Subgroups — C₁₃×#32906 #15719245

Order 3328.

1436 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#451	C₂	1	2	yes	maximal
4	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1878	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1872	C₂	1	2	yes	maximal
7	C₁₃×#1803	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	—	2	1	no	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#462	—	2	8	no	—
23	C₁₃×#451	—	2	8	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	4	yes	—
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	2	yes	—
29	C₁₃×#389	—	2	1	no	—
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#380	—	2	1	no	—
33	C₁₃×#380	—	2	1	no	—
34	C₁₃×#340	C₂²	1	4	yes	—
35	C₁₃×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₃	—	2	4	no	—
37	C₂²×Q₈×C₁₃	—	2	4	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	D₄	1	4	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×Q₁₆	—	2	8	no	—
49	C₂×C₁₃×Q₁₆	—	2	8	no	—
50	C₂×C₁₃×Q₁₆	—	2	8	no	—
51	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
52	C₁₃×C₄⋊Q₈	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	2	8	no	—
56	C₄×Q₈×C₁₃	—	2	8	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	4	no	—
60	C₄×Q₈×C₁₃	D₄	1	8	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	8	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	4	no	—
78	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊C₈	—	2	4	no	—
83	C₁₃×#103	—	2	8	no	—
84	C₁₃×#103	—	2	8	no	—
85	C₁₃×C₂²⋊C₈	—	2	4	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	#32906	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	16	no	—
92	C₂×Q₈×C₁₃	—	2	4	no	—
93	C₂×Q₈×C₁₃	—	2	16	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
104	C₂×Q₈×C₁₃	#41	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
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	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	complemented
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	#41	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×Q₁₆	—	4	16	no	—
132	C₂×C₈×C₁₃	—	2	4	no	—
133	C₂×C₈×C₁₃	—	2	4	no	—
134	C₂×C₈×C₁₃	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	8	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	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	4	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₄²×C₁₃	—	2	8	no	—
149	C₄²×C₁₃	—	2	8	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
155	C₂×#462	C₂×C₁₃	1	2	yes	complemented
156	C₂×#451	C₂×C₁₃	1	2	yes	—
157	#2857	C₂×C₁₃	1	1	yes	characteristic
158	#1878	C₂×C₁₃	1	4	yes	complemented
159	#1872	C₂×C₁₃	1	2	yes	—
160	#1803	C₂×C₁₃	1	2	yes	complemented
161	#1797	C₂×C₁₃	1	1	yes	characteristic
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	1	no	—
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	#121	1	2	yes	—
167	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
168	C₂³×C₁₃	#137	1	2	yes	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	16	no	—
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	—	2	4	no	—
173	Q₈×C₁₃	—	2	4	no	—
174	Q₈×C₁₃	—	4	4	no	—
175	Q₈×C₁₃	—	4	4	no	—
176	Q₈×C₁₃	#121	1	8	yes	—
177	C₂×C₄×C₁₃	—	2	16	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	#120	1	2	yes	—
205	C₂×C₄×C₁₃	#120	1	2	yes	—
206	C₂×C₄×C₁₃	#121	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
208	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
209	C₂×C₄×C₁₃	#137	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₈×C₁₃	—	4	4	no	—
215	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
217	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×Q₈	—	2	8	no	—
220	C₂×C₄×Q₈	—	2	1	no	—
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₄⋊C₄	—	2	1	no	—
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄²	—	2	1	no	—
227	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
228	#462	—	2	8	no	—
229	#451	—	2	8	no	—
230	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
231	C₂×#103	C₂²×C₁₃	1	4	yes	—
232	C₂×#103	C₂²×C₁₃	1	4	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
234	#391	C₂²×C₁₃	1	2	yes	—
235	#389	—	2	1	no	—
236	#389	—	2	1	no	—
237	#384	C₂²×C₁₃	1	1	yes	characteristic
238	#380	—	2	1	no	—
239	#380	—	2	1	no	—
240	#340	C₂²×C₁₃	1	4	yes	—
241	#336	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	2	2	no	—
248	C₂²×C₁₃	#462	1	4	yes	complemented
249	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
251	C₂²×C₁₃	#525	1	1	yes	characteristic
252	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
255	C₂²×C₁₃	#575	1	1	yes	characteristic
256	C₄×C₁₃	—	2	8	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	4	1	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	8	2	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	#451	1	4	yes	complemented
265	C₄×C₁₃	C₂×#121	1	2	yes	—
266	C₄×C₁₃	#525	1	2	yes	—
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	—	2	4	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×Q₈	D₄×C₁₃	1	4	yes	—
272	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
277	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×Q₁₆	—	2	8	no	—
280	C₂×Q₁₆	—	2	8	no	—
281	C₂×Q₁₆	—	2	8	no	—
282	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	8	no	—
287	C₄×Q₈	—	2	8	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	D₄×C₁₃	1	8	yes	—
292	C₂×C₄⋊C₄	—	2	8	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₄²	—	2	8	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
313	C₄⋊C₈	—	2	4	no	—
314	#103	—	2	8	no	—
315	#103	—	2	8	no	—
316	C₂²⋊C₈	—	2	4	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	C₂×C₁₃	—	2	4	no	—
320	C₂×C₁₃	#2847	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
322	C₂×C₁₃	#3007	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
324	C₂×C₁₃	#3037	1	1	yes	characteristic
325	C₂×C₁₃	#3104	1	1	yes	characteristic
326	C₂×C₁₃	#3113	1	1	yes	characteristic
327	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	16	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	16	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
341	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
342	C₂×Q₈	C₁₃×#41	1	4	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	complemented
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₁₃×#41	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
369	Q₁₆	—	4	16	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₄²	—	2	8	no	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	C₂×D₄×C₁₃	1	4	yes	—
392	C₁₃	#32906	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	C₁₃×#121	1	2	yes	—
398	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
399	C₂³	C₁₃×#137	1	2	yes	—
400	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
401	Q₈	—	2	16	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	4	no	—
406	Q₈	—	4	4	no	—
407	Q₈	C₁₃×#121	1	8	yes	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	C₁₃×#120	1	2	yes	—
436	C₂×C₄	C₁₃×#120	1	2	yes	—
437	C₂×C₄	C₁₃×#121	1	2	yes	—
438	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
439	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
440	C₂×C₄	C₁₃×#137	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
443	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
444	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
445	C₈	—	4	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	C₁₃×#462	1	4	yes	complemented
453	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
454	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
455	C₂²	C₁₃×#525	1	1	yes	characteristic
456	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
457	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
458	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
459	C₂²	C₁₃×#575	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	2	8	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	4	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	2	no	—
468	C₄	C₁₃×#451	1	4	yes	complemented
469	C₄	C₂×C₁₃×#121	1	2	yes	—
470	C₄	C₁₃×#525	1	2	yes	—
471	C₂	—	2	4	no	—
472	C₂	C₁₃×#2847	1	1	yes	characteristic
473	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
474	C₂	C₁₃×#3007	1	1	yes	characteristic
475	C₂	C₂×C₁₃×#462	1	1	yes	characteristic
476	C₂	C₁₃×#3037	1	1	yes	characteristic
477	C₂	C₁₃×#3104	1	1	yes	characteristic
478	C₂	C₁₃×#3113	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#462	C₂	semidirect
5. C₁₃×#1878	C₂	semidirect
7. C₁₃×#1803	C₂	semidirect
88. #32906	C₁₃	direct (N × H)
122. C₂²×C₄×C₁₃	Q₁₆	semidirect
155. C₂×#462	C₂×C₁₃	semidirect
158. #1878	C₂×C₁₃	semidirect
160. #1803	C₂×C₁₃	semidirect
248. C₂²×C₁₃	#462	semidirect
264. C₄×C₁₃	#451	semidirect
360. C₂²×C₄	C₁₃×Q₁₆	semidirect
392. C₁₃	#32906	direct (N × H)
452. C₂²	C₁₃×#462	semidirect
468. C₄	C₁₃×#451	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₃	2
C₂×C₁₃×#462	2
C₂×C₁₃×#451	2
C₁₃×#2857	2
C₁₃×#1878	2
C₁₃×#1872	2
C₁₃×#1803	2
C₁₃×#1797	2
#32906	13

Subgroups — C13×#32906 #15719245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32906 #15719245