Subgroups — C₂×C₁₃×#2833 #15723007

Order 3328.

1718 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2833	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₃×#401	C₂	1	2	yes	maximal
3	C₂×C₁₃×#400	C₂	1	2	yes	maximal
4	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#400	C₂	1	2	yes	maximal
6	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#398	C₂	1	2	yes	maximal
8	C₂×C₁₃×#395	C₂	1	2	yes	maximal
9	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#387	C₂	1	2	yes	maximal
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#401	C₂²	1	16	yes	—
21	C₁₃×#400	C₂²	1	8	yes	—
22	C₁₃×#400	C₂²	1	16	yes	—
23	C₁₃×#400	C₂²	1	16	yes	—
24	C₁₃×#398	C₂²	1	16	yes	—
25	C₁₃×#398	C₂²	1	8	yes	—
26	C₁₃×#395	C₂²	1	16	yes	—
27	C₁₃×#391	C₂²	1	8	yes	—
28	C₁₃×#387	C₂²	1	16	yes	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	2	yes	—
31	C₂×C₁₃×#95	C₂²	1	2	yes	—
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	—	2	4	no	—
42	C₂²×Q₈×C₁₃	—	4	2	no	—
43	C₂²×Q₈×C₁₃	—	4	2	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
55	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
57	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₄²×C₁₃	—	4	2	no	—
69	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
70	C₁₃×#95	C₂³	1	8	yes	—
71	C₁₃×#95	C₂³	1	8	yes	—
72	C₁₃×#95	C₂³	1	8	yes	—
73	C₁₃×#95	C₂³	1	8	yes	—
74	C₁₃×#95	C₂³	1	8	yes	—
75	C₁₃×#95	C₂³	1	8	yes	—
76	C₁₃×#95	C₂³	1	8	yes	—
77	C₁₃×#95	C₂³	1	8	yes	—
78	C₁₃×#95	C₂³	1	8	yes	—
79	C₁₃×#95	C₂³	1	8	yes	—
80	C₁₃×#95	C₂³	1	4	yes	—
81	C₁₃×#95	C₂³	1	4	yes	—
82	C₂×#2833	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
84	C₂×Q₈×C₁₃	—	2	8	no	—
85	C₂×Q₈×C₁₃	—	4	4	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×Q₈×C₁₃	—	4	16	no	—
88	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	#41	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
121	C₁₃×C₄⋊C₄	—	2	16	no	—
122	C₁₃×C₄⋊C₄	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	4	8	no	—
124	C₁₃×C₄⋊C₄	—	4	4	no	—
125	C₁₃×C₄⋊C₄	—	4	4	no	—
126	C₁₃×C₄⋊C₄	—	4	8	no	—
127	C₁₃×C₄⋊C₄	—	4	8	no	—
128	C₄²×C₁₃	—	4	4	no	—
129	#2833	C₂×C₁₃	1	16	yes	direct product factor
130	C₂×#401	C₂×C₁₃	1	2	yes	—
131	C₂×#400	C₂×C₁₃	1	2	yes	—
132	C₂×#400	C₂×C₁₃	1	2	yes	—
133	C₂×#400	C₂×C₁₃	1	1	yes	characteristic
134	C₂×#398	C₂×C₁₃	1	1	yes	characteristic
135	C₂×#398	C₂×C₁₃	1	2	yes	—
136	C₂×#395	C₂×C₁₃	1	2	yes	—
137	C₂×#391	C₂×C₁₃	1	1	yes	characteristic
138	C₂×#387	C₂×C₁₃	1	2	yes	—
139	C₂³×C₁₃	C₂×#41	1	2	yes	—
140	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
141	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
142	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
143	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
144	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
145	Q₈×C₁₃	—	4	16	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	4	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	4	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	8	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	—	4	8	no	—
171	C₂×C₄×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	—	4	8	no	—
173	C₂×C₄×C₁₃	—	4	8	no	—
174	C₂×C₄×C₁₃	—	4	8	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	—	4	8	no	—
178	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
179	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
181	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
186	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
188	#401	C₂²×C₁₃	1	16	yes	—
189	#400	C₂²×C₁₃	1	8	yes	—
190	#400	C₂²×C₁₃	1	16	yes	—
191	#400	C₂²×C₁₃	1	16	yes	—
192	#398	C₂²×C₁₃	1	16	yes	—
193	#398	C₂²×C₁₃	1	8	yes	—
194	#395	C₂²×C₁₃	1	16	yes	—
195	#391	C₂²×C₁₃	1	8	yes	—
196	#387	C₂²×C₁₃	1	16	yes	—
197	C₂×#95	C₂²×C₁₃	1	2	yes	—
198	C₂×#95	C₂²×C₁₃	1	2	yes	—
199	C₂×#95	C₂²×C₁₃	1	2	yes	—
200	C₂×#95	C₂²×C₁₃	1	2	yes	—
201	C₂×#95	C₂²×C₁₃	1	2	yes	—
202	C₂×#95	C₂²×C₁₃	1	2	yes	—
203	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#95	C₂²×C₁₃	1	2	yes	—
205	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#95	C₂²×C₁₃	1	2	yes	—
207	C₂×#95	C₂²×C₁₃	1	2	yes	—
208	C₂×#95	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₁₃	#538	1	4	yes	—
210	C₂²×C₁₃	#541	1	8	yes	—
211	C₂²×C₁₃	#563	1	8	yes	—
212	C₂²×C₁₃	#563	1	4	yes	—
213	C₂²×C₁₃	#563	1	4	yes	—
214	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
218	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
219	C₄×C₁₃	—	2	4	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	4	4	no	—
222	C₄×C₁₃	—	4	4	no	—
223	C₄×C₁₃	—	4	4	no	—
224	C₄×C₁₃	—	4	4	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	4	no	—
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	—	4	2	no	—
230	C₂²×Q₈	—	4	2	no	—
231	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
236	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
240	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	—	2	8	no	—
242	C₂×C₄⋊C₄	—	4	2	no	—
243	C₂×C₄⋊C₄	—	4	4	no	—
244	C₂×C₄⋊C₄	—	4	2	no	—
245	C₂×C₄⋊C₄	—	4	2	no	—
246	C₂×C₄⋊C₄	—	4	4	no	—
247	C₂×C₄⋊C₄	—	4	4	no	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
255	C₂×C₄²	—	4	2	no	—
256	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
257	#95	C₂³×C₁₃	1	8	yes	—
258	#95	C₂³×C₁₃	1	8	yes	—
259	#95	C₂³×C₁₃	1	8	yes	—
260	#95	C₂³×C₁₃	1	8	yes	—
261	#95	C₂³×C₁₃	1	8	yes	—
262	#95	C₂³×C₁₃	1	8	yes	—
263	#95	C₂³×C₁₃	1	8	yes	—
264	#95	C₂³×C₁₃	1	8	yes	—
265	#95	C₂³×C₁₃	1	8	yes	—
266	#95	C₂³×C₁₃	1	8	yes	—
267	#95	C₂³×C₁₃	1	4	yes	—
268	#95	C₂³×C₁₃	1	4	yes	—
269	C₂×C₁₃	#2833	1	8	yes	direct product factor
270	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#541	1	2	yes	—
272	C₂×C₁₃	C₂×#563	1	2	yes	—
273	C₂×C₁₃	C₂×#563	1	1	yes	characteristic
274	C₂×C₁₃	C₂×#563	1	1	yes	characteristic
275	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	16	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	8	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	C₁₃×#41	1	4	yes	—
304	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	8	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	8	no	—
319	C₄⋊C₄	—	4	8	no	—
320	C₄²	—	4	4	no	—
321	C₁₃	C₂×#2833	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	C₂×C₁₃×#41	1	2	yes	—
323	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
324	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
325	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
326	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
327	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
328	Q₈	—	4	16	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	4	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	—	4	8	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
362	C₂²	C₁₃×#538	1	4	yes	—
363	C₂²	C₁₃×#541	1	8	yes	—
364	C₂²	C₁₃×#563	1	8	yes	—
365	C₂²	C₁₃×#563	1	4	yes	—
366	C₂²	C₁₃×#563	1	4	yes	—
367	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
368	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
371	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	4	4	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	4	no	—
379	C₄	—	4	4	no	—
380	C₄	—	4	4	no	—
381	C₂	C₁₃×#2833	1	8	yes	direct product factor
382	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
383	C₂	C₂×C₁₃×#541	1	2	yes	—
384	C₂	C₂×C₁₃×#563	1	2	yes	—
385	C₂	C₂×C₁₃×#563	1	1	yes	characteristic
386	C₂	C₂×C₁₃×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×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
1. C₁₃×#2833	C₂	direct (N × H)
82. C₂×#2833	C₁₃	direct (N × H)
129. #2833	C₂×C₁₃	direct (N × H)
269. C₂×C₁₃	#2833	direct (N × H)
321. C₁₃	C₂×#2833	direct (N × H)
381. C₂	C₁₃×#2833	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2833	2
C₂×C₁₃×#401	2
C₂×C₁₃×#400	2
C₂×C₁₃×#398	2
C₂×C₁₃×#395	2
C₂×C₁₃×#391	2
C₂×C₁₃×#387	2
C₂×#2833	13

Subgroups — C2×C13×#2833 #15723007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2833 #15723007