Subgroups — C₁₃×#61009 #15747348

Order 3328.

1696 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3261	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3260	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3259	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3232	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3212	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3204	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3203	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3183	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3120	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3119	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#553	—	2	4	no	—
15	C₁₃×#553	—	2	4	no	—
16	C₁₃×#553	—	2	4	no	—
17	C₁₃×#552	—	2	4	no	—
18	C₁₃×#541	C₂²	1	2	yes	—
19	C₁₃×#541	C₂²	1	2	yes	—
20	C₁₃×#540	C₂²	1	2	yes	—
21	C₁₃×#540	C₂²	1	2	yes	—
22	C₁₃×#537	C₂²	1	4	yes	—
23	C₁₃×#532	C₂²	1	2	yes	—
24	C₁₃×#529	C₂²	1	4	yes	—
25	C₁₃×#529	C₂²	1	4	yes	—
26	C₂×C₁₃×#125	C₂²	1	2	yes	—
27	C₁₃×#520	C₂²	1	4	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#499	C₂²	1	2	yes	—
30	C₁₃×#499	C₂²	1	2	yes	—
31	C₁₃×#495	C₂²	1	2	yes	—
32	C₁₃×#495	C₂²	1	2	yes	—
33	C₁₃×#488	C₂²	1	4	yes	—
34	C₁₃×#488	C₂²	1	4	yes	—
35	C₁₃×#484	C₂²	1	4	yes	—
36	C₁₃×#483	C₂²	1	4	yes	—
37	C₁₃×#481	C₂²	1	4	yes	—
38	C₁₃×#480	C₂²	1	4	yes	—
39	C₁₃×#479	C₂²	1	4	yes	—
40	C₁₃×#479	C₂²	1	4	yes	—
41	C₁₃×#478	C₂²	1	4	yes	—
42	C₁₃×#478	C₂²	1	4	yes	—
43	C₁₃×#470	C₂²	1	2	yes	—
44	C₁₃×#469	C₂²	1	2	yes	—
45	C₁₃×#468	C₂²	1	4	yes	—
46	C₁₃×#467	C₂²	1	2	yes	—
47	C₁₃×#466	C₂²	1	2	yes	—
48	C₁₃×#465	C₂²	1	4	yes	—
49	C₁₃×#462	C₂²	1	4	yes	—
50	C₁₃×#461	C₂²	1	4	yes	—
51	C₁₃×#460	C₂²	1	4	yes	—
52	C₁₃×#459	C₂²	1	4	yes	—
53	C₁₃×#452	C₂²	1	4	yes	—
54	C₁₃×#452	C₂²	1	4	yes	—
55	C₁₃×#449	C₂²	1	4	yes	—
56	C₁₃×#449	C₂²	1	4	yes	—
57	C₁₃×#442	C₂²	1	2	yes	—
58	C₁₃×#441	C₂²	1	2	yes	—
59	C₁₃×#440	C₂²	1	4	yes	—
60	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
61	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
62	C₄×C₁₃×D₈	C₂²	1	2	yes	—
63	C₁₃×#433	C₂²	1	4	yes	—
64	C₁₃×#431	C₂²	1	4	yes	—
65	C₁₃×#424	C₂²	1	1	yes	characteristic
66	C₁₃×#424	C₂²	1	1	yes	characteristic
67	C₁₃×#408	C₂²	1	1	yes	characteristic
68	C₁₃×#408	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
70	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	C₂³	1	4	yes	—
72	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×D₈	C₂³	1	2	yes	—
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₃×#127	C₂³	1	2	yes	—
85	C₁₃×#126	—	2	4	no	—
86	C₁₃×#126	—	2	4	no	—
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	4	no	—
92	C₁₃×#125	C₂³	1	2	yes	—
93	C₁₃×#125	C₂³	1	2	yes	—
94	C₁₃×#125	C₂³	1	4	yes	—
95	C₁₃×#124	C₂³	1	4	yes	—
96	C₁₃×#123	—	2	4	no	—
97	C₁₃×#123	—	2	4	no	—
98	C₁₃×#123	—	2	4	no	—
99	C₁₃×#123	—	2	4	no	—
100	C₁₃×C₂²⋊Q₈	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
103	C₁₃×#121	—	2	4	no	—
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	—	2	4	no	—
106	C₁₃×#121	—	2	4	no	—
107	C₁₃×#121	—	2	4	no	—
108	C₁₃×#121	—	2	4	no	—
109	C₁₃×#121	C₂³	1	4	yes	—
110	C₁₃×#121	C₂³	1	4	yes	—
111	C₄×Q₈×C₁₃	D₄	1	2	yes	—
112	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
113	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
114	C₄×D₄×C₁₃	—	2	4	no	—
115	C₄×D₄×C₁₃	—	2	4	no	—
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₄×D₄×C₁₃	D₄	1	2	yes	—
120	C₄×D₄×C₁₃	D₄	1	4	yes	—
121	C₄×D₄×C₁₃	C₂³	1	4	yes	—
122	C₄×D₄×C₁₃	C₂³	1	4	yes	—
123	C₁₃×#117	—	2	4	no	—
124	C₁₃×#117	—	2	4	no	—
125	C₁₃×#117	—	2	4	no	—
126	C₁₃×#117	C₂³	1	1	yes	characteristic
127	C₁₃×#117	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₁₃×#107	C₂³	1	2	yes	—
134	C₁₃×#107	C₂³	1	2	yes	—
135	C₁₃×#107	C₂³	1	4	yes	—
136	C₁₃×#106	C₂³	1	4	yes	—
137	C₁₃×#106	C₂³	1	2	yes	—
138	C₁₃×#106	C₂³	1	2	yes	—
139	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
140	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
141	C₁₃×#103	C₂³	1	4	yes	—
142	C₁₃×#103	C₂³	1	4	yes	—
143	C₁₃×#103	C₂³	1	4	yes	—
144	C₁₃×#103	C₂³	1	4	yes	—
145	C₁₃×#102	C₂³	1	4	yes	—
146	C₁₃×#102	C₂³	1	4	yes	—
147	C₁₃×#102	C₂³	1	4	yes	—
148	C₁₃×#102	C₂³	1	4	yes	—
149	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
151	C₁₃×#97	C₂³	1	2	yes	—
152	C₄×C₈×C₁₃	C₂³	1	2	yes	—
153	C₄×C₈×C₁₃	C₂³	1	2	yes	—
154	C₄×C₈×C₁₃	C₂³	1	2	yes	—
155	#61009	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₁₃×#41	—	4	1	no	—
157	C₁₃×#41	—	4	1	no	—
158	C₁₃×#41	—	4	4	no	—
159	C₁₃×#41	—	4	4	no	—
160	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	4	no	—
166	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×Q₁₆	—	4	2	no	—
178	C₁₃×Q₁₆	—	4	2	no	—
179	C₁₃×SD₁₆	—	4	4	no	—
180	C₁₃×SD₁₆	—	4	4	no	—
181	C₁₃×D₈	—	4	2	no	—
182	C₁₃×D₈	—	4	2	no	—
183	C₁₃×M₁₆	—	4	1	no	—
184	C₁₃×M₁₆	—	4	1	no	—
185	C₂×C₈×C₁₃	—	4	1	no	—
186	C₂×C₈×C₁₃	—	4	1	no	—
187	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
188	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
189	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
190	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
214	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	—	2	4	no	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂×D₄	1	4	yes	—
219	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₄²×C₁₃	C₂⁴	1	2	yes	—
222	#3512	C₂×C₁₃	1	2	yes	complemented
223	#3261	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#3260	C₂×C₁₃	1	2	yes	complemented
225	#3259	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#3232	C₂×C₁₃	1	4	yes	complemented
227	#3212	C₂×C₁₃	1	4	yes	complemented
228	#3204	C₂×C₁₃	1	2	yes	complemented
229	#3203	C₂×C₁₃	1	2	yes	complemented
230	#3183	C₂×C₁₃	1	2	yes	complemented
231	#3168	C₂×C₁₃	1	2	yes	complemented
232	#3120	C₂×C₁₃	1	4	yes	complemented
233	#3119	C₂×C₁₃	1	4	yes	complemented
234	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
238	Q₈×C₁₃	—	2	4	no	—
239	Q₈×C₁₃	—	2	4	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	8	no	—
246	D₄×C₁₃	—	8	4	no	—
247	D₄×C₁₃	—	8	4	no	—
248	D₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	4	8	no	—
259	C₂×C₄×C₁₃	—	8	4	no	—
260	C₂×C₄×C₁₃	—	8	4	no	—
261	C₂×C₄×C₁₃	—	8	4	no	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	2	2	no	—
272	#553	—	2	4	no	—
273	#553	—	2	4	no	—
274	#553	—	2	4	no	—
275	#552	—	2	4	no	—
276	#541	C₂²×C₁₃	1	2	yes	—
277	#541	C₂²×C₁₃	1	2	yes	—
278	#540	C₂²×C₁₃	1	2	yes	—
279	#540	C₂²×C₁₃	1	2	yes	—
280	#537	C₂²×C₁₃	1	4	yes	—
281	#532	C₂²×C₁₃	1	2	yes	—
282	#529	C₂²×C₁₃	1	4	yes	—
283	#529	C₂²×C₁₃	1	4	yes	—
284	C₂×#125	C₂²×C₁₃	1	2	yes	—
285	#520	C₂²×C₁₃	1	4	yes	—
286	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
287	#499	C₂²×C₁₃	1	2	yes	—
288	#499	C₂²×C₁₃	1	2	yes	—
289	#495	C₂²×C₁₃	1	2	yes	—
290	#495	C₂²×C₁₃	1	2	yes	—
291	#488	C₂²×C₁₃	1	4	yes	—
292	#488	C₂²×C₁₃	1	4	yes	—
293	#484	C₂²×C₁₃	1	4	yes	—
294	#483	C₂²×C₁₃	1	4	yes	—
295	#481	C₂²×C₁₃	1	4	yes	—
296	#480	C₂²×C₁₃	1	4	yes	—
297	#479	C₂²×C₁₃	1	4	yes	—
298	#479	C₂²×C₁₃	1	4	yes	—
299	#478	C₂²×C₁₃	1	4	yes	—
300	#478	C₂²×C₁₃	1	4	yes	—
301	#470	C₂²×C₁₃	1	2	yes	—
302	#469	C₂²×C₁₃	1	2	yes	—
303	#468	C₂²×C₁₃	1	4	yes	—
304	#467	C₂²×C₁₃	1	2	yes	—
305	#466	C₂²×C₁₃	1	2	yes	—
306	#465	C₂²×C₁₃	1	4	yes	—
307	#462	C₂²×C₁₃	1	4	yes	—
308	#461	C₂²×C₁₃	1	4	yes	—
309	#460	C₂²×C₁₃	1	4	yes	—
310	#459	C₂²×C₁₃	1	4	yes	—
311	#452	C₂²×C₁₃	1	4	yes	—
312	#452	C₂²×C₁₃	1	4	yes	—
313	#449	C₂²×C₁₃	1	4	yes	—
314	#449	C₂²×C₁₃	1	4	yes	—
315	#442	C₂²×C₁₃	1	2	yes	—
316	#441	C₂²×C₁₃	1	2	yes	—
317	#440	C₂²×C₁₃	1	4	yes	—
318	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
319	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
320	C₄×D₈	C₂²×C₁₃	1	2	yes	—
321	#433	C₂²×C₁₃	1	4	yes	—
322	#431	C₂²×C₁₃	1	4	yes	—
323	#424	C₂²×C₁₃	1	1	yes	characteristic
324	#424	C₂²×C₁₃	1	1	yes	characteristic
325	#408	C₂²×C₁₃	1	1	yes	characteristic
326	#408	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	1	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	4	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	—	4	4	no	—
345	C₄×C₁₃	#585	1	1	yes	characteristic
346	C₄×C₁₃	#585	1	1	yes	characteristic
347	C₂×#41	C₂³×C₁₃	1	4	yes	—
348	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
350	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
351	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
352	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
353	C₂×D₈	C₂³×C₁₃	1	2	yes	—
354	C₂×D₈	C₂³×C₁₃	1	2	yes	—
355	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
360	#127	C₂³×C₁₃	1	2	yes	—
361	#126	—	2	4	no	—
362	#126	—	2	4	no	—
363	#126	—	2	4	no	—
364	#126	—	2	4	no	—
365	#125	—	2	4	no	—
366	#125	—	2	4	no	—
367	#125	—	2	4	no	—
368	#125	C₂³×C₁₃	1	4	yes	—
369	#125	C₂³×C₁₃	1	2	yes	—
370	#125	C₂³×C₁₃	1	2	yes	—
371	#124	C₂³×C₁₃	1	4	yes	—
372	#123	—	2	4	no	—
373	#123	—	2	4	no	—
374	#123	—	2	4	no	—
375	#123	—	2	4	no	—
376	C₂²⋊Q₈	—	2	4	no	—
377	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
378	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
379	#121	—	2	4	no	—
380	#121	—	2	4	no	—
381	#121	—	2	4	no	—
382	#121	—	2	4	no	—
383	#121	—	2	4	no	—
384	#121	—	2	4	no	—
385	#121	C₂³×C₁₃	1	4	yes	—
386	#121	C₂³×C₁₃	1	4	yes	—
387	C₄×Q₈	D₄×C₁₃	1	2	yes	—
388	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
389	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	D₄×C₁₃	1	2	yes	—
396	C₄×D₄	D₄×C₁₃	1	4	yes	—
397	C₄×D₄	C₂³×C₁₃	1	4	yes	—
398	C₄×D₄	C₂³×C₁₃	1	4	yes	—
399	#117	—	2	4	no	—
400	#117	—	2	4	no	—
401	#117	—	2	4	no	—
402	#117	C₂³×C₁₃	1	2	yes	—
403	#117	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	—	2	4	no	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
409	#107	C₂³×C₁₃	1	2	yes	—
410	#107	C₂³×C₁₃	1	2	yes	—
411	#107	C₂³×C₁₃	1	4	yes	—
412	#106	C₂³×C₁₃	1	4	yes	—
413	#106	C₂³×C₁₃	1	2	yes	—
414	#106	C₂³×C₁₃	1	2	yes	—
415	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
416	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
417	#103	C₂³×C₁₃	1	4	yes	—
418	#103	C₂³×C₁₃	1	4	yes	—
419	#103	C₂³×C₁₃	1	4	yes	—
420	#103	C₂³×C₁₃	1	4	yes	—
421	#102	C₂³×C₁₃	1	4	yes	—
422	#102	C₂³×C₁₃	1	4	yes	—
423	#102	C₂³×C₁₃	1	4	yes	—
424	#102	C₂³×C₁₃	1	4	yes	—
425	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
426	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
427	#97	C₂³×C₁₃	1	2	yes	—
428	C₄×C₈	C₂³×C₁₃	1	2	yes	—
429	C₄×C₈	C₂³×C₁₃	1	2	yes	—
430	C₄×C₈	C₂³×C₁₃	1	2	yes	—
431	C₂×C₁₃	—	4	2	no	—
432	C₂×C₁₃	—	4	1	no	—
433	C₂×C₁₃	—	8	4	no	—
434	C₂×C₁₃	#3449	1	1	yes	characteristic
435	C₂×C₁₃	#3584	1	2	yes	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	4	no	—
439	#41	—	4	4	no	—
440	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
457	Q₁₆	—	4	2	no	—
458	Q₁₆	—	4	2	no	—
459	SD₁₆	—	4	4	no	—
460	SD₁₆	—	4	4	no	—
461	D₈	—	4	2	no	—
462	D₈	—	4	2	no	—
463	M₁₆	—	4	1	no	—
464	M₁₆	—	4	1	no	—
465	C₂×C₈	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
468	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
469	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
470	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
482	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
483	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
484	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
494	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
495	C₄²	—	2	4	no	—
496	C₄²	—	2	4	no	—
497	C₄²	C₂×D₄×C₁₃	1	2	yes	—
498	C₄²	C₂×D₄×C₁₃	1	4	yes	—
499	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₄²	C₂⁴×C₁₃	1	2	yes	—
502	C₁₃	#61009	1	1	yes	characteristic, direct product factor, Sylow
503	C₂³	—	2	4	no	—
504	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
505	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
506	Q₈	—	2	4	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	4	1	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	4	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	8	no	—
514	D₄	—	8	4	no	—
515	D₄	—	8	4	no	—
516	D₄	—	8	4	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	—	8	4	no	—
530	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
532	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
533	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
535	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
536	C₈	—	2	2	no	—
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	4	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	C₁₃×#585	1	1	yes	characteristic
557	C₄	C₁₃×#585	1	1	yes	characteristic
558	C₂	—	4	2	no	—
559	C₂	—	4	1	no	—
560	C₂	—	8	4	no	—
561	C₂	C₁₃×#3449	1	1	yes	characteristic
562	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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×#3512	C₂	semidirect
2. C₁₃×#3261	C₂	semidirect
3. C₁₃×#3260	C₂	semidirect
4. C₁₃×#3259	C₂	semidirect
5. C₁₃×#3232	C₂	semidirect
6. C₁₃×#3212	C₂	semidirect
7. C₁₃×#3204	C₂	semidirect
8. C₁₃×#3203	C₂	semidirect
9. C₁₃×#3183	C₂	semidirect
10. C₁₃×#3168	C₂	semidirect
11. C₁₃×#3120	C₂	semidirect
12. C₁₃×#3119	C₂	semidirect
13. C₁₃×#2922	C₂	semidirect
155. #61009	C₁₃	direct (N × H)
222. #3512	C₂×C₁₃	semidirect
223. #3261	C₂×C₁₃	semidirect
224. #3260	C₂×C₁₃	semidirect
225. #3259	C₂×C₁₃	semidirect
226. #3232	C₂×C₁₃	semidirect
227. #3212	C₂×C₁₃	semidirect
228. #3204	C₂×C₁₃	semidirect
229. #3203	C₂×C₁₃	semidirect
230. #3183	C₂×C₁₃	semidirect
231. #3168	C₂×C₁₃	semidirect
232. #3120	C₂×C₁₃	semidirect
233. #3119	C₂×C₁₃	semidirect
234. #2922	C₂×C₁₃	semidirect
502. C₁₃	#61009	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×#3512	2
C₁₃×#3261	2
C₁₃×#3260	2
C₁₃×#3259	2
C₁₃×#3232	2
C₁₃×#3212	2
C₁₃×#3204	2
C₁₃×#3203	2
C₁₃×#3183	2
C₁₃×#3168	2
C₁₃×#3120	2
C₁₃×#3119	2
C₁₃×#2922	2
#61009	13

Subgroups — C13×#61009 #15747348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61009 #15747348