Subgroups — C₁₃×#13936 #15700275

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1443	C₂	1	4	yes	maximal
3	C₁₃×C₄⋊#95	C₂	1	2	yes	maximal
4	C₁₃×C₄⋊#95	C₂	1	2	yes	maximal
5	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1434	C₂	1	2	yes	maximal
7	C₁₃×#1434	C₂	1	2	yes	maximal
8	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
15	C₄×C₁₃×C₄⋊C₄	C₄	1	8	yes	complemented
16	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#95	C₂²	1	2	yes	—
18	C₂×C₁₃×#95	C₂²	1	2	yes	—
19	C₂×C₁₃×#95	C₂²	1	4	yes	—
20	C₂×C₁₃×#95	C₂²	1	4	yes	—
21	C₂×C₁₃×#95	C₂²	1	4	yes	—
22	C₂×C₁₃×#95	C₂²	1	4	yes	—
23	C₂×C₁₃×#95	C₂²	1	2	yes	—
24	C₂×C₁₃×#95	C₂²	1	2	yes	—
25	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
27	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
36	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₁₃	—	2	4	no	—
43	C₂×C₄²×C₁₃	—	2	4	no	—
44	C₂×C₄²×C₁₃	—	2	4	no	—
45	C₂×C₄²×C₁₃	—	2	4	no	—
46	C₂×C₄²×C₁₃	—	4	4	no	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
49	C₁₃×#95	—	2	4	no	—
50	C₁₃×#95	—	2	2	no	—
51	C₁₃×#95	—	2	8	no	—
52	C₁₃×#95	—	2	4	no	—
53	C₁₃×#95	—	4	4	no	—
54	C₁₃×#95	—	4	4	no	—
55	C₁₃×#95	—	4	4	no	—
56	C₁₃×#95	—	4	2	no	—
57	C₁₃×#95	C₂×C₄	1	8	yes	—
58	C₁₃×#95	Q₈	1	4	yes	—
59	#13936	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	2	2	no	—
63	C₂²×C₄×C₁₃	—	2	2	no	—
64	C₂²×C₄×C₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₃	—	2	2	no	—
67	C₂²×C₄×C₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	1	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	4	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	1	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	4	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	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₃	#41	1	4	yes	—
102	C₂²×C₄×C₁₃	#41	1	2	yes	—
103	C₂²×C₄×C₁₃	#41	1	4	yes	—
104	C₂²×C₄×C₁₃	#41	1	2	yes	—
105	C₂²×C₄×C₁₃	#41	1	4	yes	—
106	C₂²×C₄×C₁₃	#41	1	2	yes	—
107	C₁₃×C₄⋊C₄	—	2	8	no	—
108	C₁₃×C₄⋊C₄	—	2	8	no	—
109	C₁₃×C₄⋊C₄	—	4	8	no	—
110	C₄²×C₁₃	—	2	8	no	—
111	C₄²×C₁₃	—	4	8	no	—
112	C₄²×C₁₃	—	4	8	no	—
113	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
114	#1443	C₂×C₁₃	1	4	yes	—
115	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
116	C₄⋊#95	C₂×C₁₃	1	2	yes	—
117	C₄⋊#95	C₂×C₁₃	1	2	yes	—
118	#1434	C₂×C₁₃	1	2	yes	—
119	#1434	C₂×C₁₃	1	2	yes	—
120	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
121	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
122	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
123	C₂³×C₁₃	C₂×#41	1	2	yes	—
124	C₂³×C₁₃	C₂×#41	1	2	yes	—
125	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
126	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
127	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
128	C₂³×C₁₃	C₂×#41	1	2	yes	—
129	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
130	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
131	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	4	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	4	no	—
167	C₂×C₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	#117	1	4	yes	—
173	C₂×C₄×C₁₃	#117	1	4	yes	—
174	C₂×C₄×C₁₃	#117	1	4	yes	—
175	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
176	C₂×C₄×C₁₃	#126	1	8	yes	—
177	C₂×C₄×C₁₃	#126	1	8	yes	—
178	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
181	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
183	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
184	C₄×C₄⋊C₄	C₄×C₁₃	1	8	yes	complemented
185	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
186	C₂×#95	C₂²×C₁₃	1	2	yes	—
187	C₂×#95	C₂²×C₁₃	1	2	yes	—
188	C₂×#95	C₂²×C₁₃	1	4	yes	—
189	C₂×#95	C₂²×C₁₃	1	4	yes	—
190	C₂×#95	C₂²×C₁₃	1	4	yes	—
191	C₂×#95	C₂²×C₁₃	1	4	yes	—
192	C₂×#95	C₂²×C₁₃	1	2	yes	—
193	C₂×#95	C₂²×C₁₃	1	2	yes	—
194	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
196	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
199	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
200	C₂²×C₁₃	#518	1	1	yes	characteristic
201	C₂²×C₁₃	#520	1	1	yes	characteristic
202	C₂²×C₁₃	C₂×#126	1	2	yes	—
203	C₂²×C₁₃	C₂×#126	1	2	yes	—
204	C₂²×C₁₃	#529	1	2	yes	—
205	C₂²×C₁₃	#533	1	2	yes	—
206	C₂²×C₁₃	#540	1	2	yes	—
207	C₂²×C₁₃	#542	1	2	yes	—
208	C₂²×C₁₃	#552	1	2	yes	—
209	C₂²×C₁₃	#553	1	2	yes	—
210	C₂²×C₁₃	#553	1	2	yes	—
211	C₂²×C₁₃	#554	1	2	yes	—
212	C₂²×C₁₃	#554	1	1	yes	characteristic
213	C₂²×C₁₃	#555	1	2	yes	—
214	C₂²×C₁₃	#556	1	1	yes	characteristic
215	C₂²×C₁₃	#557	1	1	yes	characteristic
216	C₂²×C₁₃	#559	1	1	yes	characteristic
217	C₂²×C₁₃	#559	1	2	yes	—
218	C₄×C₁₃	—	2	4	no	—
219	C₄×C₁₃	—	4	4	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	—	4	4	no	—
222	C₄×C₁₃	—	4	4	no	—
223	C₄×C₁₃	—	4	4	no	—
224	C₄×C₁₃	—	8	4	no	—
225	C₄×C₁₃	#383	1	8	yes	—
226	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
227	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
228	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
229	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
242	C₂×C₄²	—	2	4	no	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	—	4	4	no	—
247	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
248	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
249	#95	—	2	4	no	—
250	#95	—	2	2	no	—
251	#95	—	2	8	no	—
252	#95	—	2	4	no	—
253	#95	—	4	4	no	—
254	#95	—	4	4	no	—
255	#95	—	4	4	no	—
256	#95	—	4	2	no	—
257	#95	C₂×C₄×C₁₃	1	8	yes	—
258	#95	Q₈×C₁₃	1	4	yes	—
259	C₂×C₁₃	C₂×#383	1	1	yes	characteristic
260	C₂×C₁₃	#2295	1	1	yes	characteristic
261	C₂×C₁₃	#2319	1	1	yes	characteristic
262	C₂×C₁₃	#2345	1	1	yes	characteristic
263	C₂×C₁₃	#2346	1	1	yes	characteristic
264	C₂×C₁₃	#2355	1	1	yes	characteristic
265	C₂×C₁₃	#2357	1	1	yes	characteristic
266	C₂×C₁₃	#2494	1	2	yes	—
267	C₂×C₁₃	#2497	1	2	yes	—
268	C₂×C₁₃	#2511	1	2	yes	—
269	C₂×C₁₃	#2513	1	2	yes	—
270	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
309	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
310	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
311	C₂²×C₄	C₁₃×#41	1	4	yes	—
312	C₂²×C₄	C₁₃×#41	1	2	yes	—
313	C₂²×C₄	C₁₃×#41	1	4	yes	—
314	C₂²×C₄	C₁₃×#41	1	2	yes	—
315	C₂²×C₄	C₁₃×#41	1	4	yes	—
316	C₂²×C₄	C₁₃×#41	1	2	yes	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	4	8	no	—
320	C₄²	—	2	8	no	—
321	C₄²	—	4	8	no	—
322	C₄²	—	4	8	no	—
323	C₁₃	#13936	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
325	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
326	C₂³	C₂×C₁₃×#41	1	2	yes	—
327	C₂³	C₂×C₁₃×#41	1	2	yes	—
328	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
329	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
330	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
331	C₂³	C₂×C₁₃×#41	1	2	yes	—
332	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
333	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	C₁₃×#117	1	4	yes	—
376	C₂×C₄	C₁₃×#117	1	4	yes	—
377	C₂×C₄	C₁₃×#117	1	4	yes	—
378	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
379	C₂×C₄	C₁₃×#126	1	8	yes	—
380	C₂×C₄	C₁₃×#126	1	8	yes	—
381	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
382	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
383	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
384	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
385	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
386	C₂²	C₁₃×#518	1	1	yes	characteristic
387	C₂²	C₁₃×#520	1	1	yes	characteristic
388	C₂²	C₂×C₁₃×#126	1	2	yes	—
389	C₂²	C₂×C₁₃×#126	1	2	yes	—
390	C₂²	C₁₃×#529	1	2	yes	—
391	C₂²	C₁₃×#533	1	2	yes	—
392	C₂²	C₁₃×#540	1	2	yes	—
393	C₂²	C₁₃×#542	1	2	yes	—
394	C₂²	C₁₃×#552	1	2	yes	—
395	C₂²	C₁₃×#553	1	2	yes	—
396	C₂²	C₁₃×#553	1	2	yes	—
397	C₂²	C₁₃×#554	1	1	yes	characteristic
398	C₂²	C₁₃×#554	1	2	yes	—
399	C₂²	C₁₃×#555	1	2	yes	—
400	C₂²	C₁₃×#556	1	1	yes	characteristic
401	C₂²	C₁₃×#557	1	1	yes	characteristic
402	C₂²	C₁₃×#559	1	2	yes	—
403	C₂²	C₁₃×#559	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	4	no	—
411	C₄	C₁₃×#383	1	8	yes	—
412	C₂	C₂×C₁₃×#383	1	1	yes	characteristic
413	C₂	C₁₃×#2295	1	1	yes	characteristic
414	C₂	C₁₃×#2319	1	1	yes	characteristic
415	C₂	C₁₃×#2345	1	1	yes	characteristic
416	C₂	C₁₃×#2346	1	1	yes	characteristic
417	C₂	C₁₃×#2355	1	1	yes	characteristic
418	C₂	C₁₃×#2357	1	1	yes	characteristic
419	C₂	C₁₃×#2494	1	2	yes	—
420	C₂	C₁₃×#2497	1	2	yes	—
421	C₂	C₁₃×#2511	1	2	yes	—
422	C₂	C₁₃×#2513	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
15. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
59. #13936	C₁₃	direct (N × H)
184. C₄×C₄⋊C₄	C₄×C₁₃	semidirect
323. C₁₃	#13936	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×C₄⋊C₄	2
C₁₃×#1443	2
C₁₃×C₄⋊#95	2
C₁₃×#1434	2
C₄×C₁₃×#95	2
#13936	13

Subgroups — C13×#13936 #15700275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13936 #15700275