Subgroups — C₁₃×#24342 #15710681

Order 3328.

1248 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1877	C₂	1	2	yes	maximal
10	C₁₃×#1862	C₂	1	2	yes	maximal
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃	—	2	1	no	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₁₃	—	2	4	no	—
15	D₄×Q₈×C₁₃	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#477	—	2	4	no	—
25	C₁₃×#440	—	2	4	no	—
26	C₂×C₁₃×#107	C₂²	1	2	yes	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#400	—	2	1	no	—
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#387	—	2	2	no	—
39	C₁₃×#382	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	8	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	4	8	no	—
49	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	—	2	4	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
64	C₁₃×C₂²⋊Q₈	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	16	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	4	no	—
71	C₄×D₄×C₁₃	—	2	4	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	D₄	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₁₃	—	2	1	no	—
87	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#107	—	2	2	no	—
90	C₁₃×#107	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#102	—	2	2	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#97	—	2	2	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	#24342	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	8	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	4	4	no	—
114	C₂×Q₈×C₁₃	—	4	4	no	—
115	C₂×Q₈×C₁₃	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	complemented
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
123	C₂×D₄×C₁₃	#41	1	2	yes	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	—	4	4	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×SD₁₆	—	2	8	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	complemented
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₁₃×C₄⋊C₄	—	4	4	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	2	2	no	—
167	C₄²×C₁₃	—	4	2	no	—
168	C₄²×C₁₃	C₂×D₄	1	2	yes	—
169	C₄²×C₁₃	C₂×D₄	1	2	yes	—
170	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
171	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
173	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#2057	C₂×C₁₃	1	2	yes	complemented
175	#2024	C₂×C₁₃	1	2	yes	complemented
176	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1877	C₂×C₁₃	1	2	yes	—
179	#1862	C₂×C₁₃	1	2	yes	—
180	#1804	C₂×C₁₃	1	1	yes	characteristic
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	8	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	4	8	no	—
191	Q₈×C₁₃	—	4	16	no	—
192	Q₈×C₁₃	—	4	1	no	—
193	Q₈×C₁₃	—	4	1	no	—
194	D₄×C₁₃	—	2	2	no	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	2	2	no	—
197	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	4	16	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	#120	1	2	yes	—
220	C₂×C₄×C₁₃	#120	1	2	yes	—
221	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	—	4	1	no	—
230	C₈×C₁₃	—	4	2	no	—
231	C₂³×Q₈	—	2	1	no	—
232	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
233	D₄×Q₈	—	2	4	no	—
234	D₄×Q₈	—	2	4	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	—	2	2	no	—
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
243	#477	—	2	4	no	—
244	#440	—	2	4	no	—
245	C₂×#107	C₂²×C₁₃	1	2	yes	—
246	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#103	C₂²×C₁₃	1	2	yes	—
249	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
253	#400	—	2	1	no	—
254	#395	—	2	1	no	—
255	#391	C₂²×C₁₃	1	2	yes	—
256	#389	C₂²×C₁₃	1	2	yes	—
257	#387	—	2	2	no	—
258	#382	C₂²×C₁₃	1	1	yes	characteristic
259	#340	C₂²×C₁₃	1	2	yes	—
260	#340	C₂²×C₁₃	1	2	yes	—
261	#340	C₂²×C₁₃	1	2	yes	—
262	#336	C₂²×C₁₃	1	2	yes	—
263	#336	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
270	C₂²×C₁₃	#548	1	1	yes	characteristic
271	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
272	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
273	C₂²×C₁₃	#578	1	2	yes	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	4	no	—
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	4	2	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	8	2	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
284	C₄×C₁₃	#536	1	1	yes	characteristic
285	C₄×C₁₃	#548	1	1	yes	characteristic
286	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
287	C₂²×Q₈	—	2	8	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	4	8	no	—
291	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
299	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	—	2	16	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	D₄×C₁₃	1	4	yes	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
321	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	#107	—	2	2	no	—
332	#107	—	2	4	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	2	no	—
335	#103	—	2	4	no	—
336	#102	—	2	2	no	—
337	#102	—	2	4	no	—
338	#97	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	C₂×C₁₃	—	4	4	no	—
345	C₂×C₁₃	#2409	1	1	yes	characteristic
346	C₂×C₁₃	#3003	1	1	yes	characteristic
347	C₂×C₁₃	#3011	1	1	yes	characteristic
348	C₂×C₁₃	#3367	1	2	yes	—
349	C₂×C₁₃	#3386	1	2	yes	—
350	C₂⁴	—	2	1	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	4	4	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×Q₈	—	4	32	no	—
363	C₂×Q₈	—	4	4	no	—
364	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	complemented
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
370	C₂×D₄	C₁₃×#41	1	2	yes	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	SD₁₆	—	2	8	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	complemented
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	4	2	no	—
415	C₄²	C₂×D₄×C₁₃	1	2	yes	—
416	C₄²	C₂×D₄×C₁₃	1	2	yes	—
417	C₁₃	#24342	1	1	yes	characteristic, direct product factor, Sylow
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
424	Q₈	—	2	8	no	—
425	Q₈	—	2	2	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	4	8	no	—
428	Q₈	—	4	16	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	C₁₃×#120	1	2	yes	—
457	C₂×C₄	C₁₃×#120	1	2	yes	—
458	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
463	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
474	C₂²	C₁₃×#548	1	1	yes	characteristic
475	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
476	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
477	C₂²	C₁₃×#578	1	2	yes	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	2	no	—
486	C₄	—	8	1	no	—
487	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
488	C₄	C₁₃×#536	1	1	yes	characteristic
489	C₄	C₁₃×#548	1	1	yes	characteristic
490	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
491	C₂	—	4	4	no	—
492	C₂	C₁₃×#2409	1	1	yes	characteristic
493	C₂	C₁₃×#3003	1	1	yes	characteristic
494	C₂	C₁₃×#3011	1	1	yes	characteristic
495	C₂	C₁₃×#3367	1	2	yes	—
496	C₂	C₁₃×#3386	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#477	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#2024	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
56. C₂×C₁₃×SD₁₆	Q₈	semidirect
102. #24342	C₁₃	direct (N × H)
117. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
148. C₂×C₈×C₁₃	C₂×Q₈	semidirect
171. C₂×#477	C₂×C₁₃	semidirect
173. #2581	C₂×C₁₃	semidirect
174. #2057	C₂×C₁₃	semidirect
175. #2024	C₂×C₁₃	semidirect
176. #1993	C₂×C₁₃	semidirect
177. #1985	C₂×C₁₃	semidirect
298. C₂×SD₁₆	Q₈×C₁₃	semidirect
364. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
395. C₂×C₈	C₂×Q₈×C₁₃	semidirect
417. C₁₃	#24342	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×D₄×Q₈×C₁₃	2
C₂×C₁₃×#477	2
C₂×C₁₃×#440	2
C₁₃×#2581	2
C₁₃×#2057	2
C₁₃×#2024	2
C₁₃×#1993	2
C₁₃×#1985	2
C₁₃×#1877	2
C₁₃×#1862	2
C₁₃×#1804	2
#24342	13

Subgroups — C13×#24342 #15710681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24342 #15710681