Subgroups — C₂×C₁₃×#2337 #15720419

Order 3328.

3046 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2337	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#386	C₂	1	2	yes	maximal
7	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×#124	C₄	1	16	yes	complemented
15	C₂×C₁₃×#124	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×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#391	C₂²	1	16	yes	complemented
28	C₁₃×#388	C₂²	1	16	yes	complemented
29	C₁₃×#388	C₂²	1	16	yes	complemented
30	C₁₃×#386	C₂²	1	16	yes	—
31	C₁₃×#385	C₂²	1	16	yes	complemented
32	C₁₃×#383	C₂²	1	8	yes	complemented
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
34	C₄×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
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	1	yes	characteristic
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	2	yes	—
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	C₂²×D₄×C₁₃	—	4	4	no	—
47	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₃	—	2	8	no	—
50	C₂³×C₄×C₁₃	—	4	4	no	—
51	C₂³×C₄×C₁₃	—	4	4	no	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
61	C₁₃×#124	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	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
69	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
70	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₄²×C₁₃	—	4	2	no	—
77	C₂×C₄²×C₁₃	—	4	2	no	—
78	C₂×C₄²×C₁₃	—	4	4	no	—
79	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
80	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
84	C₁₃×#95	C₂³	1	8	yes	—
85	C₁₃×#95	C₂³	1	8	yes	—
86	C₁₃×#95	C₂³	1	8	yes	—
87	C₁₃×#95	C₂³	1	4	yes	—
88	C₁₃×#95	C₂³	1	8	yes	—
89	C₁₃×#95	C₂³	1	4	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₂×#2337	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	4	no	—
97	C₂⁴×C₁₃	—	2	4	no	—
98	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	4	16	no	—
102	C₂×Q₈×C₁₃	—	4	8	no	—
103	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	complemented
104	C₂×D₄×C₁₃	—	4	16	no	—
105	C₂×D₄×C₁₃	—	4	8	no	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	16	no	—
125	C₂²×C₄×C₁₃	—	4	8	no	—
126	C₂²×C₄×C₁₃	—	4	8	no	—
127	C₂²×C₄×C₁₃	—	4	32	no	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
132	C₂²×C₄×C₁₃	#41	1	8	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₁₃×C₄⋊C₄	—	2	16	no	—
142	C₁₃×C₄⋊C₄	—	4	8	no	—
143	C₁₃×C₂²⋊C₄	—	2	16	no	—
144	C₁₃×C₂²⋊C₄	—	4	8	no	—
145	C₁₃×C₂²⋊C₄	—	4	8	no	—
146	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
147	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
148	C₄²×C₁₃	—	4	4	no	—
149	C₄²×C₁₃	—	4	4	no	—
150	C₄²×C₁₃	—	4	8	no	—
151	C₄²×C₁₃	C₂²×C₄	1	16	yes	complemented
152	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
153	#2337	C₂×C₁₃	1	16	yes	direct product factor
154	C₂×#391	C₂×C₁₃	1	2	yes	complemented
155	C₂×#388	C₂×C₁₃	1	2	yes	complemented
156	C₂×#388	C₂×C₁₃	1	2	yes	complemented
157	C₂×#386	C₂×C₁₃	1	2	yes	—
158	C₂×#385	C₂×C₁₃	1	2	yes	complemented
159	C₂×#383	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
162	C₂³×C₁₃	—	2	16	no	—
163	C₂³×C₁₃	—	2	16	no	—
164	C₂³×C₁₃	—	2	16	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	2	4	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	4	8	no	—
172	C₂³×C₁₃	—	4	8	no	—
173	C₂³×C₁₃	—	4	8	no	—
174	C₂³×C₁₃	—	4	8	no	—
175	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
176	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
177	C₂³×C₁₃	C₂×#41	1	4	yes	—
178	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
179	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
180	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
181	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
182	Q₈×C₁₃	—	4	16	no	—
183	D₄×C₁₃	—	4	16	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	2	16	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	16	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	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	2	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	4	32	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	—	4	8	no	—
210	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
211	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
212	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
213	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
214	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
215	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
218	C₂×#124	C₄×C₁₃	1	16	yes	complemented
219	C₂×#124	C₂²×C₁₃	1	8	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
222	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
230	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
231	#391	C₂²×C₁₃	1	16	yes	complemented
232	#388	C₂²×C₁₃	1	16	yes	complemented
233	#388	C₂²×C₁₃	1	16	yes	complemented
234	#386	C₂²×C₁₃	1	16	yes	—
235	#385	C₂²×C₁₃	1	16	yes	complemented
236	#383	C₂²×C₁₃	1	8	yes	complemented
237	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
238	C₄×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	complemented
239	C₂×#95	C₂²×C₁₃	1	2	yes	—
240	C₂×#95	C₂²×C₁₃	1	2	yes	—
241	C₂×#95	C₂²×C₁₃	1	2	yes	—
242	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#95	C₂²×C₁₃	1	2	yes	—
244	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#95	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₁₃	—	2	8	no	—
247	C₂²×C₁₃	—	2	8	no	—
248	C₂²×C₁₃	—	2	8	no	—
249	C₂²×C₁₃	—	4	32	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	4	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	C₄×#41	1	4	yes	—
255	C₂²×C₁₃	#518	1	4	yes	—
256	C₂²×C₁₃	#520	1	4	yes	—
257	C₂²×C₁₃	#538	1	8	yes	—
258	C₂²×C₁₃	#542	1	8	yes	—
259	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
260	C₂²×C₁₃	C₂²×#41	1	2	yes	—
261	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	—	2	4	no	—
266	C₄×C₁₃	—	2	8	no	—
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	2	8	no	—
269	C₄×C₁₃	—	4	4	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	—	4	4	no	—
272	C₂⁵	C₂³×C₁₃	1	2	yes	—
273	C₂²×Q₈	—	4	4	no	—
274	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
275	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
276	C₂²×D₄	—	4	4	no	—
277	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
278	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
279	C₂³×C₄	—	2	8	no	—
280	C₂³×C₄	—	4	4	no	—
281	C₂³×C₄	—	4	4	no	—
282	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
284	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
291	#124	C₂×C₄×C₁₃	1	64	yes	complemented
292	C₂×C₄⋊C₄	—	2	8	no	—
293	C₂×C₄⋊C₄	—	4	4	no	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
296	C₂×C₂²⋊C₄	—	2	8	no	—
297	C₂×C₂²⋊C₄	—	4	4	no	—
298	C₂×C₂²⋊C₄	—	4	4	no	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
300	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
301	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
306	C₂×C₄²	—	4	2	no	—
307	C₂×C₄²	—	4	2	no	—
308	C₂×C₄²	—	4	4	no	—
309	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
310	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
311	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
312	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
313	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
314	#95	C₂³×C₁₃	1	8	yes	—
315	#95	C₂³×C₁₃	1	8	yes	—
316	#95	C₂³×C₁₃	1	8	yes	—
317	#95	C₂³×C₁₃	1	4	yes	—
318	#95	C₂³×C₁₃	1	8	yes	—
319	#95	C₂³×C₁₃	1	4	yes	—
320	#95	C₂³×C₁₃	1	8	yes	—
321	C₂×C₁₃	—	4	8	no	—
322	C₂×C₁₃	#2337	1	8	yes	direct product factor
323	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
325	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#538	1	2	yes	—
327	C₂×C₁₃	C₂×#542	1	2	yes	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
335	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
336	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
337	C₂×Q₈	—	4	16	no	—
338	C₂×Q₈	—	4	8	no	—
339	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	complemented
340	C₂×D₄	—	4	16	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	4	8	no	—
362	C₂²×C₄	—	4	8	no	—
363	C₂²×C₄	—	4	32	no	—
364	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
365	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
366	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
367	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
368	C₂²×C₄	C₁₃×#41	1	8	yes	—
369	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₄⋊C₄	—	2	16	no	—
378	C₄⋊C₄	—	4	8	no	—
379	C₂²⋊C₄	—	2	16	no	—
380	C₂²⋊C₄	—	4	8	no	—
381	C₂²⋊C₄	—	4	8	no	—
382	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
383	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
384	C₄²	—	4	4	no	—
385	C₄²	—	4	4	no	—
386	C₄²	—	4	8	no	—
387	C₄²	C₂²×C₄×C₁₃	1	16	yes	complemented
388	C₁₃	C₂×#2337	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	16	no	—
390	C₂³	—	2	16	no	—
391	C₂³	—	2	16	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	4	8	no	—
402	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
403	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
404	C₂³	C₂×C₁₃×#41	1	4	yes	—
405	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
406	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
407	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
408	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
409	Q₈	—	4	16	no	—
410	D₄	—	4	16	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	16	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	4	32	no	—
434	C₂×C₄	—	4	8	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
438	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
439	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
440	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
441	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	8	no	—
444	C₂²	—	2	8	no	—
445	C₂²	—	4	32	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	C₄×C₁₃×#41	1	4	yes	—
451	C₂²	C₁₃×#518	1	4	yes	—
452	C₂²	C₁₃×#520	1	4	yes	—
453	C₂²	C₁₃×#538	1	8	yes	—
454	C₂²	C₁₃×#542	1	8	yes	—
455	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
456	C₂²	C₂²×C₁₃×#41	1	2	yes	—
457	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
458	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
460	C₄	—	2	4	no	—
461	C₄	—	2	4	no	—
462	C₄	—	2	8	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	8	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	4	no	—
468	C₂	—	4	8	no	—
469	C₂	C₁₃×#2337	1	8	yes	direct product factor
470	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
471	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
472	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
473	C₂	C₂×C₁₃×#538	1	2	yes	—
474	C₂	C₂×C₁₃×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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×#2337	C₂	direct (N × H)
3. C₂×C₁₃×#391	C₂	semidirect
4. C₂×C₁₃×#388	C₂	semidirect
5. C₂×C₁₃×#388	C₂	semidirect
7. C₂×C₁₃×#385	C₂	semidirect
8. C₂×C₁₃×#383	C₂	semidirect
9. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
10. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
14. C₂×C₁₃×#124	C₄	semidirect
27. C₁₃×#391	C₂²	semidirect
28. C₁₃×#388	C₂²	semidirect
29. C₁₃×#388	C₂²	semidirect
31. C₁₃×#385	C₂²	semidirect
32. C₁₃×#383	C₂²	semidirect
33. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
44. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
61. C₁₃×#124	C₂×C₄	semidirect
69. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
70. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
79. C₂×C₄²×C₁₃	C₂×C₄	semidirect
91. C₂×#2337	C₁₃	direct (N × H)
103. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
146. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
147. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
151. C₄²×C₁₃	C₂²×C₄	semidirect
153. #2337	C₂×C₁₃	direct (N × H)
154. C₂×#391	C₂×C₁₃	semidirect
155. C₂×#388	C₂×C₁₃	semidirect
156. C₂×#388	C₂×C₁₃	semidirect
158. C₂×#385	C₂×C₁₃	semidirect
159. C₂×#383	C₂×C₁₃	semidirect
160. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
161. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
218. C₂×#124	C₄×C₁₃	semidirect
231. #391	C₂²×C₁₃	semidirect
232. #388	C₂²×C₁₃	semidirect
233. #388	C₂²×C₁₃	semidirect
235. #385	C₂²×C₁₃	semidirect
236. #383	C₂²×C₁₃	semidirect
237. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
238. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
274. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
291. #124	C₂×C₄×C₁₃	semidirect
299. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
300. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
309. C₂×C₄²	C₂×C₄×C₁₃	semidirect
322. C₂×C₁₃	#2337	direct (N × H)
339. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
382. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
383. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
387. C₄²	C₂²×C₄×C₁₃	semidirect
388. C₁₃	C₂×#2337	direct (N × H)
469. C₂	C₁₃×#2337	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×#124	2
C₁₃×#2337	2
C₂×C₁₃×#391	2
C₂×C₁₃×#388	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#383	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2337	13

Subgroups — C2×C13×#2337 #15720419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2337 #15720419