Subgroups — C₁₃×#21777 #15708116

Order 3328.

1318 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3485	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2883	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1913	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1890	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1828	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1782	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₁₃×#547	—	2	4	no	—
10	C₁₃×#546	—	2	4	no	—
11	C₁₃×#536	C₄	1	2	yes	complemented
12	C₁₃×#534	C₄	1	2	yes	complemented
13	C₁₃×#534	C₂²	1	2	yes	—
14	C₁₃×#525	C₄	1	2	yes	complemented
15	C₂×C₁₃×#123	C₄	1	2	yes	complemented
16	C₂×C₁₃×#123	C₂²	1	2	yes	—
17	C₁₃×#518	C₂²	1	4	yes	—
18	C₁₃×#518	C₂²	1	1	yes	characteristic
19	C₁₃×#410	—	2	4	no	—
20	C₂×C₁₃×#99	—	2	4	no	—
21	C₂×C₁₃×#99	C₂²	1	4	yes	—
22	C₂×C₁₃×#99	C₂²	1	4	yes	—
23	C₂×C₁₃×#99	C₂²	1	4	yes	complemented
24	C₁₃×#381	C₂²	1	4	yes	complemented
25	C₁₃×#342	C₂²	1	8	yes	complemented
26	C₁₃×H(5,𝔽₂)	—	4	4	no	—
27	C₂×C₁₃×#41	—	2	4	no	—
28	C₂×C₁₃×#41	—	4	4	no	—
29	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
30	C₂×C₁₃×#41	D₄	1	4	yes	—
31	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
32	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
34	C₂²×D₄×C₁₃	D₄	1	4	yes	—
35	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×#124	—	2	2	no	—
43	C₁₃×#123	—	2	4	no	—
44	C₁₃×#123	—	2	4	no	—
45	C₁₃×#123	—	2	2	no	—
46	C₁₃×#123	—	2	2	no	—
47	C₁₃×#123	C₂×C₄	1	4	yes	complemented
48	C₁₃×#123	C₂×C₄	1	4	yes	complemented
49	C₁₃×#123	C₂×C₄	1	4	yes	complemented
50	C₁₃×C₂²⋊Q₈	—	2	2	no	—
51	C₁₃×C₂²⋊Q₈	—	2	4	no	—
52	C₁₃×#121	—	2	2	no	—
53	C₁₃×#121	—	2	4	no	—
54	C₁₃×#121	—	2	4	no	—
55	C₁₃×#120	—	2	2	no	—
56	C₁₃×#120	—	2	2	no	—
57	C₁₃×#120	C₂×C₄	1	4	yes	complemented
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	—	2	4	no	—
60	C₄×D₄×C₁₃	—	4	8	no	—
61	C₁₃×#117	—	2	4	no	—
62	C₁₃×#117	C₂×C₄	1	2	yes	complemented
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
71	C₁₃×#99	—	2	8	no	—
72	C₁₃×#99	—	2	8	no	—
73	C₁₃×#99	—	4	4	no	—
74	C₁₃×#95	—	4	4	no	—
75	#21777	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	C₂²⋊C₄	1	2	yes	—
77	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₁₃×#41	—	4	4	no	—
82	C₁₃×#41	—	4	8	no	—
83	C₁₃×#41	—	4	16	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	4	2	no	—
86	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
87	C₂×D₄×C₁₃	—	2	8	no	—
88	C₂×D₄×C₁₃	—	2	4	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	2	4	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	—	4	4	no	—
95	C₂×D₄×C₁₃	—	4	8	no	—
96	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
97	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
100	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	2	4	no	—
124	C₁₃×C₂²⋊C₄	—	2	4	no	—
125	C₁₃×C₂²⋊C₄	—	2	4	no	—
126	C₁₃×C₂²⋊C₄	—	2	2	no	—
127	C₁₃×C₂²⋊C₄	—	2	2	no	—
128	C₁₃×C₂²⋊C₄	—	2	4	no	—
129	C₁₃×C₂²⋊C₄	—	2	8	no	—
130	C₁₃×C₂²⋊C₄	—	2	8	no	—
131	C₁₃×C₂²⋊C₄	—	4	4	no	—
132	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	4	4	no	—
135	#3485	C₂×C₁₃	1	1	yes	characteristic
136	#2883	C₂×C₁₃	1	2	yes	complemented
137	#1913	C₂×C₁₃	1	4	yes	complemented
138	#1890	C₂×C₁₃	1	4	yes	complemented
139	#1828	C₂×C₁₃	1	2	yes	complemented
140	#1782	C₂×C₁₃	1	2	yes	complemented
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	2	4	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	8	1	no	—
147	C₂³×C₁₃	—	8	1	no	—
148	C₂³×C₁₃	—	8	1	no	—
149	C₂³×C₁₃	—	8	2	no	—
150	C₂³×C₁₃	—	8	2	no	—
151	C₂³×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
154	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	4	no	—
158	D₄×C₁₃	—	2	8	no	—
159	D₄×C₁₃	—	2	8	no	—
160	D₄×C₁₃	—	2	8	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	4	no	—
164	D₄×C₁₃	—	4	4	no	—
165	D₄×C₁₃	—	8	4	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	8	no	—
181	C₂×C₄×C₁₃	—	8	2	no	—
182	C₂×C₄×C₁₃	—	8	2	no	—
183	C₂×C₄×C₁₃	—	8	8	no	—
184	C₂×C₄×C₁₃	—	16	4	no	—
185	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
187	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
189	#547	—	2	4	no	—
190	#546	—	2	4	no	—
191	#536	C₄×C₁₃	1	2	yes	complemented
192	#534	C₄×C₁₃	1	2	yes	complemented
193	#534	C₂²×C₁₃	1	2	yes	—
194	#525	C₄×C₁₃	1	2	yes	complemented
195	C₂×#123	C₄×C₁₃	1	2	yes	complemented
196	C₂×#123	C₂²×C₁₃	1	2	yes	—
197	#518	C₂²×C₁₃	1	4	yes	—
198	#518	C₂²×C₁₃	1	1	yes	characteristic
199	#410	—	2	4	no	—
200	C₂×#99	—	2	4	no	—
201	C₂×#99	C₂²×C₁₃	1	4	yes	—
202	C₂×#99	C₂²×C₁₃	1	4	yes	—
203	C₂×#99	C₂²×C₁₃	1	4	yes	complemented
204	#381	C₂²×C₁₃	1	4	yes	complemented
205	#342	C₂²×C₁₃	1	8	yes	complemented
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	4	no	—
208	C₂²×C₁₃	—	4	4	no	—
209	C₂²×C₁₃	—	4	2	no	—
210	C₂²×C₁₃	—	4	1	no	—
211	C₂²×C₁₃	—	4	2	no	—
212	C₂²×C₁₃	—	4	4	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	1	no	—
215	C₂²×C₁₃	—	8	4	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	16	2	no	—
219	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×C₁₃	#518	1	2	yes	—
221	C₂²×C₁₃	#534	1	4	yes	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	4	4	no	—
225	C₄×C₁₃	—	4	1	no	—
226	C₄×C₁₃	—	4	1	no	—
227	C₄×C₁₃	—	4	1	no	—
228	C₄×C₁₃	—	8	8	no	—
229	H(5,𝔽₂)	—	4	4	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	4	4	no	—
232	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
233	C₂×#41	D₄×C₁₃	1	4	yes	—
234	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
235	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
236	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
237	C₂²×D₄	D₄×C₁₃	1	4	yes	—
238	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
241	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
242	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
243	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	2	no	—
245	#124	—	2	2	no	—
246	#123	—	2	4	no	—
247	#123	—	2	4	no	—
248	#123	—	2	2	no	—
249	#123	—	2	2	no	—
250	#123	C₂×C₄×C₁₃	1	4	yes	complemented
251	#123	C₂×C₄×C₁₃	1	4	yes	complemented
252	#123	C₂×C₄×C₁₃	1	4	yes	complemented
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	—	2	4	no	—
255	#121	—	2	2	no	—
256	#121	—	2	4	no	—
257	#121	—	2	4	no	—
258	#120	—	2	2	no	—
259	#120	—	2	2	no	—
260	#120	C₂×C₄×C₁₃	1	4	yes	complemented
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	4	8	no	—
264	#117	—	2	4	no	—
265	#117	C₂×C₄×C₁₃	1	2	yes	complemented
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	complemented
272	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
274	#99	—	2	8	no	—
275	#99	—	2	8	no	—
276	#99	—	4	4	no	—
277	#95	—	4	4	no	—
278	C₂×C₁₃	—	2	1	no	—
279	C₂×C₁₃	—	2	4	no	—
280	C₂×C₁₃	—	2	2	no	—
281	C₂×C₁₃	—	4	2	no	—
282	C₂×C₁₃	—	4	4	no	—
283	C₂×C₁₃	—	8	1	no	—
284	C₂×C₁₃	#2308	1	1	yes	characteristic
285	C₂⁴	C₁₃×C₂²⋊C₄	1	2	yes	—
286	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
287	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
288	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
289	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
290	#41	—	4	4	no	—
291	#41	—	4	8	no	—
292	#41	—	4	16	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	8	no	—
305	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
306	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
307	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
308	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
309	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
321	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
322	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	4	no	—
344	C₁₃	#21777	1	1	yes	characteristic, direct product factor, Sylow
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
356	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
357	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
358	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
359	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	4	no	—
362	D₄	—	2	8	no	—
363	D₄	—	2	8	no	—
364	D₄	—	2	8	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	8	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	8	no	—
388	C₂×C₄	—	16	4	no	—
389	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
390	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	16	2	no	—
404	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
405	C₂²	C₁₃×#518	1	2	yes	—
406	C₂²	C₁₃×#534	1	4	yes	—
407	C₄	—	2	2	no	—
408	C₄	—	2	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	8	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	4	no	—
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	4	4	no	—
419	C₂	—	8	1	no	—
420	C₂	C₁₃×#2308	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2308
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₁₃×#3485	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2883	C₂	semidirect
3. C₁₃×#1913	C₂	semidirect
4. C₁₃×#1890	C₂	semidirect
5. C₁₃×#1828	C₂	semidirect
6. C₁₃×#1782	C₂	semidirect
11. C₁₃×#536	C₄	semidirect
12. C₁₃×#534	C₄	semidirect
14. C₁₃×#525	C₄	semidirect
15. C₂×C₁₃×#123	C₄	semidirect
23. C₂×C₁₃×#99	C₂²	semidirect
24. C₁₃×#381	C₂²	semidirect
25. C₁₃×#342	C₂²	semidirect
31. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
33. C₂²×D₄×C₁₃	C₂×C₄	semidirect
38. C₂³×C₄×C₁₃	C₂×C₄	semidirect
39. C₂³×C₄×C₁₃	C₂×C₄	semidirect
47. C₁₃×#123	C₂×C₄	semidirect
48. C₁₃×#123	C₂×C₄	semidirect
49. C₁₃×#123	C₂×C₄	semidirect
57. C₁₃×#120	C₂×C₄	semidirect
62. C₁₃×#117	C₂×C₄	semidirect
68. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
75. #21777	C₁₃	direct (N × H)
136. #2883	C₂×C₁₃	semidirect
137. #1913	C₂×C₁₃	semidirect
138. #1890	C₂×C₁₃	semidirect
139. #1828	C₂×C₁₃	semidirect
140. #1782	C₂×C₁₃	semidirect
191. #536	C₄×C₁₃	semidirect
192. #534	C₄×C₁₃	semidirect
194. #525	C₄×C₁₃	semidirect
195. C₂×#123	C₄×C₁₃	semidirect
203. C₂×#99	C₂²×C₁₃	semidirect
204. #381	C₂²×C₁₃	semidirect
205. #342	C₂²×C₁₃	semidirect
234. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
236. C₂²×D₄	C₂×C₄×C₁₃	semidirect
241. C₂³×C₄	C₂×C₄×C₁₃	semidirect
242. C₂³×C₄	C₂×C₄×C₁₃	semidirect
250. #123	C₂×C₄×C₁₃	semidirect
251. #123	C₂×C₄×C₁₃	semidirect
252. #123	C₂×C₄×C₁₃	semidirect
260. #120	C₂×C₄×C₁₃	semidirect
265. #117	C₂×C₄×C₁₃	semidirect
271. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
344. C₁₃	#21777	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3485	2
C₁₃×#2883	2
C₁₃×#1913	2
C₁₃×#1890	2
C₁₃×#1828	2
C₁₃×#1782	2
#21777	13

Subgroups — C13×#21777 #15708116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21777 #15708116