Subgroups — C₁₃×#17983 #15704322

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3171	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1588	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1586	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1582	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1581	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1496	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1495	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₁₃×#529	C₂²	1	1	yes	characteristic
15	C₁₃×#501	C₄	1	1	yes	characteristic
16	C₁₃×#496	C₄	1	1	yes	characteristic
17	C₁₃×#490	C₄	1	1	yes	characteristic
18	C₁₃×#489	C₄	1	1	yes	characteristic
19	C₁₃×#469	C₄	1	2	yes	—
20	C₁₃×#468	C₄	1	2	yes	—
21	C₁₃×#446	C₂²	1	1	yes	characteristic
22	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₁₃×D₈	C₂²	1	2	yes	—
25	C₁₃×#436	—	2	1	no	—
26	C₁₃×#436	C₂²	1	1	yes	characteristic
27	C₁₃×#436	C₂²	1	2	yes	—
28	C₁₃×#435	—	2	1	no	—
29	C₈×D₄×C₁₃	—	2	1	no	—
30	C₈×D₄×C₁₃	—	2	1	no	—
31	C₈×D₄×C₁₃	C₂²	1	2	yes	—
32	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#433	—	2	1	no	—
34	C₁₃×#432	C₂²	1	1	yes	characteristic
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₁₃×#408	—	2	1	no	—
38	C₁₃×#405	—	2	1	no	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	2	yes	—
42	C₁₃×#334	C₂²	1	2	yes	—
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₁₃×#322	C₂²	1	2	yes	—
48	C₁₃×#322	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
52	C₁₃×#131	—	4	4	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#126	—	2	1	no	—
64	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
65	C₁₃×#124	—	2	1	no	—
66	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
67	C₁₃×#123	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
69	C₁₃×#121	—	2	1	no	—
70	C₁₃×#121	C₂×C₄	1	2	yes	—
71	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
72	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	—	2	1	no	—
75	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#117	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	C₂×C₄	1	2	yes	—
80	C₁₃×#106	C₂×C₄	1	2	yes	—
81	C₁₃×C₄⋊C₈	—	2	1	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	—	2	1	no	—
84	C₁₃×C₄⋊C₈	—	2	1	no	—
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₃×#103	C₂×C₄	1	2	yes	—
89	C₁₃×#102	C₂×C₄	1	2	yes	—
90	C₁₃×#102	C₂×C₄	1	2	yes	—
91	C₁₃×#102	C₂×C₄	1	2	yes	—
92	C₁₃×C₂²⋊C₈	—	2	1	no	—
93	C₁₃×C₂²⋊C₈	—	2	1	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×C₂²⋊C₈	—	2	2	no	—
96	C₁₃×C₂²⋊C₈	—	2	1	no	—
97	C₁₃×C₂²⋊C₈	—	2	1	no	—
98	C₁₃×#97	—	2	1	no	—
99	C₁₃×#97	—	2	1	no	—
100	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₁₃	—	2	1	no	—
103	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₃	C₂³	1	2	yes	—
106	C₄×C₈×C₁₃	C₂³	1	2	yes	—
107	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	#17983	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₁₃×#41	—	4	2	no	—
111	C₁₃×#41	—	4	2	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₁₃×SD₁₆	—	4	2	no	—
126	C₁₃×D₈	—	4	2	no	—
127	C₁₃×M₁₆	—	4	2	no	—
128	C₁₃×M₁₆	—	4	4	no	—
129	C₁₃×M₁₆	—	4	2	no	—
130	C₁₃×M₁₆	—	4	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	4	1	no	—
137	C₂×C₈×C₁₃	—	4	2	no	—
138	C₂×C₈×C₁₃	—	4	4	no	—
139	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₃	#41	1	1	yes	characteristic
164	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
165	#3171	C₂×C₁₃	1	1	yes	characteristic
166	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1588	C₂×C₁₃	1	2	yes	complemented
169	#1586	C₂×C₁₃	1	2	yes	complemented
170	#1582	C₂×C₁₃	1	2	yes	complemented
171	#1581	C₂×C₁₃	1	2	yes	complemented
172	#1569	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1496	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1495	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	2	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×#131	—	2	1	no	—
217	#532	C₂²×C₁₃	1	1	yes	characteristic
218	#529	C₂²×C₁₃	1	1	yes	characteristic
219	#501	C₄×C₁₃	1	1	yes	characteristic
220	#496	C₄×C₁₃	1	1	yes	characteristic
221	#490	C₄×C₁₃	1	1	yes	characteristic
222	#489	C₄×C₁₃	1	1	yes	characteristic
223	#469	C₄×C₁₃	1	2	yes	—
224	#468	C₄×C₁₃	1	2	yes	—
225	#446	C₂²×C₁₃	1	1	yes	characteristic
226	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
228	C₄×D₈	C₂²×C₁₃	1	2	yes	—
229	#436	—	2	1	no	—
230	#436	C₂²×C₁₃	1	1	yes	characteristic
231	#436	C₂²×C₁₃	1	2	yes	—
232	#435	—	2	1	no	—
233	C₈×D₄	—	2	1	no	—
234	C₈×D₄	—	2	1	no	—
235	C₈×D₄	C₂²×C₁₃	1	2	yes	—
236	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	#433	—	2	1	no	—
238	#432	C₂²×C₁₃	1	1	yes	characteristic
239	#431	C₂²×C₁₃	1	1	yes	characteristic
240	#423	C₂²×C₁₃	1	1	yes	characteristic
241	#408	—	2	1	no	—
242	#405	—	2	1	no	—
243	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
245	#335	C₂²×C₁₃	1	2	yes	—
246	#334	C₂²×C₁₃	1	2	yes	—
247	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
248	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
249	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
250	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
251	#322	C₂²×C₁₃	1	2	yes	—
252	#322	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	1	no	—
262	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	1	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	1	no	—
271	C₄×C₁₃	#568	1	2	yes	—
272	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₄×C₁₃	#575	1	1	yes	characteristic
274	C₂×#41	—	2	1	no	—
275	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
276	C₂×D₈	C₂×C₄×C₁₃	1	2	yes	—
277	#131	—	4	4	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
285	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
286	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
287	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
288	#126	—	2	1	no	—
289	#125	C₂×C₄×C₁₃	1	1	yes	characteristic
290	#124	—	2	1	no	—
291	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
292	#123	—	2	1	no	—
293	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
294	#121	—	2	1	no	—
295	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
296	#121	C₂×C₄×C₁₃	1	2	yes	—
297	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₄×D₄	C₂³×C₁₃	1	2	yes	—
302	#117	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
304	#107	C₂×C₄×C₁₃	1	2	yes	—
305	#106	C₂×C₄×C₁₃	1	2	yes	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
313	#103	C₂×C₄×C₁₃	1	2	yes	—
314	#102	C₂×C₄×C₁₃	1	2	yes	—
315	#102	C₂×C₄×C₁₃	1	2	yes	—
316	#102	C₂×C₄×C₁₃	1	2	yes	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	#97	—	2	1	no	—
324	#97	—	2	1	no	—
325	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
326	#97	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
329	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₁₃	1	2	yes	—
331	C₄×C₈	C₂³×C₁₃	1	2	yes	—
332	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₁₃	—	4	1	no	—
335	C₂×C₁₃	—	8	2	no	—
336	C₂×C₁₃	—	8	1	no	—
337	C₂×C₁₃	#2932	1	1	yes	characteristic
338	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
339	C₂×C₁₃	#2955	1	1	yes	characteristic
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
349	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
355	SD₁₆	—	4	2	no	—
356	D₈	—	4	2	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	—	4	4	no	—
359	M₁₆	—	4	2	no	—
360	M₁₆	—	4	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	—	4	4	no	—
369	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
370	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
381	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
382	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
392	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₄²	C₁₃×#41	1	1	yes	characteristic
394	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₁₃	#17983	1	1	yes	characteristic, direct product factor, Sylow
396	C₂³	—	2	1	no	—
397	C₂³	—	2	2	no	—
398	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	1	no	—
454	C₄	C₁₃×#568	1	2	yes	—
455	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₄	C₁₃×#575	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	8	2	no	—
459	C₂	—	8	1	no	—
460	C₂	C₁₃×#2932	1	1	yes	characteristic
461	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
462	C₂	C₁₃×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#3171	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2966	C₂	semidirect
3. C₁₃×#2931	C₂	semidirect
4. C₁₃×#1588	C₂	semidirect
5. C₁₃×#1586	C₂	semidirect
6. C₁₃×#1582	C₂	semidirect
7. C₁₃×#1581	C₂	semidirect
8. C₁₃×#1569	C₂	semidirect
9. C₁₃×#1496	C₂	semidirect
10. C₁₃×#1495	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
109. #17983	C₁₃	direct (N × H)
166. #2966	C₂×C₁₃	semidirect
167. #2931	C₂×C₁₃	semidirect
168. #1588	C₂×C₁₃	semidirect
169. #1586	C₂×C₁₃	semidirect
170. #1582	C₂×C₁₃	semidirect
171. #1581	C₂×C₁₃	semidirect
172. #1569	C₂×C₁₃	semidirect
173. #1496	C₂×C₁₃	semidirect
174. #1495	C₂×C₁₃	semidirect
175. #1451	C₂×C₁₃	semidirect
395. C₁₃	#17983	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×#3171	2
C₁₃×#2966	2
C₁₃×#2931	2
C₁₃×#1588	2
C₁₃×#1586	2
C₁₃×#1582	2
C₁₃×#1581	2
C₁₃×#1569	2
C₁₃×#1496	2
C₁₃×#1495	2
C₁₃×#1451	2
#17983	13

Subgroups — C13×#17983 #15704322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17983 #15704322