Subgroups — C₁₃×#17602 #15703941

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1521	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1517	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1514	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1512	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1505	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1500	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#559	C₄	1	2	yes	complemented
13	C₁₃×#559	C₄	1	1	yes	characteristic, complemented
14	Q₈²×C₁₃	C₄	1	1	yes	characteristic, complemented
15	C₁₃×#554	C₄	1	1	yes	characteristic, complemented
16	C₁₃×#554	C₄	1	2	yes	complemented
17	C₁₃×#550	C₄	1	1	yes	characteristic, complemented
18	C₁₃×#548	—	2	1	no	—
19	C₁₃×#547	—	2	2	no	—
20	C₁₃×#547	—	2	1	no	—
21	C₁₃×#542	—	2	1	no	—
22	C₁₃×#542	—	2	2	no	—
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₁₃×#532	C₂²	1	2	yes	—
25	C₁₃×#529	C₂²	1	1	yes	characteristic
26	C₁₃×#529	C₂²	1	2	yes	—
27	C₁₃×#520	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#446	—	2	1	no	—
30	C₁₃×#446	—	2	2	no	—
31	C₈×Q₈×C₁₃	—	2	1	no	—
32	C₁₃×#432	C₂²	1	1	yes	characteristic
33	C₁₃×#432	C₂²	1	2	yes	—
34	C₁₃×#431	C₂²	1	1	yes	characteristic
35	C₁₃×#431	C₂²	1	2	yes	—
36	C₁₃×#391	—	2	1	no	—
37	C₁₃×#389	—	2	1	no	—
38	C₁₃×#387	—	2	2	no	—
39	C₁₃×#383	C₂²	1	2	yes	—
40	C₁₃×#382	C₂²	1	2	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#376	C₂²	1	1	yes	characteristic
43	C₁₃×#328	C₂²	1	1	yes	characteristic
44	C₁₃×#328	C₂²	1	1	yes	characteristic
45	C₁₃×#328	C₂²	1	2	yes	—
46	C₁₃×#327	C₂²	1	1	yes	characteristic
47	C₁₃×#327	C₂²	1	1	yes	characteristic
48	C₁₃×#327	C₂²	1	2	yes	—
49	C₁₃×#327	C₂²	1	2	yes	—
50	C₁₃×#327	C₂²	1	2	yes	—
51	C₁₃×#327	C₂²	1	2	yes	—
52	C₁₃×#327	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
61	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#127	C₂×C₄	1	2	yes	—
63	C₁₃×#126	—	2	2	no	—
64	C₁₃×#126	—	2	1	no	—
65	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
66	C₁₃×#125	C₂×C₄	1	2	yes	—
67	C₁₃×#124	—	2	1	no	—
68	C₁₃×#124	—	2	2	no	—
69	C₁₃×#124	—	2	2	no	—
70	C₁₃×#124	—	2	1	no	—
71	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
72	C₁₃×#124	C₂×C₄	1	2	yes	—
73	C₁₃×#123	—	2	1	no	—
74	C₁₃×#123	—	2	2	no	—
75	C₁₃×#123	—	2	2	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	1	no	—
79	C₁₃×C₂²⋊Q₈	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×#121	—	2	1	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	C₂³	1	1	yes	characteristic
89	C₁₃×#121	C₂³	1	2	yes	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	D₄	1	2	yes	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	—	2	2	no	—
105	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
108	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
110	C₁₃×#117	—	2	1	no	—
111	C₁₃×#117	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	—	2	1	no	—
119	C₂×C₄²×C₁₃	—	2	1	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	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	2	no	—
126	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
127	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
129	C₁₃×#97	—	2	2	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₄×C₈×C₁₃	—	2	1	no	—
132	C₄×C₈×C₁₃	—	2	2	no	—
133	C₁₃×#95	—	2	2	no	—
134	C₁₃×#95	—	2	2	no	—
135	C₁₃×#95	—	2	2	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	1	yes	characteristic
139	C₁₃×#95	C₂³	1	1	yes	characteristic
140	#17602	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	4	4	no	—
142	C₁₃×#41	—	8	1	no	—
143	C₁₃×#41	—	8	2	no	—
144	C₁₃×#41	—	8	1	no	—
145	C₁₃×#41	—	8	2	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	4	2	no	—
149	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
152	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
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	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	2	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	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	8	2	no	—
188	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
189	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
190	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
192	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
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	2	yes	—
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₄²×C₁₃	—	8	1	no	—
214	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
216	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
217	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
218	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₃	C₂×D₄	1	2	yes	—
220	C₄²×C₁₃	C₂×D₄	1	2	yes	—
221	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
222	#3522	C₂×C₁₃	1	1	yes	characteristic
223	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1521	C₂×C₁₃	1	2	yes	complemented
226	#1517	C₂×C₁₃	1	2	yes	complemented
227	#1514	C₂×C₁₃	1	2	yes	complemented
228	#1512	C₂×C₁₃	1	2	yes	complemented
229	#1509	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1505	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1502	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1500	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	8	1	no	—
241	Q₈×C₁₃	—	8	2	no	—
242	D₄×C₁₃	—	4	4	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	—	8	1	no	—
251	D₄×C₁₃	—	8	2	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	1	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	—	8	2	no	—
275	C₂×C₄×C₁₃	—	8	2	no	—
276	C₂×C₄×C₁₃	—	8	2	no	—
277	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	2	no	—
290	#559	C₄×C₁₃	1	2	yes	complemented
291	#559	C₄×C₁₃	1	1	yes	characteristic, complemented
292	Q₈²	C₄×C₁₃	1	1	yes	characteristic, complemented
293	#554	C₄×C₁₃	1	1	yes	characteristic, complemented
294	#554	C₄×C₁₃	1	2	yes	complemented
295	#550	C₄×C₁₃	1	1	yes	characteristic, complemented
296	#548	—	2	1	no	—
297	#547	—	2	2	no	—
298	#547	—	2	1	no	—
299	#542	—	2	1	no	—
300	#542	—	2	2	no	—
301	#532	C₂²×C₁₃	1	1	yes	characteristic
302	#532	C₂²×C₁₃	1	2	yes	—
303	#529	C₂²×C₁₃	1	1	yes	characteristic
304	#529	C₂²×C₁₃	1	2	yes	—
305	#520	—	2	1	no	—
306	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	#446	—	2	1	no	—
308	#446	—	2	2	no	—
309	C₈×Q₈	—	2	1	no	—
310	#432	C₂²×C₁₃	1	1	yes	characteristic
311	#432	C₂²×C₁₃	1	2	yes	—
312	#431	C₂²×C₁₃	1	1	yes	characteristic
313	#431	C₂²×C₁₃	1	2	yes	—
314	#391	—	2	1	no	—
315	#389	—	2	1	no	—
316	#387	—	2	2	no	—
317	#383	C₂²×C₁₃	1	2	yes	—
318	#382	C₂²×C₁₃	1	2	yes	—
319	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
320	#376	C₂²×C₁₃	1	1	yes	characteristic
321	#328	C₂²×C₁₃	1	1	yes	characteristic
322	#328	C₂²×C₁₃	1	1	yes	characteristic
323	#328	C₂²×C₁₃	1	2	yes	—
324	#327	C₂²×C₁₃	1	1	yes	characteristic
325	#327	C₂²×C₁₃	1	1	yes	characteristic
326	#327	C₂²×C₁₃	1	2	yes	—
327	#327	C₂²×C₁₃	1	2	yes	—
328	#327	C₂²×C₁₃	1	2	yes	—
329	#327	C₂²×C₁₃	1	2	yes	—
330	#327	C₂²×C₁₃	1	2	yes	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
340	C₂²×C₁₃	#576	1	1	yes	characteristic
341	C₂²×C₁₃	#577	1	1	yes	characteristic
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	2	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	#421	1	2	yes	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	2	no	—
362	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
363	C₄⋊Q₈	—	2	2	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
367	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
368	#127	C₂×C₄×C₁₃	1	2	yes	—
369	#126	—	2	2	no	—
370	#126	—	2	1	no	—
371	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
372	#125	C₂×C₄×C₁₃	1	2	yes	—
373	#124	—	2	1	no	—
374	#124	—	2	2	no	—
375	#124	—	2	2	no	—
376	#124	—	2	1	no	—
377	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
378	#124	C₂×C₄×C₁₃	1	2	yes	—
379	#123	—	2	1	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
390	#121	—	2	1	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	C₂³×C₁₃	1	1	yes	characteristic
395	#121	C₂³×C₁₃	1	2	yes	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
398	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
399	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
400	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
401	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
402	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
403	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
404	C₄×Q₈	D₄×C₁₃	1	2	yes	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
412	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
413	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
414	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
415	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
416	#117	—	2	1	no	—
417	#117	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
423	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	C₄⋊C₈	—	2	2	no	—
432	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
435	#97	—	2	2	no	—
436	#97	—	2	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	—	2	2	no	—
439	#95	—	2	1	no	—
440	#95	—	2	2	no	—
441	#95	—	2	2	no	—
442	#95	—	2	2	no	—
443	#95	C₂³×C₁₃	1	1	yes	characteristic
444	#95	C₂³×C₁₃	1	1	yes	characteristic
445	#95	C₂³×C₁₃	1	2	yes	—
446	C₂×C₁₃	—	2	1	no	—
447	C₂×C₁₃	—	2	1	no	—
448	C₂×C₁₃	—	8	2	no	—
449	C₂×C₁₃	—	8	1	no	—
450	C₂×C₁₃	#2884	1	1	yes	characteristic
451	C₂×C₁₃	#2897	1	1	yes	characteristic
452	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
453	#41	—	4	4	no	—
454	#41	—	8	1	no	—
455	#41	—	8	2	no	—
456	#41	—	8	1	no	—
457	#41	—	8	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
464	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
472	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	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	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	8	2	no	—
500	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
501	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
502	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
503	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
504	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
505	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
506	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
509	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	8	1	no	—
526	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
527	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
528	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
529	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₃	1	2	yes	—
532	C₄²	C₂×D₄×C₁₃	1	2	yes	—
533	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₁₃	#17602	1	1	yes	characteristic, direct product factor, Sylow
535	C₂³	—	2	2	no	—
536	C₂³	—	2	1	no	—
537	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	Q₈	—	2	2	no	—
539	Q₈	—	2	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	8	1	no	—
543	Q₈	—	8	2	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	2	no	—
579	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
580	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
581	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
582	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
584	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
585	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	2	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
601	C₂²	C₁₃×#576	1	1	yes	characteristic
602	C₂²	C₁₃×#577	1	1	yes	characteristic
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	2	no	—
618	C₄	—	8	1	no	—
619	C₄	C₁₃×#421	1	2	yes	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	8	2	no	—
623	C₂	—	8	1	no	—
624	C₂	C₁₃×#2884	1	1	yes	characteristic
625	C₂	C₁₃×#2897	1	1	yes	characteristic
626	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2984	C₂	semidirect
3. C₁₃×#2320	C₂	semidirect
4. C₁₃×#1521	C₂	semidirect
5. C₁₃×#1517	C₂	semidirect
6. C₁₃×#1514	C₂	semidirect
7. C₁₃×#1512	C₂	semidirect
8. C₁₃×#1509	C₂	semidirect
9. C₁₃×#1505	C₂	semidirect
10. C₁₃×#1502	C₂	semidirect
11. C₁₃×#1500	C₂	semidirect
12. C₁₃×#559	C₄	semidirect
13. C₁₃×#559	C₄	semidirect
14. Q₈²×C₁₃	C₄	semidirect
15. C₁₃×#554	C₄	semidirect
16. C₁₃×#554	C₄	semidirect
17. C₁₃×#550	C₄	semidirect
140. #17602	C₁₃	direct (N × H)
223. #2984	C₂×C₁₃	semidirect
224. #2320	C₂×C₁₃	semidirect
225. #1521	C₂×C₁₃	semidirect
226. #1517	C₂×C₁₃	semidirect
227. #1514	C₂×C₁₃	semidirect
228. #1512	C₂×C₁₃	semidirect
229. #1509	C₂×C₁₃	semidirect
230. #1505	C₂×C₁₃	semidirect
231. #1502	C₂×C₁₃	semidirect
232. #1500	C₂×C₁₃	semidirect
290. #559	C₄×C₁₃	semidirect
291. #559	C₄×C₁₃	semidirect
292. Q₈²	C₄×C₁₃	semidirect
293. #554	C₄×C₁₃	semidirect
294. #554	C₄×C₁₃	semidirect
295. #550	C₄×C₁₃	semidirect
534. C₁₃	#17602	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×#3522	2
C₁₃×#2984	2
C₁₃×#2320	2
C₁₃×#1521	2
C₁₃×#1517	2
C₁₃×#1514	2
C₁₃×#1512	2
C₁₃×#1509	2
C₁₃×#1505	2
C₁₃×#1502	2
C₁₃×#1500	2
#17602	13

Subgroups — C13×#17602 #15703941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17602 #15703941