Subgroups — C₂×C₁₃×#3495 #15749142

Order 3328.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#552	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#533	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
15	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#556	C₂²	1	32	yes	complemented
23	C₁₃×#554	C₂²	1	32	yes	complemented
24	C₁₃×#552	C₂²	1	32	yes	complemented
25	C₁₃×#552	C₂²	1	64	yes	complemented
26	C₁₃×#552	C₂²	1	32	yes	complemented
27	C₁₃×#551	C₂²	1	64	yes	complemented
28	C₁₃×#544	C₂²	1	16	yes	complemented
29	C₁₃×#542	C₂²	1	32	yes	complemented
30	C₁₃×#541	C₂²	1	32	yes	complemented
31	C₁₃×#536	C₂²	1	16	yes	complemented
32	C₁₃×#533	C₂²	1	32	yes	complemented
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₃×#529	C₂²	1	32	yes	complemented
37	C₂×C₁₃×#126	C₂²	1	4	yes	—
38	C₂×C₁₃×#126	C₂²	1	4	yes	—
39	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
45	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
46	C₂×C₁₃×#124	C₂²	1	4	yes	—
47	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
48	C₁₃×#525	C₂²	1	16	yes	—
49	C₂×C₁₃×#123	C₂²	1	2	yes	—
50	C₂×C₁₃×#123	C₂²	1	4	yes	—
51	C₂×C₁₃×#123	C₂²	1	4	yes	—
52	C₂×C₁₃×#123	C₂²	1	4	yes	—
53	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	16	yes	complemented
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#120	C₂²	1	2	yes	—
68	C₁₃×#520	C₂²	1	16	yes	complemented
69	C₁₃×#519	C₂²	1	16	yes	complemented
70	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
71	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
72	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
73	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
74	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
75	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
76	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
77	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
78	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
80	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
81	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
83	C₂×C₁₃×#117	C₂²	1	2	yes	—
84	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#117	C₂²	1	2	yes	—
86	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
88	C₂×C₁₃×#117	C₂²	1	4	yes	—
89	C₂×C₁₃×#117	C₂²	1	4	yes	—
90	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
91	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
92	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
93	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
101	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×#41	—	2	8	no	—
103	C₂×C₁₃×#41	C₂³	1	8	yes	—
104	C₂²×Q₈×C₁₃	—	2	8	no	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃	—	2	8	no	—
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
129	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
131	C₁₃×#126	C₂³	1	32	yes	—
132	C₁₃×#126	C₂³	1	32	yes	—
133	C₁₃×#126	C₂³	1	32	yes	complemented
134	C₁₃×#126	C₂³	1	32	yes	complemented
135	C₁₃×#125	C₂³	1	16	yes	complemented
136	C₁₃×#125	C₂³	1	32	yes	complemented
137	C₁₃×#125	C₂³	1	32	yes	complemented
138	C₁₃×#125	C₂³	1	32	yes	complemented
139	C₁₃×#125	C₂³	1	16	yes	complemented
140	C₁₃×#124	C₂³	1	32	yes	—
141	C₁₃×#124	C₂³	1	16	yes	complemented
142	C₁₃×#123	C₂³	1	16	yes	—
143	C₁₃×#123	C₂³	1	32	yes	—
144	C₁₃×#123	C₂³	1	32	yes	—
145	C₁₃×#123	C₂³	1	32	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
155	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
156	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	C₁₃×#121	C₂³	1	8	yes	—
158	C₁₃×#121	C₂³	1	8	yes	—
159	C₁₃×#120	C₂³	1	16	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
161	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
162	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
163	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
164	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
165	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
166	C₄×D₄×C₁₃	C₂³	1	32	yes	—
167	C₄×D₄×C₁₃	C₂³	1	16	yes	—
168	C₄×D₄×C₁₃	C₂³	1	16	yes	—
169	C₄×D₄×C₁₃	C₂³	1	32	yes	—
170	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
171	C₁₃×#117	C₂³	1	8	yes	—
172	C₁₃×#117	C₂³	1	8	yes	—
173	C₁₃×#117	C₂³	1	16	yes	—
174	C₁₃×#117	C₂³	1	8	yes	—
175	C₁₃×#117	C₂³	1	16	yes	—
176	C₁₃×#117	C₂³	1	8	yes	—
177	C₁₃×#117	C₂³	1	8	yes	—
178	C₁₃×#117	C₂³	1	32	yes	—
179	C₁₃×#117	C₂³	1	32	yes	—
180	C₁₃×#117	C₂³	1	16	yes	complemented
181	C₁₃×#117	C₂³	1	32	yes	complemented
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
209	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
229	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
230	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
231	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
234	C₂×#3495	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	4	no	—
236	C₂⁴×C₁₃	—	2	4	no	—
237	C₂⁴×C₁₃	—	4	2	no	—
238	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
241	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₁₃×#41	—	2	32	no	—
244	C₂×Q₈×C₁₃	—	2	8	no	—
245	C₂×Q₈×C₁₃	—	2	8	no	—
246	C₂×Q₈×C₁₃	—	2	32	no	—
247	C₂×Q₈×C₁₃	—	2	4	no	—
248	C₂×Q₈×C₁₃	—	4	8	no	—
249	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
252	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
253	C₂×D₄×C₁₃	—	2	8	no	—
254	C₂×D₄×C₁₃	—	2	8	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	—	2	8	no	—
263	C₂²×C₄×C₁₃	—	2	8	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	4	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	32	no	—
269	C₂²×C₄×C₁₃	—	2	8	no	—
270	C₂²×C₄×C₁₃	—	4	8	no	—
271	C₂²×C₄×C₁₃	—	4	4	no	—
272	C₂²×C₄×C₁₃	—	4	4	no	—
273	C₂²×C₄×C₁₃	#41	1	8	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
323	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₄²×C₁₃	C₂⁴	1	8	yes	—
336	C₄²×C₁₃	C₂⁴	1	8	yes	—
337	C₄²×C₁₃	C₂⁴	1	8	yes	—
338	C₄²×C₁₃	C₂⁴	1	8	yes	—
339	C₄²×C₁₃	C₂⁴	1	16	yes	—
340	C₄²×C₁₃	C₂⁴	1	16	yes	—
341	C₄²×C₁₃	C₂⁴	1	16	yes	—
342	C₄²×C₁₃	C₂⁴	1	8	yes	—
343	#3495	C₂×C₁₃	1	32	yes	direct product factor
344	C₂×#556	C₂×C₁₃	1	2	yes	complemented
345	C₂×#554	C₂×C₁₃	1	2	yes	complemented
346	C₂×#552	C₂×C₁₃	1	2	yes	complemented
347	C₂×#552	C₂×C₁₃	1	4	yes	complemented
348	C₂×#552	C₂×C₁₃	1	2	yes	complemented
349	C₂×#551	C₂×C₁₃	1	4	yes	complemented
350	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂×#542	C₂×C₁₃	1	2	yes	complemented
352	C₂×#541	C₂×C₁₃	1	2	yes	complemented
353	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₂×#533	C₂×C₁₃	1	2	yes	complemented
355	C₂×#529	C₂×C₁₃	1	2	yes	complemented
356	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
357	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	8	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	4	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	8	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	4	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	4	16	no	—
375	C₂³×C₁₃	C₂×#41	1	4	yes	—
376	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
377	C₂³×C₁₃	C₂⁵	1	2	yes	—
378	C₂³×C₁₃	C₂⁵	1	4	yes	—
379	C₂³×C₁₃	C₂⁵	1	2	yes	—
380	C₂³×C₁₃	C₂⁵	1	2	yes	—
381	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
382	Q₈×C₁₃	—	2	16	no	—
383	Q₈×C₁₃	—	2	16	no	—
384	Q₈×C₁₃	—	2	8	no	—
385	Q₈×C₁₃	—	4	16	no	—
386	D₄×C₁₃	—	2	16	no	—
387	D₄×C₁₃	—	2	16	no	—
388	D₄×C₁₃	—	2	8	no	—
389	D₄×C₁₃	—	4	8	no	—
390	C₂×C₄×C₁₃	—	2	8	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	2	16	no	—
395	C₂×C₄×C₁₃	—	2	8	no	—
396	C₂×C₄×C₁₃	—	2	16	no	—
397	C₂×C₄×C₁₃	—	2	4	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	4	no	—
401	C₂×C₄×C₁₃	—	2	8	no	—
402	C₂×C₄×C₁₃	—	2	4	no	—
403	C₂×C₄×C₁₃	—	2	4	no	—
404	C₂×C₄×C₁₃	—	2	8	no	—
405	C₂×C₄×C₁₃	—	2	8	no	—
406	C₂×C₄×C₁₃	—	2	8	no	—
407	C₂×C₄×C₁₃	—	2	8	no	—
408	C₂×C₄×C₁₃	—	2	16	no	—
409	C₂×C₄×C₁₃	—	4	16	no	—
410	C₂×C₄×C₁₃	—	4	8	no	—
411	C₂×C₄×C₁₃	—	4	8	no	—
412	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
413	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
414	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
424	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
425	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
426	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
427	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
428	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
429	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
431	#556	C₂²×C₁₃	1	32	yes	complemented
432	#554	C₂²×C₁₃	1	32	yes	complemented
433	#552	C₂²×C₁₃	1	32	yes	complemented
434	#552	C₂²×C₁₃	1	64	yes	complemented
435	#552	C₂²×C₁₃	1	32	yes	complemented
436	#551	C₂²×C₁₃	1	64	yes	complemented
437	#544	C₂²×C₁₃	1	16	yes	complemented
438	#542	C₂²×C₁₃	1	32	yes	complemented
439	#541	C₂²×C₁₃	1	32	yes	complemented
440	#536	C₂²×C₁₃	1	16	yes	complemented
441	#533	C₂²×C₁₃	1	32	yes	complemented
442	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
443	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
444	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
445	#529	C₂²×C₁₃	1	32	yes	complemented
446	C₂×#126	C₂²×C₁₃	1	4	yes	—
447	C₂×#126	C₂²×C₁₃	1	4	yes	—
448	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
449	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
450	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
451	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
452	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
453	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
454	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
455	C₂×#124	C₂²×C₁₃	1	4	yes	—
456	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
457	#525	C₂²×C₁₃	1	16	yes	—
458	C₂×#123	C₂²×C₁₃	1	2	yes	—
459	C₂×#123	C₂²×C₁₃	1	4	yes	—
460	C₂×#123	C₂²×C₁₃	1	4	yes	—
461	C₂×#123	C₂²×C₁₃	1	4	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
463	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
466	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
470	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	16	yes	complemented
471	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
473	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
474	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
476	C₂×#120	C₂²×C₁₃	1	2	yes	—
477	#520	C₂²×C₁₃	1	16	yes	complemented
478	#519	C₂²×C₁₃	1	16	yes	complemented
479	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
480	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
481	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
482	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
483	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
484	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
485	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
486	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
488	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
489	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
490	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
491	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
492	C₂×#117	C₂²×C₁₃	1	2	yes	—
493	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
494	C₂×#117	C₂²×C₁₃	1	2	yes	—
495	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
497	C₂×#117	C₂²×C₁₃	1	4	yes	—
498	C₂×#117	C₂²×C₁₃	1	4	yes	—
499	C₂×#117	C₂²×C₁₃	1	16	yes	complemented
500	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
501	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
502	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
503	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
504	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
505	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
506	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
507	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
508	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
509	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	8	no	—
515	C₂²×C₁₃	—	2	8	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	4	no	—
518	C₂²×C₁₃	—	2	4	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	4	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	4	16	no	—
523	C₂²×C₁₃	—	4	8	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	C₂²×#41	1	4	yes	—
526	C₂²×C₁₃	C₂²×#41	1	2	yes	—
527	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
528	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
529	C₂²×C₁₃	#585	1	2	yes	—
530	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	4	no	—
534	C₄×C₁₃	—	2	8	no	—
535	C₄×C₁₃	—	2	4	no	—
536	C₄×C₁₃	—	2	4	no	—
537	C₄×C₁₃	—	2	4	no	—
538	C₄×C₁₃	—	2	4	no	—
539	C₄×C₁₃	—	2	8	no	—
540	C₄×C₁₃	—	2	4	no	—
541	C₄×C₁₃	—	2	4	no	—
542	C₄×C₁₃	C₂²×#41	1	4	yes	—
543	C₄×C₁₃	C₂²×#41	1	4	yes	—
544	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×#41	—	2	8	no	—
546	C₂×#41	C₂³×C₁₃	1	8	yes	—
547	C₂²×Q₈	—	2	8	no	—
548	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
549	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
552	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
553	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
554	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
555	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
557	C₂³×C₄	—	2	8	no	—
558	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
559	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
560	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
563	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
566	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
568	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
569	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
570	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
572	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
573	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
574	#126	C₂³×C₁₃	1	32	yes	—
575	#126	C₂³×C₁₃	1	32	yes	—
576	#126	C₂³×C₁₃	1	32	yes	complemented
577	#126	C₂³×C₁₃	1	32	yes	complemented
578	#125	C₂³×C₁₃	1	16	yes	complemented
579	#125	C₂³×C₁₃	1	32	yes	complemented
580	#125	C₂³×C₁₃	1	32	yes	complemented
581	#125	C₂³×C₁₃	1	32	yes	complemented
582	#125	C₂³×C₁₃	1	16	yes	complemented
583	#124	C₂³×C₁₃	1	32	yes	—
584	#124	C₂³×C₁₃	1	16	yes	complemented
585	#123	C₂³×C₁₃	1	16	yes	—
586	#123	C₂³×C₁₃	1	32	yes	—
587	#123	C₂³×C₁₃	1	32	yes	—
588	#123	C₂³×C₁₃	1	32	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
598	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
599	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
600	#121	C₂³×C₁₃	1	8	yes	—
601	#121	C₂³×C₁₃	1	8	yes	—
602	#120	C₂³×C₁₃	1	16	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
604	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
605	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
606	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
607	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
608	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
609	C₄×D₄	C₂³×C₁₃	1	32	yes	—
610	C₄×D₄	C₂³×C₁₃	1	16	yes	—
611	C₄×D₄	C₂³×C₁₃	1	16	yes	—
612	C₄×D₄	C₂³×C₁₃	1	32	yes	—
613	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
614	#117	C₂³×C₁₃	1	8	yes	—
615	#117	C₂³×C₁₃	1	8	yes	—
616	#117	C₂³×C₁₃	1	16	yes	—
617	#117	C₂³×C₁₃	1	8	yes	—
618	#117	C₂³×C₁₃	1	16	yes	—
619	#117	C₂³×C₁₃	1	8	yes	—
620	#117	C₂³×C₁₃	1	8	yes	—
621	#117	C₂³×C₁₃	1	32	yes	—
622	#117	C₂³×C₁₃	1	32	yes	—
623	#117	C₂³×C₁₃	1	16	yes	complemented
624	#117	C₂³×C₁₃	1	32	yes	complemented
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
668	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
671	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
674	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
675	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
676	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
677	C₂×C₁₃	—	2	4	no	—
678	C₂×C₁₃	—	2	4	no	—
679	C₂×C₁₃	—	4	4	no	—
680	C₂×C₁₃	—	4	2	no	—
681	C₂×C₁₃	#3495	1	4	yes	direct product factor
682	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
683	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
684	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
685	C₂⁴	—	2	4	no	—
686	C₂⁴	—	2	4	no	—
687	C₂⁴	—	4	2	no	—
688	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
690	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
691	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
693	#41	—	2	32	no	—
694	C₂×Q₈	—	2	8	no	—
695	C₂×Q₈	—	2	8	no	—
696	C₂×Q₈	—	2	32	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	4	8	no	—
699	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
700	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
701	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
702	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
708	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
709	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
710	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	8	no	—
713	C₂²×C₄	—	2	8	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	32	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	4	8	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	4	4	no	—
723	C₂²×C₄	C₁₃×#41	1	8	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
743	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
745	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
761	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
762	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
763	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
764	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
778	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
779	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
780	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
781	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
785	C₄²	C₂⁴×C₁₃	1	8	yes	—
786	C₄²	C₂⁴×C₁₃	1	8	yes	—
787	C₄²	C₂⁴×C₁₃	1	8	yes	—
788	C₄²	C₂⁴×C₁₃	1	8	yes	—
789	C₄²	C₂⁴×C₁₃	1	16	yes	—
790	C₄²	C₂⁴×C₁₃	1	16	yes	—
791	C₄²	C₂⁴×C₁₃	1	16	yes	—
792	C₄²	C₂⁴×C₁₃	1	8	yes	—
793	C₁₃	C₂×#3495	1	1	yes	characteristic, direct product factor, Sylow
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	8	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	8	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	4	no	—
807	C₂³	—	4	16	no	—
808	C₂³	C₂×C₁₃×#41	1	4	yes	—
809	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
810	C₂³	C₂⁵×C₁₃	1	2	yes	—
811	C₂³	C₂⁵×C₁₃	1	4	yes	—
812	C₂³	C₂⁵×C₁₃	1	2	yes	—
813	C₂³	C₂⁵×C₁₃	1	2	yes	—
814	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
815	Q₈	—	2	16	no	—
816	Q₈	—	2	16	no	—
817	Q₈	—	2	8	no	—
818	Q₈	—	4	16	no	—
819	D₄	—	2	16	no	—
820	D₄	—	2	16	no	—
821	D₄	—	2	8	no	—
822	D₄	—	4	8	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	16	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	16	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	8	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	16	no	—
842	C₂×C₄	—	4	16	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
846	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
847	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
848	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
849	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
850	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
851	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
852	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
853	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
854	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
855	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
856	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
857	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
858	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
859	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
860	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	8	no	—
866	C₂²	—	2	8	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	4	16	no	—
874	C₂²	—	4	8	no	—
875	C₂²	—	4	4	no	—
876	C₂²	C₂²×C₁₃×#41	1	4	yes	—
877	C₂²	C₂²×C₁₃×#41	1	2	yes	—
878	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
879	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
880	C₂²	C₁₃×#585	1	2	yes	—
881	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	C₂²×C₁₃×#41	1	4	yes	—
894	C₄	C₂²×C₁₃×#41	1	4	yes	—
895	C₂	—	2	4	no	—
896	C₂	—	2	4	no	—
897	C₂	—	4	2	no	—
898	C₂	—	4	4	no	—
899	C₂	C₁₃×#3495	1	4	yes	direct product factor
900	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
901	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
902	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂×C₁₃×#525	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×#3495	C₂	direct (N × H)
2. C₂×C₁₃×#556	C₂	semidirect
3. C₂×C₁₃×#554	C₂	semidirect
4. C₂×C₁₃×#552	C₂	semidirect
5. C₂×C₁₃×#552	C₂	semidirect
6. C₂×C₁₃×#552	C₂	semidirect
7. C₂×C₁₃×#551	C₂	semidirect
8. C₂×C₁₃×#544	C₂	semidirect
9. C₂×C₁₃×#542	C₂	semidirect
10. C₂×C₁₃×#541	C₂	semidirect
11. C₂×C₁₃×#536	C₂	semidirect
12. C₂×C₁₃×#533	C₂	semidirect
13. C₂×C₁₃×#529	C₂	semidirect
15. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
16. C₂×C₁₃×#520	C₂	semidirect
17. C₂×C₁₃×#519	C₂	semidirect
18. C₂²×C₁₃×#117	C₂	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#552	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. C₁₃×#544	C₂²	semidirect
29. C₁₃×#542	C₂²	semidirect
30. C₁₃×#541	C₂²	semidirect
31. C₁₃×#536	C₂²	semidirect
32. C₁₃×#533	C₂²	semidirect
33. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
39. C₂×C₁₃×#126	C₂²	semidirect
40. C₂×C₁₃×#126	C₂²	semidirect
41. C₂×C₁₃×#125	C₂²	semidirect
42. C₂×C₁₃×#125	C₂²	semidirect
43. C₂×C₁₃×#125	C₂²	semidirect
44. C₂×C₁₃×#125	C₂²	semidirect
45. C₂×C₁₃×#125	C₂²	semidirect
47. C₂×C₁₃×#124	C₂²	semidirect
61. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
68. C₁₃×#520	C₂²	semidirect
69. C₁₃×#519	C₂²	semidirect
70. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
71. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
72. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
73. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
74. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
75. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
80. C₂×C₄×D₄×C₁₃	C₂²	semidirect
90. C₂×C₁₃×#117	C₂²	semidirect
91. C₂×C₁₃×#117	C₂²	semidirect
92. C₂×C₁₃×#117	C₂²	semidirect
97. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
128. C₁₃×C₄⋊Q₈	C₂³	semidirect
129. C₁₃×C₄⋊Q₈	C₂³	semidirect
130. C₁₃×C₄⋊Q₈	C₂³	semidirect
133. C₁₃×#126	C₂³	semidirect
134. C₁₃×#126	C₂³	semidirect
135. C₁₃×#125	C₂³	semidirect
136. C₁₃×#125	C₂³	semidirect
137. C₁₃×#125	C₂³	semidirect
138. C₁₃×#125	C₂³	semidirect
139. C₁₃×#125	C₂³	semidirect
141. C₁₃×#124	C₂³	semidirect
154. C₁₃×C₂²⋊Q₈	C₂³	semidirect
155. C₁₃×C₂²⋊Q₈	C₂³	semidirect
156. C₁₃×C₂²⋊Q₈	C₂³	semidirect
160. C₄×Q₈×C₁₃	C₂³	semidirect
161. C₄×Q₈×C₁₃	C₂³	semidirect
162. C₄×Q₈×C₁₃	C₂³	semidirect
163. C₄×Q₈×C₁₃	C₂³	semidirect
164. C₄×Q₈×C₁₃	C₂³	semidirect
165. C₄×Q₈×C₁₃	C₂³	semidirect
170. C₄×D₄×C₁₃	C₂³	semidirect
180. C₁₃×#117	C₂³	semidirect
181. C₁₃×#117	C₂³	semidirect
208. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
234. C₂×#3495	C₁₃	direct (N × H)
343. #3495	C₂×C₁₃	direct (N × H)
344. C₂×#556	C₂×C₁₃	semidirect
345. C₂×#554	C₂×C₁₃	semidirect
346. C₂×#552	C₂×C₁₃	semidirect
347. C₂×#552	C₂×C₁₃	semidirect
348. C₂×#552	C₂×C₁₃	semidirect
349. C₂×#551	C₂×C₁₃	semidirect
350. C₂×#544	C₂×C₁₃	semidirect
351. C₂×#542	C₂×C₁₃	semidirect
352. C₂×#541	C₂×C₁₃	semidirect
353. C₂×#536	C₂×C₁₃	semidirect
354. C₂×#533	C₂×C₁₃	semidirect
355. C₂×#529	C₂×C₁₃	semidirect
357. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
358. C₂×#520	C₂×C₁₃	semidirect
359. C₂×#519	C₂×C₁₃	semidirect
360. C₂²×#117	C₂×C₁₃	semidirect
431. #556	C₂²×C₁₃	semidirect
432. #554	C₂²×C₁₃	semidirect
433. #552	C₂²×C₁₃	semidirect
434. #552	C₂²×C₁₃	semidirect
435. #552	C₂²×C₁₃	semidirect
436. #551	C₂²×C₁₃	semidirect
437. #544	C₂²×C₁₃	semidirect
438. #542	C₂²×C₁₃	semidirect
439. #541	C₂²×C₁₃	semidirect
440. #536	C₂²×C₁₃	semidirect
441. #533	C₂²×C₁₃	semidirect
442. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
443. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
444. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
445. #529	C₂²×C₁₃	semidirect
448. C₂×#126	C₂²×C₁₃	semidirect
449. C₂×#126	C₂²×C₁₃	semidirect
450. C₂×#125	C₂²×C₁₃	semidirect
451. C₂×#125	C₂²×C₁₃	semidirect
452. C₂×#125	C₂²×C₁₃	semidirect
453. C₂×#125	C₂²×C₁₃	semidirect
454. C₂×#125	C₂²×C₁₃	semidirect
456. C₂×#124	C₂²×C₁₃	semidirect
470. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
471. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
472. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
473. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
477. #520	C₂²×C₁₃	semidirect
478. #519	C₂²×C₁₃	semidirect
479. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
480. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
481. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
482. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
483. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
484. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
489. C₂×C₄×D₄	C₂²×C₁₃	semidirect
499. C₂×#117	C₂²×C₁₃	semidirect
500. C₂×#117	C₂²×C₁₃	semidirect
501. C₂×#117	C₂²×C₁₃	semidirect
506. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
571. C₄⋊Q₈	C₂³×C₁₃	semidirect
572. C₄⋊Q₈	C₂³×C₁₃	semidirect
573. C₄⋊Q₈	C₂³×C₁₃	semidirect
576. #126	C₂³×C₁₃	semidirect
577. #126	C₂³×C₁₃	semidirect
578. #125	C₂³×C₁₃	semidirect
579. #125	C₂³×C₁₃	semidirect
580. #125	C₂³×C₁₃	semidirect
581. #125	C₂³×C₁₃	semidirect
582. #125	C₂³×C₁₃	semidirect
584. #124	C₂³×C₁₃	semidirect
597. C₂²⋊Q₈	C₂³×C₁₃	semidirect
598. C₂²⋊Q₈	C₂³×C₁₃	semidirect
599. C₂²⋊Q₈	C₂³×C₁₃	semidirect
603. C₄×Q₈	C₂³×C₁₃	semidirect
604. C₄×Q₈	C₂³×C₁₃	semidirect
605. C₄×Q₈	C₂³×C₁₃	semidirect
606. C₄×Q₈	C₂³×C₁₃	semidirect
607. C₄×Q₈	C₂³×C₁₃	semidirect
608. C₄×Q₈	C₂³×C₁₃	semidirect
613. C₄×D₄	C₂³×C₁₃	semidirect
623. #117	C₂³×C₁₃	semidirect
624. #117	C₂³×C₁₃	semidirect
651. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
681. C₂×C₁₃	#3495	direct (N × H)
793. C₁₃	C₂×#3495	direct (N × H)
899. C₂	C₁₃×#3495	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×#3495	2
C₂×C₁₃×#556	2
C₂×C₁₃×#554	2
C₂×C₁₃×#552	2
C₂×C₁₃×#551	2
C₂×C₁₃×#544	2
C₂×C₁₃×#542	2
C₂×C₁₃×#541	2
C₂×C₁₃×#536	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#520	2
C₂×C₁₃×#519	2
C₂²×C₁₃×#117	2
C₂×#3495	13

Subgroups — C2×C13×#3495 #15749142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3495 #15749142