Subgroups — C₁₃×#24341 #15710680

Order 3328.

1068 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2580	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1880	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	Q₈²×C₁₃	—	2	4	no	—
14	Q₈²×C₁₃	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#474	—	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	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#399	—	2	1	no	—
35	C₁₃×#393	—	2	1	no	—
36	C₁₃×#390	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#385	—	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	2	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	—	2	16	no	—
58	C₁₃×C₄⋊Q₈	—	2	8	no	—
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
63	C₄×Q₈×C₁₃	—	2	8	no	—
64	C₄×Q₈×C₁₃	—	2	4	no	—
65	C₄×Q₈×C₁₃	—	2	4	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	D₄	1	4	yes	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	D₄	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₄²×C₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×#107	—	2	2	no	—
91	C₁₃×#107	—	2	4	no	—
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#97	—	2	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	2	no	—
101	#24341	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	8	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	8	2	no	—
111	C₂×Q₈×C₁₃	—	8	2	no	—
112	C₂×Q₈×C₁₃	—	8	2	no	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂×Q₈×C₁₃	#41	1	2	yes	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
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×Q₈	1	2	yes	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	8	2	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×SD₁₆	—	2	8	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	8	2	no	—
157	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
158	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₁₃×C₂²⋊C₄	—	8	2	no	—
162	C₄²×C₁₃	—	2	8	no	—
163	C₄²×C₁₃	—	2	4	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	C₂×D₄	1	2	yes	—
167	C₄²×C₁₃	C₂×D₄	1	2	yes	—
168	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
170	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
171	#2580	C₂×C₁₃	1	1	yes	characteristic
172	#2057	C₂×C₁₃	1	2	yes	complemented
173	#2023	C₂×C₁₃	1	2	yes	—
174	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1880	C₂×C₁₃	1	2	yes	—
177	#1863	C₂×C₁₃	1	2	yes	complemented
178	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	8	no	—
186	Q₈×C₁₃	—	2	2	no	—
187	Q₈×C₁₃	—	2	2	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	8	4	no	—
190	Q₈×C₁₃	—	8	8	no	—
191	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
192	D₄×C₁₃	—	2	2	no	—
193	D₄×C₁₃	—	2	2	no	—
194	D₄×C₁₃	—	4	1	no	—
195	D₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
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	2	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	#120	1	2	yes	—
218	C₂×C₄×C₁₃	#120	1	2	yes	—
219	C₂×C₄×C₁₃	#137	1	4	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
225	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	—	4	1	no	—
228	C₈×C₁₃	—	4	2	no	—
229	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
230	Q₈²	—	2	4	no	—
231	Q₈²	—	2	4	no	—
232	C₂×C₄⋊Q₈	—	2	2	no	—
233	C₂×C₄⋊Q₈	—	2	1	no	—
234	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
241	#474	—	2	4	no	—
242	#440	—	2	4	no	—
243	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#107	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#103	C₂²×C₁₃	1	2	yes	—
247	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
251	#399	—	2	1	no	—
252	#393	—	2	1	no	—
253	#390	C₂²×C₁₃	1	2	yes	—
254	#389	C₂²×C₁₃	1	2	yes	—
255	#385	—	2	2	no	—
256	#382	C₂²×C₁₃	1	1	yes	characteristic
257	#340	C₂²×C₁₃	1	2	yes	—
258	#340	C₂²×C₁₃	1	2	yes	—
259	#340	C₂²×C₁₃	1	2	yes	—
260	#336	C₂²×C₁₃	1	2	yes	—
261	#336	C₂²×C₁₃	1	2	yes	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	—	8	1	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
268	C₂²×C₁₃	#548	1	1	yes	characteristic
269	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
270	C₂²×C₁₃	C₂×#137	1	2	yes	—
271	C₂²×C₁₃	#576	1	2	yes	—
272	C₄×C₁₃	—	2	4	no	—
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	2	4	no	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	4	4	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	8	2	no	—
280	C₄×C₁₃	—	8	1	no	—
281	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
282	C₄×C₁₃	#536	1	1	yes	characteristic
283	C₄×C₁₃	#548	1	1	yes	characteristic
284	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
294	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	16	no	—
298	C₄⋊Q₈	—	2	8	no	—
299	C₄⋊Q₈	—	2	4	no	—
300	C₄⋊Q₈	—	2	4	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
303	C₄×Q₈	—	2	8	no	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	D₄×C₁₃	1	4	yes	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
318	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
330	#107	—	2	2	no	—
331	#107	—	2	4	no	—
332	C₄⋊C₈	—	2	2	no	—
333	#103	—	2	2	no	—
334	#103	—	2	4	no	—
335	#102	—	2	2	no	—
336	#102	—	2	4	no	—
337	#97	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	C₂×C₁₃	—	8	2	no	—
342	C₂×C₁₃	#2409	1	1	yes	characteristic
343	C₂×C₁₃	#3004	1	1	yes	characteristic
344	C₂×C₁₃	#3008	1	1	yes	characteristic
345	C₂×C₁₃	#3375	1	2	yes	—
346	C₂×C₁₃	#3385	1	2	yes	—
347	C₂⁴	—	2	1	no	—
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	8	2	no	—
356	C₂×Q₈	—	8	2	no	—
357	C₂×Q₈	—	8	2	no	—
358	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
359	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
360	C₂×Q₈	C₁₃×#41	1	2	yes	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	8	2	no	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
379	SD₁₆	—	2	8	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	8	2	no	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	4	no	—
406	C₂²⋊C₄	—	8	2	no	—
407	C₄²	—	2	8	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	C₂×D₄×C₁₃	1	2	yes	—
412	C₄²	C₂×D₄×C₁₃	1	2	yes	—
413	C₁₃	#24341	1	1	yes	characteristic, direct product factor, Sylow
414	C₂³	—	2	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	Q₈	—	2	8	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	8	4	no	—
425	Q₈	—	8	8	no	—
426	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	4	1	no	—
430	D₄	—	4	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
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	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	4	no	—
452	C₂×C₄	C₁₃×#120	1	2	yes	—
453	C₂×C₄	C₁₃×#120	1	2	yes	—
454	C₂×C₄	C₁₃×#137	1	4	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
459	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
460	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	2	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	1	no	—
469	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
470	C₂²	C₁₃×#548	1	1	yes	characteristic
471	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
472	C₂²	C₂×C₁₃×#137	1	2	yes	—
473	C₂²	C₁₃×#576	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	4	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
484	C₄	C₁₃×#536	1	1	yes	characteristic
485	C₄	C₁₃×#548	1	1	yes	characteristic
486	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
487	C₂	—	8	2	no	—
488	C₂	C₁₃×#2409	1	1	yes	characteristic
489	C₂	C₁₃×#3004	1	1	yes	characteristic
490	C₂	C₁₃×#3008	1	1	yes	characteristic
491	C₂	C₁₃×#3375	1	2	yes	—
492	C₂	C₁₃×#3385	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
1. C₂×Q₈²×C₁₃	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1863	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
53. C₂×C₁₃×SD₁₆	Q₈	semidirect
101. #24341	C₁₃	direct (N × H)
168. C₂×Q₈²	C₂×C₁₃	semidirect
172. #2057	C₂×C₁₃	semidirect
174. #1993	C₂×C₁₃	semidirect
175. #1985	C₂×C₁₃	semidirect
177. #1863	C₂×C₁₃	semidirect
178. #1805	C₂×C₁₃	semidirect
293. C₂×SD₁₆	Q₈×C₁₃	semidirect
413. C₁₃	#24341	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×Q₈²×C₁₃	2
C₂×C₁₃×#474	2
C₂×C₁₃×#440	2
C₁₃×#2580	2
C₁₃×#2057	2
C₁₃×#2023	2
C₁₃×#1993	2
C₁₃×#1985	2
C₁₃×#1880	2
C₁₃×#1863	2
C₁₃×#1805	2
#24341	13

Subgroups — C13×#24341 #15710680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24341 #15710680