Subgroups — C₂×C₁₃×#3349 #15747580

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#552	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3349	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#556	—	2	4	no	—
21	C₁₃×#556	C₂²	1	8	yes	—
22	C₁₃×#552	—	2	4	no	—
23	C₁₃×#552	C₂²	1	8	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#126	—	2	1	no	—
26	C₂×C₁₃×#126	—	2	1	no	—
27	C₂×C₁₃×#126	—	2	1	no	—
28	C₂×C₁₃×#125	—	2	1	no	—
29	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#124	—	2	1	no	—
31	C₂×C₁₃×#123	—	2	1	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
37	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#117	—	2	1	no	—
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₃×#501	C₂²	1	8	yes	complemented
46	C₁₃×#485	C₂²	1	8	yes	complemented
47	C₁₃×#485	C₂²	1	8	yes	complemented
48	C₁₃×#485	C₂²	1	8	yes	complemented
49	C₁₃×#484	C₂²	1	8	yes	complemented
50	C₁₃×#479	C₂²	1	8	yes	complemented
51	C₁₃×#477	C₂²	1	8	yes	complemented
52	C₁₃×#470	C₂²	1	8	yes	complemented
53	C₁₃×#467	C₂²	1	8	yes	complemented
54	C₁₃×#441	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	—
56	C₁₃×#428	C₂²	1	8	yes	complemented
57	C₁₃×#427	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	—	2	1	no	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×Q₁₆	—	2	4	no	—
85	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
86	C₂×C₁₃×M₁₆	—	2	4	no	—
87	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
88	C₂²×C₈×C₁₃	—	2	4	no	—
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
96	C₁₃×#126	—	2	8	no	—
97	C₁₃×#126	—	2	8	no	—
98	C₁₃×#126	—	2	8	no	—
99	C₁₃×#125	—	2	8	no	—
100	C₁₃×#125	—	2	2	no	—
101	C₁₃×#125	C₂³	1	4	yes	—
102	C₁₃×#124	—	2	8	no	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×C₂²⋊Q₈	—	2	2	no	—
105	C₁₃×C₂²⋊Q₈	—	2	2	no	—
106	C₁₃×C₂²⋊Q₈	—	2	2	no	—
107	C₁₃×C₂²⋊Q₈	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
112	C₄×Q₈×C₁₃	—	2	8	no	—
113	C₄×Q₈×C₁₃	—	2	2	no	—
114	C₄×Q₈×C₁₃	—	2	2	no	—
115	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
116	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
117	C₄×D₄×C₁₃	D₄	1	4	yes	—
118	C₄×D₄×C₁₃	C₂³	1	4	yes	—
119	C₁₃×#117	—	2	2	no	—
120	C₁₃×#117	—	2	2	no	—
121	C₁₃×#117	—	2	2	no	—
122	C₁₃×#117	—	2	8	no	—
123	C₁₃×#117	C₂³	1	4	yes	—
124	C₁₃×#117	C₂³	1	4	yes	—
125	C₁₃×#117	C₂³	1	4	yes	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	—	2	1	no	—
155	C₂×C₄²×C₁₃	—	2	1	no	—
156	C₂×C₄²×C₁₃	—	2	1	no	—
157	C₂×C₄²×C₁₃	—	2	1	no	—
158	C₂×C₄²×C₁₃	—	2	1	no	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×#107	C₂³	1	4	yes	—
161	C₁₃×#107	C₂³	1	4	yes	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#107	C₂³	1	4	yes	—
164	C₁₃×#107	C₂³	1	4	yes	—
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	4	yes	—
167	C₁₃×#106	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	4	yes	—
172	C₁₃×#103	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×#97	C₂³	1	4	yes	—
179	C₂×#3349	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	2	no	—
189	C₂×Q₈×C₁₃	—	4	4	no	—
190	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
191	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	2	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	4	4	no	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×Q₁₆	—	2	8	no	—
218	C₁₃×M₁₆	—	2	8	no	—
219	C₂×C₈×C₁₃	—	2	2	no	—
220	C₂×C₈×C₁₃	—	2	2	no	—
221	C₂×C₈×C₁₃	—	2	2	no	—
222	C₂×C₈×C₁₃	—	2	8	no	—
223	C₂×C₈×C₁₃	#41	1	4	yes	—
224	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
225	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
245	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
246	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
247	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
248	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
249	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
250	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
259	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	4	no	—
265	C₄²×C₁₃	C₂×D₄	1	2	yes	—
266	C₄²×C₁₃	C₂⁴	1	2	yes	—
267	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
268	C₂×#552	C₂×C₁₃	1	1	yes	characteristic
269	#3349	C₂×C₁₃	1	16	yes	direct product factor
270	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#435	C₂×C₁₃	1	1	yes	characteristic
281	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
290	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
291	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₁₃	—	2	2	no	—
293	Q₈×C₁₃	—	2	2	no	—
294	Q₈×C₁₃	—	2	2	no	—
295	Q₈×C₁₃	—	2	2	no	—
296	Q₈×C₁₃	—	4	8	no	—
297	Q₈×C₁₃	—	4	2	no	—
298	Q₈×C₁₃	—	4	2	no	—
299	D₄×C₁₃	—	4	4	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	4	8	no	—
319	C₂×C₄×C₁₃	—	4	2	no	—
320	C₂×C₄×C₁₃	—	4	2	no	—
321	C₂×C₄×C₁₃	—	4	2	no	—
322	C₂×C₄×C₁₃	—	4	2	no	—
323	C₂×C₄×C₁₃	—	4	2	no	—
324	C₂×C₄×C₁₃	—	4	2	no	—
325	C₂×C₄×C₁₃	—	4	2	no	—
326	C₂×C₄×C₁₃	—	4	2	no	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
334	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
335	C₈×C₁₃	—	2	2	no	—
336	C₈×C₁₃	—	2	2	no	—
337	C₈×C₁₃	—	2	2	no	—
338	C₈×C₁₃	C₂×#41	1	4	yes	—
339	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
340	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
341	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
342	#556	—	2	4	no	—
343	#556	C₂²×C₁₃	1	8	yes	—
344	#552	—	2	4	no	—
345	#552	C₂²×C₁₃	1	8	yes	—
346	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#126	—	2	1	no	—
348	C₂×#126	—	2	1	no	—
349	C₂×#126	—	2	1	no	—
350	C₂×#125	—	2	1	no	—
351	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#124	—	2	1	no	—
353	C₂×#123	—	2	1	no	—
354	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×C₄×Q₈	—	2	1	no	—
359	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#117	—	2	1	no	—
363	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
367	#501	C₂²×C₁₃	1	8	yes	complemented
368	#485	C₂²×C₁₃	1	8	yes	complemented
369	#485	C₂²×C₁₃	1	8	yes	complemented
370	#485	C₂²×C₁₃	1	8	yes	complemented
371	#484	C₂²×C₁₃	1	8	yes	complemented
372	#479	C₂²×C₁₃	1	8	yes	complemented
373	#477	C₂²×C₁₃	1	8	yes	complemented
374	#470	C₂²×C₁₃	1	8	yes	complemented
375	#467	C₂²×C₁₃	1	8	yes	complemented
376	#441	C₂²×C₁₃	1	8	yes	complemented
377	#435	C₂²×C₁₃	1	8	yes	—
378	#428	C₂²×C₁₃	1	8	yes	complemented
379	#427	C₂²×C₁₃	1	8	yes	complemented
380	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×C₁₃	—	2	2	no	—
400	C₂²×C₁₃	—	2	2	no	—
401	C₂²×C₁₃	—	2	2	no	—
402	C₂²×C₁₃	—	2	2	no	—
403	C₂²×C₁₃	—	2	2	no	—
404	C₂²×C₁₃	—	2	2	no	—
405	C₂²×C₁₃	—	4	4	no	—
406	C₂²×C₁₃	—	4	4	no	—
407	C₂²×C₁₃	#547	1	2	yes	—
408	C₂²×C₁₃	#575	1	2	yes	—
409	C₂²×C₁₃	#578	1	2	yes	—
410	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₁₃	—	2	2	no	—
412	C₄×C₁₃	—	2	2	no	—
413	C₄×C₁₃	—	2	2	no	—
414	C₄×C₁₃	—	2	2	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	—	4	2	no	—
420	C₄×C₁₃	—	4	2	no	—
421	C₄×C₁₃	—	4	2	no	—
422	C₄×C₁₃	—	4	2	no	—
423	C₄×C₁₃	#547	1	2	yes	—
424	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
425	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
426	C₂²×Q₈	—	2	1	no	—
427	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×Q₁₆	—	2	4	no	—
434	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
435	C₂×M₁₆	—	2	4	no	—
436	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
437	C₂²×C₈	—	2	4	no	—
438	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
440	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
445	#126	—	2	8	no	—
446	#126	—	2	8	no	—
447	#126	—	2	8	no	—
448	#125	—	2	8	no	—
449	#125	—	2	2	no	—
450	#125	C₂³×C₁₃	1	4	yes	—
451	#124	—	2	8	no	—
452	#123	—	2	8	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	2	no	—
457	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
458	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
459	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
460	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
461	C₄×Q₈	—	2	8	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
465	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
466	C₄×D₄	D₄×C₁₃	1	4	yes	—
467	C₄×D₄	C₂³×C₁₃	1	4	yes	—
468	#117	—	2	2	no	—
469	#117	—	2	2	no	—
470	#117	—	2	2	no	—
471	#117	—	2	8	no	—
472	#117	C₂³×C₁₃	1	4	yes	—
473	#117	C₂³×C₁₃	1	4	yes	—
474	#117	C₂³×C₁₃	1	4	yes	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	2	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	—	2	1	no	—
507	C₂×C₄²	—	2	1	no	—
508	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
509	#107	C₂³×C₁₃	1	4	yes	—
510	#107	C₂³×C₁₃	1	4	yes	—
511	#107	C₂³×C₁₃	1	4	yes	—
512	#107	C₂³×C₁₃	1	4	yes	—
513	#107	C₂³×C₁₃	1	4	yes	—
514	#106	C₂³×C₁₃	1	4	yes	—
515	#106	C₂³×C₁₃	1	4	yes	—
516	#106	C₂³×C₁₃	1	4	yes	—
517	#106	C₂³×C₁₃	1	4	yes	—
518	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
519	#103	C₂³×C₁₃	1	4	yes	—
520	#103	C₂³×C₁₃	1	4	yes	—
521	#103	C₂³×C₁₃	1	4	yes	—
522	#103	C₂³×C₁₃	1	4	yes	—
523	#103	C₂³×C₁₃	1	4	yes	—
524	#103	C₂³×C₁₃	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
526	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
527	#97	C₂³×C₁₃	1	4	yes	—
528	C₂×C₁₃	—	4	2	no	—
529	C₂×C₁₃	—	4	2	no	—
530	C₂×C₁₃	#3349	1	4	yes	direct product factor
531	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
532	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
533	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
534	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	4	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	4	4	no	—
544	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
545	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
567	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
571	Q₁₆	—	2	8	no	—
572	M₁₆	—	2	8	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	2	2	no	—
575	C₂×C₈	—	2	2	no	—
576	C₂×C₈	—	2	8	no	—
577	C₂×C₈	C₁₃×#41	1	4	yes	—
578	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
579	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
580	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
581	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
599	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
613	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
614	C₄²	—	2	4	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	4	no	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	4	no	—
619	C₄²	C₂×D₄×C₁₃	1	2	yes	—
620	C₄²	C₂⁴×C₁₃	1	2	yes	—
621	C₁₃	C₂×#3349	1	1	yes	characteristic, direct product factor, Sylow
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
629	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
630	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	2	2	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	4	8	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	2	no	—
638	D₄	—	4	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	2	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
672	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
673	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
674	C₈	—	2	2	no	—
675	C₈	—	2	2	no	—
676	C₈	—	2	2	no	—
677	C₈	C₂×C₁₃×#41	1	4	yes	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	4	no	—
686	C₂²	C₁₃×#547	1	2	yes	—
687	C₂²	C₁₃×#575	1	2	yes	—
688	C₂²	C₁₃×#578	1	2	yes	—
689	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	C₁₃×#547	1	2	yes	—
703	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
704	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
705	C₂	—	4	2	no	—
706	C₂	—	4	2	no	—
707	C₂	C₁₃×#3349	1	4	yes	direct product factor
708	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
709	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
710	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#3349	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#485	C₂	semidirect
7. C₂×C₁₃×#485	C₂	semidirect
8. C₂×C₁₃×#485	C₂	semidirect
9. C₂×C₁₃×#479	C₂	semidirect
10. C₂×C₁₃×#477	C₂	semidirect
11. C₂×C₁₃×#470	C₂	semidirect
12. C₂×C₁₃×#467	C₂	semidirect
13. C₂×C₁₃×#441	C₂	semidirect
15. C₂×C₁₃×#428	C₂	semidirect
16. C₂×C₁₃×#427	C₂	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#485	C₂²	semidirect
47. C₁₃×#485	C₂²	semidirect
48. C₁₃×#485	C₂²	semidirect
49. C₁₃×#484	C₂²	semidirect
50. C₁₃×#479	C₂²	semidirect
51. C₁₃×#477	C₂²	semidirect
52. C₁₃×#470	C₂²	semidirect
53. C₁₃×#467	C₂²	semidirect
54. C₁₃×#441	C₂²	semidirect
56. C₁₃×#428	C₂²	semidirect
57. C₁₃×#427	C₂²	semidirect
179. C₂×#3349	C₁₃	direct (N × H)
269. #3349	C₂×C₁₃	direct (N × H)
270. C₂×#501	C₂×C₁₃	semidirect
271. C₂×#484	C₂×C₁₃	semidirect
272. C₂×#485	C₂×C₁₃	semidirect
273. C₂×#485	C₂×C₁₃	semidirect
274. C₂×#485	C₂×C₁₃	semidirect
275. C₂×#479	C₂×C₁₃	semidirect
276. C₂×#477	C₂×C₁₃	semidirect
277. C₂×#470	C₂×C₁₃	semidirect
278. C₂×#467	C₂×C₁₃	semidirect
279. C₂×#441	C₂×C₁₃	semidirect
281. C₂×#428	C₂×C₁₃	semidirect
282. C₂×#427	C₂×C₁₃	semidirect
367. #501	C₂²×C₁₃	semidirect
368. #485	C₂²×C₁₃	semidirect
369. #485	C₂²×C₁₃	semidirect
370. #485	C₂²×C₁₃	semidirect
371. #484	C₂²×C₁₃	semidirect
372. #479	C₂²×C₁₃	semidirect
373. #477	C₂²×C₁₃	semidirect
374. #470	C₂²×C₁₃	semidirect
375. #467	C₂²×C₁₃	semidirect
376. #441	C₂²×C₁₃	semidirect
378. #428	C₂²×C₁₃	semidirect
379. #427	C₂²×C₁₃	semidirect
530. C₂×C₁₃	#3349	direct (N × H)
621. C₁₃	C₂×#3349	direct (N × H)
707. C₂	C₁₃×#3349	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#556	2
C₂×C₁₃×#552	2
C₁₃×#3349	2
C₂×C₁₃×#501	2
C₂×C₁₃×#484	2
C₂×C₁₃×#485	2
C₂×C₁₃×#479	2
C₂×C₁₃×#477	2
C₂×C₁₃×#470	2
C₂×C₁₃×#467	2
C₂×C₁₃×#441	2
C₂×C₁₃×#435	2
C₂×C₁₃×#428	2
C₂×C₁₃×#427	2
C₂×#3349	13

Subgroups — C2×C13×#3349 #15747580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3349 #15747580