Subgroups — C₁₃×#25033 #15711372

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2421	C₂	1	2	yes	maximal
4	C₁₃×#2074	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2035	C₂	1	2	yes	maximal
6	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#467	—	2	4	no	—
17	C₄×C₁₃×Q₁₆	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	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×#400	—	2	2	no	—
29	C₁₃×#397	—	2	2	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#387	—	2	2	no	—
34	C₁₃×#382	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊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×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×Q₁₆	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	4	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#107	—	2	2	no	—
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#106	—	4	2	no	—
74	C₁₃×#103	—	2	4	no	—
75	C₁₃×#103	—	2	4	no	—
76	C₁₃×#103	—	2	4	no	—
77	C₁₃×C₂²⋊C₈	—	2	2	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	D₄	1	1	yes	characteristic
87	C₁₃×#95	D₄	1	1	yes	characteristic
88	#25033	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₁₃×Q₁₆	—	2	8	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	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	4	4	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₃	#41	1	2	yes	—
124	C₂×C₈×C₁₃	#41	1	2	yes	—
125	C₂×C₈×C₁₃	#41	1	2	yes	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₁₃×C₂²⋊C₄	—	2	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	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	C₄²×C₁₃	—	4	4	no	—
144	C₂×#467	C₂×C₁₃	1	1	yes	characteristic
145	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2421	C₂×C₁₃	1	2	yes	—
147	#2074	C₂×C₁₃	1	2	yes	complemented
148	#2035	C₂×C₁₃	1	2	yes	—
149	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1865	C₂×C₁₃	1	2	yes	complemented
152	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1808	C₂×C₁₃	1	1	yes	characteristic
154	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	#135	1	2	yes	—
162	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	4	no	—
164	Q₈×C₁₃	—	2	4	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	2	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	4	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	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	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	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	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	#135	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	4	1	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	#123	1	4	yes	—
208	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
212	#467	—	2	4	no	—
213	C₄×Q₁₆	—	2	4	no	—
214	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#106	C₂²×C₁₃	1	2	yes	—
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
224	#400	—	2	2	no	—
225	#397	—	2	2	no	—
226	#391	C₂²×C₁₃	1	2	yes	—
227	#389	C₂²×C₁₃	1	2	yes	—
228	#388	—	2	2	no	—
229	#387	—	2	2	no	—
230	#382	C₂²×C₁₃	1	2	yes	—
231	#380	C₂²×C₁₃	1	2	yes	—
232	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	1	yes	characteristic
236	#336	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	#532	1	1	yes	characteristic
245	C₂²×C₁₃	D₄²	1	1	yes	characteristic
246	C₂²×C₁₃	#547	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
249	C₂²×C₁₃	#578	1	1	yes	characteristic
250	C₂²×C₁₃	#578	1	1	yes	characteristic
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
261	C₄×C₁₃	#542	1	1	yes	characteristic
262	C₄×C₁₃	#547	1	1	yes	characteristic
263	C₄×C₁₃	#553	1	1	yes	characteristic
264	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×Q₁₆	—	2	2	no	—
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂²⋊Q₈	—	4	2	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	4	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#107	—	2	2	no	—
295	#107	—	2	2	no	—
296	#106	—	4	2	no	—
297	#103	—	2	4	no	—
298	#103	—	2	4	no	—
299	#103	—	2	4	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₄×C₈	—	2	2	no	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	D₄×C₁₃	1	1	yes	characteristic
310	#95	D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	#2422	1	1	yes	characteristic
313	C₂×C₁₃	#3168	1	1	yes	characteristic
314	C₂×C₁₃	#3177	1	1	yes	characteristic
315	C₂×C₁₃	#3285	1	1	yes	characteristic
316	C₂×C₁₃	#3285	1	1	yes	characteristic
317	C₂×C₁₃	#3336	1	1	yes	characteristic
318	C₂×C₁₃	#3342	1	1	yes	characteristic
319	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	4	4	no	—
352	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
353	C₂×C₈	C₁₃×#41	1	2	yes	—
354	C₂×C₈	C₁₃×#41	1	2	yes	—
355	C₂×C₈	C₁₃×#41	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	4	4	no	—
374	C₁₃	#25033	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	C₁₃×#135	1	2	yes	—
382	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	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	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₁₃×#135	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	C₁₃×#123	1	4	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	C₁₃×#532	1	1	yes	characteristic
436	C₂²	D₄²×C₁₃	1	1	yes	characteristic
437	C₂²	C₁₃×#547	1	1	yes	characteristic
438	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
439	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
440	C₂²	C₁₃×#578	1	1	yes	characteristic
441	C₂²	C₁₃×#578	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	4	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
452	C₄	C₁₃×#542	1	1	yes	characteristic
453	C₄	C₁₃×#547	1	1	yes	characteristic
454	C₄	C₁₃×#553	1	1	yes	characteristic
455	C₂	—	4	2	no	—
456	C₂	C₁₃×#2422	1	1	yes	characteristic
457	C₂	C₁₃×#3168	1	1	yes	characteristic
458	C₂	C₁₃×#3177	1	1	yes	characteristic
459	C₂	C₁₃×#3285	1	1	yes	characteristic
460	C₂	C₁₃×#3285	1	1	yes	characteristic
461	C₂	C₁₃×#3336	1	1	yes	characteristic
462	C₂	C₁₃×#3342	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2074	C₂	semidirect
6. C₁₃×#1969	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1865	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
88. #25033	C₁₃	direct (N × H)
145. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
147. #2074	C₂×C₁₃	semidirect
149. #1969	C₂×C₁₃	semidirect
150. #1942	C₂×C₁₃	semidirect
151. #1865	C₂×C₁₃	semidirect
152. #1846	C₂×C₁₃	semidirect
374. C₁₃	#25033	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×#467	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2421	2
C₁₃×#2074	2
C₁₃×#2035	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1865	2
C₁₃×#1846	2
C₁₃×#1808	2
C₈×C₁₃×C₂²⋊C₄	2
#25033	13

Subgroups — C13×#25033 #15711372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25033 #15711372