Subgroups — C₁₃×#29116 #15715455

Order 3328.

962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1825	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1786	C₂	1	2	yes	maximal
9	C₁₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#102	C₂²	1	2	yes	—
15	C₂×C₁₃×#102	C₂²	1	2	yes	—
16	C₂×C₁₃×#102	C₂²	1	2	yes	—
17	C₂×C₁₃×#102	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#400	—	2	1	no	—
22	C₁₃×#399	—	2	1	no	—
23	C₁₃×#395	—	2	1	no	—
24	C₁₃×#393	—	2	1	no	—
25	C₁₃×#390	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	complemented
30	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#380	C₂²	1	2	yes	—
32	C₁₃×#379	—	2	1	no	—
33	C₁₃×#379	—	2	1	no	—
34	C₁₃×#340	C₂²	1	2	yes	complemented
35	C₁₃×#340	C₂²	1	2	yes	complemented
36	C₁₃×#340	C₂²	1	2	yes	complemented
37	C₁₃×#340	C₂²	1	2	yes	complemented
38	C₁₃×#336	C₂²	1	2	yes	complemented
39	C₂⁵×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	—	2	4	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	—	4	1	no	—
45	C₂²×D₄×C₁₃	—	4	1	no	—
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	4	1	no	—
51	C₁₃×C₄⋊Q₈	—	4	1	no	—
52	C₁₃×#117	—	2	4	no	—
53	C₁₃×#117	—	4	1	no	—
54	C₁₃×#117	—	4	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊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	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#102	—	2	4	no	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×#102	—	4	2	no	—
76	C₁₃×#102	—	4	2	no	—
77	C₁₃×C₂²⋊C₈	—	2	4	no	—
78	C₁₃×#97	—	4	1	no	—
79	C₄×C₈×C₁₃	—	4	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	1	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	2	no	—
84	#29116	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	4	no	—
86	C₂⁴×C₁₃	—	2	2	no	—
87	C₂⁴×C₁₃	—	4	2	no	—
88	C₂⁴×C₁₃	—	4	2	no	—
89	C₂⁴×C₁₃	—	8	2	no	—
90	C₂⁴×C₁₃	—	8	2	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	8	2	no	—
94	C₂×D₄×C₁₃	—	2	4	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	4	8	no	—
101	C₂×D₄×C₁₃	—	4	8	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	#41	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	8	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	8	2	no	—
137	C₁₃×C₂²⋊C₄	—	8	2	no	—
138	C₁₃×C₂²⋊C₄	—	8	2	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	—	8	2	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	4	2	no	—
146	#2628	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2309	C₂×C₁₃	1	1	yes	characteristic
148	#2073	C₂×C₁₃	1	2	yes	complemented
149	#2023	C₂×C₁₃	1	2	yes	complemented
150	#1936	C₂×C₁₃	1	2	yes	complemented
151	#1934	C₂×C₁₃	1	2	yes	complemented
152	#1825	C₂×C₁₃	1	2	yes	complemented
153	#1786	C₂×C₁₃	1	2	yes	—
154	#1750	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	—	4	8	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	8	8	no	—
168	C₂³×C₁₃	—	8	8	no	—
169	C₂³×C₁₃	—	8	4	no	—
170	C₂³×C₁₃	—	8	4	no	—
171	C₂³×C₁₃	#124	1	2	yes	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃	—	8	4	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	2	4	no	—
176	D₄×C₁₃	—	4	8	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	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	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	#124	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
203	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₈×C₁₃	—	4	2	no	—
206	C₈×C₁₃	—	4	2	no	—
207	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#102	C₂²×C₁₃	1	2	yes	—
212	C₂×#102	C₂²×C₁₃	1	2	yes	—
213	C₂×#102	C₂²×C₁₃	1	2	yes	—
214	C₂×#102	C₂²×C₁₃	1	2	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
216	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
217	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
218	#400	—	2	1	no	—
219	#399	—	2	1	no	—
220	#395	—	2	1	no	—
221	#393	—	2	1	no	—
222	#390	—	2	1	no	—
223	#390	—	2	1	no	—
224	#390	C₂²×C₁₃	1	2	yes	—
225	#390	C₂²×C₁₃	1	2	yes	—
226	#389	C₂²×C₁₃	1	2	yes	complemented
227	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
228	#380	C₂²×C₁₃	1	2	yes	—
229	#379	—	2	1	no	—
230	#379	—	2	1	no	—
231	#340	C₂²×C₁₃	1	2	yes	complemented
232	#340	C₂²×C₁₃	1	2	yes	complemented
233	#340	C₂²×C₁₃	1	2	yes	complemented
234	#340	C₂²×C₁₃	1	2	yes	complemented
235	#336	C₂²×C₁₃	1	2	yes	complemented
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	4	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	8	16	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	#525	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
251	C₂²×C₁₃	#534	1	1	yes	characteristic
252	C₂²×C₁₃	#576	1	2	yes	—
253	C₂²×C₁₃	#577	1	2	yes	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	1	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	#551	1	2	yes	—
263	C₄×C₁₃	#551	1	2	yes	—
264	C₂⁵	—	2	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×D₄	—	2	4	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	4	no	—
269	C₂²×D₄	—	4	1	no	—
270	C₂²×D₄	—	4	1	no	—
271	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₄⋊Q₈	—	4	1	no	—
276	C₄⋊Q₈	—	4	1	no	—
277	#117	—	2	4	no	—
278	#117	—	4	1	no	—
279	#117	—	4	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
298	#102	—	2	4	no	—
299	#102	—	2	4	no	—
300	#102	—	4	2	no	—
301	#102	—	4	2	no	—
302	C₂²⋊C₈	—	2	4	no	—
303	#97	—	4	1	no	—
304	C₄×C₈	—	4	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	1	no	—
307	#95	—	2	1	no	—
308	#95	—	2	2	no	—
309	C₂×C₁₃	—	4	2	no	—
310	C₂×C₁₃	—	8	4	no	—
311	C₂×C₁₃	#2561	1	1	yes	characteristic
312	C₂×C₁₃	#3118	1	2	yes	—
313	C₂×C₁₃	#3136	1	2	yes	—
314	C₂×C₁₃	#3199	1	1	yes	characteristic
315	C₂×C₁₃	#3200	1	1	yes	characteristic
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	—	4	2	no	—
319	C₂⁴	—	4	2	no	—
320	C₂⁴	—	8	2	no	—
321	C₂⁴	—	8	2	no	—
322	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	8	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	C₁₃×#41	1	4	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₁₃×#41	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	4	2	no	—
377	C₁₃	#29116	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	8	8	no	—
391	C₂³	—	8	8	no	—
392	C₂³	—	8	4	no	—
393	C₂³	—	8	4	no	—
394	C₂³	C₁₃×#124	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	Q₈	—	8	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	8	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	C₁₃×#124	1	2	yes	—
424	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
425	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
426	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	8	16	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	C₁₃×#525	1	1	yes	characteristic
444	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
445	C₂²	C₁₃×#534	1	1	yes	characteristic
446	C₂²	C₁₃×#576	1	2	yes	—
447	C₂²	C₁₃×#577	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	2	no	—
456	C₄	C₁₃×#551	1	2	yes	—
457	C₄	C₁₃×#551	1	2	yes	—
458	C₂	—	4	2	no	—
459	C₂	—	8	4	no	—
460	C₂	C₁₃×#2561	1	1	yes	characteristic
461	C₂	C₁₃×#3118	1	2	yes	—
462	C₂	C₁₃×#3136	1	2	yes	—
463	C₂	C₁₃×#3199	1	1	yes	characteristic
464	C₂	C₁₃×#3200	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2628	C₂	semidirect
3. C₁₃×#2073	C₂	semidirect
4. C₁₃×#2023	C₂	semidirect
5. C₁₃×#1936	C₂	semidirect
6. C₁₃×#1934	C₂	semidirect
7. C₁₃×#1825	C₂	semidirect
9. C₁₃×#1750	C₂	semidirect
11. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×#97	C₂²	semidirect
20. C₂×C₄×C₈×C₁₃	C₂²	semidirect
29. C₁₃×#389	C₂²	semidirect
30. C₁₃×#382	C₂²	semidirect
34. C₁₃×#340	C₂²	semidirect
35. C₁₃×#340	C₂²	semidirect
36. C₁₃×#340	C₂²	semidirect
37. C₁₃×#340	C₂²	semidirect
38. C₁₃×#336	C₂²	semidirect
84. #29116	C₁₃	direct (N × H)
146. #2628	C₂×C₁₃	semidirect
148. #2073	C₂×C₁₃	semidirect
149. #2023	C₂×C₁₃	semidirect
150. #1936	C₂×C₁₃	semidirect
151. #1934	C₂×C₁₃	semidirect
152. #1825	C₂×C₁₃	semidirect
154. #1750	C₂×C₁₃	semidirect
208. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
216. C₂×#97	C₂²×C₁₃	semidirect
217. C₂×C₄×C₈	C₂²×C₁₃	semidirect
226. #389	C₂²×C₁₃	semidirect
227. #382	C₂²×C₁₃	semidirect
231. #340	C₂²×C₁₃	semidirect
232. #340	C₂²×C₁₃	semidirect
233. #340	C₂²×C₁₃	semidirect
234. #340	C₂²×C₁₃	semidirect
235. #336	C₂²×C₁₃	semidirect
377. C₁₃	#29116	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×#2628	2
C₁₃×#2309	2
C₁₃×#2073	2
C₁₃×#2023	2
C₁₃×#1936	2
C₁₃×#1934	2
C₁₃×#1825	2
C₁₃×#1786	2
C₁₃×#1750	2
#29116	13

Subgroups — C13×#29116 #15715455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29116 #15715455