Subgroups — C₂×C₁₃×#2332 #15720414

Order 3328.

2678 conjugacy classes of subgroups.

The subgroup lattice has 464 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×#2332	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
5	C₂×C₁₃×#388	C₂	1	2	yes	maximal
6	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	C₄	1	16	yes	complemented
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
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	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#391	C₂²	1	16	yes	complemented
28	C₁₃×#388	C₂²	1	16	yes	—
29	C₁₃×#388	C₂²	1	16	yes	—
30	C₁₃×#387	C₂²	1	16	yes	complemented
31	C₁₃×#387	C₂²	1	16	yes	complemented
32	C₁₃×#381	C₂²	1	8	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	16	yes	complemented
34	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	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	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	2	no	—
44	C₂²×Q₈×C₁₃	—	4	2	no	—
45	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₃	—	4	2	no	—
48	C₂³×C₄×C₁₃	—	4	2	no	—
49	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₁₃×C₂²⋊Q₈	C₂×C₄	1	64	yes	complemented
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	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	8	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₄²×C₁₃	—	2	8	no	—
77	C₂×C₄²×C₁₃	—	4	2	no	—
78	C₂×C₄²×C₁₃	—	4	4	no	—
79	C₂×C₄²×C₁₃	—	4	2	no	—
80	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	8	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	8	yes	—
88	C₁₃×#95	C₂³	1	8	yes	—
89	C₁₃×#95	C₂³	1	8	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₂×#2332	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	4	16	no	—
100	C₂×Q₈×C₁₃	—	4	4	no	—
101	C₂×Q₈×C₁₃	—	4	4	no	—
102	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
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	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	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	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	—	4	16	no	—
123	C₂²×C₄×C₁₃	—	4	4	no	—
124	C₂²×C₄×C₁₃	—	4	4	no	—
125	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
130	C₂²×C₄×C₁₃	#41	1	8	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
139	C₁₃×C₄⋊C₄	—	2	16	no	—
140	C₁₃×C₄⋊C₄	—	4	8	no	—
141	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
142	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	—
143	C₁₃×C₂²⋊C₄	—	2	16	no	—
144	C₁₃×C₂²⋊C₄	—	4	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
147	C₄²×C₁₃	—	2	16	no	—
148	C₄²×C₁₃	—	4	4	no	—
149	C₄²×C₁₃	—	4	8	no	—
150	C₄²×C₁₃	—	4	4	no	—
151	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
152	#2332	C₂×C₁₃	1	16	yes	direct product factor
153	C₂×#391	C₂×C₁₃	1	2	yes	complemented
154	C₂×#388	C₂×C₁₃	1	2	yes	—
155	C₂×#388	C₂×C₁₃	1	2	yes	—
156	C₂×#387	C₂×C₁₃	1	2	yes	complemented
157	C₂×#387	C₂×C₁₃	1	2	yes	complemented
158	C₂×#381	C₂×C₁₃	1	1	yes	characteristic
159	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
160	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
161	C₂³×C₁₃	—	2	8	no	—
162	C₂³×C₁₃	—	2	8	no	—
163	C₂³×C₁₃	—	2	8	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	4	8	no	—
169	C₂³×C₁₃	—	4	8	no	—
170	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
171	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
172	C₂³×C₁₃	C₂×#41	1	4	yes	—
173	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
175	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
176	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
177	Q₈×C₁₃	—	4	16	no	—
178	C₂×C₄×C₁₃	—	2	16	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	8	no	—
181	C₂×C₄×C₁₃	—	2	16	no	—
182	C₂×C₄×C₁₃	—	2	16	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	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	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	—	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	—	4	16	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	—	4	8	no	—
206	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
207	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
208	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
209	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
210	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
211	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	C₄×C₁₃	1	16	yes	complemented
214	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
227	#391	C₂²×C₁₃	1	16	yes	complemented
228	#388	C₂²×C₁₃	1	16	yes	—
229	#388	C₂²×C₁₃	1	16	yes	—
230	#387	C₂²×C₁₃	1	16	yes	complemented
231	#387	C₂²×C₁₃	1	16	yes	complemented
232	#381	C₂²×C₁₃	1	8	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₃	1	16	yes	complemented
234	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	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	C₂×#95	C₂²×C₁₃	1	2	yes	—
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	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	4	16	no	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	C₄×#41	1	4	yes	—
249	C₂²×C₁₃	#518	1	4	yes	—
250	C₂²×C₁₃	#519	1	4	yes	—
251	C₂²×C₁₃	#539	1	8	yes	—
252	C₂²×C₁₃	#542	1	8	yes	—
253	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
254	C₂²×C₁₃	C₂²×#41	1	2	yes	—
255	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
257	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
258	C₄×C₁₃	—	2	8	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	2	4	no	—
261	C₄×C₁₃	—	2	8	no	—
262	C₄×C₁₃	—	2	8	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	4	no	—
266	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×Q₈	—	4	2	no	—
268	C₂²×Q₈	—	4	2	no	—
269	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	—
270	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
271	C₂³×C₄	—	4	2	no	—
272	C₂³×C₄	—	4	2	no	—
273	C₂³×C₄	C₂×C₄×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	2	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
278	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
282	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
283	C₂²⋊Q₈	C₂×C₄×C₁₃	1	64	yes	complemented
284	C₂×C₄⋊C₄	—	2	8	no	—
285	C₂×C₄⋊C₄	—	4	4	no	—
286	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
287	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
292	C₂×C₂²⋊C₄	—	2	8	no	—
293	C₂×C₂²⋊C₄	—	4	2	no	—
294	C₂×C₂²⋊C₄	—	4	2	no	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
300	C₂×C₄²	—	2	8	no	—
301	C₂×C₄²	—	4	2	no	—
302	C₂×C₄²	—	4	4	no	—
303	C₂×C₄²	—	4	2	no	—
304	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
305	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
306	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
307	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
308	#95	C₂³×C₁₃	1	8	yes	—
309	#95	C₂³×C₁₃	1	8	yes	—
310	#95	C₂³×C₁₃	1	8	yes	—
311	#95	C₂³×C₁₃	1	8	yes	—
312	#95	C₂³×C₁₃	1	8	yes	—
313	#95	C₂³×C₁₃	1	8	yes	—
314	#95	C₂³×C₁₃	1	8	yes	—
315	C₂×C₁₃	—	4	4	no	—
316	C₂×C₁₃	#2332	1	8	yes	direct product factor
317	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#539	1	2	yes	—
321	C₂×C₁₃	C₂×#542	1	2	yes	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	2	no	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
327	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
328	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
329	C₂×Q₈	—	4	16	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	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	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	4	16	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
360	C₂²×C₄	C₁₃×#41	1	8	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	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
369	C₄⋊C₄	—	2	16	no	—
370	C₄⋊C₄	—	4	8	no	—
371	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
372	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
373	C₂²⋊C₄	—	2	16	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
377	C₄²	—	2	16	no	—
378	C₄²	—	4	4	no	—
379	C₄²	—	4	8	no	—
380	C₄²	—	4	4	no	—
381	C₁₃	C₂×#2332	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	8	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	8	no	—
391	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
392	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
393	C₂³	C₂×C₁₃×#41	1	4	yes	—
394	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
395	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
396	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
397	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
398	Q₈	—	4	16	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	16	no	—
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	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	—	4	16	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
428	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
429	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
430	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
431	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	16	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	C₄×C₁₃×#41	1	4	yes	—
439	C₂²	C₁₃×#518	1	4	yes	—
440	C₂²	C₁₃×#519	1	4	yes	—
441	C₂²	C₁₃×#539	1	8	yes	—
442	C₂²	C₁₃×#542	1	8	yes	—
443	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
444	C₂²	C₂²×C₁₃×#41	1	2	yes	—
445	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
448	C₄	—	2	8	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	8	no	—
452	C₄	—	2	8	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₂	—	4	4	no	—
457	C₂	C₁₃×#2332	1	8	yes	direct product factor
458	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
460	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#539	1	2	yes	—
462	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	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×#2332	C₂	direct (N × H)
3. C₂×C₁₃×#391	C₂	semidirect
6. C₂×C₁₃×#387	C₂	semidirect
7. C₂×C₁₃×#387	C₂	semidirect
9. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₂×C₁₃×C₂²⋊Q₈	C₄	semidirect
27. C₁₃×#391	C₂²	semidirect
30. C₁₃×#387	C₂²	semidirect
31. C₁₃×#387	C₂²	semidirect
33. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₂×#2332	C₁₃	direct (N × H)
152. #2332	C₂×C₁₃	direct (N × H)
153. C₂×#391	C₂×C₁₃	semidirect
156. C₂×#387	C₂×C₁₃	semidirect
157. C₂×#387	C₂×C₁₃	semidirect
159. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
213. C₂×C₂²⋊Q₈	C₄×C₁₃	semidirect
227. #391	C₂²×C₁₃	semidirect
230. #387	C₂²×C₁₃	semidirect
231. #387	C₂²×C₁₃	semidirect
233. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
283. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
316. C₂×C₁₃	#2332	direct (N × H)
381. C₁₃	C₂×#2332	direct (N × H)
457. C₂	C₁₃×#2332	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×#2332	2
C₂×C₁₃×#391	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#381	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2332	13

Subgroups — C2×C13×#2332 #15720414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2332 #15720414