Subgroups — C₁₃×#21070 #15707409

Order 3328.

1026 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×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1929	C₂	1	8	yes	maximal, complemented
7	C₁₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₁₃×#430	—	2	4	no	—
17	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
18	C₁₃×#421	—	2	4	no	—
19	C₂×C₁₃×#104	C₂²	1	4	yes	—
20	C₁₃×#419	C₄	1	2	yes	complemented
21	C₁₃×#418	C₄	1	2	yes	complemented
22	C₁₃×#417	C₄	1	4	yes	complemented
23	C₁₃×#416	C₂²	1	4	yes	—
24	C₁₃×#408	—	2	1	no	—
25	C₁₃×#408	—	2	1	no	—
26	C₁₃×#408	C₂²	1	4	yes	—
27	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
28	C₁₃×#405	—	2	2	no	—
29	C₁₃×#405	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#97	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃	—	2	1	no	—
32	C₁₃×#339	C₂²	1	4	yes	complemented
33	C₁₃×#336	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#41	—	2	1	no	—
35	C₂×C₁₃×#41	—	2	1	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×#41	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	—	2	1	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	D₄	1	2	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
68	C₁₃×#117	—	2	1	no	—
69	C₁₃×#117	—	2	1	no	—
70	C₁₃×#117	—	2	2	no	—
71	C₁₃×#117	—	2	2	no	—
72	C₁₃×#117	C₂×C₄	1	2	yes	—
73	C₁₃×#117	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
80	C₁₃×#108	—	2	8	no	—
81	C₁₃×#104	—	2	8	no	—
82	C₁₃×#103	C₂×C₄	1	8	yes	—
83	C₁₃×#102	C₂×C₄	1	8	yes	—
84	C₁₃×C₂²⋊C₈	—	2	4	no	—
85	C₁₃×C₂²⋊C₈	—	2	4	no	—
86	C₁₃×#97	—	2	4	no	—
87	C₄×C₈×C₁₃	—	2	4	no	—
88	#21070	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	1	no	—
90	C₂⁴×C₁₃	#41	1	1	yes	characteristic
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	2	4	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₁₃×#41	—	2	2	no	—
95	C₁₃×#41	—	2	2	no	—
96	C₁₃×#41	—	2	2	no	—
97	C₁₃×#41	—	4	2	no	—
98	C₁₃×#41	—	4	2	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₁₃×#41	—	4	2	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	4	2	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	2	yes	—
126	C₂²×C₄×C₁₃	#41	1	2	yes	—
127	C₂²×C₄×C₁₃	#41	1	2	yes	—
128	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×M₁₆	—	2	4	no	—
131	C₁₃×M₁₆	—	2	4	no	—
132	C₁₃×M₁₆	—	2	4	no	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	—	2	2	no	—
136	C₁₃×M₁₆	—	4	2	no	—
137	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
138	C₂×C₈×C₁₃	—	2	4	no	—
139	C₂×C₈×C₁₃	—	2	4	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	4	2	no	—
149	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
150	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
155	C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂×#421	C₂×C₁₃	1	1	yes	characteristic
164	#2896	C₂×C₁₃	1	1	yes	characteristic
165	C₂×#408	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1929	C₂×C₁₃	1	8	yes	complemented
168	#1733	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	4	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂³×C₁₃	#124	1	2	yes	—
177	C₂³×C₁₃	#126	1	2	yes	—
178	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	2	no	—
180	Q₈×C₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	4	4	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	#117	1	2	yes	—
198	C₂×C₄×C₁₃	#117	1	2	yes	—
199	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	#121	1	2	yes	—
204	C₂×C₄×C₁₃	#121	1	2	yes	—
205	C₂×C₄×C₁₃	#123	1	2	yes	—
206	C₂×C₄×C₁₃	#123	1	2	yes	—
207	C₂×C₄×C₁₃	#124	1	2	yes	—
208	C₂×C₄×C₁₃	#126	1	2	yes	—
209	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₈×C₁₃	—	2	4	no	—
216	C₈×C₁₃	—	2	4	no	—
217	C₈×C₁₃	—	2	2	no	—
218	C₈×C₁₃	—	2	2	no	—
219	C₈×C₁₃	—	4	2	no	—
220	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
224	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
227	#430	—	2	4	no	—
228	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
229	#421	—	2	4	no	—
230	C₂×#104	C₂²×C₁₃	1	4	yes	—
231	#419	C₄×C₁₃	1	2	yes	complemented
232	#418	C₄×C₁₃	1	2	yes	complemented
233	#417	C₄×C₁₃	1	4	yes	complemented
234	#416	C₂²×C₁₃	1	4	yes	—
235	#408	—	2	1	no	—
236	#408	—	2	1	no	—
237	#408	C₂²×C₁₃	1	4	yes	—
238	C₂×C₂²⋊C₈	—	2	2	no	—
239	#405	—	2	2	no	—
240	#405	C₂²×C₁₃	1	4	yes	complemented
241	C₂×#97	—	2	1	no	—
242	C₂×C₄×C₈	—	2	1	no	—
243	#339	C₂²×C₁₃	1	4	yes	complemented
244	#336	C₂²×C₁₃	1	4	yes	complemented
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	2	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	—	8	4	no	—
253	C₂²×C₁₃	#388	1	2	yes	—
254	C₂²×C₁₃	#388	1	2	yes	—
255	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	#388	1	2	yes	—
262	C₄×C₁₃	#388	1	2	yes	—
263	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
264	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
266	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
267	C₂×#41	—	2	1	no	—
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
274	C₂×#41	C₂³×C₁₃	1	2	yes	—
275	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
288	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
289	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
290	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
291	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	D₄×C₁₃	1	2	yes	—
299	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
300	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
301	#117	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	C₂×C₄×C₁₃	1	2	yes	—
306	#117	C₂³×C₁₃	1	2	yes	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
313	#108	—	2	8	no	—
314	#104	—	2	8	no	—
315	#103	C₂×C₄×C₁₃	1	8	yes	—
316	#102	C₂×C₄×C₁₃	1	8	yes	—
317	C₂²⋊C₈	—	2	4	no	—
318	C₂²⋊C₈	—	2	4	no	—
319	#97	—	2	4	no	—
320	C₄×C₈	—	2	4	no	—
321	C₂×C₁₃	—	2	1	no	—
322	C₂×C₁₃	—	2	2	no	—
323	C₂×C₁₃	—	2	1	no	—
324	C₂×C₁₃	—	2	2	no	—
325	C₂×C₁₃	—	8	2	no	—
326	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
327	C₂×C₁₃	#2955	1	2	yes	—
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₁₃×#41	1	1	yes	characteristic
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	2	no	—
338	#41	—	4	2	no	—
339	#41	—	4	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₁₃×#41	1	2	yes	—
365	C₂²×C₄	C₁₃×#41	1	2	yes	—
366	C₂²×C₄	C₁₃×#41	1	2	yes	—
367	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	4	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	4	2	no	—
376	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
389	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
390	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₁₃	#21070	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³	—	2	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
407	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
408	C₂³	C₁₃×#124	1	2	yes	—
409	C₂³	C₁₃×#126	1	2	yes	—
410	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
411	Q₈	—	2	2	no	—
412	Q₈	—	2	2	no	—
413	Q₈	—	4	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₁₃×#117	1	2	yes	—
430	C₂×C₄	C₁₃×#117	1	2	yes	—
431	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
434	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
435	C₂×C₄	C₁₃×#121	1	2	yes	—
436	C₂×C₄	C₁₃×#121	1	2	yes	—
437	C₂×C₄	C₁₃×#123	1	2	yes	—
438	C₂×C₄	C₁₃×#123	1	2	yes	—
439	C₂×C₄	C₁₃×#124	1	2	yes	—
440	C₂×C₄	C₁₃×#126	1	2	yes	—
441	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₈	—	2	4	no	—
448	C₈	—	2	4	no	—
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	8	4	no	—
460	C₂²	C₁₃×#388	1	2	yes	—
461	C₂²	C₁₃×#388	1	2	yes	—
462	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
463	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
464	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
465	C₄	—	4	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	8	2	no	—
468	C₄	C₁₃×#388	1	2	yes	—
469	C₄	C₁₃×#388	1	2	yes	—
470	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
471	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
472	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
473	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
474	C₂	—	2	1	no	—
475	C₂	—	2	2	no	—
476	C₂	—	2	2	no	—
477	C₂	—	2	1	no	—
478	C₂	—	8	2	no	—
479	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
480	C₂	C₁₃×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#430	C₂	semidirect
5. C₂×C₁₃×#405	C₂	semidirect
6. C₁₃×#1929	C₂	semidirect
7. C₁₃×#1733	C₂	semidirect
8. C₁₃×#1729	C₂	semidirect
17. C₂×C₁₃×#108	C₂²	semidirect
20. C₁₃×#419	C₄	semidirect
21. C₁₃×#418	C₄	semidirect
22. C₁₃×#417	C₄	semidirect
29. C₁₃×#405	C₂²	semidirect
32. C₁₃×#339	C₂²	semidirect
33. C₁₃×#336	C₂²	semidirect
88. #21070	C₁₃	direct (N × H)
162. C₂×#430	C₂×C₁₃	semidirect
166. C₂×#405	C₂×C₁₃	semidirect
167. #1929	C₂×C₁₃	semidirect
168. #1733	C₂×C₁₃	semidirect
169. #1729	C₂×C₁₃	semidirect
228. C₂×#108	C₂²×C₁₃	semidirect
231. #419	C₄×C₁₃	semidirect
232. #418	C₄×C₁₃	semidirect
233. #417	C₄×C₁₃	semidirect
240. #405	C₂²×C₁₃	semidirect
243. #339	C₂²×C₁₃	semidirect
244. #336	C₂²×C₁₃	semidirect
401. C₁₃	#21070	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×#430	2
C₂×C₁₃×#421	2
C₁₃×#2896	2
C₂×C₁₃×#408	2
C₂×C₁₃×#405	2
C₁₃×#1929	2
C₁₃×#1733	2
C₁₃×#1729	2
#21070	13

Subgroups — C13×#21070 #15707409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21070 #15707409