Subgroups — C₂×C₁₃×#3510 #15749147

Order 3328.

7302 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#559	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#556	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#551	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#559	C₂²	1	64	yes	complemented
18	C₁₃×#556	C₂²	1	64	yes	complemented
19	C₁₃×#551	C₂²	1	128	yes	complemented
20	C₁₃×#542	C₂²	1	64	yes	complemented
21	C₁₃×#536	C₂²	1	16	yes	complemented
22	C₁₃×#535	C₂²	1	16	yes	—
23	C₁₃×#533	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#127	C₂²	1	2	yes	—
27	C₁₃×#529	C₂²	1	64	yes	complemented
28	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
30	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#124	C₂²	1	2	yes	—
32	C₂×C₁₃×#124	C₂²	1	2	yes	—
33	C₂×C₁₃×#124	C₂²	1	4	yes	—
34	C₂×C₁₃×#124	C₂²	1	2	yes	—
35	C₂×C₁₃×#124	C₂²	1	16	yes	complemented
36	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
38	C₂×C₁₃×#123	C₂²	1	4	yes	—
39	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
44	C₂×C₁₃×#121	C₂²	1	4	yes	—
45	C₂×C₁₃×#120	C₂²	1	4	yes	—
46	C₁₃×#519	C₂²	1	16	yes	complemented
47	C₁₃×#518	C₂²	1	16	yes	complemented
48	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
51	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
52	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
53	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
54	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
55	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
56	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#117	C₂²	1	4	yes	—
62	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
63	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
64	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
68	C₂⁵×C₁₃	C₂³	1	2	yes	—
69	C₂×C₁₃×#41	—	2	8	no	—
70	C₂×C₁₃×#41	C₂³	1	8	yes	—
71	C₂²×Q₈×C₁₃	—	2	8	no	—
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃	—	2	8	no	—
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
91	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
92	C₁₃×#127	C₂³	1	16	yes	—
93	C₁₃×#126	C₂³	1	64	yes	complemented
94	C₁₃×#126	C₂³	1	64	yes	complemented
95	C₁₃×#125	C₂³	1	16	yes	complemented
96	C₁₃×#124	C₂³	1	16	yes	—
97	C₁₃×#124	C₂³	1	16	yes	—
98	C₁₃×#124	C₂³	1	32	yes	—
99	C₁₃×#124	C₂³	1	16	yes	—
100	C₁₃×#124	C₂³	1	16	yes	complemented
101	C₁₃×#124	C₂³	1	64	yes	complemented
102	C₁₃×#123	C₂³	1	32	yes	—
103	C₁₃×#123	C₂³	1	64	yes	complemented
104	C₁₃×#123	C₂³	1	64	yes	complemented
105	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
107	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
108	C₁₃×#121	C₂³	1	32	yes	—
109	C₁₃×#120	C₂³	1	32	yes	—
110	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
111	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
112	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
113	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
114	C₄×D₄×C₁₃	C₂³	1	32	yes	—
115	C₄×D₄×C₁₃	C₂³	1	32	yes	—
116	C₄×D₄×C₁₃	C₂³	1	32	yes	—
117	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
118	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
119	C₁₃×#117	C₂³	1	8	yes	—
120	C₁₃×#117	C₂³	1	8	yes	—
121	C₁₃×#117	C₂³	1	8	yes	—
122	C₁₃×#117	C₂³	1	32	yes	—
123	C₁₃×#117	C₂³	1	16	yes	complemented
124	C₁₃×#117	C₂³	1	64	yes	complemented
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
155	C₂×#3510	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂⁴×C₁₃	—	2	8	no	—
157	C₂⁴×C₁₃	—	4	8	no	—
158	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
159	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
160	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
162	C₁₃×#41	—	2	32	no	—
163	C₂×Q₈×C₁₃	—	2	8	no	—
164	C₂×Q₈×C₁₃	—	2	8	no	—
165	C₂×Q₈×C₁₃	—	2	32	no	—
166	C₂×Q₈×C₁₃	—	2	4	no	—
167	C₂×Q₈×C₁₃	—	4	8	no	—
168	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
169	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
170	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
171	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
172	C₂×D₄×C₁₃	—	2	8	no	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	32	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	4	16	no	—
178	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
179	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
183	C₂²×C₄×C₁₃	—	2	8	no	—
184	C₂²×C₄×C₁₃	—	2	8	no	—
185	C₂²×C₄×C₁₃	—	4	8	no	—
186	C₂²×C₄×C₁₃	—	4	16	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	#41	1	8	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
206	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
211	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
212	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
213	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
214	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
215	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
216	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
217	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
218	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
219	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
220	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
221	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
222	C₄²×C₁₃	C₂⁴	1	4	yes	—
223	C₄²×C₁₃	C₂⁴	1	4	yes	—
224	C₄²×C₁₃	C₂⁴	1	8	yes	—
225	C₄²×C₁₃	C₂⁴	1	8	yes	—
226	C₄²×C₁₃	C₂⁴	1	16	yes	—
227	C₄²×C₁₃	C₂⁴	1	32	yes	—
228	C₄²×C₁₃	C₂⁴	1	8	yes	—
229	C₄²×C₁₃	C₂⁴	1	8	yes	—
230	#3510	C₂×C₁₃	1	32	yes	direct product factor
231	C₂×#559	C₂×C₁₃	1	4	yes	complemented
232	C₂×#556	C₂×C₁₃	1	4	yes	complemented
233	C₂×#551	C₂×C₁₃	1	8	yes	complemented
234	C₂×#542	C₂×C₁₃	1	4	yes	complemented
235	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#535	C₂×C₁₃	1	1	yes	characteristic
237	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂×#529	C₂×C₁₃	1	4	yes	complemented
239	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
242	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	2	8	no	—
246	C₂³×C₁₃	—	2	8	no	—
247	C₂³×C₁₃	—	2	16	no	—
248	C₂³×C₁₃	—	2	16	no	—
249	C₂³×C₁₃	—	4	16	no	—
250	C₂³×C₁₃	—	8	16	no	—
251	C₂³×C₁₃	C₂×#41	1	4	yes	—
252	C₂³×C₁₃	C₂⁵	1	8	yes	—
253	C₂³×C₁₃	C₂⁵	1	4	yes	—
254	C₂³×C₁₃	C₂⁵	1	2	yes	—
255	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
256	Q₈×C₁₃	—	2	16	no	—
257	Q₈×C₁₃	—	2	16	no	—
258	Q₈×C₁₃	—	2	8	no	—
259	Q₈×C₁₃	—	4	16	no	—
260	D₄×C₁₃	—	2	16	no	—
261	D₄×C₁₃	—	2	16	no	—
262	D₄×C₁₃	—	2	16	no	—
263	D₄×C₁₃	—	2	8	no	—
264	D₄×C₁₃	—	4	32	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	16	no	—
267	C₂×C₄×C₁₃	—	2	8	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	2	8	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	8	no	—
273	C₂×C₄×C₁₃	—	2	16	no	—
274	C₂×C₄×C₁₃	—	4	16	no	—
275	C₂×C₄×C₁₃	—	4	32	no	—
276	C₂×C₄×C₁₃	—	4	8	no	—
277	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
278	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
279	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
280	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
283	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
284	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
285	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
286	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
287	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
288	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
289	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
290	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
292	#559	C₂²×C₁₃	1	64	yes	complemented
293	#556	C₂²×C₁₃	1	64	yes	complemented
294	#551	C₂²×C₁₃	1	128	yes	complemented
295	#542	C₂²×C₁₃	1	64	yes	complemented
296	#536	C₂²×C₁₃	1	16	yes	complemented
297	#535	C₂²×C₁₃	1	16	yes	—
298	#533	C₂²×C₁₃	1	16	yes	complemented
299	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
300	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
301	C₂×#127	C₂²×C₁₃	1	2	yes	—
302	#529	C₂²×C₁₃	1	64	yes	complemented
303	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
304	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
305	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
306	C₂×#124	C₂²×C₁₃	1	2	yes	—
307	C₂×#124	C₂²×C₁₃	1	2	yes	—
308	C₂×#124	C₂²×C₁₃	1	4	yes	—
309	C₂×#124	C₂²×C₁₃	1	2	yes	—
310	C₂×#124	C₂²×C₁₃	1	16	yes	complemented
311	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
312	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
313	C₂×#123	C₂²×C₁₃	1	4	yes	—
314	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
315	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
316	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
317	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
318	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
319	C₂×#121	C₂²×C₁₃	1	4	yes	—
320	C₂×#120	C₂²×C₁₃	1	4	yes	—
321	#519	C₂²×C₁₃	1	16	yes	complemented
322	#518	C₂²×C₁₃	1	16	yes	complemented
323	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
324	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
325	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
326	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
327	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
328	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
329	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
330	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
331	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
332	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
333	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#117	C₂²×C₁₃	1	4	yes	—
337	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
338	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
339	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
340	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
341	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	2	8	no	—
345	C₂²×C₁₃	—	2	4	no	—
346	C₂²×C₁₃	—	2	8	no	—
347	C₂²×C₁₃	—	2	8	no	—
348	C₂²×C₁₃	—	2	16	no	—
349	C₂²×C₁₃	—	4	8	no	—
350	C₂²×C₁₃	—	4	16	no	—
351	C₂²×C₁₃	—	8	16	no	—
352	C₂²×C₁₃	C₂²×#41	1	4	yes	—
353	C₂²×C₁₃	C₂²×#41	1	2	yes	—
354	C₂²×C₁₃	#585	1	4	yes	—
355	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	2	8	no	—
358	C₄×C₁₃	—	2	4	no	—
359	C₄×C₁₃	—	2	8	no	—
360	C₄×C₁₃	—	2	8	no	—
361	C₄×C₁₃	—	2	4	no	—
362	C₄×C₁₃	—	2	8	no	—
363	C₄×C₁₃	C₂²×#41	1	4	yes	—
364	C₄×C₁₃	C₂²×#41	1	4	yes	—
365	C₂⁵	C₂³×C₁₃	1	2	yes	—
366	C₂×#41	—	2	8	no	—
367	C₂×#41	C₂³×C₁₃	1	8	yes	—
368	C₂²×Q₈	—	2	8	no	—
369	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
370	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
371	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
373	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
374	C₂²×D₄	—	2	8	no	—
375	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
378	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
380	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
381	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
383	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
388	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
389	#127	C₂³×C₁₃	1	16	yes	—
390	#126	C₂³×C₁₃	1	64	yes	complemented
391	#126	C₂³×C₁₃	1	64	yes	complemented
392	#125	C₂³×C₁₃	1	16	yes	complemented
393	#124	C₂³×C₁₃	1	16	yes	—
394	#124	C₂³×C₁₃	1	16	yes	—
395	#124	C₂³×C₁₃	1	32	yes	—
396	#124	C₂³×C₁₃	1	16	yes	—
397	#124	C₂³×C₁₃	1	16	yes	complemented
398	#124	C₂³×C₁₃	1	64	yes	complemented
399	#123	C₂³×C₁₃	1	32	yes	—
400	#123	C₂³×C₁₃	1	64	yes	complemented
401	#123	C₂³×C₁₃	1	64	yes	complemented
402	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
403	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
404	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
405	#121	C₂³×C₁₃	1	32	yes	—
406	#120	C₂³×C₁₃	1	32	yes	—
407	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
408	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
409	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
410	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
411	C₄×D₄	C₂³×C₁₃	1	32	yes	—
412	C₄×D₄	C₂³×C₁₃	1	32	yes	—
413	C₄×D₄	C₂³×C₁₃	1	32	yes	—
414	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
415	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
416	#117	C₂³×C₁₃	1	8	yes	—
417	#117	C₂³×C₁₃	1	8	yes	—
418	#117	C₂³×C₁₃	1	8	yes	—
419	#117	C₂³×C₁₃	1	32	yes	—
420	#117	C₂³×C₁₃	1	16	yes	complemented
421	#117	C₂³×C₁₃	1	64	yes	complemented
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
442	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
444	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
447	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
449	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
450	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
452	C₂×C₁₃	—	2	4	no	—
453	C₂×C₁₃	—	4	4	no	—
454	C₂×C₁₃	—	4	8	no	—
455	C₂×C₁₃	#3510	1	4	yes	direct product factor
456	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
457	C₂×C₁₃	C₂×#585	1	2	yes	—
458	C₂⁴	—	2	8	no	—
459	C₂⁴	—	4	8	no	—
460	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
461	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
462	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
464	#41	—	2	32	no	—
465	C₂×Q₈	—	2	8	no	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	2	32	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	4	8	no	—
470	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
471	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
472	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
473	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	8	no	—
477	C₂×D₄	—	2	32	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	4	16	no	—
480	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
481	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
482	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
483	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
484	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	4	8	no	—
488	C₂²×C₄	—	4	16	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	C₁₃×#41	1	8	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
500	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
506	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
507	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
508	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
509	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
510	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
511	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
512	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
513	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
514	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
515	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
516	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
517	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
518	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
519	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
520	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
521	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
522	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
523	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
524	C₄²	C₂⁴×C₁₃	1	4	yes	—
525	C₄²	C₂⁴×C₁₃	1	4	yes	—
526	C₄²	C₂⁴×C₁₃	1	8	yes	—
527	C₄²	C₂⁴×C₁₃	1	8	yes	—
528	C₄²	C₂⁴×C₁₃	1	16	yes	—
529	C₄²	C₂⁴×C₁₃	1	32	yes	—
530	C₄²	C₂⁴×C₁₃	1	8	yes	—
531	C₄²	C₂⁴×C₁₃	1	8	yes	—
532	C₁₃	C₂×#3510	1	1	yes	characteristic, direct product factor, Sylow
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	2	8	no	—
537	C₂³	—	2	16	no	—
538	C₂³	—	2	16	no	—
539	C₂³	—	4	16	no	—
540	C₂³	—	8	16	no	—
541	C₂³	C₂×C₁₃×#41	1	4	yes	—
542	C₂³	C₂⁵×C₁₃	1	8	yes	—
543	C₂³	C₂⁵×C₁₃	1	4	yes	—
544	C₂³	C₂⁵×C₁₃	1	2	yes	—
545	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
546	Q₈	—	2	16	no	—
547	Q₈	—	2	16	no	—
548	Q₈	—	2	8	no	—
549	Q₈	—	4	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	16	no	—
552	D₄	—	2	16	no	—
553	D₄	—	2	8	no	—
554	D₄	—	4	32	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	16	no	—
564	C₂×C₄	—	4	16	no	—
565	C₂×C₄	—	4	32	no	—
566	C₂×C₄	—	4	8	no	—
567	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
568	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
569	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
570	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
571	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
572	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
573	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
574	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
575	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
576	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
577	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
578	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	16	no	—
585	C₂²	—	4	8	no	—
586	C₂²	—	4	16	no	—
587	C₂²	—	8	16	no	—
588	C₂²	C₂²×C₁₃×#41	1	4	yes	—
589	C₂²	C₂²×C₁₃×#41	1	2	yes	—
590	C₂²	C₁₃×#585	1	4	yes	—
591	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	4	no	—
595	C₄	—	2	8	no	—
596	C₄	—	2	8	no	—
597	C₄	—	2	4	no	—
598	C₄	—	2	8	no	—
599	C₄	C₂²×C₁₃×#41	1	4	yes	—
600	C₄	C₂²×C₁₃×#41	1	4	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	4	8	no	—
603	C₂	—	4	4	no	—
604	C₂	C₁₃×#3510	1	4	yes	direct product factor
605	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
606	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂×C₁₃×#535	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	direct (N × H)
2. C₂×C₁₃×#559	C₂	semidirect
3. C₂×C₁₃×#556	C₂	semidirect
4. C₂×C₁₃×#551	C₂	semidirect
5. C₂×C₁₃×#542	C₂	semidirect
6. C₂×C₁₃×#536	C₂	semidirect
8. C₂×C₁₃×#533	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂²×C₁₃×#124	C₂	semidirect
11. C₂×C₁₃×#519	C₂	semidirect
12. C₂×C₁₃×#518	C₂	semidirect
13. C₂×C₄×C₁₃×#41	C₂	semidirect
17. C₁₃×#559	C₂²	semidirect
18. C₁₃×#556	C₂²	semidirect
19. C₁₃×#551	C₂²	semidirect
20. C₁₃×#542	C₂²	semidirect
21. C₁₃×#536	C₂²	semidirect
23. C₁₃×#533	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₁₃×#529	C₂²	semidirect
28. C₂×C₁₃×#126	C₂²	semidirect
29. C₂×C₁₃×#126	C₂²	semidirect
30. C₂×C₁₃×#125	C₂²	semidirect
35. C₂×C₁₃×#124	C₂²	semidirect
36. C₂×C₁₃×#124	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
39. C₂×C₁₃×#123	C₂²	semidirect
40. C₂×C₁₃×#123	C₂²	semidirect
42. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
43. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₁₃×#519	C₂²	semidirect
47. C₁₃×#518	C₂²	semidirect
48. C₄×C₁₃×#41	C₂²	semidirect
49. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
50. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
51. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
52. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
56. C₂×C₄×D₄×C₁₃	C₂²	semidirect
57. C₂×C₄×D₄×C₁₃	C₂²	semidirect
62. C₂×C₁₃×#117	C₂²	semidirect
63. C₂×C₁₃×#117	C₂²	semidirect
67. C₂²×C₄²×C₁₃	C₂²	semidirect
90. C₁₃×C₄⋊Q₈	C₂³	semidirect
91. C₁₃×C₄⋊Q₈	C₂³	semidirect
93. C₁₃×#126	C₂³	semidirect
94. C₁₃×#126	C₂³	semidirect
95. C₁₃×#125	C₂³	semidirect
100. C₁₃×#124	C₂³	semidirect
101. C₁₃×#124	C₂³	semidirect
103. C₁₃×#123	C₂³	semidirect
104. C₁₃×#123	C₂³	semidirect
106. C₁₃×C₂²⋊Q₈	C₂³	semidirect
107. C₁₃×C₂²⋊Q₈	C₂³	semidirect
110. C₄×Q₈×C₁₃	C₂³	semidirect
111. C₄×Q₈×C₁₃	C₂³	semidirect
112. C₄×Q₈×C₁₃	C₂³	semidirect
113. C₄×Q₈×C₁₃	C₂³	semidirect
117. C₄×D₄×C₁₃	C₂³	semidirect
118. C₄×D₄×C₁₃	C₂³	semidirect
123. C₁₃×#117	C₂³	semidirect
124. C₁₃×#117	C₂³	semidirect
154. C₂×C₄²×C₁₃	C₂³	semidirect
155. C₂×#3510	C₁₃	direct (N × H)
230. #3510	C₂×C₁₃	direct (N × H)
231. C₂×#559	C₂×C₁₃	semidirect
232. C₂×#556	C₂×C₁₃	semidirect
233. C₂×#551	C₂×C₁₃	semidirect
234. C₂×#542	C₂×C₁₃	semidirect
235. C₂×#536	C₂×C₁₃	semidirect
237. C₂×#533	C₂×C₁₃	semidirect
238. C₂×#529	C₂×C₁₃	semidirect
239. C₂²×#124	C₂×C₁₃	semidirect
240. C₂×#519	C₂×C₁₃	semidirect
241. C₂×#518	C₂×C₁₃	semidirect
242. C₂×C₄×#41	C₂×C₁₃	semidirect
292. #559	C₂²×C₁₃	semidirect
293. #556	C₂²×C₁₃	semidirect
294. #551	C₂²×C₁₃	semidirect
295. #542	C₂²×C₁₃	semidirect
296. #536	C₂²×C₁₃	semidirect
298. #533	C₂²×C₁₃	semidirect
299. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
300. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
302. #529	C₂²×C₁₃	semidirect
303. C₂×#126	C₂²×C₁₃	semidirect
304. C₂×#126	C₂²×C₁₃	semidirect
305. C₂×#125	C₂²×C₁₃	semidirect
310. C₂×#124	C₂²×C₁₃	semidirect
311. C₂×#124	C₂²×C₁₃	semidirect
312. C₂×#124	C₂²×C₁₃	semidirect
314. C₂×#123	C₂²×C₁₃	semidirect
315. C₂×#123	C₂²×C₁₃	semidirect
317. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
318. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
321. #519	C₂²×C₁₃	semidirect
322. #518	C₂²×C₁₃	semidirect
323. C₄×#41	C₂²×C₁₃	semidirect
324. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
325. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
326. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
327. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
331. C₂×C₄×D₄	C₂²×C₁₃	semidirect
332. C₂×C₄×D₄	C₂²×C₁₃	semidirect
337. C₂×#117	C₂²×C₁₃	semidirect
338. C₂×#117	C₂²×C₁₃	semidirect
342. C₂²×C₄²	C₂²×C₁₃	semidirect
387. C₄⋊Q₈	C₂³×C₁₃	semidirect
388. C₄⋊Q₈	C₂³×C₁₃	semidirect
390. #126	C₂³×C₁₃	semidirect
391. #126	C₂³×C₁₃	semidirect
392. #125	C₂³×C₁₃	semidirect
397. #124	C₂³×C₁₃	semidirect
398. #124	C₂³×C₁₃	semidirect
400. #123	C₂³×C₁₃	semidirect
401. #123	C₂³×C₁₃	semidirect
403. C₂²⋊Q₈	C₂³×C₁₃	semidirect
404. C₂²⋊Q₈	C₂³×C₁₃	semidirect
407. C₄×Q₈	C₂³×C₁₃	semidirect
408. C₄×Q₈	C₂³×C₁₃	semidirect
409. C₄×Q₈	C₂³×C₁₃	semidirect
410. C₄×Q₈	C₂³×C₁₃	semidirect
414. C₄×D₄	C₂³×C₁₃	semidirect
415. C₄×D₄	C₂³×C₁₃	semidirect
420. #117	C₂³×C₁₃	semidirect
421. #117	C₂³×C₁₃	semidirect
451. C₂×C₄²	C₂³×C₁₃	semidirect
455. C₂×C₁₃	#3510	direct (N × H)
532. C₁₃	C₂×#3510	direct (N × H)
604. C₂	C₁₃×#3510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3510	2
C₂×C₁₃×#559	2
C₂×C₁₃×#556	2
C₂×C₁₃×#551	2
C₂×C₁₃×#542	2
C₂×C₁₃×#536	2
C₂×C₁₃×#535	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#124	2
C₂×C₁₃×#519	2
C₂×C₁₃×#518	2
C₂×C₄×C₁₃×#41	2
C₂×#3510	13

Subgroups — C2×C13×#3510 #15749147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3510 #15749147