Subgroups — C₂×C₁₃×#2407 #15721048

Order 3328.

5998 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2407	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#392	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	8	no	—
14	C₂²×C₁₃×#41	—	2	8	no	—
15	C₂²×C₁₃×#41	—	2	8	no	—
16	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#121	—	2	8	no	—
28	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
29	C₂×C₄×D₄×C₁₃	—	2	8	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#394	C₂²	1	16	yes	complemented
44	C₁₃×#392	C₂²	1	16	yes	complemented
45	C₁₃×#391	C₂²	1	8	yes	complemented
46	C₁₃×#390	C₂²	1	8	yes	complemented
47	C₁₃×#386	C₂²	1	16	yes	complemented
48	C₁₃×#385	C₂²	1	16	yes	complemented
49	C₁₃×#380	C₂²	1	8	yes	complemented
50	C₂×C₁₃×#95	C₂²	1	2	yes	—
51	C₂×C₁₃×#95	C₂²	1	2	yes	—
52	C₂×C₁₃×#95	C₂²	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	2	yes	—
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×#41	—	2	128	no	—
57	C₂×C₁₃×#41	—	2	32	no	—
58	C₂×C₁₃×#41	—	2	32	no	—
59	C₂×C₁₃×#41	—	2	32	no	—
60	C₂²×Q₈×C₁₃	—	2	4	no	—
61	C₂²×Q₈×C₁₃	—	2	4	no	—
62	C₂²×Q₈×C₁₃	D₄	1	8	yes	complemented
63	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	—	2	4	no	—
65	C₂²×D₄×C₁₃	—	2	8	no	—
66	C₂²×D₄×C₁₃	—	2	8	no	—
67	C₂²×D₄×C₁₃	—	2	4	no	—
68	C₂²×D₄×C₁₃	—	2	8	no	—
69	C₂²×D₄×C₁₃	—	2	8	no	—
70	C₂²×D₄×C₁₃	—	2	8	no	—
71	C₂²×D₄×C₁₃	—	2	4	no	—
72	C₂²×D₄×C₁₃	—	2	4	no	—
73	C₂²×D₄×C₁₃	—	2	4	no	—
74	C₂²×D₄×C₁₃	—	4	4	no	—
75	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
76	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃	—	2	8	no	—
81	C₂³×C₄×C₁₃	—	2	8	no	—
82	C₂³×C₄×C₁₃	—	2	8	no	—
83	C₂³×C₄×C₁₃	—	2	4	no	—
84	C₂³×C₄×C₁₃	—	2	4	no	—
85	C₂³×C₄×C₁₃	—	2	4	no	—
86	C₂³×C₄×C₁₃	—	2	4	no	—
87	C₂³×C₄×C₁₃	—	2	4	no	—
88	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
89	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₂²⋊Q₈	—	2	32	no	—
101	C₁₃×#121	—	2	32	no	—
102	C₄×D₄×C₁₃	—	2	32	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
125	C₂×C₄²×C₁₃	—	2	4	no	—
126	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	8	yes	—
128	C₁₃×#95	C₂³	1	8	yes	—
129	C₁₃×#95	C₂³	1	8	yes	—
130	C₂×#2407	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₂⁴×C₁₃	—	2	4	no	—
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₂⁴×C₁₃	—	2	4	no	—
136	C₂⁴×C₁₃	—	2	2	no	—
137	C₂⁴×C₁₃	—	2	2	no	—
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	2	2	no	—
140	C₂⁴×C₁₃	—	2	2	no	—
141	C₂⁴×C₁₃	—	2	2	no	—
142	C₂⁴×C₁₃	—	2	4	no	—
143	C₂⁴×C₁₃	—	2	2	no	—
144	C₂⁴×C₁₃	—	2	4	no	—
145	C₂⁴×C₁₃	—	2	2	no	—
146	C₂⁴×C₁₃	—	2	2	no	—
147	C₂⁴×C₁₃	—	2	4	no	—
148	C₂⁴×C₁₃	—	2	2	no	—
149	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
150	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
151	C₂⁴×C₁₃	#41	1	4	yes	complemented
152	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
154	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
155	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₁₃×#41	—	2	256	no	—
157	C₂×Q₈×C₁₃	—	2	32	no	—
158	C₂×Q₈×C₁₃	—	2	8	no	—
159	C₂×Q₈×C₁₃	—	2	8	no	—
160	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	complemented
161	C₂×D₄×C₁₃	—	2	32	no	—
162	C₂×D₄×C₁₃	—	2	64	no	—
163	C₂×D₄×C₁₃	—	2	8	no	—
164	C₂×D₄×C₁₃	—	2	16	no	—
165	C₂×D₄×C₁₃	—	2	16	no	—
166	C₂×D₄×C₁₃	—	2	8	no	—
167	C₂×D₄×C₁₃	—	2	16	no	—
168	C₂×D₄×C₁₃	—	2	16	no	—
169	C₂×D₄×C₁₃	—	2	32	no	—
170	C₂×D₄×C₁₃	—	2	16	no	—
171	C₂×D₄×C₁₃	—	2	8	no	—
172	C₂×D₄×C₁₃	—	2	8	no	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	4	8	no	—
175	C₂×D₄×C₁₃	—	4	32	no	—
176	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
177	C₂²×C₄×C₁₃	—	2	64	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	16	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	32	no	—
186	C₂²×C₄×C₁₃	—	2	16	no	—
187	C₂²×C₄×C₁₃	—	2	16	no	—
188	C₂²×C₄×C₁₃	—	2	8	no	—
189	C₂²×C₄×C₁₃	—	2	8	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	8	no	—
203	C₂²×C₄×C₁₃	—	2	8	no	—
204	C₂²×C₄×C₁₃	—	2	8	no	—
205	C₂²×C₄×C₁₃	—	4	16	no	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
212	C₂²×C₄×C₁₃	#41	1	4	yes	complemented
213	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₁₃×C₄⋊C₄	—	2	8	no	—
222	C₁₃×C₄⋊C₄	—	2	8	no	—
223	C₁₃×C₄⋊C₄	—	2	8	no	—
224	C₁₃×C₄⋊C₄	—	2	16	no	—
225	C₁₃×C₂²⋊C₄	—	2	8	no	—
226	C₁₃×C₂²⋊C₄	—	2	16	no	—
227	C₁₃×C₂²⋊C₄	—	2	8	no	—
228	C₁₃×C₂²⋊C₄	—	2	16	no	—
229	C₁₃×C₂²⋊C₄	—	2	16	no	—
230	C₁₃×C₂²⋊C₄	—	4	8	no	—
231	C₁₃×C₂²⋊C₄	—	4	8	no	—
232	C₄²×C₁₃	—	2	8	no	—
233	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2407	C₂×C₁₃	1	16	yes	direct product factor
238	C₂×#394	C₂×C₁₃	1	2	yes	complemented
239	C₂×#392	C₂×C₁₃	1	2	yes	complemented
240	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
242	C₂×#386	C₂×C₁₃	1	2	yes	complemented
243	C₂×#385	C₂×C₁₃	1	2	yes	complemented
244	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	16	no	—
246	C₂³×C₁₃	—	2	8	no	—
247	C₂³×C₁₃	—	2	8	no	—
248	C₂³×C₁₃	—	2	8	no	—
249	C₂³×C₁₃	—	2	8	no	—
250	C₂³×C₁₃	—	2	8	no	—
251	C₂³×C₁₃	—	2	16	no	—
252	C₂³×C₁₃	—	2	16	no	—
253	C₂³×C₁₃	—	2	8	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	4	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	4	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	4	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	4	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	4	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	—	2	2	no	—
270	C₂³×C₁₃	—	2	4	no	—
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	4	4	no	—
273	C₂³×C₁₃	—	4	8	no	—
274	C₂³×C₁₃	—	4	4	no	—
275	C₂³×C₁₃	—	4	8	no	—
276	C₂³×C₁₃	—	4	4	no	—
277	C₂³×C₁₃	—	4	4	no	—
278	C₂³×C₁₃	—	4	4	no	—
279	C₂³×C₁₃	—	4	4	no	—
280	C₂³×C₁₃	—	4	8	no	—
281	C₂³×C₁₃	—	4	4	no	—
282	C₂³×C₁₃	—	4	8	no	—
283	C₂³×C₁₃	—	4	4	no	—
284	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
285	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
289	C₂³×C₁₃	C₂×#41	1	2	yes	—
290	C₂³×C₁₃	C₂×#41	1	2	yes	—
291	C₂³×C₁₃	C₂×#41	1	4	yes	complemented
292	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
293	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
294	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
295	Q₈×C₁₃	—	2	32	no	—
296	D₄×C₁₃	—	2	32	no	—
297	D₄×C₁₃	—	2	64	no	—
298	D₄×C₁₃	—	2	32	no	—
299	D₄×C₁₃	—	4	32	no	—
300	C₂×C₄×C₁₃	—	2	64	no	—
301	C₂×C₄×C₁₃	—	2	8	no	—
302	C₂×C₄×C₁₃	—	2	16	no	—
303	C₂×C₄×C₁₃	—	2	8	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	32	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	4	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	4	no	—
318	C₂×C₄×C₁₃	—	2	4	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	4	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	4	4	no	—
325	C₂×C₄×C₁₃	—	4	8	no	—
326	C₂×C₄×C₁₃	—	4	8	no	—
327	C₂×C₄×C₁₃	—	4	16	no	—
328	C₂×C₄×C₁₃	#120	1	16	yes	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
330	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₁₃	C₂×#41	1	4	yes	complemented
335	C₂²×#41	—	2	8	no	—
336	C₂²×#41	—	2	8	no	—
337	C₂²×#41	—	2	8	no	—
338	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
339	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
340	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
341	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
343	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
344	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
345	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₂²⋊Q₈	—	2	8	no	—
348	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
349	C₂×#121	—	2	8	no	—
350	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
351	C₂×C₄×D₄	—	2	8	no	—
352	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
353	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
354	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
358	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
359	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
360	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
361	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
363	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
364	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
365	#394	C₂²×C₁₃	1	16	yes	complemented
366	#392	C₂²×C₁₃	1	16	yes	complemented
367	#391	C₂²×C₁₃	1	8	yes	complemented
368	#390	C₂²×C₁₃	1	8	yes	complemented
369	#386	C₂²×C₁₃	1	16	yes	complemented
370	#385	C₂²×C₁₃	1	16	yes	complemented
371	#380	C₂²×C₁₃	1	8	yes	complemented
372	C₂×#95	C₂²×C₁₃	1	2	yes	—
373	C₂×#95	C₂²×C₁₃	1	2	yes	—
374	C₂×#95	C₂²×C₁₃	1	2	yes	—
375	C₂²×C₁₃	—	2	8	no	—
376	C₂²×C₁₃	—	2	4	no	—
377	C₂²×C₁₃	—	2	4	no	—
378	C₂²×C₁₃	—	2	4	no	—
379	C₂²×C₁₃	—	2	4	no	—
380	C₂²×C₁₃	—	2	4	no	—
381	C₂²×C₁₃	—	2	8	no	—
382	C₂²×C₁₃	—	2	8	no	—
383	C₂²×C₁₃	—	2	4	no	—
384	C₂²×C₁₃	—	4	16	no	—
385	C₂²×C₁₃	—	4	32	no	—
386	C₂²×C₁₃	—	4	16	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	4	4	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	4	4	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	—	4	4	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	2	no	—
399	C₂²×C₁₃	C₂×#120	1	4	yes	—
400	C₂²×C₁₃	#525	1	4	yes	—
401	C₂²×C₁₃	#537	1	4	yes	—
402	C₂²×C₁₃	#546	1	4	yes	—
403	C₂²×C₁₃	#547	1	4	yes	—
404	C₂²×C₁₃	#548	1	4	yes	—
405	C₂²×C₁₃	#550	1	4	yes	—
406	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
407	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
408	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
409	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
413	C₄×C₁₃	—	2	4	no	—
414	C₄×C₁₃	—	2	8	no	—
415	C₄×C₁₃	—	2	4	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	4	4	no	—
419	C₄×C₁₃	—	4	4	no	—
420	C₄×C₁₃	C₂×#120	1	8	yes	—
421	C₂⁵	C₂³×C₁₃	1	2	yes	—
422	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
423	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×#41	—	2	128	no	—
425	C₂×#41	—	2	32	no	—
426	C₂×#41	—	2	32	no	—
427	C₂×#41	—	2	32	no	—
428	C₂²×Q₈	—	2	4	no	—
429	C₂²×Q₈	—	2	4	no	—
430	C₂²×Q₈	D₄×C₁₃	1	8	yes	complemented
431	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
432	C₂²×D₄	—	2	4	no	—
433	C₂²×D₄	—	2	8	no	—
434	C₂²×D₄	—	2	8	no	—
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	2	8	no	—
437	C₂²×D₄	—	2	8	no	—
438	C₂²×D₄	—	2	8	no	—
439	C₂²×D₄	—	2	4	no	—
440	C₂²×D₄	—	2	4	no	—
441	C₂²×D₄	—	2	4	no	—
442	C₂²×D₄	—	4	4	no	—
443	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
444	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
445	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
446	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
447	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
448	C₂³×C₄	—	2	8	no	—
449	C₂³×C₄	—	2	8	no	—
450	C₂³×C₄	—	2	8	no	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	—	2	4	no	—
453	C₂³×C₄	—	2	4	no	—
454	C₂³×C₄	—	2	4	no	—
455	C₂³×C₄	—	2	4	no	—
456	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
457	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
461	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
462	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
463	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
465	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
466	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²⋊Q₈	—	2	32	no	—
469	#121	—	2	32	no	—
470	C₄×D₄	—	2	32	no	—
471	C₂×C₄⋊C₄	—	2	4	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	—	2	8	no	—
475	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
479	C₂×C₂²⋊C₄	—	2	4	no	—
480	C₂×C₂²⋊C₄	—	2	8	no	—
481	C₂×C₂²⋊C₄	—	2	4	no	—
482	C₂×C₂²⋊C₄	—	2	8	no	—
483	C₂×C₂²⋊C₄	—	2	8	no	—
484	C₂×C₂²⋊C₄	—	4	4	no	—
485	C₂×C₂²⋊C₄	—	4	4	no	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
493	C₂×C₄²	—	2	4	no	—
494	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
495	#95	C₂³×C₁₃	1	8	yes	—
496	#95	C₂³×C₁₃	1	8	yes	—
497	#95	C₂³×C₁₃	1	8	yes	—
498	C₂×C₁₃	—	4	4	no	—
499	C₂×C₁₃	—	4	8	no	—
500	C₂×C₁₃	—	4	4	no	—
501	C₂×C₁₃	#2407	1	8	yes	direct product factor
502	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
503	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
504	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
505	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
506	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
507	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
508	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
509	C₂⁴	—	2	2	no	—
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	2	2	no	—
513	C₂⁴	—	2	4	no	—
514	C₂⁴	—	2	2	no	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	2	4	no	—
521	C₂⁴	—	2	2	no	—
522	C₂⁴	—	2	4	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	2	4	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
528	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
529	C₂⁴	C₁₃×#41	1	4	yes	complemented
530	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
531	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
532	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
533	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
534	#41	—	2	256	no	—
535	C₂×Q₈	—	2	32	no	—
536	C₂×Q₈	—	2	8	no	—
537	C₂×Q₈	—	2	8	no	—
538	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	complemented
539	C₂×D₄	—	2	64	no	—
540	C₂×D₄	—	2	32	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	16	no	—
543	C₂×D₄	—	2	16	no	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	2	16	no	—
546	C₂×D₄	—	2	16	no	—
547	C₂×D₄	—	2	32	no	—
548	C₂×D₄	—	2	16	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	8	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	4	8	no	—
553	C₂×D₄	—	4	32	no	—
554	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	complemented
555	C₂²×C₄	—	2	64	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	16	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	32	no	—
564	C₂²×C₄	—	2	16	no	—
565	C₂²×C₄	—	2	16	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	8	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	2	8	no	—
583	C₂²×C₄	—	4	16	no	—
584	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
585	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
586	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
587	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
588	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
589	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
590	C₂²×C₄	C₁₃×#41	1	4	yes	complemented
591	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
592	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
597	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	16	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	16	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	16	no	—
607	C₂²⋊C₄	—	2	16	no	—
608	C₂²⋊C₄	—	4	8	no	—
609	C₂²⋊C₄	—	4	8	no	—
610	C₄²	—	2	8	no	—
611	C₁₃	C₂×#2407	1	1	yes	characteristic, direct product factor, Sylow
612	C₂³	—	2	16	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	8	no	—
617	C₂³	—	2	8	no	—
618	C₂³	—	2	16	no	—
619	C₂³	—	2	16	no	—
620	C₂³	—	2	8	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	4	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	4	4	no	—
640	C₂³	—	4	8	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	4	8	no	—
643	C₂³	—	4	4	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	8	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	8	no	—
650	C₂³	—	4	4	no	—
651	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
652	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
653	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
654	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
655	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
656	C₂³	C₂×C₁₃×#41	1	2	yes	—
657	C₂³	C₂×C₁₃×#41	1	2	yes	—
658	C₂³	C₂×C₁₃×#41	1	4	yes	complemented
659	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
660	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
661	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
662	Q₈	—	2	32	no	—
663	D₄	—	2	32	no	—
664	D₄	—	2	64	no	—
665	D₄	—	2	32	no	—
666	D₄	—	4	32	no	—
667	C₂×C₄	—	2	64	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	2	16	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	32	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	16	no	—
695	C₂×C₄	C₁₃×#120	1	16	yes	—
696	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
697	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
699	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
700	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
701	C₂×C₄	C₂×C₁₃×#41	1	4	yes	complemented
702	C₂²	—	2	8	no	—
703	C₂²	—	2	4	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	8	no	—
709	C₂²	—	2	8	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	16	no	—
712	C₂²	—	4	32	no	—
713	C₂²	—	4	16	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	C₂×C₁₃×#120	1	4	yes	—
727	C₂²	C₁₃×#525	1	4	yes	—
728	C₂²	C₁₃×#537	1	4	yes	—
729	C₂²	C₁₃×#546	1	4	yes	—
730	C₂²	C₁₃×#547	1	4	yes	—
731	C₂²	C₁₃×#548	1	4	yes	—
732	C₂²	C₁₃×#550	1	4	yes	—
733	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
734	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
735	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
736	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
737	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
738	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
739	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
740	C₄	—	2	4	no	—
741	C₄	—	2	8	no	—
742	C₄	—	2	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	4	no	—
747	C₄	C₂×C₁₃×#120	1	8	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	8	no	—
750	C₂	—	4	4	no	—
751	C₂	C₁₃×#2407	1	8	yes	direct product factor
752	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
753	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
754	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
755	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
756	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
757	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
758	C₂	C₂×C₁₃×#550	1	1	yes	characteristic

	subgroup	G/H
center, socle	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
1. C₂³×C₁₃×#41	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₂²×C₁₃×#121	C₂	semidirect
4. C₂²×C₄×D₄×C₁₃	C₂	semidirect
5. C₁₃×#2407	C₂	direct (N × H)
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#392	C₂	semidirect
8. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#390	C₂	semidirect
10. C₂×C₁₃×#386	C₂	semidirect
11. C₂×C₁₃×#385	C₂	semidirect
12. C₂×C₁₃×#380	C₂	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#394	C₂²	semidirect
44. C₁₃×#392	C₂²	semidirect
45. C₁₃×#391	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#386	C₂²	semidirect
48. C₁₃×#385	C₂²	semidirect
49. C₁₃×#380	C₂²	semidirect
62. C₂²×Q₈×C₁₃	D₄	semidirect
75. C₂²×D₄×C₁₃	D₄	semidirect
88. C₂³×C₄×C₁₃	D₄	semidirect
130. C₂×#2407	C₁₃	direct (N × H)
151. C₂⁴×C₁₃	#41	semidirect
160. C₂×Q₈×C₁₃	C₂×D₄	semidirect
176. C₂×D₄×C₁₃	C₂×D₄	semidirect
211. C₂²×C₄×C₁₃	C₂×D₄	semidirect
212. C₂²×C₄×C₁₃	#41	semidirect
233. C₂³×#41	C₂×C₁₃	semidirect
234. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
235. C₂²×#121	C₂×C₁₃	semidirect
236. C₂²×C₄×D₄	C₂×C₁₃	semidirect
237. #2407	C₂×C₁₃	direct (N × H)
238. C₂×#394	C₂×C₁₃	semidirect
239. C₂×#392	C₂×C₁₃	semidirect
240. C₂×#391	C₂×C₁₃	semidirect
241. C₂×#390	C₂×C₁₃	semidirect
242. C₂×#386	C₂×C₁₃	semidirect
243. C₂×#385	C₂×C₁₃	semidirect
244. C₂×#380	C₂×C₁₃	semidirect
291. C₂³×C₁₃	C₂×#41	semidirect
334. C₂×C₄×C₁₃	C₂×#41	semidirect
338. C₂²×#41	C₂²×C₁₃	semidirect
348. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
350. C₂×#121	C₂²×C₁₃	semidirect
352. C₂×C₄×D₄	C₂²×C₁₃	semidirect
365. #394	C₂²×C₁₃	semidirect
366. #392	C₂²×C₁₃	semidirect
367. #391	C₂²×C₁₃	semidirect
368. #390	C₂²×C₁₃	semidirect
369. #386	C₂²×C₁₃	semidirect
370. #385	C₂²×C₁₃	semidirect
371. #380	C₂²×C₁₃	semidirect
430. C₂²×Q₈	D₄×C₁₃	semidirect
443. C₂²×D₄	D₄×C₁₃	semidirect
456. C₂³×C₄	D₄×C₁₃	semidirect
501. C₂×C₁₃	#2407	direct (N × H)
529. C₂⁴	C₁₃×#41	semidirect
538. C₂×Q₈	C₂×D₄×C₁₃	semidirect
554. C₂×D₄	C₂×D₄×C₁₃	semidirect
589. C₂²×C₄	C₂×D₄×C₁₃	semidirect
590. C₂²×C₄	C₁₃×#41	semidirect
611. C₁₃	C₂×#2407	direct (N × H)
658. C₂³	C₂×C₁₃×#41	semidirect
701. C₂×C₄	C₂×C₁₃×#41	semidirect
751. C₂	C₁₃×#2407	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₃×#41	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2407	2
C₂×C₁₃×#394	2
C₂×C₁₃×#392	2
C₂×C₁₃×#391	2
C₂×C₁₃×#390	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂×#2407	13

Subgroups — C2×C13×#2407 #15721048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2407 #15721048