Subgroups — C₂×C₁₃×#3520 #15749111

Order 3328.

7910 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#533	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×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#520	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	—
20	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
21	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
22	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
24	C₁₃×#556	C₂²	1	16	yes	complemented
25	C₁₃×#554	C₂²	1	32	yes	complemented
26	C₁₃×#552	C₂²	1	32	yes	complemented
27	C₁₃×#551	C₂²	1	64	yes	complemented
28	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
29	C₁₃×#548	C₂²	1	32	yes	complemented
30	C₁₃×#547	C₂²	1	16	yes	complemented
31	C₁₃×#547	C₂²	1	16	yes	complemented
32	C₁₃×#546	C₂²	1	32	yes	complemented
33	C₁₃×#542	C₂²	1	32	yes	complemented
34	C₁₃×#539	C₂²	1	64	yes	complemented
35	C₁₃×#533	C₂²	1	16	yes	complemented
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₁₃×#529	C₂²	1	16	yes	complemented
40	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
46	C₂×C₁₃×#124	C₂²	1	2	yes	—
47	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
49	C₁₃×#525	C₂²	1	32	yes	complemented
50	C₂×C₁₃×#123	C₂²	1	2	yes	—
51	C₂×C₁₃×#123	C₂²	1	4	yes	—
52	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
53	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
54	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
55	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
58	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	32	yes	complemented
67	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#121	C₂²	1	4	yes	—
69	C₂×C₁₃×#121	C₂²	1	2	yes	—
70	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
71	C₂×C₁₃×#120	C₂²	1	4	yes	—
72	C₁₃×#520	C₂²	1	32	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	1	yes	characteristic, complemented
76	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
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	1	yes	characteristic
80	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
83	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
84	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
85	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
86	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
87	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
89	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₁₃×#117	C₂²	1	2	yes	—
91	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
92	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
93	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
94	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
96	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
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	4	yes	—
100	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
101	C₂⁵×C₁₃	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	—	2	16	no	—
103	C₂×C₁₃×#41	—	4	8	no	—
104	C₂×C₁₃×#41	C₂³	1	16	yes	—
105	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
106	C₂²×Q₈×C₁₃	—	4	8	no	—
107	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
111	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
112	C₂²×D₄×C₁₃	—	2	8	no	—
113	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₁₃	—	4	8	no	—
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
136	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
137	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
138	C₁₃×#126	C₂³	1	16	yes	complemented
139	C₁₃×#126	C₂³	1	32	yes	complemented
140	C₁₃×#126	C₂³	1	32	yes	complemented
141	C₁₃×#125	C₂³	1	8	yes	complemented
142	C₁₃×#125	C₂³	1	16	yes	complemented
143	C₁₃×#125	C₂³	1	32	yes	complemented
144	C₁₃×#124	C₂³	1	16	yes	—
145	C₁₃×#124	C₂³	1	8	yes	complemented
146	C₁₃×#124	C₂³	1	32	yes	complemented
147	C₁₃×#123	C₂³	1	16	yes	—
148	C₁₃×#123	C₂³	1	32	yes	—
149	C₁₃×#123	C₂³	1	32	yes	complemented
150	C₁₃×#123	C₂³	1	32	yes	complemented
151	C₁₃×#123	C₂³	1	32	yes	complemented
152	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
158	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
159	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
160	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
161	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
162	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
163	C₁₃×#121	C₂³	1	8	yes	—
164	C₁₃×#121	C₂³	1	32	yes	—
165	C₁₃×#121	C₂³	1	16	yes	—
166	C₁₃×#121	C₂³	1	16	yes	complemented
167	C₁₃×#120	C₂³	1	32	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
169	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
170	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
171	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
172	C₄×D₄×C₁₃	C₂³	1	8	yes	—
173	C₄×D₄×C₁₃	C₂³	1	16	yes	—
174	C₄×D₄×C₁₃	C₂³	1	8	yes	—
175	C₄×D₄×C₁₃	C₂³	1	8	yes	—
176	C₄×D₄×C₁₃	C₂³	1	8	yes	—
177	C₄×D₄×C₁₃	C₂³	1	16	yes	—
178	C₄×D₄×C₁₃	C₂³	1	16	yes	—
179	C₄×D₄×C₁₃	C₂³	1	32	yes	—
180	C₄×D₄×C₁₃	C₂³	1	16	yes	—
181	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
182	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
183	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
184	C₁₃×#117	C₂³	1	16	yes	—
185	C₁₃×#117	C₂³	1	16	yes	complemented
186	C₁₃×#117	C₂³	1	32	yes	complemented
187	C₁₃×#117	C₂³	1	16	yes	complemented
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	16	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
234	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
235	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
236	C₂×#3520	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂⁴×C₁₃	—	2	8	no	—
238	C₂⁴×C₁₃	—	2	8	no	—
239	C₂⁴×C₁₃	—	4	4	no	—
240	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
241	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
242	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
243	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
244	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×#41	—	2	64	no	—
246	C₁₃×#41	—	4	32	no	—
247	C₂×Q₈×C₁₃	—	2	8	no	—
248	C₂×Q₈×C₁₃	—	2	4	no	—
249	C₂×Q₈×C₁₃	—	2	8	no	—
250	C₂×Q₈×C₁₃	—	4	8	no	—
251	C₂×Q₈×C₁₃	—	4	32	no	—
252	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
253	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
255	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
256	C₂×D₄×C₁₃	—	2	8	no	—
257	C₂×D₄×C₁₃	—	2	16	no	—
258	C₂×D₄×C₁₃	—	2	8	no	—
259	C₂×D₄×C₁₃	—	2	32	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	4	8	no	—
263	C₂×D₄×C₁₃	#41	1	8	yes	complemented
264	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
268	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
269	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
270	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₁₃	—	2	16	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	8	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	8	no	—
277	C₂²×C₄×C₁₃	—	2	8	no	—
278	C₂²×C₄×C₁₃	—	4	32	no	—
279	C₂²×C₄×C₁₃	—	4	4	no	—
280	C₂²×C₄×C₁₃	—	4	4	no	—
281	C₂²×C₄×C₁₃	—	4	4	no	—
282	C₂²×C₄×C₁₃	—	4	8	no	—
283	C₂²×C₄×C₁₃	—	4	8	no	—
284	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	8	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	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
338	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
339	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
340	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
343	C₄²×C₁₃	C₂⁴	1	4	yes	—
344	C₄²×C₁₃	C₂⁴	1	4	yes	—
345	C₄²×C₁₃	C₂⁴	1	4	yes	—
346	C₄²×C₁₃	C₂⁴	1	4	yes	—
347	C₄²×C₁₃	C₂⁴	1	16	yes	—
348	C₄²×C₁₃	C₂⁴	1	16	yes	—
349	C₄²×C₁₃	C₂⁴	1	8	yes	—
350	#3520	C₂×C₁₃	1	32	yes	direct product factor
351	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#554	C₂×C₁₃	1	2	yes	complemented
353	C₂×#552	C₂×C₁₃	1	2	yes	complemented
354	C₂×#551	C₂×C₁₃	1	4	yes	complemented
355	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#548	C₂×C₁₃	1	2	yes	complemented
357	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#546	C₂×C₁₃	1	2	yes	complemented
360	C₂×#542	C₂×C₁₃	1	2	yes	complemented
361	C₂×#539	C₂×C₁₃	1	4	yes	complemented
362	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂×#525	C₂×C₁₃	1	2	yes	complemented
365	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
366	C₂×#520	C₂×C₁₃	1	2	yes	complemented
367	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	4	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	4	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	2	16	no	—
374	C₂³×C₁₃	—	2	4	no	—
375	C₂³×C₁₃	—	2	4	no	—
376	C₂³×C₁₃	—	2	4	no	—
377	C₂³×C₁₃	—	2	4	no	—
378	C₂³×C₁₃	—	2	16	no	—
379	C₂³×C₁₃	—	2	4	no	—
380	C₂³×C₁₃	—	4	8	no	—
381	C₂³×C₁₃	—	4	32	no	—
382	C₂³×C₁₃	C₂×#41	1	8	yes	—
383	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
384	C₂³×C₁₃	C₂⁵	1	4	yes	—
385	C₂³×C₁₃	C₂⁵	1	4	yes	—
386	C₂³×C₁₃	C₂⁵	1	4	yes	—
387	C₂³×C₁₃	C₂⁵	1	2	yes	—
388	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
389	Q₈×C₁₃	—	2	16	no	—
390	Q₈×C₁₃	—	2	8	no	—
391	Q₈×C₁₃	—	2	16	no	—
392	Q₈×C₁₃	—	4	16	no	—
393	D₄×C₁₃	—	2	16	no	—
394	D₄×C₁₃	—	2	32	no	—
395	D₄×C₁₃	—	2	16	no	—
396	D₄×C₁₃	—	2	8	no	—
397	D₄×C₁₃	—	2	8	no	—
398	D₄×C₁₃	—	4	16	no	—
399	D₄×C₁₃	C₂×#41	1	16	yes	complemented
400	C₂×C₄×C₁₃	—	2	4	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	8	no	—
403	C₂×C₄×C₁₃	—	2	32	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	4	no	—
406	C₂×C₄×C₁₃	—	2	4	no	—
407	C₂×C₄×C₁₃	—	2	8	no	—
408	C₂×C₄×C₁₃	—	2	4	no	—
409	C₂×C₄×C₁₃	—	2	8	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	8	no	—
414	C₂×C₄×C₁₃	—	2	16	no	—
415	C₂×C₄×C₁₃	—	2	8	no	—
416	C₂×C₄×C₁₃	—	2	16	no	—
417	C₂×C₄×C₁₃	—	2	16	no	—
418	C₂×C₄×C₁₃	—	4	8	no	—
419	C₂×C₄×C₁₃	—	4	8	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	—	4	16	no	—
422	C₂×C₄×C₁₃	—	4	16	no	—
423	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
424	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
425	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
426	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
427	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
428	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
429	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
432	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
436	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
437	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
438	C₂²×#41	C₂²×C₁₃	1	2	yes	—
439	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
440	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
441	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
442	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
443	#556	C₂²×C₁₃	1	16	yes	complemented
444	#554	C₂²×C₁₃	1	32	yes	complemented
445	#552	C₂²×C₁₃	1	32	yes	complemented
446	#551	C₂²×C₁₃	1	64	yes	complemented
447	D₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
448	#548	C₂²×C₁₃	1	32	yes	complemented
449	#547	C₂²×C₁₃	1	16	yes	complemented
450	#547	C₂²×C₁₃	1	16	yes	complemented
451	#546	C₂²×C₁₃	1	32	yes	complemented
452	#542	C₂²×C₁₃	1	32	yes	complemented
453	#539	C₂²×C₁₃	1	64	yes	complemented
454	#533	C₂²×C₁₃	1	16	yes	complemented
455	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
458	#529	C₂²×C₁₃	1	16	yes	complemented
459	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
460	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
461	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
462	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
464	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
465	C₂×#124	C₂²×C₁₃	1	2	yes	—
466	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
468	#525	C₂²×C₁₃	1	32	yes	complemented
469	C₂×#123	C₂²×C₁₃	1	2	yes	—
470	C₂×#123	C₂²×C₁₃	1	4	yes	—
471	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
472	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
473	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
474	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
477	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
478	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
479	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
480	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
481	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
482	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
483	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
484	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
485	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	32	yes	complemented
486	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×#121	C₂²×C₁₃	1	4	yes	—
488	C₂×#121	C₂²×C₁₃	1	2	yes	—
489	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
490	C₂×#120	C₂²×C₁₃	1	4	yes	—
491	#520	C₂²×C₁₃	1	32	yes	complemented
492	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
493	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
494	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
496	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
502	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
503	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
504	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
506	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
507	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
508	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	C₂×#117	C₂²×C₁₃	1	2	yes	—
510	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
511	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
512	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
513	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
514	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
515	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
516	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
517	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
518	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
519	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	2	4	no	—
524	C₂²×C₁₃	—	2	8	no	—
525	C₂²×C₁₃	—	2	16	no	—
526	C₂²×C₁₃	—	2	4	no	—
527	C₂²×C₁₃	—	2	4	no	—
528	C₂²×C₁₃	—	2	4	no	—
529	C₂²×C₁₃	—	2	4	no	—
530	C₂²×C₁₃	—	2	4	no	—
531	C₂²×C₁₃	—	2	4	no	—
532	C₂²×C₁₃	—	4	32	no	—
533	C₂²×C₁₃	—	4	8	no	—
534	C₂²×C₁₃	—	4	8	no	—
535	C₂²×C₁₃	C₂²×#41	1	8	yes	—
536	C₂²×C₁₃	C₂²×#41	1	2	yes	—
537	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
538	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
539	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
540	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
541	C₄×C₁₃	—	2	4	no	—
542	C₄×C₁₃	—	2	2	no	—
543	C₄×C₁₃	—	2	8	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	4	no	—
546	C₄×C₁₃	—	2	4	no	—
547	C₄×C₁₃	—	2	8	no	—
548	C₄×C₁₃	—	2	4	no	—
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	—	2	2	no	—
551	C₄×C₁₃	—	2	4	no	—
552	C₄×C₁₃	C₂²×#41	1	4	yes	—
553	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
554	C₂⁵	C₂³×C₁₃	1	2	yes	—
555	C₂×#41	—	2	16	no	—
556	C₂×#41	—	4	8	no	—
557	C₂×#41	C₂³×C₁₃	1	16	yes	—
558	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
559	C₂²×Q₈	—	4	8	no	—
560	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
561	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
563	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
564	C₂²×Q₈	C₂³×C₁₃	1	16	yes	complemented
565	C₂²×D₄	—	2	8	no	—
566	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
567	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
568	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
570	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
571	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
573	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂³×C₄	—	4	8	no	—
575	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
577	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
579	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
580	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
581	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
584	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
585	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
586	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
587	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
588	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
589	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
590	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
591	#126	C₂³×C₁₃	1	16	yes	complemented
592	#126	C₂³×C₁₃	1	32	yes	complemented
593	#126	C₂³×C₁₃	1	32	yes	complemented
594	#125	C₂³×C₁₃	1	8	yes	complemented
595	#125	C₂³×C₁₃	1	16	yes	complemented
596	#125	C₂³×C₁₃	1	32	yes	complemented
597	#124	C₂³×C₁₃	1	16	yes	—
598	#124	C₂³×C₁₃	1	8	yes	complemented
599	#124	C₂³×C₁₃	1	32	yes	complemented
600	#123	C₂³×C₁₃	1	16	yes	—
601	#123	C₂³×C₁₃	1	32	yes	—
602	#123	C₂³×C₁₃	1	32	yes	complemented
603	#123	C₂³×C₁₃	1	32	yes	complemented
604	#123	C₂³×C₁₃	1	32	yes	complemented
605	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
606	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
608	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
609	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
610	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
611	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
612	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
613	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
614	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
615	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
616	#121	C₂³×C₁₃	1	8	yes	—
617	#121	C₂³×C₁₃	1	32	yes	—
618	#121	C₂³×C₁₃	1	16	yes	—
619	#121	C₂³×C₁₃	1	16	yes	complemented
620	#120	C₂³×C₁₃	1	32	yes	—
621	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
622	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
623	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
624	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
625	C₄×D₄	C₂³×C₁₃	1	8	yes	—
626	C₄×D₄	C₂³×C₁₃	1	16	yes	—
627	C₄×D₄	C₂³×C₁₃	1	8	yes	—
628	C₄×D₄	C₂³×C₁₃	1	8	yes	—
629	C₄×D₄	C₂³×C₁₃	1	8	yes	—
630	C₄×D₄	C₂³×C₁₃	1	16	yes	—
631	C₄×D₄	C₂³×C₁₃	1	16	yes	—
632	C₄×D₄	C₂³×C₁₃	1	32	yes	—
633	C₄×D₄	C₂³×C₁₃	1	16	yes	—
634	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
635	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
636	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
637	#117	C₂³×C₁₃	1	16	yes	—
638	#117	C₂³×C₁₃	1	16	yes	complemented
639	#117	C₂³×C₁₃	1	32	yes	complemented
640	#117	C₂³×C₁₃	1	16	yes	complemented
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
684	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
689	C₂×C₁₃	—	2	4	no	—
690	C₂×C₁₃	—	2	8	no	—
691	C₂×C₁₃	—	4	4	no	—
692	C₂×C₁₃	—	4	4	no	—
693	C₂×C₁₃	#3520	1	4	yes	direct product factor
694	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
695	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
697	C₂⁴	—	2	8	no	—
698	C₂⁴	—	2	8	no	—
699	C₂⁴	—	4	4	no	—
700	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
701	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
702	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
703	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
704	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
705	#41	—	2	64	no	—
706	#41	—	4	32	no	—
707	C₂×Q₈	—	2	8	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	2	8	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	—	4	32	no	—
712	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
713	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
714	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
715	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
716	C₂×D₄	—	2	8	no	—
717	C₂×D₄	—	2	16	no	—
718	C₂×D₄	—	2	8	no	—
719	C₂×D₄	—	2	32	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	4	8	no	—
723	C₂×D₄	C₁₃×#41	1	8	yes	complemented
724	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
725	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
726	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
727	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
728	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
729	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
730	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
731	C₂²×C₄	—	2	16	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	8	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	8	no	—
737	C₂²×C₄	—	2	8	no	—
738	C₂²×C₄	—	4	32	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	—	4	4	no	—
741	C₂²×C₄	—	4	4	no	—
742	C₂²×C₄	—	4	8	no	—
743	C₂²×C₄	—	4	8	no	—
744	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
753	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
754	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
759	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
772	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
773	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
782	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
785	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
787	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
788	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
790	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
797	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
798	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
799	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
800	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
801	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
802	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
803	C₄²	C₂⁴×C₁₃	1	4	yes	—
804	C₄²	C₂⁴×C₁₃	1	4	yes	—
805	C₄²	C₂⁴×C₁₃	1	4	yes	—
806	C₄²	C₂⁴×C₁₃	1	4	yes	—
807	C₄²	C₂⁴×C₁₃	1	16	yes	—
808	C₄²	C₂⁴×C₁₃	1	16	yes	—
809	C₄²	C₂⁴×C₁₃	1	8	yes	—
810	C₁₃	C₂×#3520	1	1	yes	characteristic, direct product factor, Sylow
811	C₂³	—	2	2	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	16	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	2	4	no	—
820	C₂³	—	2	4	no	—
821	C₂³	—	2	16	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	4	8	no	—
824	C₂³	—	4	32	no	—
825	C₂³	C₂×C₁₃×#41	1	8	yes	—
826	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
827	C₂³	C₂⁵×C₁₃	1	4	yes	—
828	C₂³	C₂⁵×C₁₃	1	4	yes	—
829	C₂³	C₂⁵×C₁₃	1	4	yes	—
830	C₂³	C₂⁵×C₁₃	1	2	yes	—
831	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
832	Q₈	—	2	16	no	—
833	Q₈	—	2	8	no	—
834	Q₈	—	2	16	no	—
835	Q₈	—	4	16	no	—
836	D₄	—	2	16	no	—
837	D₄	—	2	32	no	—
838	D₄	—	2	16	no	—
839	D₄	—	2	8	no	—
840	D₄	—	2	8	no	—
841	D₄	—	4	16	no	—
842	D₄	C₂×C₁₃×#41	1	16	yes	complemented
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	32	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	8	no	—
857	C₂×C₄	—	2	16	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	16	no	—
860	C₂×C₄	—	2	16	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	16	no	—
865	C₂×C₄	—	4	16	no	—
866	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
867	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
868	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
869	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
870	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
871	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
872	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
873	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
874	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
875	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
876	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
877	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
878	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
879	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
880	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	16	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	4	32	no	—
894	C₂²	—	4	8	no	—
895	C₂²	—	4	8	no	—
896	C₂²	C₂²×C₁₃×#41	1	8	yes	—
897	C₂²	C₂²×C₁₃×#41	1	2	yes	—
898	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
899	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
900	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
901	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	8	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	4	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	8	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	4	no	—
913	C₄	C₂²×C₁₃×#41	1	4	yes	—
914	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	—	2	8	no	—
917	C₂	—	4	4	no	—
918	C₂	—	4	4	no	—
919	C₂	C₁₃×#3520	1	4	yes	direct product factor
920	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
921	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
922	C₂	C₂²×C₁₃×2₋¹⁺⁴	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×#3520	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×#551	C₂	semidirect
6. C₂×D₄×Q₈×C₁₃	C₂	semidirect
7. C₂×C₁₃×#548	C₂	semidirect
8. C₂×C₁₃×#547	C₂	semidirect
9. C₂×C₁₃×#547	C₂	semidirect
10. C₂×C₁₃×#546	C₂	semidirect
11. C₂×C₁₃×#542	C₂	semidirect
12. C₂×C₁₃×#539	C₂	semidirect
13. C₂×C₁₃×#533	C₂	semidirect
14. C₂×C₁₃×#529	C₂	semidirect
15. C₂×C₁₃×#525	C₂	semidirect
16. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
17. C₂×C₁₃×#520	C₂	semidirect
18. C₂²×C₄×D₄×C₁₃	C₂	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂³×Q₈×C₁₃	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
31. C₁₃×#547	C₂²	semidirect
32. C₁₃×#546	C₂²	semidirect
33. C₁₃×#542	C₂²	semidirect
34. C₁₃×#539	C₂²	semidirect
35. C₁₃×#533	C₂²	semidirect
36. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₁₃×#529	C₂²	semidirect
40. C₂×C₁₃×#126	C₂²	semidirect
41. C₂×C₁₃×#126	C₂²	semidirect
42. C₂×C₁₃×#126	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
48. C₂×C₁₃×#124	C₂²	semidirect
49. C₁₃×#525	C₂²	semidirect
52. C₂×C₁₃×#123	C₂²	semidirect
53. C₂×C₁₃×#123	C₂²	semidirect
54. C₂×C₁₃×#123	C₂²	semidirect
59. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊Q₈	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
65. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
66. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
70. C₂×C₁₃×#121	C₂²	semidirect
72. C₁₃×#520	C₂²	semidirect
73. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
74. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
75. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
76. C₂×C₄×Q₈×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
91. C₂×C₁₃×#117	C₂²	semidirect
92. C₂×C₁₃×#117	C₂²	semidirect
93. C₂×C₁₃×#117	C₂²	semidirect
95. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
97. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
105. C₂×C₁₃×#41	C₂³	semidirect
111. C₂²×Q₈×C₁₃	C₂³	semidirect
135. C₁₃×C₄⋊Q₈	C₂³	semidirect
136. C₁₃×C₄⋊Q₈	C₂³	semidirect
137. C₁₃×C₄⋊Q₈	C₂³	semidirect
138. C₁₃×#126	C₂³	semidirect
139. C₁₃×#126	C₂³	semidirect
140. C₁₃×#126	C₂³	semidirect
141. C₁₃×#125	C₂³	semidirect
142. C₁₃×#125	C₂³	semidirect
143. C₁₃×#125	C₂³	semidirect
145. C₁₃×#124	C₂³	semidirect
146. C₁₃×#124	C₂³	semidirect
149. C₁₃×#123	C₂³	semidirect
150. C₁₃×#123	C₂³	semidirect
151. C₁₃×#123	C₂³	semidirect
156. C₁₃×C₂²⋊Q₈	C₂³	semidirect
157. C₁₃×C₂²⋊Q₈	C₂³	semidirect
158. C₁₃×C₂²⋊Q₈	C₂³	semidirect
159. C₁₃×C₂²⋊Q₈	C₂³	semidirect
160. C₁₃×C₂²⋊Q₈	C₂³	semidirect
161. C₁₃×C₂²⋊Q₈	C₂³	semidirect
162. C₁₃×C₂²⋊Q₈	C₂³	semidirect
166. C₁₃×#121	C₂³	semidirect
168. C₄×Q₈×C₁₃	C₂³	semidirect
169. C₄×Q₈×C₁₃	C₂³	semidirect
170. C₄×Q₈×C₁₃	C₂³	semidirect
171. C₄×Q₈×C₁₃	C₂³	semidirect
181. C₄×D₄×C₁₃	C₂³	semidirect
182. C₄×D₄×C₁₃	C₂³	semidirect
183. C₄×D₄×C₁₃	C₂³	semidirect
185. C₁₃×#117	C₂³	semidirect
186. C₁₃×#117	C₂³	semidirect
187. C₁₃×#117	C₂³	semidirect
208. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
209. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
210. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
236. C₂×#3520	C₁₃	direct (N × H)
263. C₂×D₄×C₁₃	#41	semidirect
350. #3520	C₂×C₁₃	direct (N × H)
351. C₂×#556	C₂×C₁₃	semidirect
352. C₂×#554	C₂×C₁₃	semidirect
353. C₂×#552	C₂×C₁₃	semidirect
354. C₂×#551	C₂×C₁₃	semidirect
355. C₂×D₄×Q₈	C₂×C₁₃	semidirect
356. C₂×#548	C₂×C₁₃	semidirect
357. C₂×#547	C₂×C₁₃	semidirect
358. C₂×#547	C₂×C₁₃	semidirect
359. C₂×#546	C₂×C₁₃	semidirect
360. C₂×#542	C₂×C₁₃	semidirect
361. C₂×#539	C₂×C₁₃	semidirect
362. C₂×#533	C₂×C₁₃	semidirect
363. C₂×#529	C₂×C₁₃	semidirect
364. C₂×#525	C₂×C₁₃	semidirect
365. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
366. C₂×#520	C₂×C₁₃	semidirect
367. C₂²×C₄×D₄	C₂×C₁₃	semidirect
399. D₄×C₁₃	C₂×#41	semidirect
439. C₂²×#41	C₂²×C₁₃	semidirect
440. C₂³×Q₈	C₂²×C₁₃	semidirect
443. #556	C₂²×C₁₃	semidirect
444. #554	C₂²×C₁₃	semidirect
445. #552	C₂²×C₁₃	semidirect
446. #551	C₂²×C₁₃	semidirect
447. D₄×Q₈	C₂²×C₁₃	semidirect
448. #548	C₂²×C₁₃	semidirect
449. #547	C₂²×C₁₃	semidirect
450. #547	C₂²×C₁₃	semidirect
451. #546	C₂²×C₁₃	semidirect
452. #542	C₂²×C₁₃	semidirect
453. #539	C₂²×C₁₃	semidirect
454. #533	C₂²×C₁₃	semidirect
455. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
456. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
458. #529	C₂²×C₁₃	semidirect
459. C₂×#126	C₂²×C₁₃	semidirect
460. C₂×#126	C₂²×C₁₃	semidirect
461. C₂×#126	C₂²×C₁₃	semidirect
462. C₂×#125	C₂²×C₁₃	semidirect
463. C₂×#125	C₂²×C₁₃	semidirect
464. C₂×#125	C₂²×C₁₃	semidirect
466. C₂×#124	C₂²×C₁₃	semidirect
467. C₂×#124	C₂²×C₁₃	semidirect
468. #525	C₂²×C₁₃	semidirect
471. C₂×#123	C₂²×C₁₃	semidirect
472. C₂×#123	C₂²×C₁₃	semidirect
473. C₂×#123	C₂²×C₁₃	semidirect
478. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
479. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
480. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
481. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
482. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
483. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
484. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
485. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
489. C₂×#121	C₂²×C₁₃	semidirect
491. #520	C₂²×C₁₃	semidirect
492. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
493. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
494. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
495. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
505. C₂×C₄×D₄	C₂²×C₁₃	semidirect
506. C₂×C₄×D₄	C₂²×C₁₃	semidirect
507. C₂×C₄×D₄	C₂²×C₁₃	semidirect
508. C₂×C₄×D₄	C₂²×C₁₃	semidirect
510. C₂×#117	C₂²×C₁₃	semidirect
511. C₂×#117	C₂²×C₁₃	semidirect
512. C₂×#117	C₂²×C₁₃	semidirect
514. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
515. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
516. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
558. C₂×#41	C₂³×C₁₃	semidirect
564. C₂²×Q₈	C₂³×C₁₃	semidirect
588. C₄⋊Q₈	C₂³×C₁₃	semidirect
589. C₄⋊Q₈	C₂³×C₁₃	semidirect
590. C₄⋊Q₈	C₂³×C₁₃	semidirect
591. #126	C₂³×C₁₃	semidirect
592. #126	C₂³×C₁₃	semidirect
593. #126	C₂³×C₁₃	semidirect
594. #125	C₂³×C₁₃	semidirect
595. #125	C₂³×C₁₃	semidirect
596. #125	C₂³×C₁₃	semidirect
598. #124	C₂³×C₁₃	semidirect
599. #124	C₂³×C₁₃	semidirect
602. #123	C₂³×C₁₃	semidirect
603. #123	C₂³×C₁₃	semidirect
604. #123	C₂³×C₁₃	semidirect
609. C₂²⋊Q₈	C₂³×C₁₃	semidirect
610. C₂²⋊Q₈	C₂³×C₁₃	semidirect
611. C₂²⋊Q₈	C₂³×C₁₃	semidirect
612. C₂²⋊Q₈	C₂³×C₁₃	semidirect
613. C₂²⋊Q₈	C₂³×C₁₃	semidirect
614. C₂²⋊Q₈	C₂³×C₁₃	semidirect
615. C₂²⋊Q₈	C₂³×C₁₃	semidirect
619. #121	C₂³×C₁₃	semidirect
621. C₄×Q₈	C₂³×C₁₃	semidirect
622. C₄×Q₈	C₂³×C₁₃	semidirect
623. C₄×Q₈	C₂³×C₁₃	semidirect
624. C₄×Q₈	C₂³×C₁₃	semidirect
634. C₄×D₄	C₂³×C₁₃	semidirect
635. C₄×D₄	C₂³×C₁₃	semidirect
636. C₄×D₄	C₂³×C₁₃	semidirect
638. #117	C₂³×C₁₃	semidirect
639. #117	C₂³×C₁₃	semidirect
640. #117	C₂³×C₁₃	semidirect
661. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
662. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
663. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
693. C₂×C₁₃	#3520	direct (N × H)
723. C₂×D₄	C₁₃×#41	semidirect
810. C₁₃	C₂×#3520	direct (N × H)
842. D₄	C₂×C₁₃×#41	semidirect
919. C₂	C₁₃×#3520	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×#3520	2
C₂×C₁₃×#556	2
C₂×C₁₃×#554	2
C₂×C₁₃×#552	2
C₂×C₁₃×#551	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₂×C₁₃×#546	2
C₂×C₁₃×#542	2
C₂×C₁₃×#539	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂×C₁₃×#525	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#520	2
C₂²×C₄×D₄×C₁₃	2
C₂×#3520	13

Subgroups — C2×C13×#3520 #15749111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3520 #15749111