Subgroups — C₁₃×#21071 #15707410

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 474 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	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2896	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	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1728	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	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#430	—	2	4	no	—
17	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#104	—	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	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	—	2	1	no	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	—	2	1	no	—
47	C₂×C₁₃×M₁₆	—	2	2	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	2	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
58	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
59	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	C₂×C₄	1	2	yes	—
69	C₁₃×#117	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	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	complemented
80	C₁₃×#102	C₂×C₄	1	8	yes	complemented
81	C₁₃×C₂²⋊C₈	—	2	8	no	—
82	C₁₃×#97	—	2	4	no	—
83	C₄×C₈×C₁₃	—	2	4	no	—
84	#21071	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	4	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	2	yes	—
124	C₂²×C₄×C₁₃	#41	1	2	yes	—
125	C₂²×C₄×C₁₃	#41	1	2	yes	—
126	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×M₁₆	—	2	4	no	—
129	C₁₃×M₁₆	—	2	4	no	—
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	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	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	4	2	no	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
147	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
150	C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₁₃×C₂²⋊C₄	—	2	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	C₄²×C₁₃	—	4	2	no	—
157	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic
159	#2896	C₂×C₁₃	1	1	yes	characteristic
160	#2879	C₂×C₁₃	1	1	yes	characteristic
161	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1929	C₂×C₁₃	1	8	yes	complemented
163	C₂×#339	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	8	2	no	—
169	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₁₃	#124	1	2	yes	—
172	C₂³×C₁₃	#126	1	2	yes	—
173	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	4	no	—
182	D₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	8	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	8	2	no	—
194	C₂×C₄×C₁₃	#117	1	2	yes	—
195	C₂×C₄×C₁₃	#117	1	2	yes	—
196	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#121	1	2	yes	—
201	C₂×C₄×C₁₃	#121	1	2	yes	—
202	C₂×C₄×C₁₃	#123	1	2	yes	—
203	C₂×C₄×C₁₃	#123	1	2	yes	—
204	C₂×C₄×C₁₃	#124	1	2	yes	—
205	C₂×C₄×C₁₃	#126	1	2	yes	—
206	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₈×C₁₃	—	2	4	no	—
213	C₈×C₁₃	—	2	4	no	—
214	C₈×C₁₃	—	2	4	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
220	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
223	#430	—	2	4	no	—
224	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
225	C₂×#104	—	2	4	no	—
226	C₂×#104	C₂²×C₁₃	1	4	yes	—
227	#419	C₄×C₁₃	1	2	yes	complemented
228	#418	C₄×C₁₃	1	2	yes	complemented
229	#417	C₄×C₁₃	1	4	yes	complemented
230	#416	C₂²×C₁₃	1	4	yes	—
231	#408	—	2	2	no	—
232	#408	C₂²×C₁₃	1	4	yes	—
233	#407	—	2	2	no	—
234	#405	—	2	2	no	—
235	#405	C₂²×C₁₃	1	4	yes	complemented
236	C₄×M₁₆	—	2	2	no	—
237	#339	C₂²×C₁₃	1	4	yes	complemented
238	#336	C₂²×C₁₃	1	4	yes	complemented
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	8	4	no	—
247	C₂²×C₁₃	#388	1	2	yes	—
248	C₂²×C₁₃	#388	1	2	yes	—
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	#388	1	2	yes	—
256	C₄×C₁₃	#388	1	2	yes	—
257	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
258	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
260	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
261	C₂×#41	—	2	1	no	—
262	C₂×#41	—	2	1	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
268	C₂×#41	C₂³×C₁₃	1	2	yes	—
269	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
285	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
286	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
287	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
288	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
289	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	C₂×C₄×C₁₃	1	2	yes	—
298	#117	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
306	#108	—	2	8	no	—
307	#104	—	2	8	no	—
308	#103	C₂×C₄×C₁₃	1	8	yes	complemented
309	#102	C₂×C₄×C₁₃	1	8	yes	complemented
310	C₂²⋊C₈	—	2	8	no	—
311	#97	—	2	4	no	—
312	C₄×C₈	—	2	4	no	—
313	C₂×C₁₃	—	2	1	no	—
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	2	1	no	—
316	C₂×C₁₃	—	2	2	no	—
317	C₂×C₁₃	—	8	2	no	—
318	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
319	C₂×C₁₃	#2956	1	2	yes	—
320	C₂⁴	—	2	1	no	—
321	C₂⁴	C₁₃×#41	1	1	yes	characteristic
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₁₃×#41	1	2	yes	—
359	C₂²×C₄	C₁₃×#41	1	2	yes	—
360	C₂²×C₄	C₁₃×#41	1	2	yes	—
361	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
363	M₁₆	—	2	4	no	—
364	M₁₆	—	2	4	no	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	—	2	4	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
382	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	2	no	—
392	C₁₃	#21071	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
398	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
399	C₂³	C₁₃×#124	1	2	yes	—
400	C₂³	C₁₃×#126	1	2	yes	—
401	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	C₁₃×#117	1	2	yes	—
423	C₂×C₄	C₁₃×#117	1	2	yes	—
424	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
427	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
428	C₂×C₄	C₁₃×#121	1	2	yes	—
429	C₂×C₄	C₁₃×#121	1	2	yes	—
430	C₂×C₄	C₁₃×#123	1	2	yes	—
431	C₂×C₄	C₁₃×#123	1	2	yes	—
432	C₂×C₄	C₁₃×#124	1	2	yes	—
433	C₂×C₄	C₁₃×#126	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
437	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
438	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
439	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	2	4	no	—
442	C₈	—	2	4	no	—
443	C₈	—	4	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₁₃×#388	1	2	yes	—
453	C₂²	C₁₃×#388	1	2	yes	—
454	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
455	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
456	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	C₁₃×#388	1	2	yes	—
461	C₄	C₁₃×#388	1	2	yes	—
462	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
463	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
464	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
465	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	2	no	—
469	C₂	—	2	1	no	—
470	C₂	—	8	2	no	—
471	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
472	C₂	C₁₃×#2956	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. C₂×C₁₃×#430	C₂	semidirect
5. C₁₃×#2873	C₂	semidirect
6. C₁₃×#1929	C₂	semidirect
7. C₂×C₁₃×#339	C₂	semidirect
8. C₁₃×#1728	C₂	semidirect
17. C₂×C₁₃×#108	C₂²	semidirect
20. C₁₃×#419	C₄	semidirect
21. C₁₃×#418	C₄	semidirect
22. C₁₃×#417	C₄	semidirect
28. C₁₃×#405	C₂²	semidirect
30. C₁₃×#339	C₂²	semidirect
31. C₁₃×#336	C₂²	semidirect
79. C₁₃×#103	C₂×C₄	semidirect
80. C₁₃×#102	C₂×C₄	semidirect
84. #21071	C₁₃	direct (N × H)
157. C₂×#430	C₂×C₁₃	semidirect
161. #2873	C₂×C₁₃	semidirect
162. #1929	C₂×C₁₃	semidirect
163. C₂×#339	C₂×C₁₃	semidirect
164. #1728	C₂×C₁₃	semidirect
224. C₂×#108	C₂²×C₁₃	semidirect
227. #419	C₄×C₁₃	semidirect
228. #418	C₄×C₁₃	semidirect
229. #417	C₄×C₁₃	semidirect
235. #405	C₂²×C₁₃	semidirect
237. #339	C₂²×C₁₃	semidirect
238. #336	C₂²×C₁₃	semidirect
308. #103	C₂×C₄×C₁₃	semidirect
309. #102	C₂×C₄×C₁₃	semidirect
392. C₁₃	#21071	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
C₂²×C₁₃×#104	2
C₁₃×#2896	2
C₁₃×#2879	2
C₁₃×#2873	2
C₁₃×#1929	2
C₂×C₁₃×#339	2
C₁₃×#1728	2
#21071	13

Subgroups — C13×#21071 #15707410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21071 #15707410