Subgroups — C₁₃×#23612 #15709951

Order 3328.

1214 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2067	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2065	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#427	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
20	C₁₃×#424	—	2	4	no	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₁₃×#418	—	2	4	no	—
24	C₂×C₁₃×#102	—	2	4	no	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	4	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₁₃×#390	—	2	1	no	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#390	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	complemented
32	C₁₃×#385	—	2	2	no	—
33	C₁₃×#384	—	2	1	no	—
34	C₁₃×#382	—	2	1	no	—
35	C₁₃×#379	—	2	2	no	—
36	C₁₃×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	D₄	1	4	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	—	2	2	no	—
60	C₁₃×#117	—	2	2	no	—
61	C₁₃×#117	—	2	2	no	—
62	C₁₃×#117	D₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
80	C₁₃×#107	—	2	4	no	—
81	C₁₃×#106	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	4	no	—
83	C₁₃×C₄⋊C₈	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#102	—	2	4	no	—
86	C₁₃×#102	—	2	8	no	—
87	C₁₃×#95	—	2	4	no	—
88	#23612	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	4	2	no	—
92	C₂⁴×C₁₃	—	4	2	no	—
93	C₂⁴×C₁₃	—	8	2	no	—
94	C₂⁴×C₁₃	—	8	2	no	—
95	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₁₃	—	2	8	no	—
97	C₂×D₄×C₁₃	—	2	8	no	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	4	4	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	8	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	#41	1	2	yes	—
122	C₂²×C₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₁₃×M₁₆	—	4	4	no	—
125	C₂×C₈×C₁₃	—	2	8	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	8	4	no	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	2	no	—
148	C₁₃×C₂²⋊C₄	—	8	4	no	—
149	C₁₃×C₂²⋊C₄	—	8	4	no	—
150	C₄²×C₁₃	—	2	4	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	4	2	no	—
154	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
157	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic
158	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2309	C₂×C₁₃	1	1	yes	characteristic
160	#2067	C₂×C₁₃	1	4	yes	complemented
161	#2065	C₂×C₁₃	1	4	yes	complemented
162	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	4	no	—
169	C₂³×C₁₃	—	4	4	no	—
170	C₂³×C₁₃	—	4	8	no	—
171	C₂³×C₁₃	—	8	8	no	—
172	C₂³×C₁₃	—	8	8	no	—
173	C₂³×C₁₃	—	8	4	no	—
174	C₂³×C₁₃	—	8	4	no	—
175	C₂³×C₁₃	#121	1	2	yes	—
176	C₂³×C₁₃	#121	1	2	yes	—
177	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	8	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	8	4	no	—
197	C₂×C₄×C₁₃	#121	1	4	yes	—
198	C₂×C₄×C₁₃	#121	1	2	yes	—
199	C₂×C₄×C₁₃	#121	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
201	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
202	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
203	C₂×C₄×C₁₃	#126	1	4	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
215	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	#427	—	2	4	no	—
221	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
222	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
223	#424	—	2	4	no	—
224	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
225	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
226	#418	—	2	4	no	—
227	C₂×#102	—	2	4	no	—
228	C₂×#102	C₂²×C₁₃	1	2	yes	—
229	C₂×#102	C₂²×C₁₃	1	4	yes	—
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	#390	—	2	1	no	—
232	#390	—	2	1	no	—
233	#390	C₂²×C₁₃	1	4	yes	—
234	#389	C₂²×C₁₃	1	4	yes	complemented
235	#385	—	2	2	no	—
236	#384	—	2	1	no	—
237	#382	—	2	1	no	—
238	#379	—	2	2	no	—
239	#340	C₂²×C₁₃	1	4	yes	complemented
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	4	no	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	4	8	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	8	16	no	—
247	C₂²×C₁₃	—	8	4	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	#396	1	4	yes	—
251	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
254	C₂²×C₁₃	#576	1	2	yes	—
255	C₂²×C₁₃	#577	1	2	yes	—
256	C₄×C₁₃	—	4	4	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	#396	1	4	yes	—
262	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
263	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
266	C₂⁵	—	2	1	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
274	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	D₄×C₁₃	1	4	yes	—
283	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	2	no	—
289	#117	—	2	2	no	—
290	#117	—	2	2	no	—
291	#117	D₄×C₁₃	1	4	yes	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
309	#107	—	2	4	no	—
310	#106	—	2	4	no	—
311	C₄⋊C₈	—	2	4	no	—
312	C₄⋊C₈	—	2	4	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	8	no	—
316	#95	—	2	4	no	—
317	C₂×C₁₃	—	2	4	no	—
318	C₂×C₁₃	—	8	4	no	—
319	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
320	C₂×C₁₃	#3045	1	2	yes	—
321	C₂×C₁₃	#3057	1	1	yes	characteristic
322	C₂×C₁₃	#3058	1	1	yes	characteristic
323	C₂×C₁₃	#3081	1	2	yes	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	4	2	no	—
327	C₂⁴	—	4	2	no	—
328	C₂⁴	—	8	2	no	—
329	C₂⁴	—	8	2	no	—
330	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
354	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
355	C₂²×C₄	C₁₃×#41	1	2	yes	—
356	C₂²×C₄	C₁₃×#41	1	2	yes	—
357	C₂²×C₄	C₁₃×#41	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	M₁₆	—	4	4	no	—
360	C₂×C₈	—	2	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	8	4	no	—
379	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	8	4	no	—
384	C₂²⋊C₄	—	8	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	2	no	—
389	C₁₃	#23612	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	8	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	8	8	no	—
399	C₂³	—	8	8	no	—
400	C₂³	—	8	4	no	—
401	C₂³	—	8	4	no	—
402	C₂³	C₁₃×#121	1	2	yes	—
403	C₂³	C₁₃×#121	1	2	yes	—
404	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
405	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	C₁₃×#121	1	2	yes	—
425	C₂×C₄	C₁₃×#121	1	2	yes	—
426	C₂×C₄	C₁₃×#121	1	4	yes	—
427	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
428	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
429	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
430	C₂×C₄	C₁₃×#126	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	2	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	8	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	16	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	C₁₃×#396	1	4	yes	—
451	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
452	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
453	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
454	C₂²	C₁₃×#576	1	2	yes	—
455	C₂²	C₁₃×#577	1	2	yes	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	2	no	—
461	C₄	C₁₃×#396	1	4	yes	—
462	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
463	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
464	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
465	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
466	C₂	—	2	4	no	—
467	C₂	—	8	4	no	—
468	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
469	C₂	C₁₃×#3045	1	2	yes	—
470	C₂	C₁₃×#3057	1	1	yes	characteristic
471	C₂	C₁₃×#3058	1	1	yes	characteristic
472	C₂	C₁₃×#3081	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	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×#427	C₂	semidirect
2. C₂×C₁₃×#424	C₂	semidirect
5. C₁₃×#2317	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2065	C₂	semidirect
9. C₁₃×#1736	C₂	semidirect
18. C₂×C₁₃×#107	C₂²	semidirect
19. C₂×C₁₃×#106	C₂²	semidirect
21. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
22. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
31. C₁₃×#389	C₂²	semidirect
36. C₁₃×#340	C₂²	semidirect
88. #23612	C₁₃	direct (N × H)
154. C₂×#427	C₂×C₁₃	semidirect
155. C₂×#424	C₂×C₁₃	semidirect
158. #2317	C₂×C₁₃	semidirect
160. #2067	C₂×C₁₃	semidirect
161. #2065	C₂×C₁₃	semidirect
162. #1736	C₂×C₁₃	semidirect
221. C₂×#107	C₂²×C₁₃	semidirect
222. C₂×#106	C₂²×C₁₃	semidirect
224. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
225. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
234. #389	C₂²×C₁₃	semidirect
239. #340	C₂²×C₁₃	semidirect
389. C₁₃	#23612	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×#427	2
C₂×C₁₃×#424	2
C₂×C₁₃×#418	2
C₂²×C₁₃×#102	2
C₁₃×#2317	2
C₁₃×#2309	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1736	2
#23612	13

Subgroups — C13×#23612 #15709951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23612 #15709951