Subgroups — C₂×C₁₃×#2821 #15723025

Order 3328.

2370 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	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#126	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2821	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#399	C₂	1	2	yes	maximal
6	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#397	C₂	1	2	yes	maximal
8	C₂×C₁₃×#395	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#393	C₂	1	2	yes	maximal
10	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
14	C₂×C₁₃×#126	—	2	8	no	—
15	C₂×C₁₃×#126	C₂²	1	8	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#400	C₂²	1	16	yes	complemented
28	C₁₃×#399	C₂²	1	16	yes	—
29	C₁₃×#398	C₂²	1	16	yes	complemented
30	C₁₃×#397	C₂²	1	16	yes	—
31	C₁₃×#395	C₂²	1	16	yes	complemented
32	C₁₃×#393	C₂²	1	16	yes	—
33	C₁₃×#383	C₂²	1	8	yes	complemented
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	4	yes	—
38	C₂×C₁₃×#95	C₂²	1	4	yes	—
39	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	—	4	8	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	32	no	—
52	C₁₃×#126	—	2	32	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
58	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	16	yes	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
73	C₂×C₄²×C₁₃	D₄	1	8	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	4	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	16	yes	—
79	C₁₃×#95	C₂³	1	16	yes	—
80	C₂×#2821	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	2	no	—
82	C₂⁴×C₁₃	—	2	4	no	—
83	C₂⁴×C₁₃	—	2	4	no	—
84	C₂⁴×C₁₃	—	2	4	no	—
85	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	—	2	16	no	—
88	C₂×Q₈×C₁₃	—	4	16	no	—
89	C₂×Q₈×C₁₃	—	4	32	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	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	8	no	—
97	C₂²×C₄×C₁₃	—	2	8	no	—
98	C₂²×C₄×C₁₃	—	2	8	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	8	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	8	no	—
104	C₂²×C₄×C₁₃	—	2	8	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₁₃×C₄⋊C₄	—	2	8	no	—
119	C₁₃×C₄⋊C₄	—	2	16	no	—
120	C₁₃×C₄⋊C₄	—	2	16	no	—
121	C₁₃×C₄⋊C₄	—	4	16	no	—
122	C₁₃×C₂²⋊C₄	—	2	8	no	—
123	C₁₃×C₂²⋊C₄	—	2	8	no	—
124	C₁₃×C₂²⋊C₄	—	2	8	no	—
125	C₁₃×C₂²⋊C₄	—	4	16	no	—
126	C₄²×C₁₃	C₂×D₄	1	16	yes	—
127	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂²×#126	C₂×C₁₃	1	1	yes	characteristic
129	#2821	C₂×C₁₃	1	16	yes	direct product factor
130	C₂×#400	C₂×C₁₃	1	2	yes	complemented
131	C₂×#399	C₂×C₁₃	1	2	yes	—
132	C₂×#398	C₂×C₁₃	1	2	yes	complemented
133	C₂×#397	C₂×C₁₃	1	2	yes	—
134	C₂×#395	C₂×C₁₃	1	2	yes	complemented
135	C₂×#393	C₂×C₁₃	1	2	yes	—
136	C₂×#383	C₂×C₁₃	1	1	yes	characteristic, complemented
137	C₂³×C₁₃	—	2	2	no	—
138	C₂³×C₁₃	—	2	4	no	—
139	C₂³×C₁₃	—	2	4	no	—
140	C₂³×C₁₃	—	2	4	no	—
141	C₂³×C₁₃	—	4	4	no	—
142	C₂³×C₁₃	—	4	4	no	—
143	C₂³×C₁₃	—	4	4	no	—
144	C₂³×C₁₃	—	4	16	no	—
145	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
146	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
147	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
148	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
149	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
150	Q₈×C₁₃	—	4	32	no	—
151	C₂×C₄×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	2	8	no	—
153	C₂×C₄×C₁₃	—	2	8	no	—
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	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	8	no	—
161	C₂×C₄×C₁₃	—	2	8	no	—
162	C₂×C₄×C₁₃	—	2	8	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	8	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	8	no	—
168	C₂×C₄×C₁₃	—	2	8	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	4	16	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	16	no	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
176	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
177	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
178	C₂×C₄⋊Q₈	—	2	8	no	—
179	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
180	C₂×#126	—	2	8	no	—
181	C₂×#126	C₂²×C₁₃	1	8	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
183	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
184	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
186	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
189	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
192	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
193	#400	C₂²×C₁₃	1	16	yes	complemented
194	#399	C₂²×C₁₃	1	16	yes	—
195	#398	C₂²×C₁₃	1	16	yes	complemented
196	#397	C₂²×C₁₃	1	16	yes	—
197	#395	C₂²×C₁₃	1	16	yes	complemented
198	#393	C₂²×C₁₃	1	16	yes	—
199	#383	C₂²×C₁₃	1	8	yes	complemented
200	C₂×#95	C₂²×C₁₃	1	2	yes	—
201	C₂×#95	C₂²×C₁₃	1	4	yes	—
202	C₂×#95	C₂²×C₁₃	1	4	yes	—
203	C₂×#95	C₂²×C₁₃	1	2	yes	—
204	C₂×#95	C₂²×C₁₃	1	2	yes	—
205	C₂²×C₁₃	—	4	2	no	—
206	C₂²×C₁₃	—	4	2	no	—
207	C₂²×C₁₃	—	4	2	no	—
208	C₂²×C₁₃	—	4	8	no	—
209	C₂²×C₁₃	—	8	8	no	—
210	C₂²×C₁₃	#535	1	4	yes	—
211	C₂²×C₁₃	#536	1	4	yes	—
212	C₂²×C₁₃	#536	1	4	yes	—
213	C₂²×C₁₃	#563	1	16	yes	—
214	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
216	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
217	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
218	C₄×C₁₃	—	2	4	no	—
219	C₄×C₁₃	—	2	4	no	—
220	C₄×C₁₃	—	2	4	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	8	no	—
223	C₄×C₁₃	—	4	2	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	8	no	—
226	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
227	C₂²×Q₈	—	2	8	no	—
228	C₂²×Q₈	—	4	8	no	—
229	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
230	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
231	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
235	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	32	no	—
239	#126	—	2	32	no	—
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	4	8	no	—
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₂²⋊C₄	—	4	8	no	—
256	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
260	C₂×C₄²	D₄×C₁₃	1	8	yes	—
261	C₂×C₄²	C₂³×C₁₃	1	4	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	16	yes	—
266	#95	C₂³×C₁₃	1	16	yes	—
267	C₂×C₁₃	—	8	2	no	—
268	C₂×C₁₃	#2821	1	8	yes	direct product factor
269	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
270	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#563	1	4	yes	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
278	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
279	C₂×Q₈	—	2	16	no	—
280	C₂×Q₈	—	4	16	no	—
281	C₂×Q₈	—	4	32	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	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	8	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
301	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
304	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	16	no	—
312	C₄⋊C₄	—	2	16	no	—
313	C₄⋊C₄	—	4	16	no	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	8	no	—
317	C₂²⋊C₄	—	4	16	no	—
318	C₄²	C₂×D₄×C₁₃	1	16	yes	—
319	C₁₃	C₂×#2821	1	1	yes	characteristic, direct product factor, Sylow
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	16	no	—
328	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
329	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
330	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
331	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
332	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
333	Q₈	—	4	32	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	16	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
359	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
360	C₂²	—	4	8	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₁₃×#535	1	4	yes	—
366	C₂²	C₁₃×#536	1	4	yes	—
367	C₂²	C₁₃×#536	1	4	yes	—
368	C₂²	C₁₃×#563	1	16	yes	—
369	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
370	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
371	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
372	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
373	C₄	—	2	4	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	4	8	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	8	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₂	—	8	2	no	—
382	C₂	C₁₃×#2821	1	8	yes	direct product factor
383	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
384	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
385	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
386	C₂	C₂×C₁₃×#563	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
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. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2821	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
6. C₂×C₁₃×#398	C₂	semidirect
8. C₂×C₁₃×#395	C₂	semidirect
10. C₂×C₁₃×#383	C₂	semidirect
13. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₁₃×#400	C₂²	semidirect
29. C₁₃×#398	C₂²	semidirect
31. C₁₃×#395	C₂²	semidirect
33. C₁₃×#383	C₂²	semidirect
80. C₂×#2821	C₁₃	direct (N × H)
127. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
129. #2821	C₂×C₁₃	direct (N × H)
130. C₂×#400	C₂×C₁₃	semidirect
132. C₂×#398	C₂×C₁₃	semidirect
134. C₂×#395	C₂×C₁₃	semidirect
136. C₂×#383	C₂×C₁₃	semidirect
179. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
193. #400	C₂²×C₁₃	semidirect
195. #398	C₂²×C₁₃	semidirect
197. #395	C₂²×C₁₃	semidirect
199. #383	C₂²×C₁₃	semidirect
268. C₂×C₁₃	#2821	direct (N × H)
319. C₁₃	C₂×#2821	direct (N × H)
382. C₂	C₁₃×#2821	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×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#126	2
C₁₃×#2821	2
C₂×C₁₃×#400	2
C₂×C₁₃×#399	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#395	2
C₂×C₁₃×#393	2
C₂×C₁₃×#383	2
C₂×#2821	13

Subgroups — C2×C13×#2821 #15723025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2821 #15723025