Subgroups — C₂×C₁₃×#2368 #15720481

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2368	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#385	C₂	1	2	yes	maximal
7	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
9	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₄	1	16	yes	complemented
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	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	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#391	C₂²	1	16	yes	complemented
27	C₁₃×#387	C₂²	1	16	yes	complemented
28	C₁₃×#387	C₂²	1	16	yes	complemented
29	C₁₃×#385	C₂²	1	16	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	16	yes	complemented
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	—
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
33	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	8	yes	—
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	4	4	no	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	—	2	8	no	—
47	C₂³×C₄×C₁₃	—	2	8	no	—
48	C₂³×C₄×C₁₃	—	4	4	no	—
49	C₂³×C₄×C₁₃	—	4	4	no	—
50	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
61	C₁₃×C₂²⋊Q₈	C₂×C₄	1	64	yes	complemented
62	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	—
72	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₂×C₄²×C₁₃	—	2	8	no	—
77	C₂×C₄²×C₁₃	—	4	4	no	—
78	C₂×C₄²×C₁₃	—	4	4	no	—
79	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
82	C₁₃×#95	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	8	yes	—
84	C₁₃×#95	C₂³	1	8	yes	—
85	C₁₃×#95	C₂³	1	4	yes	—
86	C₁₃×#95	C₂³	1	8	yes	—
87	C₁₃×#95	C₂³	1	8	yes	—
88	C₁₃×#95	C₂³	1	4	yes	—
89	C₁₃×#95	C₂³	1	8	yes	—
90	C₂×#2368	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
95	C₂⁴×C₁₃	#41	1	4	yes	—
96	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×Q₈×C₁₃	—	4	16	no	—
99	C₂×Q₈×C₁₃	—	4	8	no	—
100	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	complemented
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	4	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	16	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	16	no	—
119	C₂²×C₄×C₁₃	—	4	16	no	—
120	C₂²×C₄×C₁₃	—	4	8	no	—
121	C₂²×C₄×C₁₃	—	4	8	no	—
122	C₂²×C₄×C₁₃	—	4	32	no	—
123	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
128	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
129	C₂²×C₄×C₁₃	#41	1	8	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
138	C₁₃×C₄⋊C₄	—	2	16	no	—
139	C₁₃×C₄⋊C₄	—	4	8	no	—
140	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	complemented
142	C₁₃×C₂²⋊C₄	—	2	8	no	—
143	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
144	C₁₃×C₂²⋊C₄	C₂×Q₈	1	16	yes	complemented
145	C₄²×C₁₃	—	2	16	no	—
146	C₄²×C₁₃	—	4	8	no	—
147	C₄²×C₁₃	—	4	8	no	—
148	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
149	#2368	C₂×C₁₃	1	16	yes	direct product factor
150	C₂×#391	C₂×C₁₃	1	2	yes	complemented
151	C₂×#387	C₂×C₁₃	1	2	yes	complemented
152	C₂×#387	C₂×C₁₃	1	2	yes	complemented
153	C₂×#385	C₂×C₁₃	1	2	yes	—
154	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
155	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
156	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
157	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	8	no	—
159	C₂³×C₁₃	—	2	8	no	—
160	C₂³×C₁₃	—	2	16	no	—
161	C₂³×C₁₃	—	2	16	no	—
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	C₄×Q₈	1	16	yes	—
165	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
166	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
167	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
168	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
169	C₂³×C₁₃	C₂×#41	1	4	yes	—
170	C₂³×C₁₃	C₂×#41	1	2	yes	—
171	C₂³×C₁₃	C₂×#41	1	4	yes	—
172	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
173	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
174	Q₈×C₁₃	—	4	16	no	—
175	C₂×C₄×C₁₃	—	2	16	no	—
176	C₂×C₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	16	no	—
179	C₂×C₄×C₁₃	—	2	16	no	—
180	C₂×C₄×C₁₃	—	2	16	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	4	16	no	—
198	C₂×C₄×C₁₃	—	4	32	no	—
199	C₂×C₄×C₁₃	—	4	8	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
202	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
203	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
204	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
207	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
209	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	C₄×C₁₃	1	16	yes	complemented
211	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
213	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
222	#391	C₂²×C₁₃	1	16	yes	complemented
223	#387	C₂²×C₁₃	1	16	yes	complemented
224	#387	C₂²×C₁₃	1	16	yes	complemented
225	#385	C₂²×C₁₃	1	16	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	16	yes	complemented
227	C₄×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	—
228	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
229	C₂×#95	C₂²×C₁₃	1	8	yes	—
230	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#95	C₂²×C₁₃	1	2	yes	—
233	C₂×#95	C₂²×C₁₃	1	2	yes	—
234	C₂×#95	C₂²×C₁₃	1	2	yes	—
235	C₂×#95	C₂²×C₁₃	1	2	yes	—
236	C₂×#95	C₂²×C₁₃	1	2	yes	—
237	C₂×#95	C₂²×C₁₃	1	2	yes	—
238	C₂²×C₁₃	—	2	32	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	8	no	—
242	C₂²×C₁₃	—	2	8	no	—
243	C₂²×C₁₃	C₂×C₄×Q₈	1	8	yes	—
244	C₂²×C₁₃	C₂×C₄×Q₈	1	4	yes	—
245	C₂²×C₁₃	C₄×#41	1	4	yes	—
246	C₂²×C₁₃	#518	1	4	yes	—
247	C₂²×C₁₃	#551	1	8	yes	—
248	C₂²×C₁₃	#554	1	8	yes	—
249	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
250	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
251	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
252	C₂²×C₁₃	C₂²×#41	1	2	yes	—
253	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
254	C₄×C₁₃	—	2	8	no	—
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	2	8	no	—
258	C₄×C₁₃	—	2	8	no	—
259	C₄×C₁₃	—	2	8	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×Q₈	—	4	4	no	—
264	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
265	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
266	C₂³×C₄	—	2	8	no	—
267	C₂³×C₄	—	2	8	no	—
268	C₂³×C₄	—	4	4	no	—
269	C₂³×C₄	—	4	4	no	—
270	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	—
271	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
273	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
274	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
276	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
281	C₂²⋊Q₈	C₂×C₄×C₁₃	1	64	yes	complemented
282	C₂×C₄⋊C₄	—	2	8	no	—
283	C₂×C₄⋊C₄	—	4	4	no	—
284	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
285	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
292	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
293	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
296	C₂×C₄²	—	2	8	no	—
297	C₂×C₄²	—	4	4	no	—
298	C₂×C₄²	—	4	4	no	—
299	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
300	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
301	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
302	#95	C₂³×C₁₃	1	4	yes	—
303	#95	C₂³×C₁₃	1	4	yes	—
304	#95	C₂³×C₁₃	1	8	yes	—
305	#95	C₂³×C₁₃	1	8	yes	—
306	#95	C₂³×C₁₃	1	8	yes	—
307	#95	C₂³×C₁₃	1	8	yes	—
308	#95	C₂³×C₁₃	1	8	yes	—
309	#95	C₂³×C₁₃	1	8	yes	—
310	C₂×C₁₃	—	2	8	no	—
311	C₂×C₁₃	#2368	1	8	yes	direct product factor
312	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
313	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#551	1	2	yes	—
316	C₂×C₁₃	C₂×#554	1	2	yes	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
320	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
321	C₂⁴	C₁₃×#41	1	4	yes	—
322	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
323	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
324	C₂×Q₈	—	4	16	no	—
325	C₂×Q₈	—	4	8	no	—
326	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	complemented
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	16	no	—
345	C₂²×C₄	—	4	16	no	—
346	C₂²×C₄	—	4	8	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	—	4	32	no	—
349	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
350	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
351	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
354	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
355	C₂²×C₄	C₁₃×#41	1	8	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
364	C₄⋊C₄	—	2	16	no	—
365	C₄⋊C₄	—	4	8	no	—
366	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
367	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
370	C₂²⋊C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
371	C₄²	—	2	16	no	—
372	C₄²	—	4	8	no	—
373	C₄²	—	4	8	no	—
374	C₁₃	C₂×#2368	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	8	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	16	no	—
378	C₂³	—	2	16	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	C₄×Q₈×C₁₃	1	16	yes	—
382	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
383	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
384	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
385	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
386	C₂³	C₂×C₁₃×#41	1	4	yes	—
387	C₂³	C₂×C₁₃×#41	1	2	yes	—
388	C₂³	C₂×C₁₃×#41	1	4	yes	—
389	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
390	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
391	Q₈	—	4	16	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	2	16	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	—	4	32	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
419	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
420	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
422	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
423	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
424	C₂²	—	2	32	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	2	8	no	—
429	C₂²	C₂×C₄×Q₈×C₁₃	1	8	yes	—
430	C₂²	C₂×C₄×Q₈×C₁₃	1	4	yes	—
431	C₂²	C₄×C₁₃×#41	1	4	yes	—
432	C₂²	C₁₃×#518	1	4	yes	—
433	C₂²	C₁₃×#551	1	8	yes	—
434	C₂²	C₁₃×#554	1	8	yes	—
435	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
436	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
437	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
438	C₂²	C₂²×C₁₃×#41	1	2	yes	—
439	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
440	C₄	—	2	8	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	8	no	—
444	C₄	—	2	8	no	—
445	C₄	—	2	8	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₂	—	2	8	no	—
449	C₂	C₁₃×#2368	1	8	yes	direct product factor
450	C₂	C₂²×C₄×Q₈×C₁₃	1	1	yes	characteristic
451	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
452	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
453	C₂	C₂×C₁₃×#551	1	2	yes	—
454	C₂	C₂×C₁₃×#554	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2368	C₂	direct (N × H)
3. C₂×C₁₃×#391	C₂	semidirect
4. C₂×C₁₃×#387	C₂	semidirect
5. C₂×C₁₃×#387	C₂	semidirect
7. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
14. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
26. C₁₃×#391	C₂²	semidirect
27. C₁₃×#387	C₂²	semidirect
28. C₁₃×#387	C₂²	semidirect
30. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
44. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
61. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
64. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
65. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
72. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
90. C₂×#2368	C₁₃	direct (N × H)
100. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
140. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
141. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
144. C₁₃×C₂²⋊C₄	C₂×Q₈	semidirect
149. #2368	C₂×C₁₃	direct (N × H)
150. C₂×#391	C₂×C₁₃	semidirect
151. C₂×#387	C₂×C₁₃	semidirect
152. C₂×#387	C₂×C₁₃	semidirect
154. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
210. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
222. #391	C₂²×C₁₃	semidirect
223. #387	C₂²×C₁₃	semidirect
224. #387	C₂²×C₁₃	semidirect
226. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
264. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
281. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
284. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
285. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
292. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
311. C₂×C₁₃	#2368	direct (N × H)
326. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
366. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
367. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
370. C₂²⋊C₄	C₂×Q₈×C₁₃	semidirect
374. C₁₃	C₂×#2368	direct (N × H)
449. C₂	C₁₃×#2368	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×C₂²⋊Q₈	2
C₁₃×#2368	2
C₂×C₁₃×#391	2
C₂×C₁₃×#387	2
C₂×C₁₃×#385	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂²×C₁₃×#95	2
C₂×#2368	13

Subgroups — C2×C13×#2368 #15720481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2368 #15720481