Subgroups — C₁₃×#17681 #15704020

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1535	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1533	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1530	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1529	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1527	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#559	C₄	1	1	yes	characteristic
13	C₁₃×#556	C₄	1	1	yes	characteristic
14	C₁₃×#555	—	2	1	no	—
15	C₁₃×#551	—	2	2	no	—
16	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
17	C₁₃×#548	C₄	1	2	yes	—
18	C₁₃×#546	—	2	1	no	—
19	C₁₃×#546	C₄	1	2	yes	—
20	D₄²×C₁₃	C₄	1	1	yes	characteristic
21	C₁₃×#542	—	2	1	no	—
22	C₁₃×#538	—	2	2	no	—
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₁₃×#529	C₂²	1	2	yes	—
26	C₂×C₁₃×#124	C₂²	1	2	yes	—
27	C₁₃×#518	—	2	1	no	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₁₃	—	2	1	no	—
30	C₁₃×#436	—	2	1	no	—
31	C₁₃×#436	—	2	2	no	—
32	C₁₃×#433	—	2	2	no	—
33	C₁₃×#432	C₂²	1	2	yes	complemented
34	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#432	C₂²	1	2	yes	complemented
36	C₁₃×#432	C₂²	1	2	yes	complemented
37	C₁₃×#424	—	2	1	no	—
38	C₁₃×#408	—	2	1	no	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#330	C₂²	1	2	yes	complemented
46	C₁₃×#329	C₂²	1	1	yes	characteristic
47	C₁₃×#329	C₂²	1	1	yes	characteristic
48	C₁₃×#329	C₂²	1	2	yes	—
49	C₁₃×#329	C₂²	1	2	yes	complemented
50	C₁₃×#329	C₂²	1	2	yes	complemented
51	C₁₃×#329	C₂²	1	2	yes	complemented
52	C₁₃×#329	C₂²	1	2	yes	complemented
53	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#126	—	2	2	no	—
66	C₁₃×#126	—	2	2	no	—
67	C₁₃×#126	—	2	1	no	—
68	C₁₃×#125	C₂³	1	1	yes	characteristic
69	C₁₃×#124	—	2	1	no	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	C₂×C₄	1	2	yes	—
74	C₁₃×#124	C₂×C₄	1	2	yes	—
75	C₁₃×#124	C₂³	1	1	yes	characteristic
76	C₁₃×#124	C₂³	1	2	yes	—
77	C₁₃×#123	—	2	1	no	—
78	C₁₃×#123	—	2	2	no	—
79	C₁₃×#123	—	2	2	no	—
80	C₁₃×#123	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
85	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	C₂×C₄	1	2	yes	—
92	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#120	—	2	2	no	—
94	C₁₃×#120	—	2	2	no	—
95	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
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	1	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	1	no	—
113	C₁₃×#117	—	2	1	no	—
114	C₁₃×#117	—	2	2	no	—
115	C₁₃×#117	D₄	1	1	yes	characteristic
116	C₁₃×#117	D₄	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	—	2	2	no	—
123	C₁₃×C₄⋊C₈	—	2	2	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	2	no	—
126	C₁₃×C₂²⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	—	2	2	no	—
128	C₁₃×C₂²⋊C₈	—	2	2	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	C₂³	1	1	yes	characteristic
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	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	2	no	—
140	#17681	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	2	no	—
142	C₁₃×#41	—	4	2	no	—
143	C₁₃×#41	—	8	2	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	8	2	no	—
146	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	4	4	no	—
156	C₂×D₄×C₁₃	—	8	2	no	—
157	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
159	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₁₃×M₁₆	—	4	4	no	—
172	C₁₃×M₁₆	—	4	2	no	—
173	C₁₃×M₁₆	—	4	2	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	4	2	no	—
181	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
208	C₁₃×C₂²⋊C₄	—	2	2	no	—
209	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
210	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
211	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
217	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₁₃	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃	C₂×D₄	1	2	yes	—
220	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
221	#3514	C₂×C₁₃	1	1	yes	characteristic
222	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1535	C₂×C₁₃	1	2	yes	complemented
225	#1533	C₂×C₁₃	1	2	yes	complemented
226	#1530	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1529	C₂×C₁₃	1	2	yes	complemented
229	#1527	C₂×C₁₃	1	2	yes	complemented
230	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1524	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	8	2	no	—
236	C₂³×C₁₃	—	8	2	no	—
237	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	2	no	—
242	Q₈×C₁₃	—	8	2	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	8	1	no	—
250	D₄×C₁₃	—	8	2	no	—
251	D₄×C₁₃	—	8	1	no	—
252	D₄×C₁₃	—	8	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	8	2	no	—
265	C₂×C₄×C₁₃	—	8	2	no	—
266	C₂×C₄×C₁₃	—	8	2	no	—
267	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₈×C₁₃	—	2	2	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	2	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	2	no	—
282	#559	C₄×C₁₃	1	1	yes	characteristic
283	#556	C₄×C₁₃	1	1	yes	characteristic
284	#555	—	2	1	no	—
285	#551	—	2	2	no	—
286	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
287	#548	C₄×C₁₃	1	2	yes	—
288	#546	—	2	1	no	—
289	#546	C₄×C₁₃	1	2	yes	—
290	D₄²	C₄×C₁₃	1	1	yes	characteristic
291	#542	—	2	1	no	—
292	#538	—	2	2	no	—
293	#532	C₂²×C₁₃	1	1	yes	characteristic
294	#529	C₂²×C₁₃	1	1	yes	characteristic
295	#529	C₂²×C₁₃	1	2	yes	—
296	C₂×#124	C₂²×C₁₃	1	2	yes	—
297	#518	—	2	1	no	—
298	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
299	C₈×Q₈	—	2	1	no	—
300	#436	—	2	1	no	—
301	#436	—	2	2	no	—
302	#433	—	2	2	no	—
303	#432	C₂²×C₁₃	1	2	yes	complemented
304	#432	C₂²×C₁₃	1	2	yes	complemented
305	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
306	#432	C₂²×C₁₃	1	2	yes	complemented
307	#424	—	2	1	no	—
308	#408	—	2	1	no	—
309	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
312	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	#330	C₂²×C₁₃	1	2	yes	complemented
316	#329	C₂²×C₁₃	1	1	yes	characteristic
317	#329	C₂²×C₁₃	1	1	yes	characteristic
318	#329	C₂²×C₁₃	1	2	yes	—
319	#329	C₂²×C₁₃	1	2	yes	complemented
320	#329	C₂²×C₁₃	1	2	yes	complemented
321	#329	C₂²×C₁₃	1	2	yes	complemented
322	#329	C₂²×C₁₃	1	2	yes	complemented
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	2	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	16	4	no	—
336	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	4	2	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	#421	1	2	yes	—
350	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
351	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
352	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
361	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#126	—	2	1	no	—
365	#125	C₂³×C₁₃	1	1	yes	characteristic
366	#124	—	2	1	no	—
367	#124	—	2	2	no	—
368	#124	—	2	2	no	—
369	#124	—	2	2	no	—
370	#124	C₂×C₄×C₁₃	1	2	yes	—
371	#124	C₂×C₄×C₁₃	1	2	yes	—
372	#124	C₂³×C₁₃	1	1	yes	characteristic
373	#124	C₂³×C₁₃	1	2	yes	—
374	#123	—	2	1	no	—
375	#123	—	2	2	no	—
376	#123	—	2	2	no	—
377	#123	—	2	2	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	2	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
382	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
383	#121	—	2	2	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	2	1	no	—
387	#121	—	2	2	no	—
388	#121	C₂×C₄×C₁₃	1	2	yes	—
389	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
390	#120	—	2	2	no	—
391	#120	—	2	2	no	—
392	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
393	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
394	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
395	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
404	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
405	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
406	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
407	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
408	C₄×D₄	D₄×C₁₃	1	2	yes	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	2	no	—
412	#117	D₄×C₁₃	1	2	yes	—
413	#117	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	—	2	2	no	—
415	C₂×C₂²⋊C₄	—	2	2	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	—	2	2	no	—
424	C₂²⋊C₈	—	2	2	no	—
425	C₂²⋊C₈	—	2	2	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	#97	—	2	1	no	—
428	#97	C₂³×C₁₃	1	1	yes	characteristic
429	#97	C₂³×C₁₃	1	1	yes	characteristic
430	#97	C₂³×C₁₃	1	1	yes	characteristic
431	#97	C₂³×C₁₃	1	1	yes	characteristic
432	#97	C₂³×C₁₃	1	2	yes	—
433	#97	C₂³×C₁₃	1	2	yes	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	2	no	—
437	C₂×C₁₃	—	4	1	no	—
438	C₂×C₁₃	—	4	2	no	—
439	C₂×C₁₃	—	8	2	no	—
440	C₂×C₁₃	—	8	1	no	—
441	C₂×C₁₃	#2888	1	1	yes	characteristic
442	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
443	C₂×C₁₃	#2901	1	1	yes	characteristic
444	C₂⁴	—	2	2	no	—
445	#41	—	4	2	no	—
446	#41	—	8	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	8	2	no	—
449	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
450	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
451	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	8	2	no	—
460	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
462	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
463	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	M₁₆	—	4	4	no	—
475	M₁₆	—	4	2	no	—
476	M₁₆	—	4	2	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	4	2	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
493	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
494	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
495	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
496	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
513	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
514	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	1	no	—
517	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
518	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
519	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₄²	C₂×D₄×C₁₃	1	2	yes	—
522	C₄²	C₂×D₄×C₁₃	1	2	yes	—
523	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₁₃	#17681	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	1	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	8	2	no	—
529	C₂³	—	8	2	no	—
530	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
531	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
532	Q₈	—	2	2	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	8	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	1	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
561	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
562	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
565	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
569	C₈	—	2	2	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	16	4	no	—
588	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	C₁₃×#421	1	2	yes	—
602	C₂	—	4	2	no	—
603	C₂	—	4	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	2	no	—
606	C₂	C₁₃×#2888	1	1	yes	characteristic
607	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
608	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×#3514	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×#2971	C₂	semidirect
3. C₁₃×#2923	C₂	semidirect
4. C₁₃×#1535	C₂	semidirect
5. C₁₃×#1533	C₂	semidirect
6. C₁₃×#1530	C₂	semidirect
7. C₁₃×#1529	C₂	semidirect
8. C₁₃×#1529	C₂	semidirect
9. C₁₃×#1527	C₂	semidirect
10. C₁₃×#1525	C₂	semidirect
11. C₁₃×#1524	C₂	semidirect
33. C₁₃×#432	C₂²	semidirect
34. C₁₃×#432	C₂²	semidirect
35. C₁₃×#432	C₂²	semidirect
36. C₁₃×#432	C₂²	semidirect
39. C₄×C₁₃×M₁₆	C₂²	semidirect
40. C₄×C₁₃×M₁₆	C₂²	semidirect
41. C₄×C₁₃×M₁₆	C₂²	semidirect
42. C₂×C₁₃×#97	C₂²	semidirect
43. C₁₃×#330	C₂²	semidirect
44. C₁₃×#330	C₂²	semidirect
45. C₁₃×#330	C₂²	semidirect
49. C₁₃×#329	C₂²	semidirect
50. C₁₃×#329	C₂²	semidirect
51. C₁₃×#329	C₂²	semidirect
52. C₁₃×#329	C₂²	semidirect
140. #17681	C₁₃	direct (N × H)
222. #2971	C₂×C₁₃	semidirect
223. #2923	C₂×C₁₃	semidirect
224. #1535	C₂×C₁₃	semidirect
225. #1533	C₂×C₁₃	semidirect
226. #1530	C₂×C₁₃	semidirect
227. #1529	C₂×C₁₃	semidirect
228. #1529	C₂×C₁₃	semidirect
229. #1527	C₂×C₁₃	semidirect
230. #1525	C₂×C₁₃	semidirect
231. #1524	C₂×C₁₃	semidirect
303. #432	C₂²×C₁₃	semidirect
304. #432	C₂²×C₁₃	semidirect
305. #432	C₂²×C₁₃	semidirect
306. #432	C₂²×C₁₃	semidirect
309. C₄×M₁₆	C₂²×C₁₃	semidirect
310. C₄×M₁₆	C₂²×C₁₃	semidirect
311. C₄×M₁₆	C₂²×C₁₃	semidirect
312. C₂×#97	C₂²×C₁₃	semidirect
313. #330	C₂²×C₁₃	semidirect
314. #330	C₂²×C₁₃	semidirect
315. #330	C₂²×C₁₃	semidirect
319. #329	C₂²×C₁₃	semidirect
320. #329	C₂²×C₁₃	semidirect
321. #329	C₂²×C₁₃	semidirect
322. #329	C₂²×C₁₃	semidirect
524. C₁₃	#17681	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×#3514	2
C₁₃×#2971	2
C₁₃×#2923	2
C₁₃×#1535	2
C₁₃×#1533	2
C₁₃×#1530	2
C₁₃×#1529	2
C₁₃×#1527	2
C₁₃×#1525	2
C₁₃×#1524	2
#17681	13

Subgroups — C13×#17681 #15704020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17681 #15704020