Subgroups — C₁₃×#17704 #15704043

Order 3328.

1298 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1547	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1546	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1545	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1540	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#41	—	2	1	no	—
9	C₂²×C₁₃×M₁₆	—	2	1	no	—
10	C₁₃×#532	—	2	1	no	—
11	C₁₃×#532	—	2	1	no	—
12	C₁₃×#532	—	2	1	no	—
13	C₁₃×#532	—	2	1	no	—
14	C₁₃×#532	C₄	1	2	yes	—
15	C₁₃×#532	C₄	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#124	—	2	1	no	—
21	C₂×C₁₃×#121	—	2	1	no	—
22	C₂×C₁₃×#121	C₄	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	—	2	1	no	—
24	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#431	—	2	1	no	—
27	C₁₃×#431	—	2	1	no	—
28	C₁₃×#431	C₂²	1	2	yes	—
29	C₁₃×#431	C₂²	1	2	yes	complemented
30	C₁₃×#423	—	2	1	no	—
31	C₁₃×#423	—	2	1	no	—
32	C₁₃×#423	C₂²	1	2	yes	—
33	C₁₃×#423	C₂²	1	2	yes	complemented
34	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
37	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
38	C₂×C₄×C₈×C₁₃	—	2	1	no	—
39	C₁₃×#332	C₂²	1	8	yes	complemented
40	C₁₃×#331	C₂²	1	8	yes	complemented
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	4	4	no	—
46	C₂×C₁₃×#41	—	4	4	no	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	—	4	4	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₃×#127	—	2	1	no	—
66	C₁₃×#127	—	2	1	no	—
67	C₁₃×#127	C₂×C₄	1	2	yes	—
68	C₁₃×#127	C₂³	1	2	yes	—
69	C₁₃×#124	—	2	2	no	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	2	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#121	—	2	2	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	C₂×C₄	1	4	yes	—
80	C₁₃×#121	C₂×C₄	1	4	yes	—
81	C₄×D₄×C₁₃	—	2	2	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
88	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×C₄⋊C₈	—	2	2	no	—
107	C₁₃×C₄⋊C₈	—	2	2	no	—
108	C₁₃×C₄⋊C₈	—	2	2	no	—
109	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊C₈	—	2	2	no	—
112	C₁₃×C₂²⋊C₈	—	2	2	no	—
113	C₄×C₈×C₁₃	—	2	2	no	—
114	C₄×C₈×C₁₃	—	2	2	no	—
115	#17704	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	2	no	—
117	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₁₃×#41	—	4	8	no	—
119	C₁₃×#41	—	4	8	no	—
120	C₁₃×#41	—	4	4	no	—
121	C₁₃×#41	—	4	4	no	—
122	C₁₃×#41	—	4	4	no	—
123	C₁₃×#41	—	4	4	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	4	2	no	—
127	C₂×Q₈×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	4	4	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	—	4	8	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	4	2	no	—
140	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	4	2	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	D₈	1	4	yes	—
157	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₁₃×M₁₆	—	4	4	no	—
168	C₁₃×M₁₆	—	4	4	no	—
169	C₂×C₈×C₁₃	—	2	4	no	—
170	C₂×C₈×C₁₃	—	2	4	no	—
171	C₂×C₈×C₁₃	—	4	4	no	—
172	C₂×C₈×C₁₃	—	4	4	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	2	4	no	—
179	C₁₃×C₂²⋊C₄	—	2	4	no	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
186	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
187	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
189	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
198	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#1547	C₂×C₁₃	1	4	yes	complemented
201	#1546	C₂×C₁₃	1	2	yes	complemented
202	#1545	C₂×C₁₃	1	2	yes	complemented
203	#1540	C₂×C₁₃	1	4	yes	complemented
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	4	1	no	—
206	C₂³×C₁₃	—	4	1	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	—	4	4	no	—
209	C₂³×C₁₃	—	4	4	no	—
210	C₂³×C₁₃	#102	1	4	yes	—
211	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	4	2	no	—
216	Q₈×C₁₃	—	4	4	no	—
217	D₄×C₁₃	—	4	4	no	—
218	D₄×C₁₃	—	4	4	no	—
219	D₄×C₁₃	—	4	8	no	—
220	D₄×C₁₃	—	4	8	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	4	2	no	—
223	D₄×C₁₃	—	4	4	no	—
224	D₄×C₁₃	—	4	4	no	—
225	D₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	#102	1	4	yes	—
243	C₂×C₄×C₁₃	#102	1	4	yes	—
244	C₂×C₄×C₁₃	#102	1	4	yes	—
245	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
256	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
258	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
259	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
260	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₁₃	—	4	4	no	—
264	C₈×C₁₃	—	4	4	no	—
265	C₂²×#41	—	2	1	no	—
266	C₂²×M₁₆	—	2	1	no	—
267	#532	—	2	1	no	—
268	#532	—	2	1	no	—
269	#532	—	2	1	no	—
270	#532	—	2	1	no	—
271	#532	C₄×C₁₃	1	2	yes	—
272	#532	C₄×C₁₃	1	2	yes	—
273	#532	C₂²×C₁₃	1	2	yes	—
274	#532	C₂²×C₁₃	1	2	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#124	—	2	1	no	—
278	C₂×#121	—	2	1	no	—
279	C₂×#121	C₄×C₁₃	1	2	yes	—
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	—
282	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
283	#431	—	2	1	no	—
284	#431	—	2	1	no	—
285	#431	C₂²×C₁₃	1	2	yes	—
286	#431	C₂²×C₁₃	1	2	yes	complemented
287	#423	—	2	1	no	—
288	#423	—	2	1	no	—
289	#423	C₂²×C₁₃	1	2	yes	—
290	#423	C₂²×C₁₃	1	2	yes	complemented
291	C₂×C₄⋊C₈	—	2	1	no	—
292	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
293	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
294	C₂×C₂²⋊C₈	—	2	1	no	—
295	C₂×C₄×C₈	—	2	1	no	—
296	#332	C₂²×C₁₃	1	8	yes	complemented
297	#331	C₂²×C₁₃	1	8	yes	complemented
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	8	8	no	—
309	C₂²×C₁₃	C₂×#102	1	2	yes	—
310	C₂²×C₁₃	C₂×#102	1	2	yes	—
311	C₂²×C₁₃	C₂×#102	1	2	yes	—
312	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
313	C₄×C₁₃	—	2	1	no	—
314	C₄×C₁₃	—	2	1	no	—
315	C₄×C₁₃	—	2	1	no	—
316	C₄×C₁₃	—	2	1	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	#413	1	2	yes	—
321	C₄×C₁₃	C₂×#102	1	2	yes	—
322	C₄×C₁₃	C₂×#102	1	2	yes	—
323	C₄×C₁₃	C₂×#102	1	2	yes	—
324	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
325	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
326	C₄×C₁₃	#575	1	2	yes	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	4	4	no	—
332	C₂×#41	—	4	4	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
338	C₂³×C₄	—	2	2	no	—
339	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
340	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
341	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
342	C₂×M₁₆	—	2	2	no	—
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	4	4	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
350	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
351	#127	—	2	1	no	—
352	#127	—	2	1	no	—
353	#127	C₂×C₄×C₁₃	1	2	yes	—
354	#127	C₂³×C₁₃	1	2	yes	—
355	#124	—	2	2	no	—
356	#124	—	2	2	no	—
357	#124	—	2	2	no	—
358	#124	—	2	2	no	—
359	#121	—	2	2	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	C₂×C₄×C₁₃	1	4	yes	—
366	#121	C₂×C₄×C₁₃	1	4	yes	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
374	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	C₄⋊C₈	—	2	2	no	—
392	C₄⋊C₈	—	2	2	no	—
393	C₄⋊C₈	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
396	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
397	C₂²⋊C₈	—	2	2	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	C₄×C₈	—	2	2	no	—
400	C₄×C₈	—	2	2	no	—
401	C₂×C₁₃	—	2	2	no	—
402	C₂×C₁₃	—	2	2	no	—
403	C₂×C₁₃	—	2	2	no	—
404	C₂×C₁₃	—	8	4	no	—
405	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
406	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
407	C₂×C₁₃	#2896	1	1	yes	characteristic
408	C₂⁴	—	2	2	no	—
409	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
410	#41	—	4	8	no	—
411	#41	—	4	8	no	—
412	#41	—	4	4	no	—
413	#41	—	4	4	no	—
414	#41	—	4	4	no	—
415	#41	—	4	4	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	8	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	8	no	—
439	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
440	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
441	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
442	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
443	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
444	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
445	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
446	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
447	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
448	C₂²×C₄	C₁₃×D₈	1	4	yes	—
449	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
450	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	M₁₆	—	4	4	no	—
460	M₁₆	—	4	4	no	—
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	2	4	no	—
463	C₂×C₈	—	4	4	no	—
464	C₂×C₈	—	4	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
474	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
475	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
476	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
477	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
478	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
479	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
480	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
481	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₁₃	#17704	1	1	yes	characteristic, direct product factor, Sylow
490	C₂³	—	2	4	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	4	no	—
496	C₂³	C₁₃×#102	1	4	yes	—
497	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
498	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
499	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
500	Q₈	—	4	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	4	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	C₁₃×#102	1	4	yes	—
529	C₂×C₄	C₁₃×#102	1	4	yes	—
530	C₂×C₄	C₁₃×#102	1	4	yes	—
531	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
533	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
534	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
535	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
536	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
537	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
538	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
539	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
540	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
541	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
542	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
543	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
544	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
545	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
546	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
549	C₈	—	4	4	no	—
550	C₈	—	4	4	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	8	8	no	—
562	C₂²	C₂×C₁₃×#102	1	2	yes	—
563	C₂²	C₂×C₁₃×#102	1	2	yes	—
564	C₂²	C₂×C₁₃×#102	1	2	yes	—
565	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	4	4	no	—
573	C₄	C₁₃×#413	1	2	yes	—
574	C₄	C₂×C₁₃×#102	1	2	yes	—
575	C₄	C₂×C₁₃×#102	1	2	yes	—
576	C₄	C₂×C₁₃×#102	1	2	yes	—
577	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
578	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
579	C₄	C₁₃×#575	1	2	yes	—
580	C₂	—	2	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	8	4	no	—
584	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
585	C₂	C₂²×C₁₃×#102	1	1	yes	characteristic
586	C₂	C₁₃×#2896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#431	C₂	semidirect
3. C₂×C₁₃×#423	C₂	semidirect
4. C₁₃×#1547	C₂	semidirect
5. C₁₃×#1546	C₂	semidirect
6. C₁₃×#1545	C₂	semidirect
7. C₁₃×#1540	C₂	semidirect
29. C₁₃×#431	C₂²	semidirect
33. C₁₃×#423	C₂²	semidirect
35. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
36. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
39. C₁₃×#332	C₂²	semidirect
40. C₁₃×#331	C₂²	semidirect
115. #17704	C₁₃	direct (N × H)
198. C₂×#431	C₂×C₁₃	semidirect
199. C₂×#423	C₂×C₁₃	semidirect
200. #1547	C₂×C₁₃	semidirect
201. #1546	C₂×C₁₃	semidirect
202. #1545	C₂×C₁₃	semidirect
203. #1540	C₂×C₁₃	semidirect
286. #431	C₂²×C₁₃	semidirect
290. #423	C₂²×C₁₃	semidirect
292. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
293. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
296. #332	C₂²×C₁₃	semidirect
297. #331	C₂²×C₁₃	semidirect
489. C₁₃	#17704	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×#532	2
C₂×C₁₃×#431	2
C₂×C₁₃×#423	2
C₁₃×#1547	2
C₁₃×#1546	2
C₁₃×#1545	2
C₁₃×#1540	2
#17704	13

Subgroups — C13×#17704 #15704043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17704 #15704043