Subgroups — C₁₃×#22812 #15709151

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1973	C₂	1	2	yes	maximal
5	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1926	C₂	1	2	yes	maximal
7	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1776	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	2	yes	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#388	—	2	2	no	—
29	C₁₃×#387	—	2	2	no	—
30	C₁₃×#383	—	2	1	no	—
31	C₁₃×#382	C₂²	1	1	yes	characteristic
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#381	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
38	C₁₃×#376	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂×C₁₃×SD₁₆	—	2	2	no	—
46	C₂×C₁₃×SD₁₆	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	2	no	—
67	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#107	—	2	4	no	—
70	C₁₃×#106	—	4	2	no	—
71	C₁₃×#106	C₂×C₄	1	4	yes	—
72	C₁₃×C₄⋊C₈	—	2	2	no	—
73	C₁₃×#103	—	4	2	no	—
74	C₁₃×#103	C₂×C₄	1	4	yes	—
75	C₁₃×#102	—	4	2	no	—
76	C₁₃×#102	C₂×C₄	1	4	yes	—
77	C₁₃×#97	—	2	4	no	—
78	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	D₄	1	1	yes	characteristic
88	C₁₃×#95	D₄	1	1	yes	characteristic
89	#22812	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×SD₁₆	—	2	8	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	#41	1	2	yes	—
124	C₂×C₈×C₁₃	#41	1	2	yes	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
134	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	8	2	no	—
138	C₄²×C₁₃	—	2	4	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	4	4	no	—
142	C₄²×C₁₃	—	8	2	no	—
143	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
144	C₄²×C₁₃	#41	1	2	yes	—
145	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
146	#2357	C₂×C₁₃	1	1	yes	characteristic
147	#2356	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1973	C₂×C₁₃	1	2	yes	—
149	#1927	C₂×C₁₃	1	2	yes	complemented
150	#1926	C₂×C₁₃	1	2	yes	—
151	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1804	C₂×C₁₃	1	1	yes	characteristic
154	#1776	C₂×C₁₃	1	2	yes	complemented
155	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	—	4	1	no	—
165	Q₈×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	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	—	8	4	no	—
192	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	#117	1	4	yes	—
203	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
206	C₄×SD₁₆	C₄×C₁₃	1	8	yes	complemented
207	C₂×#107	C₂²×C₁₃	1	2	yes	—
208	C₂×#106	C₂²×C₁₃	1	2	yes	—
209	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#103	C₂²×C₁₃	1	2	yes	—
212	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#102	C₂²×C₁₃	1	2	yes	—
214	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#97	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
217	#391	C₂²×C₁₃	1	2	yes	—
218	#390	C₂²×C₁₃	1	2	yes	—
219	#388	—	2	2	no	—
220	#387	—	2	2	no	—
221	#383	—	2	1	no	—
222	#382	C₂²×C₁₃	1	1	yes	characteristic
223	#382	C₂²×C₁₃	1	1	yes	characteristic
224	#381	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
228	C₄×C₂²⋊C₄	—	2	1	no	—
229	#376	—	2	1	no	—
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	2	yes	—
232	#336	C₂²×C₁₃	1	2	yes	—
233	C₂²×C₁₃	—	4	2	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₂²×C₁₃	#547	1	1	yes	characteristic
240	C₂²×C₁₃	#550	1	1	yes	characteristic
241	C₂²×C₁₃	#575	1	2	yes	—
242	C₂²×C₁₃	#577	1	2	yes	—
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
253	C₄×C₁₃	#520	1	1	yes	characteristic
254	C₄×C₁₃	#555	1	1	yes	characteristic
255	C₄×C₁₃	#556	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂³×C₄	—	2	1	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
262	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	#107	—	2	4	no	—
284	#106	—	4	2	no	—
285	#106	C₂×C₄×C₁₃	1	4	yes	—
286	C₄⋊C₈	—	2	2	no	—
287	#103	—	4	2	no	—
288	#103	C₂×C₄×C₁₃	1	4	yes	—
289	#102	—	4	2	no	—
290	#102	C₂×C₄×C₁₃	1	4	yes	—
291	#97	—	2	4	no	—
292	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
293	#95	—	2	1	no	—
294	#95	—	2	2	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	1	no	—
299	#95	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	D₄×C₁₃	1	1	yes	characteristic
302	#95	D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₁₃	—	8	2	no	—
304	C₂×C₁₃	#2354	1	1	yes	characteristic
305	C₂×C₁₃	#2943	1	1	yes	characteristic
306	C₂×C₁₃	#2949	1	1	yes	characteristic
307	C₂×C₁₃	#3351	1	2	yes	—
308	C₂×C₁₃	#3401	1	2	yes	—
309	C₂⁴	—	2	1	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
334	SD₁₆	—	2	8	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
341	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
342	C₂×C₈	C₁₃×#41	1	2	yes	—
343	C₂×C₈	C₁₃×#41	1	2	yes	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
353	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	4	4	no	—
361	C₄²	—	8	2	no	—
362	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
363	C₄²	C₁₃×#41	1	2	yes	—
364	C₁₃	#22812	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
402	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
405	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
406	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
407	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	2	no	—
411	C₈	C₁₃×#117	1	4	yes	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
418	C₂²	C₁₃×#547	1	1	yes	characteristic
419	C₂²	C₁₃×#550	1	1	yes	characteristic
420	C₂²	C₁₃×#575	1	2	yes	—
421	C₂²	C₁₃×#577	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
432	C₄	C₁₃×#520	1	1	yes	characteristic
433	C₄	C₁₃×#555	1	1	yes	characteristic
434	C₄	C₁₃×#556	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₁₃×#2354	1	1	yes	characteristic
437	C₂	C₁₃×#2943	1	1	yes	characteristic
438	C₂	C₁₃×#2949	1	1	yes	characteristic
439	C₂	C₁₃×#3351	1	2	yes	—
440	C₂	C₁₃×#3401	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2356	C₂	semidirect
5. C₁₃×#1927	C₂	semidirect
7. C₁₃×#1846	C₂	semidirect
8. C₁₃×#1805	C₂	semidirect
10. C₁₃×#1776	C₂	semidirect
11. C₁₃×#1770	C₂	semidirect
15. C₄×C₁₃×SD₁₆	C₄	semidirect
89. #22812	C₁₃	direct (N × H)
147. #2356	C₂×C₁₃	semidirect
149. #1927	C₂×C₁₃	semidirect
151. #1846	C₂×C₁₃	semidirect
152. #1805	C₂×C₁₃	semidirect
154. #1776	C₂×C₁₃	semidirect
155. #1770	C₂×C₁₃	semidirect
206. C₄×SD₁₆	C₄×C₁₃	semidirect
364. C₁₃	#22812	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×SD₁₆	2
C₁₃×#2357	2
C₁₃×#2356	2
C₁₃×#1973	2
C₁₃×#1927	2
C₁₃×#1926	2
C₁₃×#1846	2
C₁₃×#1805	2
C₁₃×#1804	2
C₁₃×#1776	2
C₁₃×#1770	2
#22812	13

Subgroups — C13×#22812 #15709151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22812 #15709151