Subgroups — C₁₃×#10231 #15696570

Order 3328.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	—	2	1	no	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#121	—	2	1	no	—
11	C₂×C₁₃×#121	—	2	1	no	—
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#474	—	2	2	no	—
15	C₁₃×#474	—	2	2	no	—
16	C₁₃×#461	—	2	2	no	—
17	C₁₃×#461	—	2	2	no	—
18	C₂×C₁₃×#107	—	2	1	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#103	—	2	1	no	—
22	C₂×C₁₃×#102	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#394	—	2	2	no	—
25	C₁₃×#384	C₂²	1	1	yes	characteristic
26	C₁₃×#380	—	2	1	no	—
27	C₁₃×#380	—	2	1	no	—
28	C₁₃×#340	—	2	2	no	—
29	C₁₃×D₄⋊C₈	—	2	2	no	—
30	C₁₃×D₄⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	2	no	—
33	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	—	2	1	no	—
36	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂×C₁₃×SD₁₆	—	2	4	no	—
38	C₂×C₁₃×SD₁₆	—	4	2	no	—
39	C₂×C₁₃×SD₁₆	—	4	2	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	—	2	1	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	complemented
47	C₁₃×#121	—	4	2	no	—
48	C₁₃×#121	—	4	2	no	—
49	C₁₃×#121	—	4	2	no	—
50	C₁₃×#121	—	4	2	no	—
51	C₄×D₄×C₁₃	—	2	1	no	—
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	4	no	—
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	—	2	1	no	—
74	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
75	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
76	C₁₃×#103	—	2	4	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₄×C₈×C₁₃	—	2	1	no	—
79	C₄×C₈×C₁₃	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	#10231	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	—	2	1	no	—
83	C₂⁴×C₁₃	—	2	1	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	4	1	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	4	1	no	—
88	C₂×Q₈×C₁₃	—	4	1	no	—
89	C₂×Q₈×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	4	4	no	—
101	C₂×D₄×C₁₃	—	4	4	no	—
102	C₂×D₄×C₁₃	—	8	2	no	—
103	C₂×D₄×C₁₃	D₈	1	2	yes	—
104	C₂×D₄×C₁₃	SD₁₆	1	2	yes	complemented
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	—	4	1	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	1	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	—	4	1	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	—	4	1	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₁₃×SD₁₆	—	4	8	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₂×C₈×C₁₃	—	4	1	no	—
131	C₂×C₈×C₁₃	—	4	1	no	—
132	C₂×C₈×C₁₃	—	4	1	no	—
133	C₂×C₈×C₁₃	—	4	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	1	no	—
142	C₁₃×C₄⋊C₄	—	4	1	no	—
143	C₁₃×C₄⋊C₄	—	4	1	no	—
144	C₁₃×C₄⋊C₄	—	4	1	no	—
145	C₁₃×C₄⋊C₄	—	4	1	no	—
146	C₁₃×C₄⋊C₄	—	4	1	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	—	4	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	1	no	—
150	C₁₃×C₂²⋊C₄	—	4	1	no	—
151	C₁₃×C₂²⋊C₄	—	4	1	no	—
152	C₁₃×C₂²⋊C₄	—	4	1	no	—
153	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	#41	1	1	yes	characteristic
157	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2537	C₂×C₁₃	1	1	yes	characteristic
160	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1296	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	1	no	—
171	C₂³×C₁₃	—	4	1	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	#120	1	1	yes	characteristic
179	Q₈×C₁₃	—	4	2	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	Q₈×C₁₃	—	8	1	no	—
182	Q₈×C₁₃	—	8	1	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	4	1	no	—
188	D₄×C₁₃	—	4	1	no	—
189	D₄×C₁₃	—	4	1	no	—
190	D₄×C₁₃	—	4	1	no	—
191	D₄×C₁₃	—	8	8	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	4	1	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	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	—	8	1	no	—
205	C₂×C₄×C₁₃	—	8	1	no	—
206	C₂×C₄×C₁₃	—	8	1	no	—
207	C₂×C₄×C₁₃	—	8	1	no	—
208	C₂×C₄×C₁₃	—	8	1	no	—
209	C₂×C₄×C₁₃	—	8	1	no	—
210	C₂×C₄×C₁₃	—	8	1	no	—
211	C₂×C₄×C₁₃	—	8	1	no	—
212	C₂×C₄×C₁₃	—	8	1	no	—
213	C₂×C₄×C₁₃	—	8	1	no	—
214	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
216	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
224	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
228	C₈×C₁₃	—	4	2	no	—
229	C₈×C₁₃	—	4	2	no	—
230	C₈×C₁₃	—	4	2	no	—
231	C₂²×SD₁₆	—	2	1	no	—
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#121	—	2	1	no	—
234	C₂×#121	—	2	1	no	—
235	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
237	#474	—	2	2	no	—
238	#474	—	2	2	no	—
239	#461	—	2	2	no	—
240	#461	—	2	2	no	—
241	C₂×#107	—	2	1	no	—
242	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#103	—	2	1	no	—
245	C₂×#102	—	2	1	no	—
246	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
247	#394	—	2	2	no	—
248	#384	C₂²×C₁₃	1	1	yes	characteristic
249	#380	—	2	1	no	—
250	#380	—	2	1	no	—
251	#340	—	2	2	no	—
252	D₄⋊C₈	—	2	2	no	—
253	D₄⋊C₈	—	2	2	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	8	1	no	—
261	C₂²×C₁₃	—	8	1	no	—
262	C₂²×C₁₃	—	8	1	no	—
263	C₂²×C₁₃	—	8	1	no	—
264	C₂²×C₁₃	—	8	1	no	—
265	C₂²×C₁₃	—	8	1	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	#392	1	1	yes	characteristic
269	C₂²×C₁₃	#447	1	1	yes	characteristic
270	C₂²×C₁₃	#449	1	1	yes	characteristic
271	C₂²×C₁₃	#450	1	1	yes	characteristic
272	C₂²×C₁₃	#452	1	1	yes	characteristic
273	C₂²×C₁₃	#455	1	1	yes	characteristic
274	C₂²×C₁₃	#456	1	1	yes	characteristic
275	C₄×C₁₃	—	2	1	no	—
276	C₄×C₁₃	—	2	1	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	—	8	1	no	—
279	C₄×C₁₃	—	8	2	no	—
280	C₄×C₁₃	—	8	1	no	—
281	C₄×C₁₃	#447	1	1	yes	characteristic
282	C₄×C₁₃	#448	1	1	yes	characteristic
283	C₄×C₁₃	#449	1	1	yes	characteristic
284	C₄×C₁₃	#449	1	1	yes	characteristic
285	C₄×C₁₃	#465	1	1	yes	characteristic
286	C₄×C₁₃	#466	1	1	yes	characteristic
287	C₄×C₁₃	#468	1	1	yes	characteristic
288	C₄×C₁₃	#469	1	1	yes	characteristic
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
292	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	4	2	no	—
297	C₂×SD₁₆	—	4	2	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	D₄×C₁₃	1	2	yes	complemented
305	#121	—	4	2	no	—
306	#121	—	4	2	no	—
307	#121	—	4	2	no	—
308	#121	—	4	2	no	—
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	#107	—	2	4	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
333	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
334	#103	—	2	4	no	—
335	#102	—	2	4	no	—
336	C₄×C₈	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	#95	—	2	2	no	—
339	C₂×C₁₃	—	8	2	no	—
340	C₂×C₁₃	—	8	2	no	—
341	C₂×C₁₃	#1639	1	1	yes	characteristic
342	C₂×C₁₃	#1646	1	1	yes	characteristic
343	C₂×C₁₃	#1647	1	1	yes	characteristic
344	C₂×C₁₃	#1654	1	1	yes	characteristic
345	C₂×C₁₃	#1999	1	1	yes	characteristic
346	C₂×C₁₃	#2000	1	1	yes	characteristic
347	C₂×C₁₃	#2007	1	1	yes	characteristic
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	4	1	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×Q₈	—	4	1	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
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	—	4	4	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	C₁₃×D₈	1	2	yes	—
370	C₂×D₄	C₁₃×SD₁₆	1	2	yes	complemented
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	SD₁₆	—	4	8	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	4	1	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	4	1	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	4	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₂²⋊C₄	—	4	1	no	—
417	C₂²⋊C₄	—	4	1	no	—
418	C₂²⋊C₄	—	4	1	no	—
419	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₄²	C₁₃×#41	1	1	yes	characteristic
423	C₁₃	#10231	1	1	yes	characteristic, direct product factor, Sylow
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	C₁₃×#120	1	1	yes	characteristic
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	8	1	no	—
442	Q₈	—	8	1	no	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	8	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	—	8	1	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	1	no	—
473	C₂×C₄	—	8	1	no	—
474	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
475	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
476	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
477	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
478	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
479	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
480	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
481	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
482	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
483	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
484	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
485	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
488	C₈	—	4	2	no	—
489	C₈	—	4	2	no	—
490	C₈	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	C₁₃×#392	1	1	yes	characteristic
506	C₂²	C₁₃×#447	1	1	yes	characteristic
507	C₂²	C₁₃×#449	1	1	yes	characteristic
508	C₂²	C₁₃×#450	1	1	yes	characteristic
509	C₂²	C₁₃×#452	1	1	yes	characteristic
510	C₂²	C₁₃×#455	1	1	yes	characteristic
511	C₂²	C₁₃×#456	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	2	no	—
518	C₄	C₁₃×#447	1	1	yes	characteristic
519	C₄	C₁₃×#448	1	1	yes	characteristic
520	C₄	C₁₃×#449	1	1	yes	characteristic
521	C₄	C₁₃×#449	1	1	yes	characteristic
522	C₄	C₁₃×#465	1	1	yes	characteristic
523	C₄	C₁₃×#466	1	1	yes	characteristic
524	C₄	C₁₃×#468	1	1	yes	characteristic
525	C₄	C₁₃×#469	1	1	yes	characteristic
526	C₂	—	8	2	no	—
527	C₂	—	8	2	no	—
528	C₂	C₁₃×#1639	1	1	yes	characteristic
529	C₂	C₁₃×#1646	1	1	yes	characteristic
530	C₂	C₁₃×#1647	1	1	yes	characteristic
531	C₂	C₁₃×#1654	1	1	yes	characteristic
532	C₂	C₁₃×#1999	1	1	yes	characteristic
533	C₂	C₁₃×#2000	1	1	yes	characteristic
534	C₂	C₁₃×#2007	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#2537	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#474	C₂	semidirect
2. C₂×C₁₃×#461	C₂	semidirect
4. C₁₃×#1990	C₂	semidirect
5. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
6. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
7. C₁₃×#1296	C₂	semidirect
46. C₁₃×C₄⋊Q₈	D₄	semidirect
74. C₁₃×C₄⋊C₈	D₄	semidirect
75. C₁₃×C₄⋊C₈	D₄	semidirect
81. #10231	C₁₃	direct (N × H)
104. C₂×D₄×C₁₃	SD₁₆	semidirect
157. C₂×#474	C₂×C₁₃	semidirect
158. C₂×#461	C₂×C₁₃	semidirect
160. #1990	C₂×C₁₃	semidirect
161. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
162. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
163. #1296	C₂×C₁₃	semidirect
304. C₄⋊Q₈	D₄×C₁₃	semidirect
332. C₄⋊C₈	D₄×C₁₃	semidirect
333. C₄⋊C₈	D₄×C₁₃	semidirect
370. C₂×D₄	C₁₃×SD₁₆	semidirect
423. C₁₃	#10231	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×#474	2
C₂×C₁₃×#461	2
C₁₃×#2537	2
C₁₃×#1990	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1296	2
#10231	13

Subgroups — C13×#10231 #15696570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10231 #15696570