Subgroups — C₁₃×#17653 #15703992

Order 3328.

964 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1532	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1531	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1528	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1526	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1524	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1524	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#330	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#557	C₄	1	1	yes	characteristic
14	C₁₃×#554	C₄	1	1	yes	characteristic
15	C₁₃×#554	C₄	1	1	yes	characteristic
16	C₁₃×#553	C₄	1	2	yes	—
17	C₁₃×#552	—	2	2	no	—
18	C₁₃×#552	—	2	1	no	—
19	C₁₃×#552	C₄	1	2	yes	—
20	C₁₃×#547	—	2	1	no	—
21	C₁₃×#547	C₄	1	1	yes	characteristic
22	C₁₃×#541	—	2	1	no	—
23	C₁₃×#539	—	2	2	no	—
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#529	C₂²	1	1	yes	characteristic
26	C₁₃×#529	C₂²	1	2	yes	—
27	C₂×C₁₃×#125	C₂²	1	2	yes	—
28	C₁₃×#520	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₁₃×#446	—	2	1	no	—
31	C₁₃×#435	—	2	2	no	—
32	C₈×D₄×C₁₃	—	2	1	no	—
33	C₁₃×#432	C₂²	1	2	yes	—
34	C₁₃×#432	C₂²	1	1	yes	characteristic
35	C₁₃×#405	—	2	1	no	—
36	C₁₃×#405	—	2	2	no	—
37	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#97	C₂²	1	2	yes	—
41	C₂×C₁₃×#97	C₂²	1	2	yes	—
42	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
43	C₁₃×#330	C₂²	1	1	yes	characteristic
44	C₁₃×#330	C₂²	1	2	yes	—
45	C₁₃×#330	C₂²	1	2	yes	—
46	C₁₃×#330	C₂²	1	2	yes	—
47	C₁₃×#330	C₂²	1	1	yes	characteristic
48	C₁₃×#330	C₂²	1	2	yes	—
49	C₁₃×#330	C₂²	1	2	yes	—
50	C₁₃×#329	C₂²	1	1	yes	characteristic
51	C₁₃×#329	C₂²	1	2	yes	—
52	C₁₃×#329	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₁₃×#131	—	2	8	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#126	—	2	2	no	—
66	C₁₃×#126	—	2	2	no	—
67	C₁₃×#126	—	2	2	no	—
68	C₁₃×#126	—	2	1	no	—
69	C₁₃×#125	—	2	2	no	—
70	C₁₃×#125	—	2	2	no	—
71	C₁₃×#125	—	2	1	no	—
72	C₁₃×#125	—	2	2	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	C₂×C₄	1	2	yes	—
75	C₁₃×#125	C₂×C₄	1	2	yes	—
76	C₁₃×#125	C₂³	1	1	yes	characteristic
77	C₁₃×#125	C₂³	1	2	yes	—
78	C₁₃×#124	C₂³	1	1	yes	characteristic
79	C₁₃×#123	—	2	2	no	—
80	C₁₃×#123	—	2	1	no	—
81	C₁₃×#123	—	2	2	no	—
82	C₁₃×#123	—	2	2	no	—
83	C₁₃×#123	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
91	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	C₂×C₄	1	2	yes	—
94	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	—	2	2	no	—
106	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
107	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
108	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
111	C₄×D₄×C₁₃	D₄	1	2	yes	—
112	C₁₃×#117	—	2	2	no	—
113	C₁₃×#117	—	2	1	no	—
114	C₁₃×#117	—	2	2	no	—
115	C₁₃×#117	C₂×C₄	1	2	yes	—
116	C₁₃×#117	D₄	1	1	yes	characteristic
117	C₁₃×#117	D₄	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	—	2	2	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×#97	—	2	2	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	—	2	2	no	—
132	C₁₃×#97	C₂³	1	1	yes	characteristic
133	C₁₃×#97	C₂³	1	1	yes	characteristic
134	C₁₃×#97	C₂³	1	1	yes	characteristic
135	C₁₃×#97	C₂³	1	2	yes	—
136	C₁₃×#97	C₂³	1	2	yes	—
137	C₁₃×#97	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	—	2	2	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	#17653	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₁₃×#41	—	2	4	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
151	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₁₃×M₁₆	—	2	8	no	—
164	C₁₃×M₁₆	—	2	4	no	—
165	C₁₃×M₁₆	—	4	2	no	—
166	C₂×C₈×C₁₃	—	2	8	no	—
167	C₂×C₈×C₁₃	—	2	4	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	4	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	1	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
209	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
211	C₄²×C₁₃	—	2	2	no	—
212	C₄²×C₁₃	—	2	2	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
215	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₃	C₂×D₄	1	2	yes	—
220	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
221	#3515	C₂×C₁₃	1	1	yes	characteristic
222	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1532	C₂×C₁₃	1	2	yes	complemented
225	#1531	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1528	C₂×C₁₃	1	2	yes	complemented
228	#1526	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1524	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1524	C₂×C₁₃	1	2	yes	complemented
231	C₂×#330	C₂×C₁₃	1	2	yes	complemented
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	2	no	—
238	Q₈×C₁₃	—	8	1	no	—
239	D₄×C₁₃	—	2	4	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	4	no	—
242	D₄×C₁₃	—	8	1	no	—
243	D₄×C₁₃	#104	1	4	yes	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	8	2	no	—
258	C₂×C₄×C₁₃	—	8	2	no	—
259	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	2	4	no	—
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	—	4	2	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₂×#131	—	2	1	no	—
275	#557	C₄×C₁₃	1	1	yes	characteristic
276	#554	C₄×C₁₃	1	1	yes	characteristic
277	#554	C₄×C₁₃	1	1	yes	characteristic
278	#553	C₄×C₁₃	1	2	yes	—
279	#552	—	2	2	no	—
280	#552	—	2	1	no	—
281	#552	C₄×C₁₃	1	2	yes	—
282	#547	—	2	1	no	—
283	#547	C₄×C₁₃	1	1	yes	characteristic
284	#541	—	2	1	no	—
285	#539	—	2	2	no	—
286	#533	C₂²×C₁₃	1	1	yes	characteristic
287	#529	C₂²×C₁₃	1	1	yes	characteristic
288	#529	C₂²×C₁₃	1	2	yes	—
289	C₂×#125	C₂²×C₁₃	1	2	yes	—
290	#520	—	2	1	no	—
291	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
292	#446	—	2	1	no	—
293	#435	—	2	2	no	—
294	C₈×D₄	—	2	1	no	—
295	#432	C₂²×C₁₃	1	2	yes	—
296	#432	C₂²×C₁₃	1	1	yes	characteristic
297	#405	—	2	1	no	—
298	#405	—	2	2	no	—
299	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
300	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
301	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#97	C₂²×C₁₃	1	2	yes	—
303	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#97	C₂²×C₁₃	1	2	yes	—
305	#330	C₂²×C₁₃	1	1	yes	characteristic
306	#330	C₂²×C₁₃	1	2	yes	—
307	#330	C₂²×C₁₃	1	2	yes	—
308	#330	C₂²×C₁₃	1	2	yes	—
309	#330	C₂²×C₁₃	1	1	yes	characteristic
310	#330	C₂²×C₁₃	1	2	yes	—
311	#330	C₂²×C₁₃	1	2	yes	—
312	#329	C₂²×C₁₃	1	1	yes	characteristic
313	#329	C₂²×C₁₃	1	2	yes	—
314	#329	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	C₂×#104	1	4	yes	—
324	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	C₂×#104	1	2	yes	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
341	#131	—	2	8	no	—
342	C₂×M₁₆	—	2	2	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	1	no	—
347	C₂²×C₈	—	2	2	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
350	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
351	#126	—	2	2	no	—
352	#126	—	2	2	no	—
353	#126	—	2	2	no	—
354	#126	—	2	1	no	—
355	#125	—	2	2	no	—
356	#125	—	2	2	no	—
357	#125	—	2	1	no	—
358	#125	—	2	2	no	—
359	#125	—	2	2	no	—
360	#125	C₂×C₄×C₁₃	1	2	yes	—
361	#125	C₂×C₄×C₁₃	1	2	yes	—
362	#125	C₂³×C₁₃	1	1	yes	characteristic
363	#125	C₂³×C₁₃	1	2	yes	—
364	#124	C₂³×C₁₃	1	1	yes	characteristic
365	#123	—	2	2	no	—
366	#123	—	2	1	no	—
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
377	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
378	#121	—	2	2	no	—
379	#121	C₂×C₄×C₁₃	1	2	yes	—
380	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
385	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
386	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
387	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
393	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
394	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
395	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
396	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
397	C₄×D₄	D₄×C₁₃	1	2	yes	—
398	#117	—	2	2	no	—
399	#117	—	2	1	no	—
400	#117	—	2	2	no	—
401	#117	C₂×C₄×C₁₃	1	2	yes	—
402	#117	D₄×C₁₃	1	1	yes	characteristic
403	#117	D₄×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	#97	—	2	2	no	—
416	#97	—	2	1	no	—
417	#97	—	2	2	no	—
418	#97	C₂³×C₁₃	1	1	yes	characteristic
419	#97	C₂³×C₁₃	1	1	yes	characteristic
420	#97	C₂³×C₁₃	1	1	yes	characteristic
421	#97	C₂³×C₁₃	1	2	yes	—
422	#97	C₂³×C₁₃	1	2	yes	—
423	#97	C₂³×C₁₃	1	1	yes	characteristic
424	C₄×C₈	—	2	2	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₂×C₁₃	—	2	4	no	—
428	C₂×C₁₃	—	4	1	no	—
429	C₂×C₁₃	—	8	1	no	—
430	C₂×C₁₃	#2889	1	1	yes	characteristic
431	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
432	C₂×C₁₃	#2901	1	1	yes	characteristic
433	#41	—	2	4	no	—
434	#41	—	4	4	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
438	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
442	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
449	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	M₁₆	—	2	8	no	—
455	M₁₆	—	2	4	no	—
456	M₁₆	—	4	2	no	—
457	C₂×C₈	—	2	8	no	—
458	C₂×C₈	—	2	4	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	4	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
483	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
484	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
485	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
486	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
489	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
500	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
501	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
506	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₁₃	1	2	yes	—
508	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₁₃	1	2	yes	—
511	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
512	C₁₃	#17653	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	1	no	—
514	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
515	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	8	1	no	—
520	D₄	—	2	4	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	4	no	—
523	D₄	—	8	1	no	—
524	D₄	C₁₃×#104	1	4	yes	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
542	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
543	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
544	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
545	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
550	C₈	—	2	4	no	—
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	4	2	no	—
554	C₈	—	4	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×C₁₃×#104	1	4	yes	—
564	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	2	no	—
578	C₄	C₂×C₁₃×#104	1	2	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	4	1	no	—
581	C₂	—	8	1	no	—
582	C₂	C₁₃×#2889	1	1	yes	characteristic
583	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
584	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2970	C₂	semidirect
3. C₁₃×#2875	C₂	semidirect
4. C₁₃×#1532	C₂	semidirect
5. C₁₃×#1531	C₂	semidirect
6. C₁₃×#1529	C₂	semidirect
7. C₁₃×#1528	C₂	semidirect
8. C₁₃×#1526	C₂	semidirect
9. C₁₃×#1524	C₂	semidirect
10. C₁₃×#1524	C₂	semidirect
11. C₂×C₁₃×#330	C₂	semidirect
141. #17653	C₁₃	direct (N × H)
222. #2970	C₂×C₁₃	semidirect
223. #2875	C₂×C₁₃	semidirect
224. #1532	C₂×C₁₃	semidirect
225. #1531	C₂×C₁₃	semidirect
226. #1529	C₂×C₁₃	semidirect
227. #1528	C₂×C₁₃	semidirect
228. #1526	C₂×C₁₃	semidirect
229. #1524	C₂×C₁₃	semidirect
230. #1524	C₂×C₁₃	semidirect
231. C₂×#330	C₂×C₁₃	semidirect
512. C₁₃	#17653	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3515	2
C₁₃×#2970	2
C₁₃×#2875	2
C₁₃×#1532	2
C₁₃×#1531	2
C₁₃×#1529	2
C₁₃×#1528	2
C₁₃×#1526	2
C₁₃×#1524	2
C₂×C₁₃×#330	2
#17653	13

Subgroups — C13×#17653 #15703992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17653 #15703992