Subgroups — C₁₃×#24646 #15710985

Order 3328.

864 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2055	C₂	1	2	yes	maximal
6	C₁₃×#2013	C₂	1	2	yes	maximal
7	C₁₃×#1981	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1928	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	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#461	—	2	4	no	—
19	C₁₃×#440	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
30	C₁₃×#398	—	2	1	no	—
31	C₁₃×#398	—	2	1	no	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#389	—	2	2	no	—
35	C₁₃×#388	—	2	2	no	—
36	C₁₃×#382	C₂²	1	1	yes	characteristic
37	C₁₃×#381	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	4	2	no	—
52	C₂×C₁₃×SD₁₆	—	4	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	4	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	D₄	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	4	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	2	4	no	—
86	C₁₃×#103	—	4	2	no	—
87	C₁₃×#103	—	4	2	no	—
88	C₁₃×#102	—	2	2	no	—
89	C₁₃×#97	—	2	2	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	D₄	1	1	yes	characteristic
96	C₁₃×#95	D₄	1	1	yes	characteristic
97	#24646	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	#41	1	2	yes	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
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	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	8	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×SD₁₆	—	2	8	no	—
130	C₁₃×SD₁₆	—	4	8	no	—
131	C₂×C₈×C₁₃	—	2	1	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	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	#41	1	2	yes	—
140	C₁₃×C₄⋊C₄	—	2	4	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	4	4	no	—
147	C₁₃×C₄⋊C₄	—	4	4	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	8	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	4	2	no	—
158	C₄²×C₁₃	—	8	2	no	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	#41	1	2	yes	—
161	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
162	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
163	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2357	C₂×C₁₃	1	1	yes	characteristic
165	#2055	C₂×C₁₃	1	2	yes	—
166	#2013	C₂×C₁₃	1	2	yes	—
167	#1981	C₂×C₁₃	1	2	yes	complemented
168	#1960	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1928	C₂×C₁₃	1	2	yes	complemented
171	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	2	2	no	—
180	Q₈×C₁₃	—	4	1	no	—
181	Q₈×C₁₃	—	4	1	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	2	2	no	—
188	D₄×C₁₃	—	4	1	no	—
189	D₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
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	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	8	4	no	—
211	C₂×C₄×C₁₃	#121	1	2	yes	—
212	C₂×C₄×C₁₃	#121	1	2	yes	—
213	C₂×C₄×C₁₃	#137	1	4	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
220	C₈×C₁₃	—	2	2	no	—
221	C₈×C₁₃	—	4	1	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
224	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
225	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
229	#461	—	2	4	no	—
230	#440	—	2	4	no	—
231	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
234	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#103	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#103	C₂²×C₁₃	1	2	yes	—
238	C₂×#103	C₂²×C₁₃	1	2	yes	—
239	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
241	#398	—	2	1	no	—
242	#398	—	2	1	no	—
243	#391	C₂²×C₁₃	1	2	yes	—
244	#390	C₂²×C₁₃	1	2	yes	—
245	#389	—	2	2	no	—
246	#388	—	2	2	no	—
247	#382	C₂²×C₁₃	1	1	yes	characteristic
248	#381	—	2	1	no	—
249	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
251	C₄×C₂²⋊C₄	—	2	1	no	—
252	#340	C₂²×C₁₃	1	2	yes	—
253	#336	C₂²×C₁₃	1	2	yes	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	8	2	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
260	C₂²×C₁₃	#546	1	1	yes	characteristic
261	C₂²×C₁₃	#550	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×#137	1	2	yes	—
263	C₂²×C₁₃	#577	1	2	yes	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	4	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	—	8	2	no	—
272	C₄×C₁₃	—	8	1	no	—
273	C₄×C₁₃	#525	1	1	yes	characteristic
274	C₄×C₁₃	#535	1	1	yes	characteristic
275	C₄×C₁₃	#553	1	1	yes	characteristic
276	C₄×C₁₃	#555	1	1	yes	characteristic
277	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
278	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	2	4	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	4	2	no	—
286	C₂×SD₁₆	—	4	2	no	—
287	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	4	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	D₄×C₁₃	1	4	yes	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
313	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
314	#107	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	4	2	no	—
317	#103	—	2	4	no	—
318	#103	—	2	2	no	—
319	#103	—	2	4	no	—
320	#103	—	4	2	no	—
321	#103	—	4	2	no	—
322	#102	—	2	2	no	—
323	#97	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	D₄×C₁₃	1	1	yes	characteristic
330	#95	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₁₃	—	8	2	no	—
332	C₂×C₁₃	#2414	1	1	yes	characteristic
333	C₂×C₁₃	#3039	1	1	yes	characteristic
334	C₂×C₁₃	#3042	1	1	yes	characteristic
335	C₂×C₁₃	#3320	1	2	yes	—
336	C₂×C₁₃	#3400	1	2	yes	—
337	C₂⁴	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	C₁₃×#41	1	2	yes	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	8	2	no	—
363	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
368	SD₁₆	—	2	8	no	—
369	SD₁₆	—	4	8	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	C₁₃×#41	1	2	yes	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	4	2	no	—
397	C₄²	—	8	2	no	—
398	C₄²	C₂×D₄×C₁₃	1	2	yes	—
399	C₄²	C₁₃×#41	1	2	yes	—
400	C₁₃	#24646	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
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	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	C₁₃×#121	1	2	yes	—
441	C₂×C₄	C₁₃×#121	1	2	yes	—
442	C₂×C₄	C₁₃×#137	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
445	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
447	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
458	C₂²	C₁₃×#546	1	1	yes	characteristic
459	C₂²	C₁₃×#550	1	1	yes	characteristic
460	C₂²	C₂×C₁₃×#137	1	2	yes	—
461	C₂²	C₁₃×#577	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	C₁₃×#525	1	1	yes	characteristic
472	C₄	C₁₃×#535	1	1	yes	characteristic
473	C₄	C₁₃×#553	1	1	yes	characteristic
474	C₄	C₁₃×#555	1	1	yes	characteristic
475	C₂	—	8	2	no	—
476	C₂	C₁₃×#2414	1	1	yes	characteristic
477	C₂	C₁₃×#3039	1	1	yes	characteristic
478	C₂	C₁₃×#3042	1	1	yes	characteristic
479	C₂	C₁₃×#3320	1	2	yes	—
480	C₂	C₁₃×#3400	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2546	C₂	semidirect
7. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1960	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1928	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
97. #24646	C₁₃	direct (N × H)
163. #2546	C₂×C₁₃	semidirect
167. #1981	C₂×C₁₃	semidirect
168. #1960	C₂×C₁₃	semidirect
169. #1940	C₂×C₁₃	semidirect
170. #1928	C₂×C₁₃	semidirect
171. #1805	C₂×C₁₃	semidirect
400. C₁₃	#24646	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×#461	2
C₂×C₁₃×#440	2
C₁₃×#2546	2
C₁₃×#2357	2
C₁₃×#2055	2
C₁₃×#2013	2
C₁₃×#1981	2
C₁₃×#1960	2
C₁₃×#1940	2
C₁₃×#1928	2
C₁₃×#1805	2
#24646	13

Subgroups — C13×#24646 #15710985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24646 #15710985