Subgroups — C₁₃×#61012 #15747351

Order 3328.

1776 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3260	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3228	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3200	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3182	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3167	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3126	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3123	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	—	2	2	no	—
15	C₁₃×#557	—	2	2	no	—
16	C₁₃×#556	—	2	2	no	—
17	C₁₃×#552	—	2	2	no	—
18	C₁₃×#552	—	2	2	no	—
19	C₁₃×#550	—	2	2	no	—
20	C₁₃×#546	—	2	2	no	—
21	C₁₃×#546	—	2	2	no	—
22	C₁₃×#541	C₂²	1	2	yes	—
23	C₁₃×#541	C₂²	1	2	yes	complemented
24	C₁₃×#540	C₂²	1	2	yes	—
25	C₁₃×#540	C₂²	1	2	yes	—
26	C₁₃×#536	C₂²	1	2	yes	—
27	C₁₃×#535	C₂²	1	2	yes	—
28	C₁₃×#533	C₂²	1	2	yes	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic
30	C₁₃×#533	C₂²	1	2	yes	complemented
31	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#532	C₂²	1	2	yes	—
33	C₁₃×#532	C₂²	1	2	yes	—
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
36	C₁₃×#519	C₂²	1	2	yes	complemented
37	C₁₃×#518	C₂²	1	2	yes	—
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₁₃×#500	C₂²	1	2	yes	complemented
40	C₁₃×#498	C₂²	1	2	yes	complemented
41	C₁₃×#492	C₂²	1	2	yes	—
42	C₁₃×#492	C₂²	1	2	yes	—
43	C₁₃×#487	C₂²	1	2	yes	complemented
44	C₁₃×#487	C₂²	1	2	yes	complemented
45	C₁₃×#486	C₂²	1	2	yes	—
46	C₁₃×#486	C₂²	1	2	yes	—
47	C₁₃×#485	C₂²	1	8	yes	—
48	C₁₃×#482	C₂²	1	8	yes	complemented
49	C₁₃×#479	C₂²	1	8	yes	complemented
50	C₁₃×#478	C₂²	1	8	yes	complemented
51	C₁₃×#468	C₂²	1	8	yes	complemented
52	C₁₃×#465	C₂²	1	8	yes	complemented
53	C₁₃×#461	C₂²	1	8	yes	complemented
54	C₁₃×#460	C₂²	1	8	yes	—
55	C₁₃×#450	C₂²	1	8	yes	—
56	C₁₃×#448	C₂²	1	8	yes	complemented
57	C₁₃×#440	C₂²	1	8	yes	complemented
58	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
59	C₁₃×#433	C₂²	1	2	yes	—
60	C₁₃×#433	C₂²	1	2	yes	complemented
61	C₁₃×#431	C₂²	1	2	yes	—
62	C₁₃×#431	C₂²	1	2	yes	complemented
63	C₁₃×#424	C₂²	1	2	yes	complemented
64	C₁₃×#408	C₂²	1	2	yes	—
65	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	—	2	2	no	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	C₂³	1	2	yes	—
86	C₁₃×#127	C₂³	1	2	yes	—
87	C₁₃×#126	—	2	4	no	—
88	C₁₃×#126	—	2	4	no	—
89	C₁₃×#125	—	2	4	no	—
90	C₁₃×#125	—	2	4	no	—
91	C₁₃×#125	—	2	2	no	—
92	C₁₃×#125	—	2	2	no	—
93	C₁₃×#125	C₂³	1	2	yes	—
94	C₁₃×#125	C₂³	1	2	yes	—
95	C₁₃×#124	—	2	2	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	2	no	—
98	C₁₃×#124	—	2	2	no	—
99	C₁₃×#123	—	2	2	no	—
100	C₁₃×#123	—	2	2	no	—
101	C₁₃×#123	—	2	4	no	—
102	C₁₃×#123	—	2	4	no	—
103	C₁₃×C₂²⋊Q₈	—	2	2	no	—
104	C₁₃×C₂²⋊Q₈	—	2	2	no	—
105	C₁₃×C₂²⋊Q₈	—	2	2	no	—
106	C₁₃×C₂²⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	4	no	—
112	C₁₃×#121	—	2	4	no	—
113	C₁₃×#121	C₂³	1	4	yes	—
114	C₁₃×#121	C₂³	1	4	yes	—
115	C₁₃×#120	—	2	2	no	—
116	C₁₃×#120	—	2	2	no	—
117	C₄×Q₈×C₁₃	—	2	4	no	—
118	C₄×Q₈×C₁₃	—	2	2	no	—
119	C₄×Q₈×C₁₃	—	2	2	no	—
120	C₄×Q₈×C₁₃	—	2	2	no	—
121	C₄×Q₈×C₁₃	—	2	2	no	—
122	C₄×Q₈×C₁₃	D₄	1	2	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
125	C₄×D₄×C₁₃	—	2	4	no	—
126	C₄×D₄×C₁₃	—	2	2	no	—
127	C₄×D₄×C₁₃	—	2	2	no	—
128	C₄×D₄×C₁₃	D₄	1	2	yes	—
129	C₄×D₄×C₁₃	D₄	1	2	yes	—
130	C₄×D₄×C₁₃	D₄	1	2	yes	—
131	C₄×D₄×C₁₃	C₂³	1	4	yes	—
132	C₄×D₄×C₁₃	C₂³	1	4	yes	—
133	C₁₃×#117	—	2	2	no	—
134	C₁₃×#117	—	2	2	no	—
135	C₁₃×#117	—	2	4	no	—
136	C₁₃×#117	C₂³	1	2	yes	—
137	C₁₃×#117	C₂³	1	2	yes	—
138	C₁₃×#117	C₂³	1	1	yes	characteristic
139	C₁₃×#117	C₂³	1	1	yes	characteristic
140	C₁₃×#117	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#107	C₂³	1	8	yes	—
147	C₁₃×#106	C₂³	1	8	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
150	C₁₃×#103	C₂³	1	8	yes	—
151	C₁₃×#103	C₂³	1	8	yes	—
152	C₁₃×#102	C₂³	1	8	yes	—
153	C₁₃×#102	C₂³	1	8	yes	—
154	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
155	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
156	C₁₃×#97	C₂³	1	2	yes	—
157	C₄×C₈×C₁₃	C₂³	1	2	yes	—
158	C₄×C₈×C₁₃	C₂³	1	2	yes	—
159	C₄×C₈×C₁₃	C₂³	1	2	yes	—
160	#61012	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₃	—	2	2	no	—
162	C₁₃×#41	—	4	2	no	—
163	C₁₃×#41	—	8	4	no	—
164	C₁₃×#41	—	8	4	no	—
165	C₂×Q₈×C₁₃	—	2	2	no	—
166	C₂×Q₈×C₁₃	—	2	2	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	4	4	no	—
169	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
171	C₂×D₄×C₁₃	—	2	4	no	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	2	2	no	—
174	C₂×D₄×C₁₃	—	2	2	no	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	4	4	no	—
178	C₂×D₄×C₁₃	—	8	4	no	—
179	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₁₃×SD₁₆	—	4	8	no	—
193	C₁₃×SD₁₆	—	4	8	no	—
194	C₁₃×M₁₆	—	4	2	no	—
195	C₂×C₈×C₁₃	—	4	2	no	—
196	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
197	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
198	C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
210	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
211	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
212	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
213	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
214	C₁₃×C₂²⋊C₄	—	2	2	no	—
215	C₁₃×C₂²⋊C₄	—	2	2	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	4	no	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
223	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
224	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
225	C₄²×C₁₃	—	2	4	no	—
226	C₄²×C₁₃	—	2	4	no	—
227	C₄²×C₁₃	—	2	2	no	—
228	C₄²×C₁₃	—	2	2	no	—
229	C₄²×C₁₃	C₂×D₄	1	2	yes	—
230	C₄²×C₁₃	C₂×D₄	1	2	yes	—
231	C₄²×C₁₃	C₂×D₄	1	2	yes	—
232	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
236	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#3508	C₂×C₁₃	1	1	yes	characteristic
238	#3260	C₂×C₁₃	1	4	yes	complemented
239	#3231	C₂×C₁₃	1	2	yes	complemented
240	#3228	C₂×C₁₃	1	2	yes	complemented
241	#3208	C₂×C₁₃	1	2	yes	complemented
242	#3206	C₂×C₁₃	1	2	yes	complemented
243	#3200	C₂×C₁₃	1	4	yes	complemented
244	#3182	C₂×C₁₃	1	2	yes	complemented
245	#3167	C₂×C₁₃	1	2	yes	complemented
246	#3126	C₂×C₁₃	1	4	yes	complemented
247	#3123	C₂×C₁₃	1	4	yes	complemented
248	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂³×C₁₃	—	2	4	no	—
250	C₂³×C₁₃	—	4	4	no	—
251	C₂³×C₁₃	—	8	4	no	—
252	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₃	—	2	8	no	—
256	Q₈×C₁₃	—	4	1	no	—
257	Q₈×C₁₃	—	4	4	no	—
258	Q₈×C₁₃	—	4	4	no	—
259	Q₈×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	2	8	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	4	4	no	—
265	D₄×C₁₃	—	4	4	no	—
266	D₄×C₁₃	—	4	4	no	—
267	D₄×C₁₃	—	8	4	no	—
268	D₄×C₁₃	—	8	4	no	—
269	D₄×C₁₃	—	8	4	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	4	4	no	—
280	C₂×C₄×C₁₃	—	8	4	no	—
281	C₂×C₄×C₁₃	—	8	4	no	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
290	C₈×C₁₃	—	2	4	no	—
291	C₈×C₁₃	—	2	4	no	—
292	#559	—	2	2	no	—
293	#557	—	2	2	no	—
294	#556	—	2	2	no	—
295	#552	—	2	2	no	—
296	#552	—	2	2	no	—
297	#550	—	2	2	no	—
298	#546	—	2	2	no	—
299	#546	—	2	2	no	—
300	#541	C₂²×C₁₃	1	2	yes	—
301	#541	C₂²×C₁₃	1	2	yes	complemented
302	#540	C₂²×C₁₃	1	2	yes	—
303	#540	C₂²×C₁₃	1	2	yes	—
304	#536	C₂²×C₁₃	1	2	yes	—
305	#535	C₂²×C₁₃	1	2	yes	—
306	#533	C₂²×C₁₃	1	2	yes	—
307	#533	C₂²×C₁₃	1	1	yes	characteristic
308	#533	C₂²×C₁₃	1	2	yes	complemented
309	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#532	C₂²×C₁₃	1	2	yes	—
311	#532	C₂²×C₁₃	1	2	yes	—
312	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
314	#519	C₂²×C₁₃	1	2	yes	complemented
315	#518	C₂²×C₁₃	1	2	yes	—
316	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
317	#500	C₂²×C₁₃	1	2	yes	complemented
318	#498	C₂²×C₁₃	1	2	yes	complemented
319	#492	C₂²×C₁₃	1	2	yes	—
320	#492	C₂²×C₁₃	1	2	yes	—
321	#487	C₂²×C₁₃	1	2	yes	complemented
322	#487	C₂²×C₁₃	1	2	yes	complemented
323	#486	C₂²×C₁₃	1	2	yes	—
324	#486	C₂²×C₁₃	1	2	yes	—
325	#485	C₂²×C₁₃	1	8	yes	—
326	#482	C₂²×C₁₃	1	8	yes	complemented
327	#479	C₂²×C₁₃	1	8	yes	complemented
328	#478	C₂²×C₁₃	1	8	yes	complemented
329	#468	C₂²×C₁₃	1	8	yes	complemented
330	#465	C₂²×C₁₃	1	8	yes	complemented
331	#461	C₂²×C₁₃	1	8	yes	complemented
332	#460	C₂²×C₁₃	1	8	yes	—
333	#450	C₂²×C₁₃	1	8	yes	—
334	#448	C₂²×C₁₃	1	8	yes	complemented
335	#440	C₂²×C₁₃	1	8	yes	complemented
336	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
337	#433	C₂²×C₁₃	1	2	yes	—
338	#433	C₂²×C₁₃	1	2	yes	complemented
339	#431	C₂²×C₁₃	1	2	yes	—
340	#431	C₂²×C₁₃	1	2	yes	complemented
341	#424	C₂²×C₁₃	1	2	yes	complemented
342	#408	C₂²×C₁₃	1	2	yes	—
343	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
344	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
345	C₂²×C₁₃	—	2	1	no	—
346	C₂²×C₁₃	—	2	1	no	—
347	C₂²×C₁₃	—	2	1	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	4	4	no	—
352	C₂²×C₁₃	—	4	4	no	—
353	C₂²×C₁₃	—	4	4	no	—
354	C₂²×C₁₃	—	16	4	no	—
355	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	2	1	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	2	2	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	4	4	no	—
363	C₄×C₁₃	—	4	4	no	—
364	C₄×C₁₃	—	4	4	no	—
365	C₄×C₁₃	#577	1	4	yes	—
366	C₄×C₁₃	#585	1	2	yes	—
367	C₂×#41	—	2	2	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
371	C₂²×D₄	—	2	2	no	—
372	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
373	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
374	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
375	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
376	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
377	C₄⋊Q₈	—	2	2	no	—
378	C₄⋊Q₈	—	2	2	no	—
379	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
380	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
381	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
382	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
383	#127	—	2	2	no	—
384	#127	—	2	2	no	—
385	#127	C₂³×C₁₃	1	2	yes	—
386	#127	C₂³×C₁₃	1	2	yes	—
387	#126	—	2	4	no	—
388	#126	—	2	4	no	—
389	#125	—	2	4	no	—
390	#125	—	2	4	no	—
391	#125	—	2	2	no	—
392	#125	—	2	2	no	—
393	#125	C₂³×C₁₃	1	2	yes	—
394	#125	C₂³×C₁₃	1	2	yes	—
395	#124	—	2	2	no	—
396	#124	—	2	2	no	—
397	#124	—	2	2	no	—
398	#124	—	2	2	no	—
399	#123	—	2	2	no	—
400	#123	—	2	2	no	—
401	#123	—	2	4	no	—
402	#123	—	2	4	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
408	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
409	#121	—	2	2	no	—
410	#121	—	2	2	no	—
411	#121	—	2	4	no	—
412	#121	—	2	4	no	—
413	#121	C₂³×C₁₃	1	4	yes	—
414	#121	C₂³×C₁₃	1	4	yes	—
415	#120	—	2	2	no	—
416	#120	—	2	2	no	—
417	C₄×Q₈	—	2	4	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	D₄×C₁₃	1	2	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
425	C₄×D₄	—	2	4	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	D₄×C₁₃	1	2	yes	—
429	C₄×D₄	D₄×C₁₃	1	2	yes	—
430	C₄×D₄	D₄×C₁₃	1	2	yes	—
431	C₄×D₄	C₂³×C₁₃	1	4	yes	—
432	C₄×D₄	C₂³×C₁₃	1	4	yes	—
433	#117	—	2	2	no	—
434	#117	—	2	2	no	—
435	#117	—	2	4	no	—
436	#117	C₂³×C₁₃	1	2	yes	—
437	#117	C₂³×C₁₃	1	2	yes	—
438	#117	C₂³×C₁₃	1	1	yes	characteristic
439	#117	C₂³×C₁₃	1	1	yes	characteristic
440	#117	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₂²⋊C₄	—	2	4	no	—
443	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
446	#107	C₂³×C₁₃	1	8	yes	—
447	#106	C₂³×C₁₃	1	8	yes	—
448	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
449	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
450	#103	C₂³×C₁₃	1	8	yes	—
451	#103	C₂³×C₁₃	1	8	yes	—
452	#102	C₂³×C₁₃	1	8	yes	—
453	#102	C₂³×C₁₃	1	8	yes	—
454	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
455	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
456	#97	C₂³×C₁₃	1	2	yes	—
457	C₄×C₈	C₂³×C₁₃	1	2	yes	—
458	C₄×C₈	C₂³×C₁₃	1	2	yes	—
459	C₄×C₈	C₂³×C₁₃	1	2	yes	—
460	C₂×C₁₃	—	4	1	no	—
461	C₂×C₁₃	—	4	1	no	—
462	C₂×C₁₃	—	4	1	no	—
463	C₂×C₁₃	—	8	4	no	—
464	C₂×C₁₃	#3449	1	1	yes	characteristic
465	C₂×C₁₃	C₂×#577	1	2	yes	—
466	C₂⁴	—	2	2	no	—
467	#41	—	4	2	no	—
468	#41	—	8	4	no	—
469	#41	—	8	4	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	4	4	no	—
474	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	4	4	no	—
483	C₂×D₄	—	8	4	no	—
484	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	SD₁₆	—	4	8	no	—
498	SD₁₆	—	4	8	no	—
499	M₁₆	—	4	2	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
502	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
515	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
516	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
517	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
518	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
528	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
529	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	C₂×D₄×C₁₃	1	2	yes	—
535	C₄²	C₂×D₄×C₁₃	1	2	yes	—
536	C₄²	C₂×D₄×C₁₃	1	2	yes	—
537	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
538	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
539	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
540	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
541	C₁₃	#61012	1	1	yes	characteristic, direct product factor, Sylow
542	C₂³	—	2	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	8	4	no	—
545	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
546	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
547	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
548	Q₈	—	2	8	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	4	4	no	—
551	Q₈	—	4	4	no	—
552	Q₈	—	4	4	no	—
553	D₄	—	2	8	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	4	no	—
558	D₄	—	4	4	no	—
559	D₄	—	4	4	no	—
560	D₄	—	8	4	no	—
561	D₄	—	8	4	no	—
562	D₄	—	8	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	8	4	no	—
574	C₂×C₄	—	8	4	no	—
575	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
582	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	—	2	4	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	16	4	no	—
595	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	4	no	—
604	C₄	—	4	4	no	—
605	C₄	C₁₃×#577	1	4	yes	—
606	C₄	C₁₃×#585	1	2	yes	—
607	C₂	—	4	1	no	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	8	4	no	—
611	C₂	C₁₃×#3449	1	1	yes	characteristic
612	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
1. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3260	C₂	semidirect
4. C₁₃×#3231	C₂	semidirect
5. C₁₃×#3228	C₂	semidirect
6. C₁₃×#3208	C₂	semidirect
7. C₁₃×#3206	C₂	semidirect
8. C₁₃×#3200	C₂	semidirect
9. C₁₃×#3182	C₂	semidirect
10. C₁₃×#3167	C₂	semidirect
11. C₁₃×#3126	C₂	semidirect
12. C₁₃×#3123	C₂	semidirect
13. C₁₃×#2922	C₂	semidirect
23. C₁₃×#541	C₂²	semidirect
30. C₁₃×#533	C₂²	semidirect
31. C₁₃×#533	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
36. C₁₃×#519	C₂²	semidirect
39. C₁₃×#500	C₂²	semidirect
40. C₁₃×#498	C₂²	semidirect
43. C₁₃×#487	C₂²	semidirect
44. C₁₃×#487	C₂²	semidirect
48. C₁₃×#482	C₂²	semidirect
49. C₁₃×#479	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#468	C₂²	semidirect
52. C₁₃×#465	C₂²	semidirect
53. C₁₃×#461	C₂²	semidirect
56. C₁₃×#448	C₂²	semidirect
57. C₁₃×#440	C₂²	semidirect
58. C₄×C₁₃×SD₁₆	C₂²	semidirect
60. C₁₃×#433	C₂²	semidirect
62. C₁₃×#431	C₂²	semidirect
63. C₁₃×#424	C₂²	semidirect
65. C₄×C₁₃×M₁₆	C₂²	semidirect
66. C₂×C₄×C₈×C₁₃	C₂²	semidirect
160. #61012	C₁₃	direct (N × H)
236. #3509	C₂×C₁₃	semidirect
238. #3260	C₂×C₁₃	semidirect
239. #3231	C₂×C₁₃	semidirect
240. #3228	C₂×C₁₃	semidirect
241. #3208	C₂×C₁₃	semidirect
242. #3206	C₂×C₁₃	semidirect
243. #3200	C₂×C₁₃	semidirect
244. #3182	C₂×C₁₃	semidirect
245. #3167	C₂×C₁₃	semidirect
246. #3126	C₂×C₁₃	semidirect
247. #3123	C₂×C₁₃	semidirect
248. #2922	C₂×C₁₃	semidirect
301. #541	C₂²×C₁₃	semidirect
308. #533	C₂²×C₁₃	semidirect
309. #533	C₂²×C₁₃	semidirect
312. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
314. #519	C₂²×C₁₃	semidirect
317. #500	C₂²×C₁₃	semidirect
318. #498	C₂²×C₁₃	semidirect
321. #487	C₂²×C₁₃	semidirect
322. #487	C₂²×C₁₃	semidirect
326. #482	C₂²×C₁₃	semidirect
327. #479	C₂²×C₁₃	semidirect
328. #478	C₂²×C₁₃	semidirect
329. #468	C₂²×C₁₃	semidirect
330. #465	C₂²×C₁₃	semidirect
331. #461	C₂²×C₁₃	semidirect
334. #448	C₂²×C₁₃	semidirect
335. #440	C₂²×C₁₃	semidirect
336. C₄×SD₁₆	C₂²×C₁₃	semidirect
338. #433	C₂²×C₁₃	semidirect
340. #431	C₂²×C₁₃	semidirect
341. #424	C₂²×C₁₃	semidirect
343. C₄×M₁₆	C₂²×C₁₃	semidirect
344. C₂×C₄×C₈	C₂²×C₁₃	semidirect
541. C₁₃	#61012	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×#3509	2
C₁₃×#3508	2
C₁₃×#3260	2
C₁₃×#3231	2
C₁₃×#3228	2
C₁₃×#3208	2
C₁₃×#3206	2
C₁₃×#3200	2
C₁₃×#3182	2
C₁₃×#3167	2
C₁₃×#3126	2
C₁₃×#3123	2
C₁₃×#2922	2
#61012	13

Subgroups — C13×#61012 #15747351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61012 #15747351