Subgroups — C₁₃×#18026 #15704365

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#480	C₄	1	1	yes	characteristic
19	C₁₃×#480	C₄	1	1	yes	characteristic
20	C₁₃×#474	C₄	1	1	yes	characteristic
21	C₁₃×#474	C₄	1	1	yes	characteristic
22	C₁₃×#459	C₄	1	1	yes	characteristic
23	C₁₃×#459	C₄	1	1	yes	characteristic
24	C₁₃×#447	C₄	1	1	yes	characteristic
25	C₁₃×#447	C₄	1	1	yes	characteristic
26	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₁₃×#436	—	2	1	no	—
31	C₁₃×#436	C₂²	1	1	yes	characteristic
32	C₁₃×#436	C₂²	1	1	yes	characteristic
33	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#435	—	2	1	no	—
36	C₁₃×#435	—	2	1	no	—
37	C₈×D₄×C₁₃	—	2	1	no	—
38	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#432	C₂²	1	1	yes	characteristic
43	C₁₃×#431	C₂²	1	1	yes	characteristic
44	C₁₃×#431	C₂²	1	1	yes	characteristic
45	C₁₃×#431	C₂²	1	1	yes	characteristic
46	C₁₃×#431	C₂²	1	1	yes	characteristic
47	C₁₃×#408	—	2	1	no	—
48	C₁₃×#408	—	2	1	no	—
49	C₁₃×#407	—	2	1	no	—
50	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
51	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#334	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#124	—	2	1	no	—
85	C₁₃×#121	—	2	1	no	—
86	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
87	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	—	2	1	no	—
90	C₄×D₄×C₁₃	—	2	1	no	—
91	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
102	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
103	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₃×C₂²⋊C₈	—	2	1	no	—
122	C₁₃×C₂²⋊C₈	—	2	1	no	—
123	C₁₃×C₂²⋊C₈	—	2	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	1	no	—
125	C₁₃×C₂²⋊C₈	—	2	1	no	—
126	C₁₃×C₂²⋊C₈	—	2	1	no	—
127	C₁₃×C₂²⋊C₈	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×C₂²⋊C₈	—	2	1	no	—
130	C₁₃×C₂²⋊C₈	—	2	1	no	—
131	C₁₃×C₂²⋊C₈	—	2	1	no	—
132	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
135	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
136	C₁₃×#97	—	2	1	no	—
137	C₄×C₈×C₁₃	—	2	1	no	—
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#18026	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	1	no	—
146	C₁₃×#41	—	8	1	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	8	1	no	—
168	C₂²×C₄×C₁₃	—	8	1	no	—
169	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
172	C₁₃×D₈	—	2	2	no	—
173	C₁₃×D₈	—	2	2	no	—
174	C₁₃×D₈	—	4	1	no	—
175	C₁₃×D₈	—	4	1	no	—
176	C₁₃×M₁₆	—	8	1	no	—
177	C₁₃×M₁₆	—	8	1	no	—
178	C₁₃×M₁₆	—	8	1	no	—
179	C₁₃×M₁₆	—	8	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	8	1	no	—
187	C₂×C₈×C₁₃	—	8	1	no	—
188	C₂×C₈×C₁₃	—	8	1	no	—
189	C₂×C₈×C₁₃	—	8	1	no	—
190	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₁₃×C₂²⋊C₄	—	2	1	no	—
212	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	#41	1	1	yes	characteristic
215	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
216	#3100	C₂×C₁₃	1	1	yes	characteristic
217	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1594	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1589	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1586	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1572	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1496	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1478	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1454	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	4	2	no	—
236	C₂³×C₁₃	—	4	2	no	—
237	C₂³×C₁₃	—	8	1	no	—
238	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
239	Q₈×C₁₃	—	8	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	4	2	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	8	1	no	—
250	D₄×C₁₃	—	8	1	no	—
251	D₄×C₁₃	—	8	1	no	—
252	D₄×C₁₃	#131	1	2	yes	—
253	C₂×C₄×C₁₃	—	2	1	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	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	8	1	no	—
271	C₂×C₄×C₁₃	—	8	1	no	—
272	C₂×C₄×C₁₃	—	8	1	no	—
273	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	2	1	no	—
281	C₈×C₁₃	—	2	1	no	—
282	C₈×C₁₃	—	2	1	no	—
283	C₈×C₁₃	—	2	1	no	—
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	—	2	1	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₈×C₁₃	—	4	1	no	—
292	C₈×C₁₃	—	4	1	no	—
293	#532	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
295	#480	C₄×C₁₃	1	1	yes	characteristic
296	#480	C₄×C₁₃	1	1	yes	characteristic
297	#474	C₄×C₁₃	1	1	yes	characteristic
298	#474	C₄×C₁₃	1	1	yes	characteristic
299	#459	C₄×C₁₃	1	1	yes	characteristic
300	#459	C₄×C₁₃	1	1	yes	characteristic
301	#447	C₄×C₁₃	1	1	yes	characteristic
302	#447	C₄×C₁₃	1	1	yes	characteristic
303	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
307	#436	—	2	1	no	—
308	#436	C₂²×C₁₃	1	1	yes	characteristic
309	#436	C₂²×C₁₃	1	1	yes	characteristic
310	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
311	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	#435	—	2	1	no	—
313	#435	—	2	1	no	—
314	C₈×D₄	—	2	1	no	—
315	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
316	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	#432	C₂²×C₁₃	1	1	yes	characteristic
320	#431	C₂²×C₁₃	1	1	yes	characteristic
321	#431	C₂²×C₁₃	1	1	yes	characteristic
322	#431	C₂²×C₁₃	1	1	yes	characteristic
323	#431	C₂²×C₁₃	1	1	yes	characteristic
324	#408	—	2	1	no	—
325	#408	—	2	1	no	—
326	#407	—	2	1	no	—
327	C₂×C₂²⋊C₈	—	2	1	no	—
328	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	#334	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
333	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
336	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
339	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
342	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
343	C₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
344	C₂²×C₁₃	—	2	1	no	—
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	1	no	—
347	C₂²×C₁₃	—	2	1	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	—	4	1	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	4	1	no	—
354	C₂²×C₁₃	—	4	1	no	—
355	C₂²×C₁₃	—	4	1	no	—
356	C₂²×C₁₃	—	4	1	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	—	8	4	no	—
360	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
361	C₄×C₁₃	—	2	1	no	—
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	4	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
370	C₄×C₁₃	#568	1	1	yes	characteristic
371	C₄×C₁₃	#576	1	1	yes	characteristic
372	C₄×C₁₃	#576	1	1	yes	characteristic
373	C₂×#41	—	2	1	no	—
374	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	—	2	1	no	—
376	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
377	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
378	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
379	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
389	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
390	#124	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
393	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
398	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
399	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
406	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
407	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
408	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
409	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
419	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
420	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
421	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
422	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
423	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
424	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
425	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
426	#102	C₂×C₄×C₁₃	1	1	yes	characteristic
427	C₂²⋊C₈	—	2	1	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
439	C₂²⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
440	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
441	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
442	#97	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₁₃	—	4	1	no	—
451	C₂×C₁₃	—	4	2	no	—
452	C₂×C₁₃	—	8	1	no	—
453	C₂×C₁₃	—	8	1	no	—
454	C₂×C₁₃	—	8	1	no	—
455	C₂×C₁₃	#2933	1	1	yes	characteristic
456	C₂×C₁₃	#2948	1	1	yes	characteristic
457	C₂×C₁₃	#2955	1	1	yes	characteristic
458	C₂⁴	—	2	1	no	—
459	#41	—	8	1	no	—
460	#41	—	8	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	4	1	no	—
469	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
470	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
472	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	8	1	no	—
481	C₂²×C₄	—	8	1	no	—
482	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
485	D₈	—	2	2	no	—
486	D₈	—	2	2	no	—
487	D₈	—	4	1	no	—
488	D₈	—	4	1	no	—
489	M₁₆	—	8	1	no	—
490	M₁₆	—	8	1	no	—
491	M₁₆	—	8	1	no	—
492	M₁₆	—	8	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	8	1	no	—
500	C₂×C₈	—	8	1	no	—
501	C₂×C₈	—	8	1	no	—
502	C₂×C₈	—	8	1	no	—
503	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
504	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
505	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
506	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
507	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	1	no	—
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
526	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₄²	C₁₃×#41	1	1	yes	characteristic
528	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₁₃	#18026	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	8	1	no	—
537	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
538	Q₈	—	8	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	1	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	1	no	—
551	D₄	C₁₃×#131	1	2	yes	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	8	1	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	8	4	no	—
608	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
618	C₄	C₁₃×#568	1	1	yes	characteristic
619	C₄	C₁₃×#576	1	1	yes	characteristic
620	C₄	C₁₃×#576	1	1	yes	characteristic
621	C₂	—	4	1	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	1	no	—
624	C₂	—	8	1	no	—
625	C₂	—	8	1	no	—
626	C₂	C₁₃×#2933	1	1	yes	characteristic
627	C₂	C₁₃×#2948	1	1	yes	characteristic
628	C₂	C₁₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2979	C₂	semidirect
3. C₁₃×#2974	C₂	semidirect
4. C₁₃×#1594	C₂	semidirect
5. C₁₃×#1589	C₂	semidirect
6. C₁₃×#1586	C₂	semidirect
7. C₁₃×#1586	C₂	semidirect
8. C₁₃×#1581	C₂	semidirect
9. C₁₃×#1581	C₂	semidirect
10. C₁₃×#1580	C₂	semidirect
11. C₈×C₁₃×D₈	C₂	semidirect
12. C₁₃×#1572	C₂	semidirect
13. C₁₃×#1496	C₂	semidirect
14. C₁₃×#1478	C₂	semidirect
15. C₁₃×#1454	C₂	semidirect
33. C₁₃×#436	C₂²	semidirect
34. C₁₃×#436	C₂²	semidirect
40. C₈×D₄×C₁₃	C₂²	semidirect
41. C₈×D₄×C₁₃	C₂²	semidirect
51. C₁₃×#335	C₂²	semidirect
52. C₁₃×#335	C₂²	semidirect
53. C₁₃×#334	C₂²	semidirect
54. C₁₃×#334	C₂²	semidirect
59. C₁₃×D₄⋊C₈	C₂²	semidirect
60. C₁₃×D₄⋊C₈	C₂²	semidirect
61. C₁₃×D₄⋊C₈	C₂²	semidirect
62. C₁₃×D₄⋊C₈	C₂²	semidirect
63. C₁₃×#322	C₂²	semidirect
64. C₁₃×#322	C₂²	semidirect
65. C₁₃×#322	C₂²	semidirect
66. C₈²×C₁₃	C₂²	semidirect
144. #18026	C₁₃	direct (N × H)
217. #2979	C₂×C₁₃	semidirect
218. #2974	C₂×C₁₃	semidirect
219. #1594	C₂×C₁₃	semidirect
220. #1589	C₂×C₁₃	semidirect
221. #1586	C₂×C₁₃	semidirect
222. #1586	C₂×C₁₃	semidirect
223. #1581	C₂×C₁₃	semidirect
224. #1581	C₂×C₁₃	semidirect
225. #1580	C₂×C₁₃	semidirect
226. C₈×D₈	C₂×C₁₃	semidirect
227. #1572	C₂×C₁₃	semidirect
228. #1496	C₂×C₁₃	semidirect
229. #1478	C₂×C₁₃	semidirect
230. #1454	C₂×C₁₃	semidirect
310. #436	C₂²×C₁₃	semidirect
311. #436	C₂²×C₁₃	semidirect
317. C₈×D₄	C₂²×C₁₃	semidirect
318. C₈×D₄	C₂²×C₁₃	semidirect
328. #335	C₂²×C₁₃	semidirect
329. #335	C₂²×C₁₃	semidirect
330. #334	C₂²×C₁₃	semidirect
331. #334	C₂²×C₁₃	semidirect
336. D₄⋊C₈	C₂²×C₁₃	semidirect
337. D₄⋊C₈	C₂²×C₁₃	semidirect
338. D₄⋊C₈	C₂²×C₁₃	semidirect
339. D₄⋊C₈	C₂²×C₁₃	semidirect
340. #322	C₂²×C₁₃	semidirect
341. #322	C₂²×C₁₃	semidirect
342. #322	C₂²×C₁₃	semidirect
343. C₈²	C₂²×C₁₃	semidirect
529. C₁₃	#18026	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×#3100	2
C₁₃×#2979	2
C₁₃×#2974	2
C₁₃×#1594	2
C₁₃×#1589	2
C₁₃×#1586	2
C₁₃×#1581	2
C₁₃×#1580	2
C₈×C₁₃×D₈	2
C₁₃×#1572	2
C₁₃×#1496	2
C₁₃×#1478	2
C₁₃×#1454	2
#18026	13

Subgroups — C13×#18026 #15704365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18026 #15704365