Subgroups — C₄×C₁₃×#389 #15700106

Order 3328.

1918 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#389	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1436	C₂	1	4	yes	maximal
7	C₁₃×C₄⋊#95	C₂	1	2	yes	maximal
8	C₄×C₁₃×#95	C₂	1	2	yes	maximal
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#389	C₄	1	16	yes	direct product factor
21	C₄×C₁₃×C₄⋊C₄	—	2	8	no	—
22	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
23	C₄×C₁₃×C₄⋊C₄	C₄	1	8	yes	complemented
24	C₂×C₁₃×#95	C₂²	1	4	yes	—
25	C₂×C₁₃×#95	C₂²	1	2	yes	—
26	C₂×C₁₃×#95	C₂²	1	4	yes	—
27	C₂×C₁₃×#95	C₂²	1	2	yes	—
28	C₂×C₁₃×#95	C₂²	1	4	yes	—
29	C₄³×C₁₃	—	2	4	no	—
30	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
31	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
48	C₂×C₄²×C₁₃	—	2	4	no	—
49	C₂×C₄²×C₁₃	—	2	4	no	—
50	C₂×C₄²×C₁₃	—	2	4	no	—
51	C₂×C₄²×C₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₃	—	2	2	no	—
53	C₂×C₄²×C₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₃	—	2	4	no	—
55	C₂×C₄²×C₁₃	—	2	4	no	—
56	C₂×C₄²×C₁₃	—	2	4	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	—	2	4	no	—
60	C₂×C₄²×C₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₃	—	2	4	no	—
62	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
64	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₁₃	D₄	1	4	yes	—
66	C₂×C₄²×C₁₃	D₄	1	4	yes	—
67	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
68	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
69	C₁₃×#95	—	2	8	no	—
70	C₁₃×#95	—	2	4	no	—
71	C₁₃×#95	—	2	8	no	—
72	C₁₃×#95	C₂×C₄	1	8	yes	—
73	C₁₃×#95	C₂×C₄	1	16	yes	—
74	C₄×#389	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
103	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₁₃	#41	1	4	yes	—
120	C₂²×C₄×C₁₃	#41	1	4	yes	—
121	C₂²×C₄×C₁₃	#41	1	4	yes	—
122	C₂²×C₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	#41	1	2	yes	—
124	C₁₃×C₄⋊C₄	—	2	8	no	—
125	C₁₃×C₄⋊C₄	—	2	32	no	—
126	C₁₃×C₄⋊C₄	—	2	16	no	—
127	C₁₃×C₄⋊C₄	C₄²	1	16	yes	complemented
128	C₄²×C₁₃	—	2	16	no	—
129	C₄²×C₁₃	—	2	16	no	—
130	C₄²×C₁₃	—	2	16	no	—
131	C₄²×C₁₃	—	2	8	no	—
132	C₄²×C₁₃	—	2	8	no	—
133	C₄²×C₁₃	—	4	8	no	—
134	C₄²×C₁₃	C₄⋊C₄	1	16	yes	complemented
135	C₂×#389	C₂×C₁₃	1	2	yes	—
136	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
137	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
138	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
139	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic
140	#1436	C₂×C₁₃	1	4	yes	—
141	C₄⋊#95	C₂×C₁₃	1	2	yes	—
142	C₄×#95	C₂×C₁₃	1	2	yes	—
143	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
144	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
148	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
149	C₂³×C₁₃	C₂×#41	1	2	yes	—
150	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
151	C₂³×C₁₃	C₂×#41	1	2	yes	—
152	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
153	C₂³×C₁₃	C₂×#41	1	2	yes	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	8	no	—
158	C₂×C₄×C₁₃	—	2	8	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	C₂×C₄²	1	8	yes	—
187	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
188	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
189	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
190	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
191	C₂×C₄×C₁₃	#117	1	4	yes	—
192	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
193	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
194	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
195	C₂×C₄×C₁₃	C₄×Q₈	1	8	yes	—
196	C₂×C₄×C₁₃	C₄×Q₈	1	8	yes	—
197	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
198	C₂×C₄×C₁₃	#121	1	4	yes	—
199	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
200	C₂×C₄×C₁₃	#125	1	4	yes	—
201	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
208	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
213	#389	C₄×C₁₃	1	16	yes	direct product factor
214	C₄×C₄⋊C₄	—	2	8	no	—
215	C₄×C₄⋊C₄	—	2	4	no	—
216	C₄×C₄⋊C₄	C₄×C₁₃	1	8	yes	complemented
217	C₂×#95	C₂²×C₁₃	1	4	yes	—
218	C₂×#95	C₂²×C₁₃	1	4	yes	—
219	C₂×#95	C₂²×C₁₃	1	2	yes	—
220	C₂×#95	C₂²×C₁₃	1	4	yes	—
221	C₂×#95	C₂²×C₁₃	1	2	yes	—
222	C₄³	—	2	4	no	—
223	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
224	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
226	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
227	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
228	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
230	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
231	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
232	C₂²×C₁₃	C₄×#41	1	2	yes	—
233	C₂²×C₁₃	C₄×#41	1	2	yes	—
234	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
235	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
236	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
237	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₂²×C₁₃	#525	1	2	yes	—
239	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
240	C₂²×C₁₃	#529	1	2	yes	—
241	C₂²×C₁₃	#529	1	2	yes	—
242	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	C₂²×C₁₃	#532	1	2	yes	—
244	C₂²×C₁₃	#533	1	2	yes	—
245	C₂²×C₁₃	#533	1	2	yes	—
246	C₄×C₁₃	—	2	8	no	—
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	2	8	no	—
249	C₄×C₁₃	—	2	8	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	—	4	8	no	—
252	C₄×C₁₃	C₄×C₄⋊C₄	1	8	yes	complemented
253	C₄×C₁₃	#389	1	8	yes	direct product factor
254	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	2	8	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
268	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	—	2	4	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	—	2	4	no	—
285	C₂×C₄²	—	2	4	no	—
286	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
287	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
288	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
289	C₂×C₄²	D₄×C₁₃	1	4	yes	—
290	C₂×C₄²	D₄×C₁₃	1	4	yes	—
291	C₂×C₄²	Q₈×C₁₃	1	4	yes	—
292	C₂×C₄²	Q₈×C₁₃	1	4	yes	—
293	#95	—	2	8	no	—
294	#95	—	2	4	no	—
295	#95	—	2	8	no	—
296	#95	C₂×C₄×C₁₃	1	8	yes	—
297	#95	C₂×C₄×C₁₃	1	16	yes	—
298	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
300	C₂×C₁₃	C₄²×Q₈	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
302	C₂×C₁₃	#2293	1	1	yes	characteristic
303	C₂×C₁₃	#2295	1	1	yes	characteristic
304	C₂×C₁₃	#2296	1	1	yes	characteristic
305	C₂×C₁₃	C₄×#121	1	2	yes	—
306	C₂×C₁₃	C₄×C₂²⋊Q₈	1	2	yes	—
307	C₂×C₁₃	C₄×#125	1	2	yes	—
308	C₂×C₁₃	C₄×C₄⋊Q₈	1	2	yes	—
309	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
350	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
353	C₂²×C₄	C₁₃×#41	1	4	yes	—
354	C₂²×C₄	C₁₃×#41	1	4	yes	—
355	C₂²×C₄	C₁₃×#41	1	4	yes	—
356	C₂²×C₄	C₁₃×#41	1	2	yes	—
357	C₂²×C₄	C₁₃×#41	1	2	yes	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	32	no	—
360	C₄⋊C₄	—	2	16	no	—
361	C₄⋊C₄	C₄²×C₁₃	1	16	yes	complemented
362	C₄²	—	2	16	no	—
363	C₄²	—	2	16	no	—
364	C₄²	—	2	16	no	—
365	C₄²	—	2	8	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	4	8	no	—
368	C₄²	C₁₃×C₄⋊C₄	1	16	yes	complemented
369	C₁₃	C₄×#389	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
371	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
372	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
374	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
375	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
376	C₂³	C₂×C₁₃×#41	1	2	yes	—
377	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
378	C₂³	C₂×C₁₃×#41	1	2	yes	—
379	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
380	C₂³	C₂×C₁₃×#41	1	2	yes	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	C₂×C₄²×C₁₃	1	8	yes	—
414	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
415	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
416	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
417	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
418	C₂×C₄	C₁₃×#117	1	4	yes	—
419	C₂×C₄	C₄×D₄×C₁₃	1	8	yes	—
420	C₂×C₄	C₄×D₄×C₁₃	1	8	yes	—
421	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
422	C₂×C₄	C₄×Q₈×C₁₃	1	8	yes	—
423	C₂×C₄	C₄×Q₈×C₁₃	1	8	yes	—
424	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
425	C₂×C₄	C₁₃×#121	1	4	yes	—
426	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
427	C₂×C₄	C₁₃×#125	1	4	yes	—
428	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
429	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
430	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
431	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
432	C₂²	C₂×C₄×D₄×C₁₃	1	2	yes	—
433	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
434	C₂²	C₂×C₄×D₄×C₁₃	1	2	yes	—
435	C₂²	C₂×C₄×Q₈×C₁₃	1	2	yes	—
436	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
437	C₂²	C₂×C₄×Q₈×C₁₃	1	2	yes	—
438	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
439	C₂²	C₄×C₁₃×#41	1	2	yes	—
440	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
441	C₂²	C₄×C₁₃×#41	1	2	yes	—
442	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
443	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
444	C₂²	C₁₃×#525	1	2	yes	—
445	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
446	C₂²	C₁₃×#529	1	2	yes	—
447	C₂²	C₁₃×#529	1	2	yes	—
448	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
449	C₂²	C₁₃×#532	1	2	yes	—
450	C₂²	C₁₃×#533	1	2	yes	—
451	C₂²	C₁₃×#533	1	2	yes	—
452	C₄	—	2	8	no	—
453	C₄	—	2	4	no	—
454	C₄	—	2	8	no	—
455	C₄	—	2	8	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	8	no	—
458	C₄	C₄×C₁₃×C₄⋊C₄	1	8	yes	complemented
459	C₄	C₁₃×#389	1	8	yes	direct product factor
460	C₂	C₂×C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
461	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
462	C₂	C₄²×Q₈×C₁₃	1	1	yes	characteristic
463	C₂	C₂×C₁₃×#389	1	1	yes	characteristic
464	C₂	C₁₃×#2293	1	1	yes	characteristic
465	C₂	C₁₃×#2295	1	1	yes	characteristic
466	C₂	C₁₃×#2296	1	1	yes	characteristic
467	C₂	C₄×C₁₃×#121	1	2	yes	—
468	C₂	C₄×C₁₃×C₂²⋊Q₈	1	2	yes	—
469	C₂	C₄×C₁₃×#125	1	2	yes	—
470	C₂	C₄×C₁₃×C₄⋊Q₈	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
20. C₁₃×#389	C₄	direct (N × H)
23. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
74. C₄×#389	C₁₃	direct (N × H)
127. C₁₃×C₄⋊C₄	C₄²	semidirect
134. C₄²×C₁₃	C₄⋊C₄	semidirect
213. #389	C₄×C₁₃	direct (N × H)
216. C₄×C₄⋊C₄	C₄×C₁₃	semidirect
252. C₄×C₁₃	C₄×C₄⋊C₄	semidirect
253. C₄×C₁₃	#389	direct (N × H)
361. C₄⋊C₄	C₄²×C₁₃	semidirect
368. C₄²	C₁₃×C₄⋊C₄	semidirect
369. C₁₃	C₄×#389	direct (N × H)
458. C₄	C₄×C₁₃×C₄⋊C₄	semidirect
459. C₄	C₁₃×#389	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×#389	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄³×C₁₃	2
C₁₃×#1436	2
C₁₃×C₄⋊#95	2
C₄×C₁₃×#95	2
C₄×#389	13

Subgroups — C4×C13×#389 #15700106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#389 #15700106