Subgroups — C₁₃×#23696 #15710035

Order 3328.

1062 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic
10	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#121	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	—	2	2	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×D₈	—	2	4	no	—
18	C₁₃×#431	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#386	—	2	2	no	—
34	C₁₃×#380	C₂²	1	2	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×D₈	—	2	4	no	—
48	C₂×C₁₃×D₈	—	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×#121	—	2	4	no	—
54	C₁₃×#121	—	2	4	no	—
55	C₄×D₄×C₁₃	—	2	4	no	—
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	4	8	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	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×C₄²×C₁₃	—	2	2	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#102	—	2	4	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×C₂²⋊C₈	—	2	2	no	—
82	C₁₃×C₂²⋊C₈	—	2	2	no	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	#23696	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₁₃	—	2	8	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	4	4	no	—
98	C₂×D₄×C₁₃	—	4	4	no	—
99	C₂×D₄×C₁₃	#41	1	4	yes	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	D₈	1	4	yes	complemented
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×D₈	—	2	8	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	#41	1	4	yes	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	4	no	—
140	C₁₃×C₂²⋊C₄	—	4	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	4	4	no	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	#41	1	2	yes	—
149	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₄×#121	C₂×C₁₃	1	2	yes	complemented
152	#2086	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#2075	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2067	C₂×C₁₃	1	2	yes	complemented
155	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2033	C₂×C₁₃	1	2	yes	complemented
157	#1999	C₂×C₁₃	1	1	yes	characteristic
158	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₄×#102	C₂×C₁₃	1	2	yes	complemented
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	C₂×D₈	1	2	yes	—
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	D₄×C₁₃	—	2	4	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	4	16	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	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	—	8	8	no	—
200	C₂×C₄×C₁₃	#121	1	2	yes	—
201	C₂×C₄×C₁₃	#121	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
204	C₂×C₄×C₁₃	#135	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	4	1	no	—
212	C₈×C₁₃	—	4	1	no	—
213	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#121	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×D₄	—	2	2	no	—
216	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
218	C₄×D₈	—	2	4	no	—
219	#431	—	2	4	no	—
220	C₂×#107	C₂²×C₁₃	1	2	yes	—
221	C₂×#107	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	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₃	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	#390	C₂²×C₁₃	1	2	yes	—
232	#389	C₂²×C₁₃	1	2	yes	—
233	#388	—	2	2	no	—
234	#386	—	2	2	no	—
235	#380	C₂²×C₁₃	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
237	C₄×C₂²⋊C₄	—	2	2	no	—
238	#340	C₂²×C₁₃	1	1	yes	characteristic
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	2	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	—	4	1	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	—	8	2	no	—
253	C₂²×C₁₃	—	8	2	no	—
254	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
255	C₂²×C₁₃	#525	1	2	yes	—
256	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
258	C₂²×C₁₃	#575	1	2	yes	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	1	no	—
263	C₄×C₁₃	—	4	1	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	—	8	2	no	—
266	C₄×C₁₃	#466	1	4	yes	—
267	C₄×C₁₃	#525	1	1	yes	characteristic
268	C₄×C₁₃	#529	1	2	yes	—
269	C₄×C₁₃	#532	1	1	yes	characteristic
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
274	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	#121	—	2	4	no	—
283	#121	—	2	4	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	4	8	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	#107	—	2	4	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#102	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂×C₁₃	—	4	2	no	—
318	C₂×C₁₃	—	8	4	no	—
319	C₂×C₁₃	#2392	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
321	C₂×C₁₃	#3054	1	1	yes	characteristic
322	C₂×C₁₃	#3100	1	2	yes	—
323	C₂×C₁₃	#3102	1	2	yes	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂×D₄	—	2	8	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	—	2	2	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	C₁₃×#41	1	4	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	C₁₃×D₈	1	4	yes	complemented
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
356	D₈	—	2	8	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	C₁₃×#41	1	4	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	4	4	no	—
382	C₄²	C₂×D₄×C₁₃	1	2	yes	—
383	C₄²	C₁₃×#41	1	2	yes	—
384	C₁₃	#23696	1	1	yes	characteristic, direct product factor, Sylow
385	C₂³	—	2	1	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	C₂×C₁₃×D₈	1	2	yes	—
397	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	16	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	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	—	4	2	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	C₁₃×#121	1	2	yes	—
426	C₂×C₄	C₁₃×#121	1	2	yes	—
427	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
428	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
429	C₂×C₄	C₁₃×#135	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
451	C₂²	C₁₃×#525	1	2	yes	—
452	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
453	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
454	C₂²	C₁₃×#575	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₁₃×#466	1	4	yes	—
463	C₄	C₁₃×#525	1	1	yes	characteristic
464	C₄	C₁₃×#529	1	2	yes	—
465	C₄	C₁₃×#532	1	1	yes	characteristic
466	C₂	—	4	2	no	—
467	C₂	—	8	4	no	—
468	C₂	C₁₃×#2392	1	1	yes	characteristic
469	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
470	C₂	C₁₃×#3054	1	1	yes	characteristic
471	C₂	C₁₃×#3100	1	2	yes	—
472	C₂	C₁₃×#3102	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₁₃×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₃×D₈	C₂	semidirect
2. C₂×C₁₃×#431	C₂	semidirect
3. C₄×C₁₃×#121	C₂	semidirect
4. C₁₃×#2086	C₂	semidirect
5. C₁₃×#2075	C₂	semidirect
6. C₁₃×#2067	C₂	semidirect
7. C₁₃×#2054	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
10. C₄×C₁₃×#107	C₂	semidirect
11. C₄×C₁₃×#102	C₂	semidirect
84. C₄×C₈×C₁₃	D₄	semidirect
88. #23696	C₁₃	direct (N × H)
114. C₂²×C₄×C₁₃	D₈	semidirect
149. C₂×C₄×D₈	C₂×C₁₃	semidirect
150. C₂×#431	C₂×C₁₃	semidirect
151. C₄×#121	C₂×C₁₃	semidirect
152. #2086	C₂×C₁₃	semidirect
153. #2075	C₂×C₁₃	semidirect
154. #2067	C₂×C₁₃	semidirect
155. #2054	C₂×C₁₃	semidirect
156. #2033	C₂×C₁₃	semidirect
158. C₄×#107	C₂×C₁₃	semidirect
159. C₄×#102	C₂×C₁₃	semidirect
313. C₄×C₈	D₄×C₁₃	semidirect
349. C₂²×C₄	C₁₃×D₈	semidirect
384. C₁₃	#23696	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×C₄×C₁₃×D₈	2
C₂×C₁₃×#431	2
C₄×C₁₃×#121	2
C₁₃×#2086	2
C₁₃×#2075	2
C₁₃×#2067	2
C₁₃×#2054	2
C₁₃×#2033	2
C₁₃×#1999	2
C₄×C₁₃×#107	2
C₄×C₁₃×#102	2
#23696	13

Subgroups — C13×#23696 #15710035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23696 #15710035