Subgroups — C₂×C₁₃×#2639 #15720902

Order 3328.

3326 conjugacy classes of subgroups.

The subgroup lattice has 448 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, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2639	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
9	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
17	C₂×C₁₃×#121	—	2	8	no	—
18	C₂×C₁₃×#121	C₂²	1	8	yes	—
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	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₁₃×#400	C₂²	1	16	yes	complemented
27	C₁₃×#397	C₂²	1	16	yes	complemented
28	C₁₃×#394	C₂²	1	16	yes	complemented
29	C₁₃×#393	C₂²	1	16	yes	complemented
30	C₁₃×#386	C₂²	1	32	yes	complemented
31	C₂×C₁₃×#95	C₂²	1	2	yes	—
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	4	yes	—
34	C₂×C₁₃×#95	C₂²	1	4	yes	—
35	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃	—	2	4	no	—
39	C₂²×Q₈×C₁₃	—	4	4	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
41	C₂²×D₄×C₁₃	—	2	8	no	—
42	C₂²×D₄×C₁₃	—	2	16	no	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	—	4	4	no	—
45	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
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	—	4	4	no	—
51	C₂³×C₄×C₁₃	D₄	1	8	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
60	C₁₃×C₂²⋊Q₈	—	2	32	no	—
61	C₁₃×#121	—	2	32	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
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	16	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₁₃×#95	C₂³	1	16	yes	—
77	C₁₃×#95	C₂³	1	16	yes	—
78	C₁₃×#95	C₂³	1	8	yes	—
79	C₁₃×#95	C₂³	1	8	yes	—
80	C₂×#2639	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	4	no	—
82	C₂⁴×C₁₃	—	2	2	no	—
83	C₂⁴×C₁₃	—	2	2	no	—
84	C₂⁴×C₁₃	—	2	4	no	—
85	C₂⁴×C₁₃	—	2	8	no	—
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	8	no	—
88	C₂⁴×C₁₃	—	2	4	no	—
89	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
90	C₂⁴×C₁₃	#41	1	8	yes	—
91	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
92	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
93	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₂×Q₈×C₁₃	—	2	8	no	—
95	C₂×Q₈×C₁₃	—	4	8	no	—
96	C₂×Q₈×C₁₃	—	4	16	no	—
97	C₂×D₄×C₁₃	—	2	16	no	—
98	C₂×D₄×C₁₃	—	2	32	no	—
99	C₂×D₄×C₁₃	—	2	8	no	—
100	C₂×D₄×C₁₃	—	4	8	no	—
101	C₂×D₄×C₁₃	—	4	16	no	—
102	C₂×D₄×C₁₃	—	4	32	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	16	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	4	16	no	—
117	C₂²×C₄×C₁₃	—	4	8	no	—
118	C₂²×C₄×C₁₃	—	4	8	no	—
119	C₂²×C₄×C₁₃	—	4	8	no	—
120	C₂²×C₄×C₁₃	—	4	32	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	16	no	—
133	C₁₃×C₂²⋊C₄	—	2	16	no	—
134	C₁₃×C₂²⋊C₄	—	2	16	no	—
135	C₁₃×C₂²⋊C₄	—	4	16	no	—
136	C₁₃×C₂²⋊C₄	—	4	16	no	—
137	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
139	#2639	C₂×C₁₃	1	16	yes	direct product factor
140	C₂×#400	C₂×C₁₃	1	2	yes	complemented
141	C₂×#397	C₂×C₁₃	1	2	yes	complemented
142	C₂×#394	C₂×C₁₃	1	2	yes	complemented
143	C₂×#393	C₂×C₁₃	1	2	yes	complemented
144	C₂×#386	C₂×C₁₃	1	4	yes	complemented
145	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂³×C₁₃	—	2	8	no	—
147	C₂³×C₁₃	—	2	8	no	—
148	C₂³×C₁₃	—	2	16	no	—
149	C₂³×C₁₃	—	2	16	no	—
150	C₂³×C₁₃	—	2	4	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	4	no	—
154	C₂³×C₁₃	—	2	8	no	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	—	2	8	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	4	8	no	—
159	C₂³×C₁₃	—	4	8	no	—
160	C₂³×C₁₃	—	4	8	no	—
161	C₂³×C₁₃	—	4	16	no	—
162	C₂³×C₁₃	—	4	16	no	—
163	C₂³×C₁₃	#124	1	16	yes	—
164	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
165	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
166	C₂³×C₁₃	C₂×#41	1	8	yes	—
167	C₂³×C₁₃	C₂×#41	1	4	yes	—
168	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
169	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
170	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
171	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
172	Q₈×C₁₃	—	4	16	no	—
173	D₄×C₁₃	—	4	16	no	—
174	D₄×C₁₃	—	4	32	no	—
175	C₂×C₄×C₁₃	—	2	8	no	—
176	C₂×C₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	8	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	4	16	no	—
190	C₂×C₄×C₁₃	—	4	32	no	—
191	C₂×C₄×C₁₃	—	4	8	no	—
192	C₂×C₄×C₁₃	—	4	8	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	16	no	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
197	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
199	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
201	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	—	2	8	no	—
203	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
204	C₂×#121	—	2	8	no	—
205	C₂×#121	C₂²×C₁₃	1	8	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
213	#400	C₂²×C₁₃	1	16	yes	complemented
214	#397	C₂²×C₁₃	1	16	yes	complemented
215	#394	C₂²×C₁₃	1	16	yes	complemented
216	#393	C₂²×C₁₃	1	16	yes	complemented
217	#386	C₂²×C₁₃	1	32	yes	complemented
218	C₂×#95	C₂²×C₁₃	1	2	yes	—
219	C₂×#95	C₂²×C₁₃	1	4	yes	—
220	C₂×#95	C₂²×C₁₃	1	2	yes	—
221	C₂×#95	C₂²×C₁₃	1	4	yes	—
222	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
223	C₂²×C₁₃	—	2	32	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	—	2	8	no	—
227	C₂²×C₁₃	—	2	8	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	—	4	4	no	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	4	8	no	—
232	C₂²×C₁₃	—	4	8	no	—
233	C₂²×C₁₃	—	8	16	no	—
234	C₂²×C₁₃	C₂×#124	1	8	yes	—
235	C₂²×C₁₃	C₂×#124	1	4	yes	—
236	C₂²×C₁₃	#534	1	4	yes	—
237	C₂²×C₁₃	#537	1	4	yes	—
238	C₂²×C₁₃	#538	1	8	yes	—
239	C₂²×C₁₃	#539	1	8	yes	—
240	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
241	C₂²×C₁₃	C₂²×#41	1	2	yes	—
242	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
243	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	—	2	4	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	4	8	no	—
251	C₂⁵	C₂³×C₁₃	1	2	yes	—
252	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×Q₈	—	2	4	no	—
254	C₂²×Q₈	—	4	4	no	—
255	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
256	C₂²×D₄	—	2	8	no	—
257	C₂²×D₄	—	2	16	no	—
258	C₂²×D₄	—	2	4	no	—
259	C₂²×D₄	—	4	4	no	—
260	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
261	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
262	C₂³×C₄	—	2	8	no	—
263	C₂³×C₄	—	4	4	no	—
264	C₂³×C₄	—	4	4	no	—
265	C₂³×C₄	—	4	4	no	—
266	C₂³×C₄	D₄×C₁₃	1	8	yes	—
267	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
270	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
274	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
275	C₂²⋊Q₈	—	2	32	no	—
276	#121	—	2	32	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	8	no	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	—	4	8	no	—
286	C₂×C₂²⋊C₄	—	4	8	no	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
291	#95	C₂³×C₁₃	1	8	yes	—
292	#95	C₂³×C₁₃	1	8	yes	—
293	#95	C₂³×C₁₃	1	16	yes	—
294	#95	C₂³×C₁₃	1	16	yes	—
295	C₂×C₁₃	—	2	8	no	—
296	C₂×C₁₃	—	8	4	no	—
297	C₂×C₁₃	#2639	1	8	yes	direct product factor
298	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
299	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#538	1	2	yes	—
302	C₂×C₁₃	C₂×#539	1	2	yes	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	2	8	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	8	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
312	C₂⁴	C₁₃×#41	1	8	yes	—
313	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
314	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
315	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₂×Q₈	—	2	8	no	—
317	C₂×Q₈	—	4	8	no	—
318	C₂×Q₈	—	4	16	no	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	2	32	no	—
321	C₂×D₄	—	2	8	no	—
322	C₂×D₄	—	4	8	no	—
323	C₂×D₄	—	4	16	no	—
324	C₂×D₄	—	4	32	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	4	16	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	—	4	8	no	—
342	C₂²×C₄	—	4	32	no	—
343	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
347	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	16	no	—
355	C₂²⋊C₄	—	2	16	no	—
356	C₂²⋊C₄	—	2	16	no	—
357	C₂²⋊C₄	—	4	16	no	—
358	C₂²⋊C₄	—	4	16	no	—
359	C₁₃	C₂×#2639	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	16	no	—
363	C₂³	—	2	16	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	8	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	4	16	no	—
376	C₂³	—	4	16	no	—
377	C₂³	C₁₃×#124	1	16	yes	—
378	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
379	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
380	C₂³	C₂×C₁₃×#41	1	8	yes	—
381	C₂³	C₂×C₁₃×#41	1	4	yes	—
382	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
383	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
384	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
385	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
386	Q₈	—	4	16	no	—
387	D₄	—	4	16	no	—
388	D₄	—	4	32	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	16	no	—
404	C₂×C₄	—	4	32	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	16	no	—
409	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
411	C₂²	—	2	32	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	8	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	8	no	—
421	C₂²	—	8	16	no	—
422	C₂²	C₂×C₁₃×#124	1	8	yes	—
423	C₂²	C₂×C₁₃×#124	1	4	yes	—
424	C₂²	C₁₃×#534	1	4	yes	—
425	C₂²	C₁₃×#537	1	4	yes	—
426	C₂²	C₁₃×#538	1	8	yes	—
427	C₂²	C₁₃×#539	1	8	yes	—
428	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
429	C₂²	C₂²×C₁₃×#41	1	2	yes	—
430	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
431	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	8	no	—
439	C₂	—	2	8	no	—
440	C₂	—	8	4	no	—
441	C₂	C₁₃×#2639	1	8	yes	direct product factor
442	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
443	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
444	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
445	C₂	C₂×C₁₃×#538	1	2	yes	—
446	C₂	C₂×C₁₃×#539	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
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×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2639	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#397	C₂	semidirect
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#393	C₂	semidirect
8. C₂×C₁₃×#386	C₂	semidirect
9. C₂²×C₁₃×#95	C₂	semidirect
16. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₁₃×#400	C₂²	semidirect
27. C₁₃×#397	C₂²	semidirect
28. C₁₃×#394	C₂²	semidirect
29. C₁₃×#393	C₂²	semidirect
30. C₁₃×#386	C₂²	semidirect
35. C₂×C₁₃×#95	C₂²	semidirect
80. C₂×#2639	C₁₃	direct (N × H)
137. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
139. #2639	C₂×C₁₃	direct (N × H)
140. C₂×#400	C₂×C₁₃	semidirect
141. C₂×#397	C₂×C₁₃	semidirect
142. C₂×#394	C₂×C₁₃	semidirect
143. C₂×#393	C₂×C₁₃	semidirect
144. C₂×#386	C₂×C₁₃	semidirect
145. C₂²×#95	C₂×C₁₃	semidirect
203. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
213. #400	C₂²×C₁₃	semidirect
214. #397	C₂²×C₁₃	semidirect
215. #394	C₂²×C₁₃	semidirect
216. #393	C₂²×C₁₃	semidirect
217. #386	C₂²×C₁₃	semidirect
222. C₂×#95	C₂²×C₁₃	semidirect
297. C₂×C₁₃	#2639	direct (N × H)
359. C₁₃	C₂×#2639	direct (N × H)
441. C₂	C₁₃×#2639	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
C₂²×C₁₃×#121	2
C₁₃×#2639	2
C₂×C₁₃×#400	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#393	2
C₂×C₁₃×#386	2
C₂²×C₁₃×#95	2
C₂×#2639	13

Subgroups — C2×C13×#2639 #15720902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2639 #15720902