Subgroups — C₁₃×#23616 #15709955

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#428	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₁₃×#424	—	2	4	no	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₁₃×#417	—	2	4	no	—
26	C₁₃×#416	—	2	4	no	—
27	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#389	C₂²	1	2	yes	—
36	C₁₃×#389	C₂²	1	2	yes	—
37	C₁₃×#386	—	2	2	no	—
38	C₁₃×#385	—	2	2	no	—
39	C₁₃×#384	—	2	1	no	—
40	C₁₃×#382	—	2	1	no	—
41	C₁₃×#380	—	2	1	no	—
42	C₁₃×#380	—	2	1	no	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	Q₈	1	4	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₃	—	2	1	no	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	—	2	2	no	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₁₃×#117	—	2	2	no	—
68	C₁₃×#117	—	2	2	no	—
69	C₁₃×#117	—	2	2	no	—
70	C₁₃×#117	D₄	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
91	C₁₃×#107	—	2	4	no	—
92	C₁₃×#106	—	2	4	no	—
93	C₁₃×C₄⋊C₈	—	2	4	no	—
94	C₁₃×C₄⋊C₈	—	2	4	no	—
95	C₁₃×#103	—	2	4	no	—
96	C₁₃×#103	—	2	2	no	—
97	C₁₃×#103	—	2	2	no	—
98	C₁₃×#102	—	2	4	no	—
99	C₁₃×#102	—	2	2	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	C₁₃×#95	—	2	2	no	—
103	C₁₃×#95	—	2	2	no	—
104	C₁₃×#95	—	2	2	no	—
105	#23616	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₁₃×#41	—	2	8	no	—
109	C₁₃×#41	—	2	8	no	—
110	C₁₃×#41	—	4	4	no	—
111	C₁₃×#41	—	4	4	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	8	1	no	—
138	C₂²×C₄×C₁₃	—	8	1	no	—
139	C₂²×C₄×C₁₃	—	8	1	no	—
140	C₂²×C₄×C₁₃	—	8	1	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₁₃	#41	1	2	yes	—
148	C₂²×C₄×C₁₃	#41	1	2	yes	—
149	C₂²×C₄×C₁₃	#41	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×M₁₆	—	2	8	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	4	4	no	—
161	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	4	2	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	8	2	no	—
173	C₁₃×C₄⋊C₄	—	8	2	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
176	C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	8	2	no	—
179	C₁₃×C₂²⋊C₄	—	8	2	no	—
180	C₄²×C₁₃	—	2	4	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
186	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
187	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2311	C₂×C₁₃	1	1	yes	characteristic
189	#2068	C₂×C₁₃	1	2	yes	complemented
190	#2067	C₂×C₁₃	1	2	yes	complemented
191	#2066	C₂×C₁₃	1	2	yes	complemented
192	#2065	C₂×C₁₃	1	2	yes	complemented
193	C₂×#340	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	#121	1	2	yes	—
206	C₂³×C₁₃	#121	1	2	yes	—
207	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
208	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₁₃	—	2	2	no	—
210	Q₈×C₁₃	—	2	2	no	—
211	Q₈×C₁₃	—	4	1	no	—
212	Q₈×C₁₃	—	4	1	no	—
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	—	2	2	no	—
215	D₄×C₁₃	—	4	8	no	—
216	D₄×C₁₃	—	4	1	no	—
217	D₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	8	4	no	—
241	C₂×C₄×C₁₃	—	8	4	no	—
242	C₂×C₄×C₁₃	#121	1	4	yes	—
243	C₂×C₄×C₁₃	#121	1	2	yes	—
244	C₂×C₄×C₁₃	#121	1	2	yes	—
245	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
246	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
248	C₂×C₄×C₁₃	#126	1	4	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₈×C₁₃	—	2	4	no	—
256	C₈×C₁₃	—	4	1	no	—
257	C₈×C₁₃	—	4	1	no	—
258	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
260	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	#428	—	2	4	no	—
266	C₂×#107	C₂²×C₁₃	1	2	yes	—
267	C₂×#106	C₂²×C₁₃	1	2	yes	—
268	#424	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
271	#417	—	2	4	no	—
272	#416	—	2	4	no	—
273	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#103	C₂²×C₁₃	1	2	yes	—
275	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#102	C₂²×C₁₃	1	2	yes	—
278	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
279	#391	C₂²×C₁₃	1	2	yes	—
280	#390	C₂²×C₁₃	1	2	yes	—
281	#389	C₂²×C₁₃	1	2	yes	—
282	#389	C₂²×C₁₃	1	2	yes	—
283	#386	—	2	2	no	—
284	#385	—	2	2	no	—
285	#384	—	2	1	no	—
286	#382	—	2	1	no	—
287	#380	—	2	1	no	—
288	#380	—	2	1	no	—
289	#340	C₂²×C₁₃	1	2	yes	—
290	#340	C₂²×C₁₃	1	2	yes	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	8	1	no	—
301	C₂²×C₁₃	—	8	1	no	—
302	C₂²×C₁₃	—	8	1	no	—
303	C₂²×C₁₃	—	8	1	no	—
304	C₂²×C₁₃	#396	1	4	yes	—
305	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
306	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
307	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
308	C₂²×C₁₃	#576	1	1	yes	characteristic
309	C₂²×C₁₃	#577	1	1	yes	characteristic
310	C₂²×C₁₃	#577	1	1	yes	characteristic
311	C₂²×C₁₃	#578	1	1	yes	characteristic
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	2	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	4	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	8	2	no	—
318	C₄×C₁₃	—	8	2	no	—
319	C₄×C₁₃	#396	1	4	yes	—
320	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
321	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
323	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	Q₈×C₁₃	1	4	yes	—
330	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
340	C₂²×C₈	—	2	2	no	—
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
346	#117	—	2	2	no	—
347	#117	—	2	2	no	—
348	#117	—	2	2	no	—
349	#117	D₄×C₁₃	1	4	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
370	#107	—	2	4	no	—
371	#106	—	2	4	no	—
372	C₄⋊C₈	—	2	4	no	—
373	C₄⋊C₈	—	2	4	no	—
374	#103	—	2	4	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#102	—	2	4	no	—
378	#102	—	2	2	no	—
379	#102	—	2	2	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	C₂×C₁₃	—	2	4	no	—
385	C₂×C₁₃	—	8	2	no	—
386	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
387	C₂×C₁₃	#3045	1	1	yes	characteristic
388	C₂×C₁₃	#3046	1	1	yes	characteristic
389	C₂×C₁₃	#3062	1	1	yes	characteristic
390	C₂×C₁₃	#3063	1	1	yes	characteristic
391	C₂×C₁₃	#3083	1	1	yes	characteristic
392	C₂×C₁₃	#3084	1	1	yes	characteristic
393	C₂⁴	—	2	1	no	—
394	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
395	#41	—	2	8	no	—
396	#41	—	2	8	no	—
397	#41	—	4	4	no	—
398	#41	—	4	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	8	1	no	—
425	C₂²×C₄	—	8	1	no	—
426	C₂²×C₄	—	8	1	no	—
427	C₂²×C₄	—	8	1	no	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
434	C₂²×C₄	C₁₃×#41	1	2	yes	—
435	C₂²×C₄	C₁₃×#41	1	2	yes	—
436	C₂²×C₄	C₁₃×#41	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	M₁₆	—	2	8	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	4	4	no	—
448	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	8	2	no	—
460	C₄⋊C₄	—	8	2	no	—
461	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	8	2	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₁₃	#23616	1	1	yes	characteristic, direct product factor, Sylow
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	C₁₃×#121	1	2	yes	—
483	C₂³	C₁₃×#121	1	2	yes	—
484	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
485	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	Q₈	—	2	2	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	4	8	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	—	8	4	no	—
519	C₂×C₄	C₁₃×#121	1	2	yes	—
520	C₂×C₄	C₁₃×#121	1	2	yes	—
521	C₂×C₄	C₁₃×#121	1	4	yes	—
522	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
523	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
524	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
525	C₂×C₄	C₁₃×#126	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
530	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
531	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
532	C₈	—	2	4	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	C₁₃×#396	1	4	yes	—
549	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
550	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
551	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
552	C₂²	C₁₃×#576	1	1	yes	characteristic
553	C₂²	C₁₃×#577	1	1	yes	characteristic
554	C₂²	C₁₃×#577	1	1	yes	characteristic
555	C₂²	C₁₃×#578	1	1	yes	characteristic
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	8	2	no	—
562	C₄	—	8	2	no	—
563	C₄	C₁₃×#396	1	4	yes	—
564	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
565	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
566	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
567	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
568	C₂	—	2	4	no	—
569	C₂	—	8	2	no	—
570	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
571	C₂	C₁₃×#3045	1	1	yes	characteristic
572	C₂	C₁₃×#3046	1	1	yes	characteristic
573	C₂	C₁₃×#3062	1	1	yes	characteristic
574	C₂	C₁₃×#3063	1	1	yes	characteristic
575	C₂	C₁₃×#3083	1	1	yes	characteristic
576	C₂	C₁₃×#3084	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#428	C₂	semidirect
2. C₂×C₁₃×#424	C₂	semidirect
5. C₁₃×#2317	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2067	C₂	semidirect
9. C₁₃×#2066	C₂	semidirect
10. C₁₃×#2065	C₂	semidirect
11. C₂×C₁₃×#340	C₂	semidirect
105. #23616	C₁₃	direct (N × H)
183. C₂×#428	C₂×C₁₃	semidirect
184. C₂×#424	C₂×C₁₃	semidirect
187. #2317	C₂×C₁₃	semidirect
189. #2068	C₂×C₁₃	semidirect
190. #2067	C₂×C₁₃	semidirect
191. #2066	C₂×C₁₃	semidirect
192. #2065	C₂×C₁₃	semidirect
193. C₂×#340	C₂×C₁₃	semidirect
470. C₁₃	#23616	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#428	2
C₂×C₁₃×#424	2
C₂×C₁₃×#417	2
C₂×C₁₃×#416	2
C₁₃×#2317	2
C₁₃×#2311	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2066	2
C₁₃×#2065	2
C₂×C₁₃×#340	2
#23616	13

Subgroups — C13×#23616 #15709955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23616 #15709955