Subgroups — C₁₃×#24343 #15710682

Order 3328.

1064 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#475	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×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2026	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×#1864	C₂	1	2	yes	maximal
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₁₃×#554	—	2	4	no	—
14	C₁₃×#554	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₁₃×#475	—	2	4	no	—
25	C₁₃×#440	—	2	4	no	—
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	2	yes	—
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	1	no	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	2	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	2	no	—
58	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
59	C₁₃×#125	—	2	4	no	—
60	C₁₃×#125	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	—	2	8	no	—
62	C₁₃×C₂²⋊Q₈	—	2	16	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	4	no	—
68	C₄×D₄×C₁₃	—	2	4	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	D₄	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	—	2	8	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	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	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×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#107	—	2	2	no	—
89	C₁₃×#106	—	2	4	no	—
90	C₁₃×C₄⋊C₈	—	2	2	no	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	#24343	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	4	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	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	—	4	2	no	—
111	C₂×Q₈×C₁₃	—	8	2	no	—
112	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×D₄×C₁₃	#41	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	4	4	no	—
127	C₂²×C₄×C₁₃	—	8	4	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
133	C₁₃×SD₁₆	—	2	8	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
157	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	2	no	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
168	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#2059	C₂×C₁₃	1	2	yes	complemented
170	#2026	C₂×C₁₃	1	2	yes	complemented
171	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1877	C₂×C₁₃	1	2	yes	—
174	#1864	C₂×C₁₃	1	2	yes	—
175	#1804	C₂×C₁₃	1	1	yes	characteristic
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	4	2	no	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	—	2	2	no	—
184	Q₈×C₁₃	—	4	4	no	—
185	Q₈×C₁₃	—	4	1	no	—
186	Q₈×C₁₃	—	4	1	no	—
187	Q₈×C₁₃	—	8	4	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	2	2	no	—
191	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	4	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	4	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	1	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	2	no	—
212	C₂×C₄×C₁₃	—	8	8	no	—
213	C₂×C₄×C₁₃	#120	1	2	yes	—
214	C₂×C₄×C₁₃	#120	1	2	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
220	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₁₃	—	2	2	no	—
222	C₈×C₁₃	—	4	1	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
225	#554	—	2	4	no	—
226	#554	—	2	4	no	—
227	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#125	C₂²×C₁₃	1	2	yes	—
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₂²⋊Q₈	—	2	2	no	—
231	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	—	2	1	no	—
236	#475	—	2	4	no	—
237	#440	—	2	4	no	—
238	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#106	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#103	C₂²×C₁₃	1	2	yes	—
242	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#102	C₂²×C₁₃	1	2	yes	—
244	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
246	#400	—	2	1	no	—
247	#395	—	2	1	no	—
248	#391	C₂²×C₁₃	1	2	yes	—
249	#389	C₂²×C₁₃	1	2	yes	—
250	#387	—	2	2	no	—
251	#382	C₂²×C₁₃	1	1	yes	characteristic
252	#340	C₂²×C₁₃	1	2	yes	—
253	#340	C₂²×C₁₃	1	2	yes	—
254	#340	C₂²×C₁₃	1	2	yes	—
255	#336	C₂²×C₁₃	1	2	yes	—
256	#336	C₂²×C₁₃	1	2	yes	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
263	C₂²×C₁₃	#548	1	1	yes	characteristic
264	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
265	C₂²×C₁₃	#575	1	2	yes	—
266	C₂²×C₁₃	#577	1	2	yes	—
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	—	8	2	no	—
275	C₄×C₁₃	—	8	1	no	—
276	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
277	C₄×C₁₃	#536	1	1	yes	characteristic
278	C₄×C₁₃	#548	1	1	yes	characteristic
279	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
294	#125	—	2	4	no	—
295	#125	—	2	4	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₂²⋊Q₈	—	2	16	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	D₄×C₁₃	1	4	yes	—
306	C₂×C₄⋊C₄	—	2	8	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
323	#107	—	2	2	no	—
324	#106	—	2	4	no	—
325	C₄⋊C₈	—	2	2	no	—
326	#103	—	2	2	no	—
327	#103	—	2	4	no	—
328	#102	—	2	2	no	—
329	#102	—	2	4	no	—
330	#97	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	1	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂×C₁₃	—	4	4	no	—
337	C₂×C₁₃	#2409	1	1	yes	characteristic
338	C₂×C₁₃	#3005	1	1	yes	characteristic
339	C₂×C₁₃	#3009	1	1	yes	characteristic
340	C₂×C₁₃	#3376	1	2	yes	—
341	C₂×C₁₃	#3388	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	8	2	no	—
352	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
358	C₂×D₄	C₁₃×#41	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	8	4	no	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
373	SD₁₆	—	2	8	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	4	2	no	—
403	C₄²	C₂×D₄×C₁₃	1	2	yes	—
404	C₄²	C₂×D₄×C₁₃	1	2	yes	—
405	C₁₃	#24343	1	1	yes	characteristic, direct product factor, Sylow
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	4	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	4	1	no	—
417	Q₈	—	8	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	8	no	—
443	C₂×C₄	C₁₃×#120	1	2	yes	—
444	C₂×C₄	C₁₃×#120	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
448	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
449	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	4	2	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
460	C₂²	C₁₃×#548	1	1	yes	characteristic
461	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
462	C₂²	C₁₃×#575	1	2	yes	—
463	C₂²	C₁₃×#577	1	2	yes	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	1	no	—
473	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
474	C₄	C₁₃×#536	1	1	yes	characteristic
475	C₄	C₁₃×#548	1	1	yes	characteristic
476	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
477	C₂	—	4	4	no	—
478	C₂	C₁₃×#2409	1	1	yes	characteristic
479	C₂	C₁₃×#3005	1	1	yes	characteristic
480	C₂	C₁₃×#3009	1	1	yes	characteristic
481	C₂	C₁₃×#3376	1	2	yes	—
482	C₂	C₁₃×#3388	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×#475	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#2026	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
53. C₂×C₁₃×SD₁₆	Q₈	semidirect
101. #24343	C₁₃	direct (N × H)
166. C₂×#475	C₂×C₁₃	semidirect
168. #2581	C₂×C₁₃	semidirect
169. #2059	C₂×C₁₃	semidirect
170. #2026	C₂×C₁₃	semidirect
171. #1993	C₂×C₁₃	semidirect
172. #1985	C₂×C₁₃	semidirect
288. C₂×SD₁₆	Q₈×C₁₃	semidirect
405. C₁₃	#24343	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×#554	2
C₂×C₁₃×#475	2
C₂×C₁₃×#440	2
C₁₃×#2581	2
C₁₃×#2059	2
C₁₃×#2026	2
C₁₃×#1993	2
C₁₃×#1985	2
C₁₃×#1877	2
C₁₃×#1864	2
C₁₃×#1804	2
#24343	13

Subgroups — C13×#24343 #15710682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24343 #15710682