Subgroups — C₂×C₁₃×#3519 #15749110

Order 3328.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3519	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#546	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
9	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄²×C₁₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
16	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
21	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
24	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
25	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#555	C₂²	1	16	yes	complemented
27	C₁₃×#554	C₂²	1	16	yes	complemented
28	C₁₃×#553	C₂²	1	32	yes	complemented
29	C₁₃×#553	C₂²	1	32	yes	complemented
30	C₁₃×#550	C₂²	1	16	yes	complemented
31	C₁₃×#546	C₂²	1	64	yes	complemented
32	C₁₃×#546	C₂²	1	32	yes	complemented
33	D₄²×C₁₃	C₂²	1	16	yes	complemented
34	D₄²×C₁₃	C₂²	1	32	yes	complemented
35	C₁₃×#540	C₂²	1	32	yes	complemented
36	C₁₃×#538	C₂²	1	64	yes	complemented
37	C₁₃×#532	C₂²	1	16	yes	complemented
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
41	C₁₃×#529	C₂²	1	16	yes	complemented
42	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
46	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
48	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
49	C₁₃×#525	C₂²	1	32	yes	complemented
50	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
51	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
52	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
53	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
54	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
59	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
60	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
61	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
62	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
63	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
64	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
65	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
66	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
67	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
68	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
69	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
70	C₂×C₁₃×#121	C₂²	1	32	yes	complemented
71	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
72	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
73	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
74	C₁₃×#518	C₂²	1	32	yes	complemented
75	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
77	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
85	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
86	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
89	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
92	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
93	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
94	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
95	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
99	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₁₃	C₂³	1	2	yes	—
102	C₂⁵×C₁₃	C₂³	1	4	yes	—
103	C₂×C₁₃×#41	—	4	8	no	—
104	C₂×C₁₃×#41	—	4	8	no	—
105	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
106	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	—	2	8	no	—
110	C₂²×D₄×C₁₃	—	2	16	no	—
111	C₂²×D₄×C₁₃	—	4	8	no	—
112	C₂²×D₄×C₁₃	—	4	16	no	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
119	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
123	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
130	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
131	C₂³×C₄×C₁₃	—	4	8	no	—
132	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
140	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
142	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
143	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
145	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
146	C₁₃×#127	C₂³	1	8	yes	complemented
147	C₁₃×#127	C₂³	1	16	yes	complemented
148	C₁₃×#126	C₂³	1	16	yes	complemented
149	C₁₃×#126	C₂³	1	32	yes	complemented
150	C₁₃×#125	C₂³	1	8	yes	complemented
151	C₁₃×#125	C₂³	1	16	yes	complemented
152	C₁₃×#124	C₂³	1	8	yes	complemented
153	C₁₃×#124	C₂³	1	16	yes	complemented
154	C₁₃×#124	C₂³	1	32	yes	complemented
155	C₁₃×#123	C₂³	1	32	yes	complemented
156	C₁₃×#123	C₂³	1	16	yes	complemented
157	C₁₃×#123	C₂³	1	32	yes	complemented
158	C₁₃×#123	C₂³	1	32	yes	complemented
159	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
160	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
161	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
162	C₁₃×#121	C₂³	1	8	yes	—
163	C₁₃×#121	C₂³	1	16	yes	complemented
164	C₁₃×#121	C₂³	1	32	yes	complemented
165	C₁₃×#121	C₂³	1	32	yes	complemented
166	C₁₃×#121	C₂³	1	16	yes	complemented
167	C₁₃×#121	C₂³	1	16	yes	complemented
168	C₁₃×#121	C₂³	1	16	yes	complemented
169	C₁₃×#121	C₂³	1	16	yes	complemented
170	C₁₃×#121	C₂³	1	32	yes	complemented
171	C₁₃×#121	C₂³	1	32	yes	complemented
172	C₁₃×#121	C₂³	1	16	yes	complemented
173	C₁₃×#121	C₂³	1	16	yes	complemented
174	C₁₃×#121	C₂³	1	32	yes	complemented
175	C₁₃×#120	C₂³	1	32	yes	complemented
176	C₁₃×#120	C₂³	1	32	yes	complemented
177	C₁₃×#120	C₂³	1	32	yes	complemented
178	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
179	C₄×D₄×C₁₃	C₂³	1	8	yes	—
180	C₄×D₄×C₁₃	C₂³	1	8	yes	—
181	C₄×D₄×C₁₃	C₂³	1	16	yes	—
182	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
183	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
184	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
185	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
186	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
187	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
188	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
189	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
190	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
191	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
192	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
193	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
194	C₁₃×#117	C₂³	1	16	yes	complemented
195	C₁₃×#117	C₂³	1	16	yes	complemented
196	C₁₃×#117	C₂³	1	16	yes	complemented
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
211	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
228	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
229	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
230	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
231	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
236	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
237	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
238	C₂×#3519	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂⁴×C₁₃	—	2	8	no	—
240	C₂⁴×C₁₃	—	2	8	no	—
241	C₂⁴×C₁₃	—	2	16	no	—
242	C₂⁴×C₁₃	—	4	4	no	—
243	C₂⁴×C₁₃	—	4	8	no	—
244	C₂⁴×C₁₃	—	4	8	no	—
245	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
246	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
247	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
248	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
249	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
250	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
252	C₁₃×#41	—	4	32	no	—
253	C₁₃×#41	—	4	32	no	—
254	C₂×Q₈×C₁₃	—	2	4	no	—
255	C₂×Q₈×C₁₃	—	4	4	no	—
256	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
257	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
258	C₂×D₄×C₁₃	—	2	8	no	—
259	C₂×D₄×C₁₃	—	2	16	no	—
260	C₂×D₄×C₁₃	—	2	8	no	—
261	C₂×D₄×C₁₃	—	2	16	no	—
262	C₂×D₄×C₁₃	—	2	32	no	—
263	C₂×D₄×C₁₃	—	2	64	no	—
264	C₂×D₄×C₁₃	—	2	4	no	—
265	C₂×D₄×C₁₃	—	2	8	no	—
266	C₂×D₄×C₁₃	—	2	4	no	—
267	C₂×D₄×C₁₃	—	2	8	no	—
268	C₂×D₄×C₁₃	—	4	32	no	—
269	C₂×D₄×C₁₃	—	4	8	no	—
270	C₂×D₄×C₁₃	—	4	8	no	—
271	C₂×D₄×C₁₃	—	4	8	no	—
272	C₂×D₄×C₁₃	—	4	4	no	—
273	C₂×D₄×C₁₃	—	4	8	no	—
274	C₂×D₄×C₁₃	—	4	64	no	—
275	C₂×D₄×C₁₃	#41	1	8	yes	complemented
276	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
277	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
278	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
280	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
282	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
283	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
284	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
285	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
287	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₁₃	—	2	4	no	—
291	C₂²×C₄×C₁₃	—	2	4	no	—
292	C₂²×C₄×C₁₃	—	2	8	no	—
293	C₂²×C₄×C₁₃	—	2	4	no	—
294	C₂²×C₄×C₁₃	—	2	8	no	—
295	C₂²×C₄×C₁₃	—	2	8	no	—
296	C₂²×C₄×C₁₃	—	4	32	no	—
297	C₂²×C₄×C₁₃	—	4	4	no	—
298	C₂²×C₄×C₁₃	—	4	4	no	—
299	C₂²×C₄×C₁₃	—	4	4	no	—
300	C₂²×C₄×C₁₃	—	4	8	no	—
301	C₂²×C₄×C₁₃	—	4	8	no	—
302	C₂²×C₄×C₁₃	—	4	8	no	—
303	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
308	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
320	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
321	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
322	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
323	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
324	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
335	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
336	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
340	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
345	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
347	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
349	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
350	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
351	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
352	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
353	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
354	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
355	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
356	C₄²×C₁₃	C₂⁴	1	4	yes	—
357	C₄²×C₁₃	C₂⁴	1	4	yes	—
358	C₄²×C₁₃	C₂⁴	1	4	yes	—
359	C₄²×C₁₃	C₂⁴	1	4	yes	—
360	C₄²×C₁₃	C₂⁴	1	16	yes	—
361	C₄²×C₁₃	C₂⁴	1	8	yes	—
362	#3519	C₂×C₁₃	1	32	yes	direct product factor
363	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
365	C₂×#553	C₂×C₁₃	1	2	yes	complemented
366	C₂×#553	C₂×C₁₃	1	2	yes	complemented
367	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂×#546	C₂×C₁₃	1	4	yes	complemented
369	C₂×#546	C₂×C₁₃	1	2	yes	complemented
370	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
371	C₂×D₄²	C₂×C₁₃	1	2	yes	complemented
372	C₂×#540	C₂×C₁₃	1	2	yes	complemented
373	C₂×#538	C₂×C₁₃	1	4	yes	complemented
374	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
375	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
376	C₂×#525	C₂×C₁₃	1	2	yes	complemented
377	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
378	C₂×#518	C₂×C₁₃	1	2	yes	complemented
379	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	4	no	—
383	C₂³×C₁₃	—	2	4	no	—
384	C₂³×C₁₃	—	2	4	no	—
385	C₂³×C₁₃	—	2	16	no	—
386	C₂³×C₁₃	—	2	4	no	—
387	C₂³×C₁₃	—	2	8	no	—
388	C₂³×C₁₃	—	2	4	no	—
389	C₂³×C₁₃	—	2	8	no	—
390	C₂³×C₁₃	—	2	8	no	—
391	C₂³×C₁₃	—	2	4	no	—
392	C₂³×C₁₃	—	2	4	no	—
393	C₂³×C₁₃	—	2	16	no	—
394	C₂³×C₁₃	—	2	4	no	—
395	C₂³×C₁₃	—	2	32	no	—
396	C₂³×C₁₃	—	4	8	no	—
397	C₂³×C₁₃	—	4	16	no	—
398	C₂³×C₁₃	—	4	16	no	—
399	C₂³×C₁₃	—	4	32	no	—
400	C₂³×C₁₃	—	8	32	no	—
401	C₂³×C₁₃	C₂×#41	1	8	yes	—
402	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
403	C₂³×C₁₃	C₂⁵	1	4	yes	—
404	C₂³×C₁₃	C₂⁵	1	4	yes	—
405	C₂³×C₁₃	C₂⁵	1	8	yes	—
406	C₂³×C₁₃	C₂⁵	1	4	yes	—
407	C₂³×C₁₃	C₂⁵	1	2	yes	—
408	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
409	Q₈×C₁₃	—	2	8	no	—
410	Q₈×C₁₃	—	4	8	no	—
411	D₄×C₁₃	—	2	16	no	—
412	D₄×C₁₃	—	2	32	no	—
413	D₄×C₁₃	—	2	16	no	—
414	D₄×C₁₃	—	2	32	no	—
415	D₄×C₁₃	—	2	8	no	—
416	D₄×C₁₃	—	2	16	no	—
417	D₄×C₁₃	—	2	8	no	—
418	D₄×C₁₃	—	2	16	no	—
419	D₄×C₁₃	—	4	16	no	—
420	D₄×C₁₃	—	4	16	no	—
421	D₄×C₁₃	—	4	16	no	—
422	D₄×C₁₃	—	4	8	no	—
423	D₄×C₁₃	—	4	16	no	—
424	D₄×C₁₃	C₂×#41	1	16	yes	complemented
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	4	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	4	no	—
430	C₂×C₄×C₁₃	—	2	4	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	8	no	—
433	C₂×C₄×C₁₃	—	2	4	no	—
434	C₂×C₄×C₁₃	—	2	8	no	—
435	C₂×C₄×C₁₃	—	2	4	no	—
436	C₂×C₄×C₁₃	—	2	8	no	—
437	C₂×C₄×C₁₃	—	2	16	no	—
438	C₂×C₄×C₁₃	—	2	8	no	—
439	C₂×C₄×C₁₃	—	2	16	no	—
440	C₂×C₄×C₁₃	—	2	16	no	—
441	C₂×C₄×C₁₃	—	4	8	no	—
442	C₂×C₄×C₁₃	—	4	8	no	—
443	C₂×C₄×C₁₃	—	4	8	no	—
444	C₂×C₄×C₁₃	—	4	16	no	—
445	C₂×C₄×C₁₃	—	4	16	no	—
446	C₂×C₄×C₁₃	—	4	16	no	—
447	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
448	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
449	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
450	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
451	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
452	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
453	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
454	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
455	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
456	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
457	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
458	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
459	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
460	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
461	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
462	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
463	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
464	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
465	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
466	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
467	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
468	#555	C₂²×C₁₃	1	16	yes	complemented
469	#554	C₂²×C₁₃	1	16	yes	complemented
470	#553	C₂²×C₁₃	1	32	yes	complemented
471	#553	C₂²×C₁₃	1	32	yes	complemented
472	#550	C₂²×C₁₃	1	16	yes	complemented
473	#546	C₂²×C₁₃	1	64	yes	complemented
474	#546	C₂²×C₁₃	1	32	yes	complemented
475	D₄²	C₂²×C₁₃	1	16	yes	complemented
476	D₄²	C₂²×C₁₃	1	32	yes	complemented
477	#540	C₂²×C₁₃	1	32	yes	complemented
478	#538	C₂²×C₁₃	1	64	yes	complemented
479	#532	C₂²×C₁₃	1	16	yes	complemented
480	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
483	#529	C₂²×C₁₃	1	16	yes	complemented
484	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
485	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
486	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
488	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
490	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
491	#525	C₂²×C₁₃	1	32	yes	complemented
492	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
493	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
494	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
495	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
496	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
498	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
499	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
501	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
502	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
503	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
504	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
505	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
506	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
507	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
508	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
509	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
510	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
511	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
512	C₂×#121	C₂²×C₁₃	1	32	yes	complemented
513	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
514	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
515	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
516	#518	C₂²×C₁₃	1	32	yes	complemented
517	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
520	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
522	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
524	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
526	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
527	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
528	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
529	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
530	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
531	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
533	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
534	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
535	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
536	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
537	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
539	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
540	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
541	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
542	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
543	C₂²×C₁₃	—	2	2	no	—
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	2	4	no	—
546	C₂²×C₁₃	—	2	4	no	—
547	C₂²×C₁₃	—	2	8	no	—
548	C₂²×C₁₃	—	2	16	no	—
549	C₂²×C₁₃	—	2	4	no	—
550	C₂²×C₁₃	—	2	4	no	—
551	C₂²×C₁₃	—	2	8	no	—
552	C₂²×C₁₃	—	2	4	no	—
553	C₂²×C₁₃	—	2	8	no	—
554	C₂²×C₁₃	—	2	8	no	—
555	C₂²×C₁₃	—	2	4	no	—
556	C₂²×C₁₃	—	2	4	no	—
557	C₂²×C₁₃	—	2	4	no	—
558	C₂²×C₁₃	—	4	32	no	—
559	C₂²×C₁₃	—	4	8	no	—
560	C₂²×C₁₃	—	4	16	no	—
561	C₂²×C₁₃	—	4	8	no	—
562	C₂²×C₁₃	—	8	32	no	—
563	C₂²×C₁₃	C₂²×#41	1	8	yes	—
564	C₂²×C₁₃	C₂²×#41	1	2	yes	—
565	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
566	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
567	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
568	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
569	C₄×C₁₃	—	2	2	no	—
570	C₄×C₁₃	—	2	4	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	2	2	no	—
573	C₄×C₁₃	—	2	4	no	—
574	C₄×C₁₃	—	2	4	no	—
575	C₄×C₁₃	—	2	2	no	—
576	C₄×C₁₃	—	2	4	no	—
577	C₄×C₁₃	—	2	8	no	—
578	C₄×C₁₃	—	2	4	no	—
579	C₄×C₁₃	C₂²×#41	1	4	yes	—
580	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
581	C₂⁵	C₂³×C₁₃	1	2	yes	—
582	C₂⁵	C₂³×C₁₃	1	4	yes	—
583	C₂×#41	—	4	8	no	—
584	C₂×#41	—	4	8	no	—
585	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
586	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
587	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
588	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
589	C₂²×D₄	—	2	8	no	—
590	C₂²×D₄	—	2	16	no	—
591	C₂²×D₄	—	4	8	no	—
592	C₂²×D₄	—	4	16	no	—
593	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
594	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
595	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
597	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
598	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
599	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
600	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
603	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
604	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
606	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
607	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
608	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
610	C₂²×D₄	C₂³×C₁₃	1	32	yes	complemented
611	C₂³×C₄	—	4	8	no	—
612	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
616	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
617	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
619	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
620	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
621	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
622	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
623	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
624	C₂³×C₄	C₂³×C₁₃	1	16	yes	complemented
625	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
626	#127	C₂³×C₁₃	1	8	yes	complemented
627	#127	C₂³×C₁₃	1	16	yes	complemented
628	#126	C₂³×C₁₃	1	16	yes	complemented
629	#126	C₂³×C₁₃	1	32	yes	complemented
630	#125	C₂³×C₁₃	1	8	yes	complemented
631	#125	C₂³×C₁₃	1	16	yes	complemented
632	#124	C₂³×C₁₃	1	8	yes	complemented
633	#124	C₂³×C₁₃	1	16	yes	complemented
634	#124	C₂³×C₁₃	1	32	yes	complemented
635	#123	C₂³×C₁₃	1	32	yes	complemented
636	#123	C₂³×C₁₃	1	16	yes	complemented
637	#123	C₂³×C₁₃	1	32	yes	complemented
638	#123	C₂³×C₁₃	1	32	yes	complemented
639	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
640	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
641	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
642	#121	C₂³×C₁₃	1	8	yes	—
643	#121	C₂³×C₁₃	1	16	yes	complemented
644	#121	C₂³×C₁₃	1	32	yes	complemented
645	#121	C₂³×C₁₃	1	32	yes	complemented
646	#121	C₂³×C₁₃	1	16	yes	complemented
647	#121	C₂³×C₁₃	1	16	yes	complemented
648	#121	C₂³×C₁₃	1	16	yes	complemented
649	#121	C₂³×C₁₃	1	16	yes	complemented
650	#121	C₂³×C₁₃	1	32	yes	complemented
651	#121	C₂³×C₁₃	1	32	yes	complemented
652	#121	C₂³×C₁₃	1	16	yes	complemented
653	#121	C₂³×C₁₃	1	16	yes	complemented
654	#121	C₂³×C₁₃	1	32	yes	complemented
655	#120	C₂³×C₁₃	1	32	yes	complemented
656	#120	C₂³×C₁₃	1	32	yes	complemented
657	#120	C₂³×C₁₃	1	32	yes	complemented
658	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
659	C₄×D₄	C₂³×C₁₃	1	8	yes	—
660	C₄×D₄	C₂³×C₁₃	1	8	yes	—
661	C₄×D₄	C₂³×C₁₃	1	16	yes	—
662	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
663	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
664	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
665	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
666	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
667	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
668	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
669	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
670	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
671	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
672	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
673	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
674	#117	C₂³×C₁₃	1	16	yes	complemented
675	#117	C₂³×C₁₃	1	16	yes	complemented
676	#117	C₂³×C₁₃	1	16	yes	complemented
677	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
683	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
691	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
692	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
709	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
710	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
711	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
713	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
714	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
718	C₂×C₁₃	—	2	4	no	—
719	C₂×C₁₃	—	2	8	no	—
720	C₂×C₁₃	—	4	4	no	—
721	C₂×C₁₃	—	4	8	no	—
722	C₂×C₁₃	—	4	4	no	—
723	C₂×C₁₃	#3519	1	4	yes	direct product factor
724	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
725	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂⁴	—	2	8	no	—
728	C₂⁴	—	2	8	no	—
729	C₂⁴	—	2	16	no	—
730	C₂⁴	—	4	4	no	—
731	C₂⁴	—	4	8	no	—
732	C₂⁴	—	4	8	no	—
733	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
734	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
735	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
736	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
737	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
738	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
740	#41	—	4	32	no	—
741	#41	—	4	32	no	—
742	C₂×Q₈	—	2	4	no	—
743	C₂×Q₈	—	4	4	no	—
744	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
745	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
746	C₂×D₄	—	2	8	no	—
747	C₂×D₄	—	2	16	no	—
748	C₂×D₄	—	2	8	no	—
749	C₂×D₄	—	2	16	no	—
750	C₂×D₄	—	2	32	no	—
751	C₂×D₄	—	2	64	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	8	no	—
754	C₂×D₄	—	2	4	no	—
755	C₂×D₄	—	2	8	no	—
756	C₂×D₄	—	4	32	no	—
757	C₂×D₄	—	4	8	no	—
758	C₂×D₄	—	4	8	no	—
759	C₂×D₄	—	4	8	no	—
760	C₂×D₄	—	4	4	no	—
761	C₂×D₄	—	4	8	no	—
762	C₂×D₄	—	4	64	no	—
763	C₂×D₄	C₁₃×#41	1	8	yes	complemented
764	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
765	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
766	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
767	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
768	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
769	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
770	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
771	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
772	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
773	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
774	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
775	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
776	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
777	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	8	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	8	no	—
783	C₂²×C₄	—	2	8	no	—
784	C₂²×C₄	—	4	32	no	—
785	C₂²×C₄	—	4	4	no	—
786	C₂²×C₄	—	4	4	no	—
787	C₂²×C₄	—	4	4	no	—
788	C₂²×C₄	—	4	8	no	—
789	C₂²×C₄	—	4	8	no	—
790	C₂²×C₄	—	4	8	no	—
791	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
798	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
801	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
802	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
803	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
805	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
806	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
807	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
808	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
809	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
810	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
811	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
812	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
813	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
816	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
817	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
818	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
819	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
820	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
821	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
822	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
823	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
824	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
825	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
826	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
827	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
828	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
829	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
830	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
831	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
833	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
834	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
835	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
836	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
837	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
838	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
839	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
840	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
841	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
842	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
843	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
844	C₄²	C₂⁴×C₁₃	1	4	yes	—
845	C₄²	C₂⁴×C₁₃	1	4	yes	—
846	C₄²	C₂⁴×C₁₃	1	4	yes	—
847	C₄²	C₂⁴×C₁₃	1	4	yes	—
848	C₄²	C₂⁴×C₁₃	1	16	yes	—
849	C₄²	C₂⁴×C₁₃	1	8	yes	—
850	C₁₃	C₂×#3519	1	1	yes	characteristic, direct product factor, Sylow
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	4	no	—
856	C₂³	—	2	16	no	—
857	C₂³	—	2	4	no	—
858	C₂³	—	2	8	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	8	no	—
861	C₂³	—	2	8	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	2	16	no	—
865	C₂³	—	2	4	no	—
866	C₂³	—	2	32	no	—
867	C₂³	—	4	8	no	—
868	C₂³	—	4	16	no	—
869	C₂³	—	4	16	no	—
870	C₂³	—	4	32	no	—
871	C₂³	—	8	32	no	—
872	C₂³	C₂×C₁₃×#41	1	8	yes	—
873	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
874	C₂³	C₂⁵×C₁₃	1	4	yes	—
875	C₂³	C₂⁵×C₁₃	1	4	yes	—
876	C₂³	C₂⁵×C₁₃	1	8	yes	—
877	C₂³	C₂⁵×C₁₃	1	4	yes	—
878	C₂³	C₂⁵×C₁₃	1	2	yes	—
879	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	4	8	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	32	no	—
884	D₄	—	2	16	no	—
885	D₄	—	2	32	no	—
886	D₄	—	2	8	no	—
887	D₄	—	2	16	no	—
888	D₄	—	2	8	no	—
889	D₄	—	2	16	no	—
890	D₄	—	4	16	no	—
891	D₄	—	4	16	no	—
892	D₄	—	4	16	no	—
893	D₄	—	4	8	no	—
894	D₄	—	4	16	no	—
895	D₄	C₂×C₁₃×#41	1	16	yes	complemented
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	4	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	4	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	8	no	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	4	no	—
907	C₂×C₄	—	2	8	no	—
908	C₂×C₄	—	2	16	no	—
909	C₂×C₄	—	2	8	no	—
910	C₂×C₄	—	2	16	no	—
911	C₂×C₄	—	2	16	no	—
912	C₂×C₄	—	4	8	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	—	4	16	no	—
916	C₂×C₄	—	4	16	no	—
917	C₂×C₄	—	4	16	no	—
918	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
919	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
920	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
921	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
922	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
923	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
924	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
925	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
926	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
927	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
928	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
929	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
930	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
931	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
932	C₂²	—	2	8	no	—
933	C₂²	—	2	16	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	4	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	2	8	no	—
941	C₂²	—	2	4	no	—
942	C₂²	—	2	8	no	—
943	C₂²	—	2	8	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	4	32	no	—
948	C₂²	—	4	8	no	—
949	C₂²	—	4	16	no	—
950	C₂²	—	4	8	no	—
951	C₂²	—	8	32	no	—
952	C₂²	C₂²×C₁₃×#41	1	8	yes	—
953	C₂²	C₂²×C₁₃×#41	1	2	yes	—
954	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
955	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
956	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
957	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	4	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	4	no	—
966	C₄	—	2	8	no	—
967	C₄	—	2	4	no	—
968	C₄	C₂²×C₁₃×#41	1	4	yes	—
969	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	2	8	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	—	4	8	no	—
975	C₂	C₁₃×#3519	1	4	yes	direct product factor
976	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
977	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
978	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
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×#3519	C₂	direct (N × H)
2. C₂×C₁₃×#555	C₂	semidirect
3. C₂×C₁₃×#554	C₂	semidirect
4. C₂×C₁₃×#553	C₂	semidirect
5. C₂×C₁₃×#553	C₂	semidirect
6. C₂×C₁₃×#550	C₂	semidirect
7. C₂×C₁₃×#546	C₂	semidirect
8. C₂×C₁₃×#546	C₂	semidirect
9. C₂×D₄²×C₁₃	C₂	semidirect
10. C₂×D₄²×C₁₃	C₂	semidirect
11. C₂×C₁₃×#540	C₂	semidirect
12. C₂×C₁₃×#538	C₂	semidirect
13. C₂×C₁₃×#532	C₂	semidirect
14. C₂×C₁₃×#529	C₂	semidirect
15. C₂×C₁₃×#525	C₂	semidirect
16. C₂²×C₁₃×#121	C₂	semidirect
17. C₂×C₁₃×#518	C₂	semidirect
18. C₂²×C₄×D₄×C₁₃	C₂	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
23. C₂³×D₄×C₁₃	C₂²	semidirect
24. C₂³×D₄×C₁₃	C₂²	semidirect
25. C₂⁴×C₄×C₁₃	C₂²	semidirect
26. C₁₃×#555	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
31. C₁₃×#546	C₂²	semidirect
32. C₁₃×#546	C₂²	semidirect
33. D₄²×C₁₃	C₂²	semidirect
34. D₄²×C₁₃	C₂²	semidirect
35. C₁₃×#540	C₂²	semidirect
36. C₁₃×#538	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
38. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×#127	C₂²	semidirect
40. C₂×C₁₃×#127	C₂²	semidirect
41. C₁₃×#529	C₂²	semidirect
42. C₂×C₁₃×#126	C₂²	semidirect
43. C₂×C₁₃×#126	C₂²	semidirect
44. C₂×C₁₃×#125	C₂²	semidirect
45. C₂×C₁₃×#125	C₂²	semidirect
46. C₂×C₁₃×#124	C₂²	semidirect
47. C₂×C₁₃×#124	C₂²	semidirect
48. C₂×C₁₃×#124	C₂²	semidirect
49. C₁₃×#525	C₂²	semidirect
50. C₂×C₁₃×#123	C₂²	semidirect
51. C₂×C₁₃×#123	C₂²	semidirect
52. C₂×C₁₃×#123	C₂²	semidirect
53. C₂×C₁₃×#123	C₂²	semidirect
54. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₁₃×#121	C₂²	semidirect
59. C₂×C₁₃×#121	C₂²	semidirect
60. C₂×C₁₃×#121	C₂²	semidirect
61. C₂×C₁₃×#121	C₂²	semidirect
62. C₂×C₁₃×#121	C₂²	semidirect
63. C₂×C₁₃×#121	C₂²	semidirect
64. C₂×C₁₃×#121	C₂²	semidirect
65. C₂×C₁₃×#121	C₂²	semidirect
66. C₂×C₁₃×#121	C₂²	semidirect
67. C₂×C₁₃×#121	C₂²	semidirect
68. C₂×C₁₃×#121	C₂²	semidirect
69. C₂×C₁₃×#121	C₂²	semidirect
70. C₂×C₁₃×#121	C₂²	semidirect
71. C₂×C₁₃×#120	C₂²	semidirect
72. C₂×C₁₃×#120	C₂²	semidirect
73. C₂×C₁₃×#120	C₂²	semidirect
74. C₁₃×#518	C₂²	semidirect
75. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
79. C₂×C₄×D₄×C₁₃	C₂²	semidirect
80. C₂×C₄×D₄×C₁₃	C₂²	semidirect
81. C₂×C₄×D₄×C₁₃	C₂²	semidirect
82. C₂×C₄×D₄×C₁₃	C₂²	semidirect
83. C₂×C₄×D₄×C₁₃	C₂²	semidirect
84. C₂×C₄×D₄×C₁₃	C₂²	semidirect
85. C₂×C₄×D₄×C₁₃	C₂²	semidirect
86. C₂×C₄×D₄×C₁₃	C₂²	semidirect
87. C₂×C₄×D₄×C₁₃	C₂²	semidirect
88. C₂×C₄×D₄×C₁₃	C₂²	semidirect
89. C₂×C₄×D₄×C₁₃	C₂²	semidirect
90. C₂×C₄×D₄×C₁₃	C₂²	semidirect
91. C₂×C₄×D₄×C₁₃	C₂²	semidirect
92. C₂×C₁₃×#117	C₂²	semidirect
93. C₂×C₁₃×#117	C₂²	semidirect
94. C₂×C₁₃×#117	C₂²	semidirect
95. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
97. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
98. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
99. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
100. C₂²×C₄²×C₁₃	C₂²	semidirect
105. C₂×C₁₃×#41	C₂³	semidirect
106. C₂×C₁₃×#41	C₂³	semidirect
129. C₂²×D₄×C₁₃	C₂³	semidirect
130. C₂²×D₄×C₁₃	C₂³	semidirect
144. C₂³×C₄×C₁₃	C₂³	semidirect
145. C₁₃×C₄⋊Q₈	C₂³	semidirect
146. C₁₃×#127	C₂³	semidirect
147. C₁₃×#127	C₂³	semidirect
148. C₁₃×#126	C₂³	semidirect
149. C₁₃×#126	C₂³	semidirect
150. C₁₃×#125	C₂³	semidirect
151. C₁₃×#125	C₂³	semidirect
152. C₁₃×#124	C₂³	semidirect
153. C₁₃×#124	C₂³	semidirect
154. C₁₃×#124	C₂³	semidirect
155. C₁₃×#123	C₂³	semidirect
156. C₁₃×#123	C₂³	semidirect
157. C₁₃×#123	C₂³	semidirect
158. C₁₃×#123	C₂³	semidirect
159. C₁₃×C₂²⋊Q₈	C₂³	semidirect
160. C₁₃×C₂²⋊Q₈	C₂³	semidirect
161. C₁₃×C₂²⋊Q₈	C₂³	semidirect
163. C₁₃×#121	C₂³	semidirect
164. C₁₃×#121	C₂³	semidirect
165. C₁₃×#121	C₂³	semidirect
166. C₁₃×#121	C₂³	semidirect
167. C₁₃×#121	C₂³	semidirect
168. C₁₃×#121	C₂³	semidirect
169. C₁₃×#121	C₂³	semidirect
170. C₁₃×#121	C₂³	semidirect
171. C₁₃×#121	C₂³	semidirect
172. C₁₃×#121	C₂³	semidirect
173. C₁₃×#121	C₂³	semidirect
174. C₁₃×#121	C₂³	semidirect
175. C₁₃×#120	C₂³	semidirect
176. C₁₃×#120	C₂³	semidirect
177. C₁₃×#120	C₂³	semidirect
178. C₄×Q₈×C₁₃	C₂³	semidirect
182. C₄×D₄×C₁₃	C₂³	semidirect
183. C₄×D₄×C₁₃	C₂³	semidirect
184. C₄×D₄×C₁₃	C₂³	semidirect
185. C₄×D₄×C₁₃	C₂³	semidirect
186. C₄×D₄×C₁₃	C₂³	semidirect
187. C₄×D₄×C₁₃	C₂³	semidirect
188. C₄×D₄×C₁₃	C₂³	semidirect
189. C₄×D₄×C₁₃	C₂³	semidirect
190. C₄×D₄×C₁₃	C₂³	semidirect
191. C₄×D₄×C₁₃	C₂³	semidirect
192. C₄×D₄×C₁₃	C₂³	semidirect
193. C₄×D₄×C₁₃	C₂³	semidirect
194. C₁₃×#117	C₂³	semidirect
195. C₁₃×#117	C₂³	semidirect
196. C₁₃×#117	C₂³	semidirect
210. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
211. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
228. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
229. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
230. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
237. C₂×C₄²×C₁₃	C₂³	semidirect
238. C₂×#3519	C₁₃	direct (N × H)
275. C₂×D₄×C₁₃	#41	semidirect
362. #3519	C₂×C₁₃	direct (N × H)
363. C₂×#555	C₂×C₁₃	semidirect
364. C₂×#554	C₂×C₁₃	semidirect
365. C₂×#553	C₂×C₁₃	semidirect
366. C₂×#553	C₂×C₁₃	semidirect
367. C₂×#550	C₂×C₁₃	semidirect
368. C₂×#546	C₂×C₁₃	semidirect
369. C₂×#546	C₂×C₁₃	semidirect
370. C₂×D₄²	C₂×C₁₃	semidirect
371. C₂×D₄²	C₂×C₁₃	semidirect
372. C₂×#540	C₂×C₁₃	semidirect
373. C₂×#538	C₂×C₁₃	semidirect
374. C₂×#532	C₂×C₁₃	semidirect
375. C₂×#529	C₂×C₁₃	semidirect
376. C₂×#525	C₂×C₁₃	semidirect
377. C₂²×#121	C₂×C₁₃	semidirect
378. C₂×#518	C₂×C₁₃	semidirect
379. C₂²×C₄×D₄	C₂×C₁₃	semidirect
424. D₄×C₁₃	C₂×#41	semidirect
461. C₂²×#41	C₂²×C₁₃	semidirect
462. C₂²×#41	C₂²×C₁₃	semidirect
465. C₂³×D₄	C₂²×C₁₃	semidirect
466. C₂³×D₄	C₂²×C₁₃	semidirect
467. C₂⁴×C₄	C₂²×C₁₃	semidirect
468. #555	C₂²×C₁₃	semidirect
469. #554	C₂²×C₁₃	semidirect
470. #553	C₂²×C₁₃	semidirect
471. #553	C₂²×C₁₃	semidirect
472. #550	C₂²×C₁₃	semidirect
473. #546	C₂²×C₁₃	semidirect
474. #546	C₂²×C₁₃	semidirect
475. D₄²	C₂²×C₁₃	semidirect
476. D₄²	C₂²×C₁₃	semidirect
477. #540	C₂²×C₁₃	semidirect
478. #538	C₂²×C₁₃	semidirect
479. #532	C₂²×C₁₃	semidirect
480. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
481. C₂×#127	C₂²×C₁₃	semidirect
482. C₂×#127	C₂²×C₁₃	semidirect
483. #529	C₂²×C₁₃	semidirect
484. C₂×#126	C₂²×C₁₃	semidirect
485. C₂×#126	C₂²×C₁₃	semidirect
486. C₂×#125	C₂²×C₁₃	semidirect
487. C₂×#125	C₂²×C₁₃	semidirect
488. C₂×#124	C₂²×C₁₃	semidirect
489. C₂×#124	C₂²×C₁₃	semidirect
490. C₂×#124	C₂²×C₁₃	semidirect
491. #525	C₂²×C₁₃	semidirect
492. C₂×#123	C₂²×C₁₃	semidirect
493. C₂×#123	C₂²×C₁₃	semidirect
494. C₂×#123	C₂²×C₁₃	semidirect
495. C₂×#123	C₂²×C₁₃	semidirect
496. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
497. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
498. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
500. C₂×#121	C₂²×C₁₃	semidirect
501. C₂×#121	C₂²×C₁₃	semidirect
502. C₂×#121	C₂²×C₁₃	semidirect
503. C₂×#121	C₂²×C₁₃	semidirect
504. C₂×#121	C₂²×C₁₃	semidirect
505. C₂×#121	C₂²×C₁₃	semidirect
506. C₂×#121	C₂²×C₁₃	semidirect
507. C₂×#121	C₂²×C₁₃	semidirect
508. C₂×#121	C₂²×C₁₃	semidirect
509. C₂×#121	C₂²×C₁₃	semidirect
510. C₂×#121	C₂²×C₁₃	semidirect
511. C₂×#121	C₂²×C₁₃	semidirect
512. C₂×#121	C₂²×C₁₃	semidirect
513. C₂×#120	C₂²×C₁₃	semidirect
514. C₂×#120	C₂²×C₁₃	semidirect
515. C₂×#120	C₂²×C₁₃	semidirect
516. #518	C₂²×C₁₃	semidirect
517. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
521. C₂×C₄×D₄	C₂²×C₁₃	semidirect
522. C₂×C₄×D₄	C₂²×C₁₃	semidirect
523. C₂×C₄×D₄	C₂²×C₁₃	semidirect
524. C₂×C₄×D₄	C₂²×C₁₃	semidirect
525. C₂×C₄×D₄	C₂²×C₁₃	semidirect
526. C₂×C₄×D₄	C₂²×C₁₃	semidirect
527. C₂×C₄×D₄	C₂²×C₁₃	semidirect
528. C₂×C₄×D₄	C₂²×C₁₃	semidirect
529. C₂×C₄×D₄	C₂²×C₁₃	semidirect
530. C₂×C₄×D₄	C₂²×C₁₃	semidirect
531. C₂×C₄×D₄	C₂²×C₁₃	semidirect
532. C₂×C₄×D₄	C₂²×C₁₃	semidirect
533. C₂×C₄×D₄	C₂²×C₁₃	semidirect
534. C₂×#117	C₂²×C₁₃	semidirect
535. C₂×#117	C₂²×C₁₃	semidirect
536. C₂×#117	C₂²×C₁₃	semidirect
537. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
538. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
539. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
540. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
541. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
542. C₂²×C₄²	C₂²×C₁₃	semidirect
585. C₂×#41	C₂³×C₁₃	semidirect
586. C₂×#41	C₂³×C₁₃	semidirect
609. C₂²×D₄	C₂³×C₁₃	semidirect
610. C₂²×D₄	C₂³×C₁₃	semidirect
624. C₂³×C₄	C₂³×C₁₃	semidirect
625. C₄⋊Q₈	C₂³×C₁₃	semidirect
626. #127	C₂³×C₁₃	semidirect
627. #127	C₂³×C₁₃	semidirect
628. #126	C₂³×C₁₃	semidirect
629. #126	C₂³×C₁₃	semidirect
630. #125	C₂³×C₁₃	semidirect
631. #125	C₂³×C₁₃	semidirect
632. #124	C₂³×C₁₃	semidirect
633. #124	C₂³×C₁₃	semidirect
634. #124	C₂³×C₁₃	semidirect
635. #123	C₂³×C₁₃	semidirect
636. #123	C₂³×C₁₃	semidirect
637. #123	C₂³×C₁₃	semidirect
638. #123	C₂³×C₁₃	semidirect
639. C₂²⋊Q₈	C₂³×C₁₃	semidirect
640. C₂²⋊Q₈	C₂³×C₁₃	semidirect
641. C₂²⋊Q₈	C₂³×C₁₃	semidirect
643. #121	C₂³×C₁₃	semidirect
644. #121	C₂³×C₁₃	semidirect
645. #121	C₂³×C₁₃	semidirect
646. #121	C₂³×C₁₃	semidirect
647. #121	C₂³×C₁₃	semidirect
648. #121	C₂³×C₁₃	semidirect
649. #121	C₂³×C₁₃	semidirect
650. #121	C₂³×C₁₃	semidirect
651. #121	C₂³×C₁₃	semidirect
652. #121	C₂³×C₁₃	semidirect
653. #121	C₂³×C₁₃	semidirect
654. #121	C₂³×C₁₃	semidirect
655. #120	C₂³×C₁₃	semidirect
656. #120	C₂³×C₁₃	semidirect
657. #120	C₂³×C₁₃	semidirect
658. C₄×Q₈	C₂³×C₁₃	semidirect
662. C₄×D₄	C₂³×C₁₃	semidirect
663. C₄×D₄	C₂³×C₁₃	semidirect
664. C₄×D₄	C₂³×C₁₃	semidirect
665. C₄×D₄	C₂³×C₁₃	semidirect
666. C₄×D₄	C₂³×C₁₃	semidirect
667. C₄×D₄	C₂³×C₁₃	semidirect
668. C₄×D₄	C₂³×C₁₃	semidirect
669. C₄×D₄	C₂³×C₁₃	semidirect
670. C₄×D₄	C₂³×C₁₃	semidirect
671. C₄×D₄	C₂³×C₁₃	semidirect
672. C₄×D₄	C₂³×C₁₃	semidirect
673. C₄×D₄	C₂³×C₁₃	semidirect
674. #117	C₂³×C₁₃	semidirect
675. #117	C₂³×C₁₃	semidirect
676. #117	C₂³×C₁₃	semidirect
690. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
691. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
708. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
709. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
710. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
717. C₂×C₄²	C₂³×C₁₃	semidirect
723. C₂×C₁₃	#3519	direct (N × H)
763. C₂×D₄	C₁₃×#41	semidirect
850. C₁₃	C₂×#3519	direct (N × H)
895. D₄	C₂×C₁₃×#41	semidirect
975. C₂	C₁₃×#3519	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×#3519	2
C₂×C₁₃×#555	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#550	2
C₂×C₁₃×#546	2
C₂×D₄²×C₁₃	2
C₂×C₁₃×#540	2
C₂×C₁₃×#538	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂²×C₁₃×#121	2
C₂×C₁₃×#518	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3519	13

Subgroups — C2×C13×#3519 #15749110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3519 #15749110