Subgroups — C₁₃×#29192 #15715531

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2067	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1862	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#125	—	2	1	no	—
12	C₂×C₄×D₄×C₁₃	—	2	1	no	—
13	C₂×C₄×D₄×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#107	C₂²	1	4	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	4	yes	—
18	C₂×C₁₃×#102	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#390	—	2	1	no	—
22	C₁₃×#390	—	2	1	no	—
23	C₁₃×#390	C₂²	1	2	yes	—
24	C₁₃×#389	—	2	1	no	—
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#389	C₂²	1	2	yes	—
27	C₁₃×#389	C₂²	1	2	yes	—
28	C₁₃×#384	C₂²	1	1	yes	characteristic
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#382	—	2	1	no	—
32	C₄³×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#340	C₂²	1	4	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₁₃×#127	—	2	2	no	—
42	C₁₃×#127	Q₈	1	4	yes	—
43	C₁₃×#125	—	4	4	no	—
44	C₄×D₄×C₁₃	—	4	4	no	—
45	C₄×D₄×C₁₃	—	4	4	no	—
46	C₄×D₄×C₁₃	—	4	4	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#107	—	4	4	no	—
69	C₁₃×C₄⋊C₈	—	2	4	no	—
70	C₁₃×#102	—	2	8	no	—
71	C₁₃×#102	—	4	4	no	—
72	C₄×C₈×C₁₃	—	2	2	no	—
73	C₄×C₈×C₁₃	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	#29192	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	4	no	—
79	C₂×D₄×C₁₃	—	2	4	no	—
80	C₂×D₄×C₁₃	—	2	4	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	4	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	4	4	no	—
92	C₂²×C₄×C₁₃	—	4	4	no	—
93	C₂²×C₄×C₁₃	—	4	4	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	#41	1	4	yes	—
107	C₁₃×C₄⋊C₄	—	2	4	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	4	2	no	—
111	C₁₃×C₄⋊C₄	—	4	4	no	—
112	C₁₃×C₄⋊C₄	—	4	4	no	—
113	C₁₃×C₄⋊C₄	—	4	2	no	—
114	C₁₃×C₄⋊C₄	—	4	2	no	—
115	C₁₃×C₄⋊C₄	—	4	2	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₂²⋊C₄	—	4	4	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₁₃×C₂²⋊C₄	—	4	4	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	D₈	1	4	yes	—
127	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
128	C₄²×C₁₃	#41	1	2	yes	—
129	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
130	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
131	#2067	C₂×C₁₃	1	4	yes	complemented
132	#1957	C₂×C₁₃	1	1	yes	characteristic
133	#1957	C₂×C₁₃	1	1	yes	characteristic
134	#1862	C₂×C₁₃	1	4	yes	complemented
135	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	2	4	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	D₄×C₁₃	—	2	8	no	—
147	D₄×C₁₃	—	4	4	no	—
148	D₄×C₁₃	—	4	8	no	—
149	D₄×C₁₃	—	4	8	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	8	8	no	—
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₁₃	#135	1	2	yes	—
176	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₁₃	#137	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
182	C₈×C₁₃	—	2	4	no	—
183	C₈×C₁₃	—	4	2	no	—
184	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#125	—	2	1	no	—
186	C₂×C₄×D₄	—	2	1	no	—
187	C₂×C₄×D₄	—	2	1	no	—
188	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
189	C₂×#107	C₂²×C₁₃	1	4	yes	—
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
191	C₂×#102	C₂²×C₁₃	1	4	yes	—
192	C₂×#102	C₂²×C₁₃	1	4	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
195	#390	—	2	1	no	—
196	#390	—	2	1	no	—
197	#390	C₂²×C₁₃	1	2	yes	—
198	#389	—	2	1	no	—
199	#389	—	2	1	no	—
200	#389	C₂²×C₁₃	1	2	yes	—
201	#389	C₂²×C₁₃	1	2	yes	—
202	#384	C₂²×C₁₃	1	1	yes	characteristic
203	#384	C₂²×C₁₃	1	1	yes	characteristic
204	#384	C₂²×C₁₃	1	1	yes	characteristic
205	#382	—	2	1	no	—
206	C₄³	C₂²×C₁₃	1	1	yes	characteristic
207	#340	C₂²×C₁₃	1	4	yes	—
208	#336	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₁₃	—	4	4	no	—
210	C₂²×C₁₃	—	4	4	no	—
211	C₂²×C₁₃	—	4	4	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	2	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₂²×C₁₃	#532	1	1	yes	characteristic
218	C₂²×C₁₃	#535	1	1	yes	characteristic
219	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
221	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	4	1	no	—
226	C₄×C₁₃	—	4	1	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	#474	1	4	yes	—
231	C₄×C₁₃	#478	1	4	yes	—
232	C₄×C₁₃	#553	1	2	yes	—
233	C₄×C₁₃	#554	1	2	yes	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
237	C₂³×C₄	—	2	2	no	—
238	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
239	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
240	#127	—	2	2	no	—
241	#127	Q₈×C₁₃	1	4	yes	—
242	#125	—	4	4	no	—
243	C₄×D₄	—	4	4	no	—
244	C₄×D₄	—	4	4	no	—
245	C₄×D₄	—	4	4	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	#107	—	4	4	no	—
268	C₄⋊C₈	—	2	4	no	—
269	#102	—	2	8	no	—
270	#102	—	4	4	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	C₂×C₁₃	—	8	4	no	—
276	C₂×C₁₃	#2566	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
279	C₂×C₁₃	#3169	1	1	yes	characteristic
280	C₂×C₁₃	#3182	1	1	yes	characteristic
281	C₂×C₁₃	#3205	1	1	yes	characteristic
282	C₂×C₁₃	#3210	1	1	yes	characteristic
283	C₂⁴	—	2	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₁₃×#41	1	4	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₁₃×D₈	1	4	yes	—
333	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
334	C₄²	C₁₃×#41	1	2	yes	—
335	C₁₃	#29192	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	D₄	—	2	8	no	—
345	D₄	—	4	8	no	—
346	D₄	—	4	8	no	—
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
369	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
370	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
371	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
372	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
373	C₂×C₄	C₁₃×#135	1	2	yes	—
374	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
375	C₂×C₄	C₁₃×#137	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
379	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂²	C₁₃×#532	1	1	yes	characteristic
391	C₂²	C₁₃×#535	1	1	yes	characteristic
392	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
393	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
394	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₁₃×#474	1	4	yes	—
404	C₄	C₁₃×#478	1	4	yes	—
405	C₄	C₁₃×#553	1	2	yes	—
406	C₄	C₁₃×#554	1	2	yes	—
407	C₂	—	8	4	no	—
408	C₂	C₁₃×#2566	1	1	yes	characteristic
409	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
410	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
411	C₂	C₁₃×#3169	1	1	yes	characteristic
412	C₂	C₁₃×#3182	1	1	yes	characteristic
413	C₂	C₁₃×#3205	1	1	yes	characteristic
414	C₂	C₁₃×#3210	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2859	C₂	semidirect
3. C₁₃×#2067	C₂	semidirect
6. C₁₃×#1862	C₂	semidirect
7. C₁₃×#1845	C₂	semidirect
8. C₁₃×#1834	C₂	semidirect
9. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
76. #29192	C₁₃	direct (N × H)
129. #2859	C₂×C₁₃	semidirect
131. #2067	C₂×C₁₃	semidirect
134. #1862	C₂×C₁₃	semidirect
135. #1845	C₂×C₁₃	semidirect
136. #1834	C₂×C₁₃	semidirect
137. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
335. C₁₃	#29192	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×#2859	2
C₄×C₁₃×#127	2
C₁₃×#2067	2
C₁₃×#1957	2
C₁₃×#1862	2
C₁₃×#1845	2
C₁₃×#1834	2
C₄×C₁₃×C₄⋊C₈	2
#29192	13

Subgroups — C13×#29192 #15715531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29192 #15715531