Subgroups — C₂×C₁₃×#2584 #15721231

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2584	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#398	C₂	1	2	yes	maximal
5	C₂×C₁₃×#395	C₂	1	2	yes	maximal
6	C₂×C₁₃×#389	C₂	1	2	yes	maximal
7	C₂×C₁₃×#389	C₂	1	2	yes	maximal
8	C₂×C₁₃×#389	C₂	1	4	yes	maximal
9	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#125	—	2	8	no	—
12	C₂×C₁₃×#125	C₂²	1	8	yes	—
13	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#398	C₂²	1	16	yes	—
28	C₁₃×#395	C₂²	1	16	yes	—
29	C₁₃×#389	C₂²	1	16	yes	—
30	C₁₃×#389	C₂²	1	32	yes	—
31	C₁₃×#389	C₂²	1	16	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	4	yes	—
35	C₂×C₁₃×#95	C₂²	1	4	yes	—
36	C₂²×Q₈×C₁₃	—	2	4	no	—
37	C₂²×Q₈×C₁₃	—	2	8	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×#125	—	2	32	no	—
48	C₄×Q₈×C₁₃	—	2	32	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
56	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
57	C₂×C₁₃×C₄⋊C₄	Q₈	1	16	yes	complemented
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	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	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
67	C₂×C₄²×C₁₃	—	2	8	no	—
68	C₂×C₄²×C₁₃	—	4	4	no	—
69	C₂×C₄²×C₁₃	D₄	1	8	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
73	C₁₃×#95	C₂³	1	8	yes	—
74	C₁₃×#95	C₂³	1	16	yes	—
75	C₁₃×#95	C₂³	1	16	yes	—
76	C₂×#2584	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
78	C₂×Q₈×C₁₃	—	2	32	no	—
79	C₂×Q₈×C₁₃	—	2	8	no	—
80	C₂×Q₈×C₁₃	—	2	16	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	8	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	2	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	8	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	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	—
100	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
101	C₂²×C₄×C₁₃	#41	1	8	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
110	C₁₃×C₄⋊C₄	—	2	16	no	—
111	C₁₃×C₄⋊C₄	—	2	8	no	—
112	C₁₃×C₄⋊C₄	—	2	16	no	—
113	C₁₃×C₄⋊C₄	—	2	16	no	—
114	C₁₃×C₄⋊C₄	—	2	8	no	—
115	C₁₃×C₄⋊C₄	—	2	8	no	—
116	C₁₃×C₄⋊C₄	—	2	32	no	—
117	C₁₃×C₄⋊C₄	—	4	16	no	—
118	C₁₃×C₄⋊C₄	C₂×Q₈	1	32	yes	complemented
119	C₄²×C₁₃	—	2	16	no	—
120	C₄²×C₁₃	—	4	8	no	—
121	C₄²×C₁₃	C₂×D₄	1	16	yes	—
122	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic
123	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
124	#2584	C₂×C₁₃	1	16	yes	direct product factor
125	C₂×#398	C₂×C₁₃	1	2	yes	—
126	C₂×#395	C₂×C₁₃	1	2	yes	—
127	C₂×#389	C₂×C₁₃	1	2	yes	—
128	C₂×#389	C₂×C₁₃	1	4	yes	—
129	C₂×#389	C₂×C₁₃	1	2	yes	—
130	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
131	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
132	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
133	C₂³×C₁₃	C₂×#41	1	4	yes	—
134	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
135	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
136	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
137	Q₈×C₁₃	—	2	32	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	16	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	2	32	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	8	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	8	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	8	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	4	no	—
157	C₂×C₄×C₁₃	—	4	8	no	—
158	C₂×C₄×C₁₃	—	4	8	no	—
159	C₂×C₄×C₁₃	—	4	8	no	—
160	C₂×C₄×C₁₃	C₄⋊Q₈	1	16	yes	—
161	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
164	C₂×C₄×C₁₃	C₂²×Q₈	1	16	yes	—
165	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
166	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
167	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
168	C₂×#125	—	2	8	no	—
169	C₂×#125	C₂²×C₁₃	1	8	yes	—
170	C₂×C₄×Q₈	—	2	8	no	—
171	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	—
172	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
173	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
174	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
175	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
176	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
177	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
178	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
179	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
181	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
183	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
184	#398	C₂²×C₁₃	1	16	yes	—
185	#395	C₂²×C₁₃	1	16	yes	—
186	#389	C₂²×C₁₃	1	16	yes	—
187	#389	C₂²×C₁₃	1	32	yes	—
188	#389	C₂²×C₁₃	1	16	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
190	C₂×#95	C₂²×C₁₃	1	2	yes	—
191	C₂×#95	C₂²×C₁₃	1	4	yes	—
192	C₂×#95	C₂²×C₁₃	1	4	yes	—
193	C₂²×C₁₃	#525	1	4	yes	—
194	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
195	C₂²×C₁₃	#537	1	4	yes	—
196	C₂²×C₁₃	#554	1	8	yes	—
197	C₂²×C₁₃	#557	1	8	yes	—
198	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
199	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
200	C₂²×C₁₃	C₂²×#41	1	2	yes	—
201	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₄×C₁₃	—	2	4	no	—
204	C₄×C₁₃	—	2	8	no	—
205	C₄×C₁₃	—	2	4	no	—
206	C₄×C₁₃	—	2	16	no	—
207	C₄×C₁₃	—	4	4	no	—
208	C₄×C₁₃	—	4	4	no	—
209	C₄×C₁₃	—	4	4	no	—
210	C₄×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
211	C₂²×Q₈	—	2	4	no	—
212	C₂²×Q₈	—	2	8	no	—
213	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
214	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
215	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
216	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
217	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
221	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
222	#125	—	2	32	no	—
223	C₄×Q₈	—	2	32	no	—
224	C₂×C₄⋊C₄	—	2	8	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	8	no	—
227	C₂×C₄⋊C₄	—	2	8	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	16	no	—
231	C₂×C₄⋊C₄	—	4	8	no	—
232	C₂×C₄⋊C₄	Q₈×C₁₃	1	16	yes	complemented
233	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
242	C₂×C₄²	—	2	8	no	—
243	C₂×C₄²	—	4	4	no	—
244	C₂×C₄²	D₄×C₁₃	1	8	yes	—
245	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
246	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
247	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
248	#95	C₂³×C₁₃	1	8	yes	—
249	#95	C₂³×C₁₃	1	16	yes	—
250	#95	C₂³×C₁₃	1	16	yes	—
251	C₂×C₁₃	#2584	1	8	yes	direct product factor
252	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
253	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
255	C₂×C₁₃	C₂×#554	1	2	yes	—
256	C₂×C₁₃	C₂×#557	1	2	yes	—
257	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
258	C₂×Q₈	—	2	32	no	—
259	C₂×Q₈	—	2	8	no	—
260	C₂×Q₈	—	2	16	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
279	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	—
280	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
281	C₂²×C₄	C₁₃×#41	1	8	yes	—
282	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
284	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
290	C₄⋊C₄	—	2	16	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	16	no	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	32	no	—
297	C₄⋊C₄	—	4	16	no	—
298	C₄⋊C₄	C₂×Q₈×C₁₃	1	32	yes	complemented
299	C₄²	—	2	16	no	—
300	C₄²	—	4	8	no	—
301	C₄²	C₂×D₄×C₁₃	1	16	yes	—
302	C₁₃	C₂×#2584	1	1	yes	characteristic, direct product factor, Sylow
303	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
304	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
305	C₂³	C₂×C₁₃×#41	1	4	yes	—
306	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
307	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
308	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
309	Q₈	—	2	32	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	16	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	32	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₁₃×C₄⋊Q₈	1	16	yes	—
333	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
334	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
335	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
336	C₂×C₄	C₂²×Q₈×C₁₃	1	16	yes	—
337	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
338	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
339	C₂²	C₁₃×#525	1	4	yes	—
340	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
341	C₂²	C₁₃×#537	1	4	yes	—
342	C₂²	C₁₃×#554	1	8	yes	—
343	C₂²	C₁₃×#557	1	8	yes	—
344	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
345	C₂²	C₂³×Q₈×C₁₃	1	2	yes	—
346	C₂²	C₂²×C₁₃×#41	1	2	yes	—
347	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	8	no	—
351	C₄	—	2	4	no	—
352	C₄	—	2	16	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	4	4	no	—
356	C₄	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
357	C₂	C₁₃×#2584	1	8	yes	direct product factor
358	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
359	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
360	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
361	C₂	C₂×C₁₃×#554	1	2	yes	—
362	C₂	C₂×C₁₃×#557	1	2	yes	—

	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
3. C₁₃×#2584	C₂	direct (N × H)
57. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
76. C₂×#2584	C₁₃	direct (N × H)
118. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
124. #2584	C₂×C₁₃	direct (N × H)
232. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
251. C₂×C₁₃	#2584	direct (N × H)
298. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
302. C₁₃	C₂×#2584	direct (N × H)
357. C₂	C₁₃×#2584	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×#125	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2584	2
C₂×C₁₃×#398	2
C₂×C₁₃×#395	2
C₂×C₁₃×#389	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2584	13

Subgroups — C2×C13×#2584 #15721231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2584 #15721231