Subgroups — C₄×C₁₃×#392 #15700196

Order 3328.

3502 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃	C₂	1	3	yes	maximal, complemented
2	C₂×C₁₃×#392	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₁₃×#1444	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1439	C₂	1	3	yes	maximal, complemented
6	C₁₃×#1438	C₂	1	3	yes	maximal, complemented
7	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₃	C₂²	1	3	yes	—
9	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	—
10	C₂×C₄×D₄×C₁₃	—	2	24	no	—
11	C₂×C₄×D₄×C₁₃	—	2	12	no	—
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
13	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
14	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	6	yes	—
15	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
18	C₁₃×#392	C₄	1	8	yes	direct product factor
19	C₄×C₁₃×C₂²⋊C₄	—	2	12	no	—
20	C₂×C₁₃×#95	C₂²	1	3	yes	—
21	C₂×C₁₃×#95	C₂²	1	3	yes	—
22	C₂×C₁₃×#95	C₂²	1	3	yes	—
23	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
24	C₂⁵×C₁₃	C₂³	1	3	yes	—
25	C₂²×D₄×C₁₃	—	2	12	no	—
26	C₂²×D₄×C₁₃	—	2	12	no	—
27	C₂²×D₄×C₁₃	—	2	6	no	—
28	C₂²×D₄×C₁₃	—	2	6	no	—
29	C₂²×D₄×C₁₃	C₂×C₄	1	12	yes	complemented
30	C₂³×C₄×C₁₃	—	2	6	no	—
31	C₂³×C₄×C₁₃	—	2	12	no	—
32	C₂³×C₄×C₁₃	—	2	12	no	—
33	C₂³×C₄×C₁₃	—	2	6	no	—
34	C₂³×C₄×C₁₃	D₄	1	12	yes	complemented
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
37	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₄×D₄×C₁₃	—	2	96	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
44	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
45	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
46	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
47	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
48	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	12	yes	complemented
53	C₂×C₄²×C₁₃	—	2	12	no	—
54	C₂×C₄²×C₁₃	—	2	6	no	—
55	C₂×C₄²×C₁₃	D₄	1	12	yes	complemented
56	C₁₃×#95	—	2	6	no	—
57	C₁₃×#95	—	2	6	no	—
58	C₁₃×#95	—	2	6	no	—
59	C₁₃×#95	C₂×C₄	1	4	yes	complemented
60	C₄×#392	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₃	—	2	3	no	—
62	C₂⁴×C₁₃	—	2	6	no	—
63	C₂⁴×C₁₃	—	2	6	no	—
64	C₂⁴×C₁₃	—	2	3	no	—
65	C₂⁴×C₁₃	—	2	3	no	—
66	C₂⁴×C₁₃	—	2	3	no	—
67	C₂⁴×C₁₃	—	2	6	no	—
68	C₂⁴×C₁₃	—	2	6	no	—
69	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	—
70	C₂⁴×C₁₃	C₂×D₄	1	6	yes	—
71	C₂⁴×C₁₃	#41	1	6	yes	—
72	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
73	C₂×D₄×C₁₃	—	2	24	no	—
74	C₂×D₄×C₁₃	—	2	24	no	—
75	C₂×D₄×C₁₃	—	2	48	no	—
76	C₂×D₄×C₁₃	—	2	48	no	—
77	C₂×D₄×C₁₃	—	2	24	no	—
78	C₂²×C₄×C₁₃	—	2	6	no	—
79	C₂²×C₄×C₁₃	—	2	6	no	—
80	C₂²×C₄×C₁₃	—	2	3	no	—
81	C₂²×C₄×C₁₃	—	2	3	no	—
82	C₂²×C₄×C₁₃	—	2	3	no	—
83	C₂²×C₄×C₁₃	—	2	6	no	—
84	C₂²×C₄×C₁₃	—	2	6	no	—
85	C₂²×C₄×C₁₃	—	2	6	no	—
86	C₂²×C₄×C₁₃	—	2	6	no	—
87	C₂²×C₄×C₁₃	—	2	3	no	—
88	C₂²×C₄×C₁₃	—	2	3	no	—
89	C₂²×C₄×C₁₃	—	2	3	no	—
90	C₂²×C₄×C₁₃	—	2	3	no	—
91	C₂²×C₄×C₁₃	—	2	3	no	—
92	C₂²×C₄×C₁₃	—	2	48	no	—
93	C₂²×C₄×C₁₃	—	2	24	no	—
94	C₂²×C₄×C₁₃	—	4	12	no	—
95	C₂²×C₄×C₁₃	—	4	24	no	—
96	C₂²×C₄×C₁₃	—	4	12	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₁₃	#41	1	2	yes	—
105	C₂²×C₄×C₁₃	#41	1	6	yes	—
106	C₂²×C₄×C₁₃	#41	1	2	yes	—
107	C₁₃×C₄⋊C₄	—	2	24	no	—
108	C₁₃×C₂²⋊C₄	—	2	24	no	—
109	C₁₃×C₂²⋊C₄	—	2	48	no	—
110	C₁₃×C₂²⋊C₄	—	2	24	no	—
111	C₄²×C₁₃	—	2	24	no	—
112	C₄²×C₁₃	—	4	4	no	—
113	C₂²×C₄×D₄	C₂×C₁₃	1	3	yes	complemented
114	C₂×#392	C₂×C₁₃	1	1	yes	characteristic
115	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	3	yes	complemented
116	#1444	C₂×C₁₃	1	1	yes	characteristic, complemented
117	#1439	C₂×C₁₃	1	3	yes	complemented
118	#1438	C₂×C₁₃	1	3	yes	complemented
119	C₄×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
120	C₂³×C₁₃	—	2	6	no	—
121	C₂³×C₁₃	—	2	12	no	—
122	C₂³×C₁₃	—	2	12	no	—
123	C₂³×C₁₃	—	2	6	no	—
124	C₂³×C₁₃	—	2	12	no	—
125	C₂³×C₁₃	—	2	6	no	—
126	C₂³×C₁₃	—	2	6	no	—
127	C₂³×C₁₃	—	2	12	no	—
128	C₂³×C₁₃	—	2	12	no	—
129	C₂³×C₁₃	—	2	12	no	—
130	C₂³×C₁₃	—	2	6	no	—
131	C₂³×C₁₃	—	2	6	no	—
132	C₂³×C₁₃	—	4	3	no	—
133	C₂³×C₁₃	—	4	6	no	—
134	C₂³×C₁₃	—	4	6	no	—
135	C₂³×C₁₃	—	4	6	no	—
136	C₂³×C₁₃	—	4	3	no	—
137	C₂³×C₁₃	—	4	6	no	—
138	C₂³×C₁₃	—	4	3	no	—
139	C₂³×C₁₃	—	4	3	no	—
140	C₂³×C₁₃	—	4	6	no	—
141	C₂³×C₁₃	—	4	6	no	—
142	C₂³×C₁₃	C₄×D₄	1	12	yes	complemented
143	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
144	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
145	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
146	C₂³×C₁₃	C₂×#41	1	3	yes	—
147	C₂³×C₁₃	C₂×#41	1	3	yes	—
148	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
149	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
150	D₄×C₁₃	—	2	96	no	—
151	C₂×C₄×C₁₃	—	2	12	no	—
152	C₂×C₄×C₁₃	—	2	6	no	—
153	C₂×C₄×C₁₃	—	2	6	no	—
154	C₂×C₄×C₁₃	—	2	12	no	—
155	C₂×C₄×C₁₃	—	2	6	no	—
156	C₂×C₄×C₁₃	—	2	6	no	—
157	C₂×C₄×C₁₃	—	2	12	no	—
158	C₂×C₄×C₁₃	—	2	6	no	—
159	C₂×C₄×C₁₃	—	2	6	no	—
160	C₂×C₄×C₁₃	—	2	6	no	—
161	C₂×C₄×C₁₃	—	2	6	no	—
162	C₂×C₄×C₁₃	—	4	3	no	—
163	C₂×C₄×C₁₃	—	4	6	no	—
164	C₂×C₄×C₁₃	—	4	6	no	—
165	C₂×C₄×C₁₃	—	4	3	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	3	no	—
169	C₂×C₄×C₁₃	—	4	3	no	—
170	C₂×C₄×C₁₃	—	4	6	no	—
171	C₂×C₄×C₁₃	—	4	48	no	—
172	C₂×C₄×C₁₃	C₄×D₄	1	12	yes	complemented
173	C₂×C₄×C₁₃	#120	1	12	yes	—
174	C₂×C₄×C₁₃	#121	1	12	yes	—
175	C₂×C₄×C₁₃	#127	1	4	yes	—
176	C₂³×D₄	C₂²×C₁₃	1	3	yes	—
177	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	—
178	C₂×C₄×D₄	—	2	24	no	—
179	C₂×C₄×D₄	—	2	12	no	—
180	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
181	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	6	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
184	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
186	#392	C₄×C₁₃	1	8	yes	direct product factor
187	C₄×C₂²⋊C₄	—	2	12	no	—
188	C₂×#95	C₂²×C₁₃	1	3	yes	—
189	C₂×#95	C₂²×C₁₃	1	3	yes	—
190	C₂×#95	C₂²×C₁₃	1	3	yes	—
191	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
192	C₂²×C₁₃	—	2	24	no	—
193	C₂²×C₁₃	—	2	12	no	—
194	C₂²×C₁₃	—	4	6	no	—
195	C₂²×C₁₃	—	4	6	no	—
196	C₂²×C₁₃	—	4	12	no	—
197	C₂²×C₁₃	—	4	6	no	—
198	C₂²×C₁₃	—	4	6	no	—
199	C₂²×C₁₃	—	4	12	no	—
200	C₂²×C₁₃	—	4	6	no	—
201	C₂²×C₁₃	—	4	6	no	—
202	C₂²×C₁₃	—	4	12	no	—
203	C₂²×C₁₃	C₂×C₄×D₄	1	3	yes	—
204	C₂²×C₁₃	C₂×C₄×D₄	1	3	yes	—
205	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×#120	1	3	yes	—
207	C₂²×C₁₃	C₂×#121	1	3	yes	—
208	C₂²×C₁₃	#525	1	6	yes	—
209	C₂²×C₁₃	#525	1	3	yes	—
210	C₂²×C₁₃	#525	1	3	yes	—
211	C₂²×C₁₃	#529	1	3	yes	—
212	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
213	C₂²×C₁₃	#532	1	3	yes	—
214	C₂²×C₁₃	#532	1	3	yes	—
215	C₄×C₁₃	—	2	12	no	—
216	C₄×C₁₃	—	4	2	no	—
217	C₄×C₁₃	—	4	6	no	—
218	C₄×C₁₃	—	4	6	no	—
219	C₄×C₁₃	—	4	2	no	—
220	C₄×C₁₃	#392	1	8	yes	direct product factor
221	C₂⁵	C₂³×C₁₃	1	3	yes	—
222	C₂²×D₄	—	2	12	no	—
223	C₂²×D₄	—	2	12	no	—
224	C₂²×D₄	—	2	6	no	—
225	C₂²×D₄	—	2	6	no	—
226	C₂²×D₄	C₂×C₄×C₁₃	1	12	yes	complemented
227	C₂³×C₄	—	2	12	no	—
228	C₂³×C₄	—	2	12	no	—
229	C₂³×C₄	—	2	6	no	—
230	C₂³×C₄	—	2	6	no	—
231	C₂³×C₄	D₄×C₁₃	1	12	yes	complemented
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
235	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
237	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₄×D₄	—	2	96	no	—
239	C₂×C₄⋊C₄	—	2	12	no	—
240	C₂×C₄⋊C₄	—	2	6	no	—
241	C₂×C₂²⋊C₄	—	2	12	no	—
242	C₂×C₂²⋊C₄	—	2	6	no	—
243	C₂×C₂²⋊C₄	—	2	12	no	—
244	C₂×C₂²⋊C₄	—	2	12	no	—
245	C₂×C₂²⋊C₄	—	2	6	no	—
246	C₂×C₂²⋊C₄	—	2	6	no	—
247	C₂×C₂²⋊C₄	—	2	6	no	—
248	C₂×C₂²⋊C₄	—	2	6	no	—
249	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	12	yes	complemented
250	C₂×C₄²	—	2	12	no	—
251	C₂×C₄²	—	2	6	no	—
252	C₂×C₄²	D₄×C₁₃	1	12	yes	complemented
253	#95	—	2	6	no	—
254	#95	—	2	6	no	—
255	#95	—	2	6	no	—
256	#95	C₂×C₄×C₁₃	1	4	yes	complemented
257	C₂×C₁₃	—	4	12	no	—
258	C₂×C₁₃	C₄×#120	1	3	yes	—
259	C₂×C₁₃	C₄×#121	1	3	yes	—
260	C₂×C₁₃	C₄×#127	1	1	yes	characteristic
261	C₂×C₁₃	C₂×#392	1	1	yes	characteristic
262	C₂×C₁₃	#2388	1	3	yes	—
263	C₂×C₁₃	#2392	1	3	yes	—
264	C₂×C₁₃	#2397	1	1	yes	characteristic
265	C₂⁴	—	2	3	no	—
266	C₂⁴	—	2	6	no	—
267	C₂⁴	—	2	6	no	—
268	C₂⁴	—	2	3	no	—
269	C₂⁴	—	2	3	no	—
270	C₂⁴	—	2	3	no	—
271	C₂⁴	—	2	6	no	—
272	C₂⁴	—	2	6	no	—
273	C₂⁴	C₂²×C₄×C₁₃	1	6	yes	—
274	C₂⁴	C₂×D₄×C₁₃	1	6	yes	—
275	C₂⁴	C₁₃×#41	1	6	yes	—
276	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
277	C₂×D₄	—	2	24	no	—
278	C₂×D₄	—	2	24	no	—
279	C₂×D₄	—	2	48	no	—
280	C₂×D₄	—	2	48	no	—
281	C₂×D₄	—	2	24	no	—
282	C₂²×C₄	—	2	6	no	—
283	C₂²×C₄	—	2	6	no	—
284	C₂²×C₄	—	2	3	no	—
285	C₂²×C₄	—	2	3	no	—
286	C₂²×C₄	—	2	3	no	—
287	C₂²×C₄	—	2	6	no	—
288	C₂²×C₄	—	2	6	no	—
289	C₂²×C₄	—	2	6	no	—
290	C₂²×C₄	—	2	6	no	—
291	C₂²×C₄	—	2	3	no	—
292	C₂²×C₄	—	2	3	no	—
293	C₂²×C₄	—	2	3	no	—
294	C₂²×C₄	—	2	3	no	—
295	C₂²×C₄	—	2	3	no	—
296	C₂²×C₄	—	2	48	no	—
297	C₂²×C₄	—	2	24	no	—
298	C₂²×C₄	—	4	12	no	—
299	C₂²×C₄	—	4	24	no	—
300	C₂²×C₄	—	4	12	no	—
301	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
308	C₂²×C₄	C₁₃×#41	1	2	yes	—
309	C₂²×C₄	C₁₃×#41	1	6	yes	—
310	C₂²×C₄	C₁₃×#41	1	2	yes	—
311	C₄⋊C₄	—	2	24	no	—
312	C₂²⋊C₄	—	2	48	no	—
313	C₂²⋊C₄	—	2	24	no	—
314	C₂²⋊C₄	—	2	24	no	—
315	C₄²	—	2	24	no	—
316	C₄²	—	4	4	no	—
317	C₁₃	C₄×#392	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	2	6	no	—
319	C₂³	—	2	12	no	—
320	C₂³	—	2	12	no	—
321	C₂³	—	2	6	no	—
322	C₂³	—	2	12	no	—
323	C₂³	—	2	6	no	—
324	C₂³	—	2	6	no	—
325	C₂³	—	2	12	no	—
326	C₂³	—	2	12	no	—
327	C₂³	—	2	12	no	—
328	C₂³	—	2	6	no	—
329	C₂³	—	2	6	no	—
330	C₂³	—	4	3	no	—
331	C₂³	—	4	6	no	—
332	C₂³	—	4	6	no	—
333	C₂³	—	4	3	no	—
334	C₂³	—	4	6	no	—
335	C₂³	—	4	6	no	—
336	C₂³	—	4	3	no	—
337	C₂³	—	4	6	no	—
338	C₂³	—	4	3	no	—
339	C₂³	—	4	6	no	—
340	C₂³	C₄×D₄×C₁₃	1	12	yes	complemented
341	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
342	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
343	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
344	C₂³	C₂×C₁₃×#41	1	3	yes	—
345	C₂³	C₂×C₁₃×#41	1	3	yes	—
346	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
347	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
348	D₄	—	2	96	no	—
349	C₂×C₄	—	2	12	no	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	2	12	no	—
353	C₂×C₄	—	2	6	no	—
354	C₂×C₄	—	2	6	no	—
355	C₂×C₄	—	2	12	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	6	no	—
359	C₂×C₄	—	2	6	no	—
360	C₂×C₄	—	4	3	no	—
361	C₂×C₄	—	4	6	no	—
362	C₂×C₄	—	4	6	no	—
363	C₂×C₄	—	4	3	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	3	no	—
367	C₂×C₄	—	4	3	no	—
368	C₂×C₄	—	4	6	no	—
369	C₂×C₄	—	4	48	no	—
370	C₂×C₄	C₄×D₄×C₁₃	1	12	yes	complemented
371	C₂×C₄	C₁₃×#120	1	12	yes	—
372	C₂×C₄	C₁₃×#121	1	12	yes	—
373	C₂×C₄	C₁₃×#127	1	4	yes	—
374	C₂²	—	2	24	no	—
375	C₂²	—	2	12	no	—
376	C₂²	—	4	6	no	—
377	C₂²	—	4	12	no	—
378	C₂²	—	4	6	no	—
379	C₂²	—	4	6	no	—
380	C₂²	—	4	12	no	—
381	C₂²	—	4	6	no	—
382	C₂²	—	4	6	no	—
383	C₂²	—	4	12	no	—
384	C₂²	—	4	6	no	—
385	C₂²	C₂×C₄×D₄×C₁₃	1	3	yes	—
386	C₂²	C₂×C₄×D₄×C₁₃	1	3	yes	—
387	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
388	C₂²	C₂×C₁₃×#120	1	3	yes	—
389	C₂²	C₂×C₁₃×#121	1	3	yes	—
390	C₂²	C₁₃×#525	1	6	yes	—
391	C₂²	C₁₃×#525	1	3	yes	—
392	C₂²	C₁₃×#525	1	3	yes	—
393	C₂²	C₁₃×#529	1	3	yes	—
394	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
395	C₂²	C₁₃×#532	1	3	yes	—
396	C₂²	C₁₃×#532	1	3	yes	—
397	C₄	—	2	12	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	6	no	—
400	C₄	—	4	6	no	—
401	C₄	—	4	2	no	—
402	C₄	C₁₃×#392	1	8	yes	direct product factor
403	C₂	—	4	12	no	—
404	C₂	C₄×C₁₃×#120	1	3	yes	—
405	C₂	C₄×C₁₃×#121	1	3	yes	—
406	C₂	C₄×C₁₃×#127	1	1	yes	characteristic
407	C₂	C₂×C₁₃×#392	1	1	yes	characteristic
408	C₂	C₁₃×#2388	1	3	yes	—
409	C₂	C₁₃×#2392	1	3	yes	—
410	C₂	C₁₃×#2397	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂×C₁₃×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#1444	C₂	semidirect
5. C₁₃×#1439	C₂	semidirect
6. C₁₃×#1438	C₂	semidirect
7. C₄×C₁₃×#95	C₂	semidirect
18. C₁₃×#392	C₄	direct (N × H)
29. C₂²×D₄×C₁₃	C₂×C₄	semidirect
34. C₂³×C₄×C₁₃	D₄	semidirect
52. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
55. C₂×C₄²×C₁₃	D₄	semidirect
59. C₁₃×#95	C₂×C₄	semidirect
60. C₄×#392	C₁₃	direct (N × H)
113. C₂²×C₄×D₄	C₂×C₁₃	semidirect
115. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
116. #1444	C₂×C₁₃	semidirect
117. #1439	C₂×C₁₃	semidirect
118. #1438	C₂×C₁₃	semidirect
119. C₄×#95	C₂×C₁₃	semidirect
142. C₂³×C₁₃	C₄×D₄	semidirect
172. C₂×C₄×C₁₃	C₄×D₄	semidirect
186. #392	C₄×C₁₃	direct (N × H)
220. C₄×C₁₃	#392	direct (N × H)
226. C₂²×D₄	C₂×C₄×C₁₃	semidirect
231. C₂³×C₄	D₄×C₁₃	semidirect
249. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
252. C₂×C₄²	D₄×C₁₃	semidirect
256. #95	C₂×C₄×C₁₃	semidirect
317. C₁₃	C₄×#392	direct (N × H)
340. C₂³	C₄×D₄×C₁₃	semidirect
370. C₂×C₄	C₄×D₄×C₁₃	semidirect
402. C₄	C₁₃×#392	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×D₄×C₁₃	2
C₂×C₁₃×#392	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₁₃×#1444	2
C₁₃×#1439	2
C₁₃×#1438	2
C₄×C₁₃×#95	2
C₄×#392	13

Subgroups — C4×C13×#392 #15700196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#392 #15700196