	1	yes	characteristic
346	C₂²×C₁₃	#575	1	1	yes	characteristic
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	4	4	no	—
351	C₄×C₁₃	—	4	2	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	D₄²	1	2	yes	—
358	C₄×C₁₃	#546	1	2	yes	—
359	C₂⁵	—	2	1	no	—
360	C₂²×Q₈	—	2	4	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂²×Q₈	—	2	2	no	—
363	C₂²×Q₈	—	2	2	no	—
364	C₂²×Q₈	—	4	2	no	—
365	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	—	2	2	no	—
370	C₂²×D₄	—	2	2	no	—
371	C₂²×D₄	—	4	2	no	—
372	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×Q₁₆	—	2	4	no	—
378	C₂×Q₁₆	—	2	4	no	—
379	C₂×Q₁₆	—	4	2	no	—
380	C₂×SD₁₆	—	2	4	no	—
381	C₂×SD₁₆	—	2	4	no	—
382	C₂×SD₁₆	—	4	2	no	—
383	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
384	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
385	#124	—	2	8	no	—
386	#124	—	2	8	no	—
387	#124	—	2	4	no	—
388	#124	—	2	4	no	—
389	#124	—	2	4	no	—
390	#124	D₄×C₁₃	1	8	yes	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
393	C₄×Q₈	—	2	4	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	8	no	—
401	C₂×C₂²⋊C₄	—	2	8	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	—	2	2	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₄²	—	2	4	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	C₄⋊C₈	—	2	4	no	—
416	#103	—	2	4	no	—
417	#103	—	2	4	no	—
418	#103	—	4	2	no	—
419	#102	—	2	4	no	—
420	#102	—	2	4	no	—
421	#102	—	4	2	no	—
422	C₂²⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	—	2	2	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	C₂×C₁₃	—	2	4	no	—
430	C₂×C₁₃	—	8	4	no	—
431	C₂×C₁₃	#2408	1	1	yes	characteristic
432	C₂×C₁₃	#3002	1	1	yes	characteristic
433	C₂×C₁₃	#3007	1	1	yes	characteristic
434	C₂×C₁₃	C₂×#464	1	1	yes	characteristic
435	C₂×C₁₃	#3040	1	1	yes	characteristic
436	C₂×C₁₃	#3211	1	1	yes	characteristic
437	C₂×C₁₃	#3215	1	1	yes	characteristic
438	C₂⁴	—	2	4	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	4	2	no	—
441	C₂⁴	—	4	2	no	—
442	C₂⁴	—	4	2	no	—
443	C₂⁴	—	4	2	no	—
444	C₂⁴	—	4	2	no	—
445	C₂⁴	—	4	2	no	—
446	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	4	8	no	—
457	C₂×Q₈	—	4	8	no	—
458	C₂×Q₈	—	4	2	no	—
459	C₂×Q₈	—	4	2	no	—
460	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
461	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	4	8	no	—
469	C₂×D₄	—	4	8	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
495	C₂²×C₄	C₁₃×#41	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	Q₁₆	—	4	8	no	—
498	SD₁₆	—	4	8	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
512	C₂²⋊C₄	—	2	8	no	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	4	2	no	—
522	C₄²	—	4	2	no	—
523	C₄²	C₂×D₄×C₁₃	1	4	yes	—
524	C₁₃	#24217	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	4	8	no	—
531	C₂³	—	4	8	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	8	4	no	—
540	C₂³	—	8	4	no	—
541	C₂³	—	8	4	no	—
542	C₂³	—	8	4	no	—
543	C₂³	C₁₃×#121	1	2	yes	—
544	C₂³	C₁₃×#135	1	2	yes	—
545	C₂³	C₁₃×#137	1	2	yes	—
546	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
547	Q₈	—	2	4	no	—
548	Q₈	—	2	4	no	—
549	Q₈	—	2	4	no	—
550	Q₈	—	4	8	no	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	2	no	—
553	Q₈	—	4	2	no	—
554	D₄	—	2	4	no	—
555	D₄	—	2	4	no	—
556	D₄	—	4	8	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	8	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	C₁₃×#120	1	2	yes	—
592	C₂×C₄	C₁₃×#120	1	2	yes	—
593	C₂×C₄	C₁₃×#121	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
596	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
597	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
598	C₈	—	4	2	no	—
599	C₈	—	4	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	8	16	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	—	8	2	no	—
613	C₂²	—	8	2	no	—
614	C₂²	C₁₃×#464	1	4	yes	complemented
615	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
616	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
617	C₂²	C₁₃×#535	1	1	yes	characteristic
618	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
619	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
620	C₂²	C₁₃×#575	1	1	yes	characteristic
621	C₂²	C₁₃×#575	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	4	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	D₄²×C₁₃	1	2	yes	—
633	C₄	C₁₃×#546	1	2	yes	—
634	C₂	—	2	4	no	—
635	C₂	—	8	4	no	—
636	C₂	C₁₃×#2408	1	1	yes	characteristic
637	C₂	C₁₃×#3002	1	1	yes	characteristic
638	C₂	C₁₃×#3007	1	1	yes	characteristic
639	C₂	C₂×C₁₃×#464	1	1	yes	characteristic
640	C₂	C₁₃×#3040	1	1	yes	characteristic
641	C₂	C₁₃×#3211	1	1	yes	characteristic
642	C₂	C₁₃×#3215	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#464	C₂	semidirect
3. C₂×C₁₃×#451	C₂	semidirect
5. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#2015	C₂	semidirect
8. C₁₃×#1983	C₂	semidirect
9. C₁₃×#1797	C₂	semidirect
10. C₁₃×#1787	C₂	semidirect
14. C₂²×C₁₃×Q₁₆	C₂²	semidirect
22. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
30. C₂×C₁₃×#103	C₂²	semidirect
31. C₂×C₁₃×#103	C₂²	semidirect
32. C₂×C₁₃×#103	C₂²	semidirect
38. C₁₃×#391	C₂²	semidirect
39. C₁₃×#389	C₂²	semidirect
44. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
46. C₁₃×#336	C₂²	semidirect
117. #24217	C₁₃	direct (N × H)
205. C₂×#464	C₂×C₁₃	semidirect
206. C₂×#451	C₂×C₁₃	semidirect
208. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
209. #2042	C₂×C₁₃	semidirect
210. #2015	C₂×C₁₃	semidirect
211. #1983	C₂×C₁₃	semidirect
212. #1797	C₂×C₁₃	semidirect
213. #1787	C₂×C₁₃	semidirect
292. C₂²×Q₁₆	C₂²×C₁₃	semidirect
300. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
307. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
308. C₂×#103	C₂²×C₁₃	semidirect
309. C₂×#103	C₂²×C₁₃	semidirect
310. C₂×#103	C₂²×C₁₃	semidirect
316. #391	C₂²×C₁₃	semidirect
317. #389	C₂²×C₁₃	semidirect
322. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
324. #336	C₂²×C₁₃	semidirect
339. C₂²×C₁₃	#464	semidirect
524. C₁₃	#24217	direct (N × H)
614. C₂²	C₁₃×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#124	2
C₂×C₁₃×#464	2
C₂×C₁₃×#451	2
C₂×C₁₃×#450	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2042	2
C₁₃×#2015	2
C₁₃×#1983	2
C₁₃×#1797	2
C₁₃×#1787	2
C₁₃×#1786	2
#24217	13

Subgroups — C13×#24217 #15710556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24217 #15710556