Subgroups — C₁₃×#26482 #15712821

Order 3328.

846 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2454	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
15	C₁₃×#499	—	2	4	no	—
16	C₄×C₁₃×D₈	—	2	4	no	—
17	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#399	—	2	2	no	—
29	C₁₃×#396	—	2	2	no	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#385	—	2	2	no	—
35	C₁₃×#380	—	2	2	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	2	no	—
43	C₂×C₁₃×D₈	—	2	2	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	Q₈	1	4	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#125	—	2	4	no	—
51	C₁₃×#125	—	4	2	no	—
52	C₄×D₄×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	4	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	D₄	1	4	yes	—
74	C₁₃×#106	—	2	4	no	—
75	C₁₃×C₄⋊C₈	—	2	2	no	—
76	C₁₃×#102	—	2	4	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₁₃×#102	—	4	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	D₄	1	1	yes	characteristic
85	C₁₃×#95	D₄	1	1	yes	characteristic
86	#26482	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	4	4	no	—
98	C₂²×C₄×C₁₃	—	4	4	no	—
99	C₂²×C₄×C₁₃	—	8	2	no	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×D₈	—	2	8	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×C₈×C₁₃	#41	1	2	yes	—
119	C₂×C₈×C₁₃	#41	1	2	yes	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	4	no	—
129	C₁₃×C₄⋊C₄	—	8	2	no	—
130	C₁₃×C₄⋊C₄	—	8	2	no	—
131	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
132	C₁₃×C₂²⋊C₄	—	4	4	no	—
133	C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₁₃×C₂²⋊C₄	—	8	2	no	—
135	C₁₃×C₂²⋊C₄	—	8	2	no	—
136	C₁₃×C₂²⋊C₄	—	8	2	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
145	#2454	C₂×C₁₃	1	2	yes	complemented
146	#2065	C₂×C₁₃	1	2	yes	complemented
147	#2025	C₂×C₁₃	1	2	yes	complemented
148	#1970	C₂×C₁₃	1	1	yes	characteristic
149	#1970	C₂×C₁₃	1	1	yes	characteristic
150	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1864	C₂×C₁₃	1	2	yes	complemented
153	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	—	2	4	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₁₃	—	2	4	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	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	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	4	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	2	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	—	8	8	no	—
192	C₂×C₄×C₁₃	#135	1	2	yes	—
193	C₂×C₄×C₁₃	#135	1	2	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	4	1	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
204	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#125	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
207	#499	—	2	4	no	—
208	C₄×D₈	—	2	4	no	—
209	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#106	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#102	C₂²×C₁₃	1	2	yes	—
215	C₂×#102	C₂²×C₁₃	1	2	yes	—
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#399	—	2	2	no	—
221	#396	—	2	2	no	—
222	#390	C₂²×C₁₃	1	2	yes	—
223	#390	C₂²×C₁₃	1	2	yes	—
224	#389	C₂²×C₁₃	1	2	yes	—
225	#389	C₂²×C₁₃	1	2	yes	—
226	#385	—	2	2	no	—
227	#380	—	2	2	no	—
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
229	#340	C₂²×C₁₃	1	2	yes	—
230	#340	C₂²×C₁₃	1	2	yes	—
231	#336	C₂²×C₁₃	1	1	yes	characteristic
232	#336	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	—	4	4	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	#532	1	1	yes	characteristic
241	C₂²×C₁₃	D₄²	1	1	yes	characteristic
242	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
245	C₂²×C₁₃	#576	1	1	yes	characteristic
246	C₂²×C₁₃	#576	1	1	yes	characteristic
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	4	1	no	—
251	C₄×C₁₃	—	4	4	no	—
252	C₄×C₁₃	—	4	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₄×C₁₃	#542	1	1	yes	characteristic
258	C₄×C₁₃	#548	1	1	yes	characteristic
259	C₄×C₁₃	#554	1	1	yes	characteristic
260	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
261	C₂³×C₄	—	2	2	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	Q₈×C₁₃	1	4	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	#125	—	2	4	no	—
270	#125	—	4	2	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	4	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
290	#107	—	2	2	no	—
291	#107	—	2	2	no	—
292	#107	D₄×C₁₃	1	4	yes	—
293	#106	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	#102	—	2	4	no	—
296	#102	—	2	4	no	—
297	#102	—	4	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	D₄×C₁₃	1	1	yes	characteristic
304	#95	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₁₃	—	8	4	no	—
306	C₂×C₁₃	#2452	1	1	yes	characteristic
307	C₂×C₁₃	#3168	1	1	yes	characteristic
308	C₂×C₁₃	#3176	1	1	yes	characteristic
309	C₂×C₁₃	#3280	1	1	yes	characteristic
310	C₂×C₁₃	#3287	1	1	yes	characteristic
311	C₂×C₁₃	#3380	1	1	yes	characteristic
312	C₂×C₁₃	#3380	1	1	yes	characteristic
313	C₂⁴	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	8	2	no	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
333	D₈	—	2	8	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
343	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
344	C₂×C₈	C₁₃×#41	1	2	yes	—
345	C₂×C₈	C₁₃×#41	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₁₃	#26482	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	D₄	—	2	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	8	no	—
408	C₂×C₄	C₁₃×#135	1	2	yes	—
409	C₂×C₄	C₁₃×#135	1	2	yes	—
410	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
413	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
414	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	C₁₃×#532	1	1	yes	characteristic
428	C₂²	D₄²×C₁₃	1	1	yes	characteristic
429	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
430	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
431	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
432	C₂²	C₁₃×#576	1	1	yes	characteristic
433	C₂²	C₁₃×#576	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	2	no	—
443	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
444	C₄	C₁₃×#542	1	1	yes	characteristic
445	C₄	C₁₃×#548	1	1	yes	characteristic
446	C₄	C₁₃×#554	1	1	yes	characteristic
447	C₂	—	8	4	no	—
448	C₂	C₁₃×#2452	1	1	yes	characteristic
449	C₂	C₁₃×#3168	1	1	yes	characteristic
450	C₂	C₁₃×#3176	1	1	yes	characteristic
451	C₂	C₁₃×#3280	1	1	yes	characteristic
452	C₂	C₁₃×#3287	1	1	yes	characteristic
453	C₂	C₁₃×#3380	1	1	yes	characteristic
454	C₂	C₁₃×#3380	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#499	C₂	semidirect
3. C₁₃×#2454	C₂	semidirect
4. C₁₃×#2065	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
8. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1864	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
86. #26482	C₁₃	direct (N × H)
143. C₂×#499	C₂×C₁₃	semidirect
145. #2454	C₂×C₁₃	semidirect
146. #2065	C₂×C₁₃	semidirect
147. #2025	C₂×C₁₃	semidirect
150. #1942	C₂×C₁₃	semidirect
151. #1942	C₂×C₁₃	semidirect
152. #1864	C₂×C₁₃	semidirect
153. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
369. C₁₃	#26482	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×#499	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2454	2
C₁₃×#2065	2
C₁₃×#2025	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1864	2
C₈×C₁₃×C₄⋊C₄	2
#26482	13

Subgroups — C13×#26482 #15712821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26482 #15712821