Subgroups — C₁₃×#21072 #15707411

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2879	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2873	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	C₂×C₁₃×#108	—	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×#416	C₄	1	4	yes	complemented
21	C₁₃×#416	C₂²	1	4	yes	—
22	C₂×C₁₃×#103	C₄	1	2	yes	complemented
23	C₂×C₁₃×#102	C₄	1	2	yes	complemented
24	C₁₃×#408	—	2	2	no	—
25	C₁₃×#408	C₂²	1	4	yes	—
26	C₁₃×#407	—	2	2	no	—
27	C₁₃×#405	—	2	2	no	—
28	C₁₃×#405	C₂²	1	4	yes	complemented
29	C₄×C₁₃×M₁₆	—	2	2	no	—
30	C₁₃×#339	C₂²	1	4	yes	complemented
31	C₁₃×#336	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#41	—	2	1	no	—
33	C₂×C₁₃×#41	—	2	1	no	—
34	C₂×C₁₃×#41	—	2	2	no	—
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	2	no	—
38	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
39	C₂×C₁₃×#41	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	—	2	1	no	—
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
53	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
54	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×#117	—	2	1	no	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	2	2	no	—
68	C₁₃×#117	—	2	2	no	—
69	C₁₃×#117	C₂×C₄	1	2	yes	—
70	C₁₃×#117	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₁₃×#108	—	2	8	no	—
78	C₁₃×#104	—	2	8	no	—
79	C₁₃×#103	C₂×C₄	1	8	yes	—
80	C₁₃×#102	C₂×C₄	1	8	yes	—
81	C₁₃×C₂²⋊C₈	—	2	8	no	—
82	C₁₃×#97	—	2	4	no	—
83	C₄×C₈×C₁₃	—	2	4	no	—
84	#21072	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	1	no	—
86	C₂⁴×C₁₃	#41	1	1	yes	characteristic
87	C₁₃×#41	—	2	4	no	—
88	C₁₃×#41	—	2	4	no	—
89	C₁₃×#41	—	2	2	no	—
90	C₁₃×#41	—	2	2	no	—
91	C₁₃×#41	—	2	2	no	—
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	4	2	no	—
94	C₁₃×#41	—	4	2	no	—
95	C₁₃×#41	—	4	2	no	—
96	C₁₃×#41	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	2	yes	—
122	C₂²×C₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	#41	1	2	yes	—
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×M₁₆	—	2	4	no	—
127	C₁₃×M₁₆	—	2	4	no	—
128	C₁₃×M₁₆	—	2	4	no	—
129	C₁₃×M₁₆	—	2	2	no	—
130	C₁₃×M₁₆	—	2	2	no	—
131	C₁₃×M₁₆	—	2	2	no	—
132	C₁₃×M₁₆	—	4	2	no	—
133	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
134	C₂×C₈×C₁₃	—	2	4	no	—
135	C₂×C₈×C₁₃	—	2	4	no	—
136	C₂×C₈×C₁₃	—	2	4	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	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	—	4	2	no	—
144	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
145	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	4	2	no	—
148	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
149	C₁₃×C₂²⋊C₄	—	2	2	no	—
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₂²×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂×#421	C₂×C₁₃	1	1	yes	characteristic
158	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
159	#2879	C₂×C₁₃	1	1	yes	characteristic
160	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1929	C₂×C₁₃	1	8	yes	complemented
162	#1733	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	8	2	no	—
168	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
169	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂³×C₁₃	#124	1	2	yes	—
171	C₂³×C₁₃	#126	1	2	yes	—
172	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	4	4	no	—
181	D₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	4	4	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	#117	1	2	yes	—
192	C₂×C₄×C₁₃	#117	1	2	yes	—
193	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	#121	1	2	yes	—
198	C₂×C₄×C₁₃	#121	1	2	yes	—
199	C₂×C₄×C₁₃	#123	1	2	yes	—
200	C₂×C₄×C₁₃	#123	1	2	yes	—
201	C₂×C₄×C₁₃	#124	1	2	yes	—
202	C₂×C₄×C₁₃	#126	1	2	yes	—
203	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₈×C₁₃	—	2	4	no	—
210	C₈×C₁₃	—	2	4	no	—
211	C₈×C₁₃	—	2	4	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#108	—	2	4	no	—
221	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
222	#421	—	2	4	no	—
223	C₂×#104	C₂²×C₁₃	1	4	yes	—
224	#416	C₄×C₁₃	1	4	yes	complemented
225	#416	C₂²×C₁₃	1	4	yes	—
226	C₂×#103	C₄×C₁₃	1	2	yes	complemented
227	C₂×#102	C₄×C₁₃	1	2	yes	complemented
228	#408	—	2	2	no	—
229	#408	C₂²×C₁₃	1	4	yes	—
230	#407	—	2	2	no	—
231	#405	—	2	2	no	—
232	#405	C₂²×C₁₃	1	4	yes	complemented
233	C₄×M₁₆	—	2	2	no	—
234	#339	C₂²×C₁₃	1	4	yes	complemented
235	#336	C₂²×C₁₃	1	4	yes	complemented
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	8	4	no	—
244	C₂²×C₁₃	#388	1	2	yes	—
245	C₂²×C₁₃	#388	1	2	yes	—
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	#388	1	2	yes	—
253	C₄×C₁₃	#388	1	2	yes	—
254	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
255	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
265	C₂×#41	C₂³×C₁₃	1	2	yes	—
266	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
279	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
280	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
281	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
282	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
288	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	—	2	2	no	—
294	#117	—	2	2	no	—
295	#117	C₂×C₄×C₁₃	1	2	yes	—
296	#117	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
303	#108	—	2	8	no	—
304	#104	—	2	8	no	—
305	#103	C₂×C₄×C₁₃	1	8	yes	—
306	#102	C₂×C₄×C₁₃	1	8	yes	—
307	C₂²⋊C₈	—	2	8	no	—
308	#97	—	2	4	no	—
309	C₄×C₈	—	2	4	no	—
310	C₂×C₁₃	—	2	1	no	—
311	C₂×C₁₃	—	2	2	no	—
312	C₂×C₁₃	—	2	1	no	—
313	C₂×C₁₃	—	2	2	no	—
314	C₂×C₁₃	—	8	2	no	—
315	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
316	C₂×C₁₃	#2957	1	2	yes	—
317	C₂⁴	—	2	1	no	—
318	C₂⁴	C₁₃×#41	1	1	yes	characteristic
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	4	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₁₃×#41	1	2	yes	—
354	C₂²×C₄	C₁₃×#41	1	2	yes	—
355	C₂²×C₄	C₁₃×#41	1	2	yes	—
356	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
377	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	2	no	—
380	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₁₃	#21072	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	8	2	no	—
393	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
394	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
395	C₂³	C₁₃×#124	1	2	yes	—
396	C₂³	C₁₃×#126	1	2	yes	—
397	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	4	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	C₁₃×#117	1	2	yes	—
417	C₂×C₄	C₁₃×#117	1	2	yes	—
418	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
422	C₂×C₄	C₁₃×#121	1	2	yes	—
423	C₂×C₄	C₁₃×#121	1	2	yes	—
424	C₂×C₄	C₁₃×#123	1	2	yes	—
425	C₂×C₄	C₁₃×#123	1	2	yes	—
426	C₂×C₄	C₁₃×#124	1	2	yes	—
427	C₂×C₄	C₁₃×#126	1	2	yes	—
428	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₈	—	2	4	no	—
435	C₈	—	2	4	no	—
436	C₈	—	2	4	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	8	4	no	—
446	C₂²	C₁₃×#388	1	2	yes	—
447	C₂²	C₁₃×#388	1	2	yes	—
448	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
449	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
450	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
451	C₄	—	4	2	no	—
452	C₄	—	4	4	no	—
453	C₄	—	8	2	no	—
454	C₄	C₁₃×#388	1	2	yes	—
455	C₄	C₁₃×#388	1	2	yes	—
456	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
457	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
458	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
459	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	2	1	no	—
464	C₂	—	8	2	no	—
465	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
466	C₂	C₁₃×#2957	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 ◁ C₂²×C₁₃×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#108	C₂	semidirect
5. C₁₃×#2873	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×#416	C₄	semidirect
22. C₂×C₁₃×#103	C₄	semidirect
23. C₂×C₁₃×#102	C₄	semidirect
28. C₁₃×#405	C₂²	semidirect
30. C₁₃×#339	C₂²	semidirect
31. C₁₃×#336	C₂²	semidirect
84. #21072	C₁₃	direct (N × H)
156. C₂²×#108	C₂×C₁₃	semidirect
160. #2873	C₂×C₁₃	semidirect
161. #1929	C₂×C₁₃	semidirect
162. #1733	C₂×C₁₃	semidirect
163. #1729	C₂×C₁₃	semidirect
221. C₂×#108	C₂²×C₁₃	semidirect
224. #416	C₄×C₁₃	semidirect
226. C₂×#103	C₄×C₁₃	semidirect
227. C₂×#102	C₄×C₁₃	semidirect
232. #405	C₂²×C₁₃	semidirect
234. #339	C₂²×C₁₃	semidirect
235. #336	C₂²×C₁₃	semidirect
388. C₁₃	#21072	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#108	2
C₂×C₁₃×#421	2
C₂×C₁₃×#416	2
C₁₃×#2879	2
C₁₃×#2873	2
C₁₃×#1929	2
C₁₃×#1733	2
C₁₃×#1729	2
#21072	13

Subgroups — C13×#21072 #15707411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21072 #15707411