Subgroups — C₂×C₁₃×#3561 #15749070

Order 3328.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#543	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
12	C₂×C₁₃×#538	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#563	C₂²	1	32	yes	complemented
22	C₁₃×#562	C₂²	1	32	yes	complemented
23	C₁₃×#556	C₂²	1	32	yes	complemented
24	C₁₃×#551	C₂²	1	64	yes	complemented
25	D₄×Q₈×C₁₃	C₂²	1	32	yes	complemented
26	C₁₃×#548	C₂²	1	32	yes	complemented
27	C₁₃×#546	C₂²	1	32	yes	complemented
28	C₁₃×#543	C₂²	1	32	yes	complemented
29	C₁₃×#542	C₂²	1	32	yes	complemented
30	C₁₃×#542	C₂²	1	64	yes	complemented
31	C₁₃×#538	C₂²	1	32	yes	complemented
32	C₁₃×#536	C₂²	1	32	yes	complemented
33	C₁₃×#533	C₂²	1	16	yes	complemented
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₁₃×#529	C₂²	1	16	yes	complemented
39	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#124	C₂²	1	2	yes	—
46	C₂×C₁₃×#124	C₂²	1	2	yes	—
47	C₂×C₁₃×#124	C₂²	1	2	yes	—
48	C₂×C₁₃×#124	C₂²	1	2	yes	—
49	C₂×C₁₃×#124	C₂²	1	2	yes	—
50	C₂×C₁₃×#124	C₂²	1	16	yes	complemented
51	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
53	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
54	C₂×C₁₃×#123	C₂²	1	4	yes	—
55	C₂×C₁₃×#123	C₂²	1	2	yes	—
56	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
57	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
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	4	yes	complemented
66	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
67	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
68	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
69	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₂×C₁₃×#121	C₂²	1	4	yes	—
71	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#121	C₂²	1	2	yes	—
73	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
74	C₂×C₁₃×#120	C₂²	1	4	yes	—
75	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
77	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
78	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
79	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
81	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
82	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
84	C₂×C₁₃×#117	C₂²	1	2	yes	—
85	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
86	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
87	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
88	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
89	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
90	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
91	C₂⁵×C₁₃	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	—	4	8	no	—
93	C₂×C₁₃×#41	C₂³	1	16	yes	—
94	C₂²×Q₈×C₁₃	—	4	4	no	—
95	C₂²×Q₈×C₁₃	—	4	8	no	—
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
100	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
101	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
104	C₂²×D₄×C₁₃	—	4	4	no	—
105	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
108	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
121	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
122	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
123	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	complemented
124	C₁₃×#126	C₂³	1	16	yes	complemented
125	C₁₃×#126	C₂³	1	32	yes	complemented
126	C₁₃×#126	C₂³	1	32	yes	complemented
127	C₁₃×#126	C₂³	1	32	yes	complemented
128	C₁₃×#125	C₂³	1	8	yes	complemented
129	C₁₃×#125	C₂³	1	16	yes	complemented
130	C₁₃×#124	C₂³	1	16	yes	—
131	C₁₃×#124	C₂³	1	16	yes	—
132	C₁₃×#124	C₂³	1	16	yes	—
133	C₁₃×#124	C₂³	1	16	yes	—
134	C₁₃×#124	C₂³	1	16	yes	—
135	C₁₃×#124	C₂³	1	8	yes	complemented
136	C₁₃×#124	C₂³	1	32	yes	complemented
137	C₁₃×#124	C₂³	1	32	yes	complemented
138	C₁₃×#123	C₂³	1	16	yes	—
139	C₁₃×#123	C₂³	1	32	yes	—
140	C₁₃×#123	C₂³	1	32	yes	complemented
141	C₁₃×#123	C₂³	1	32	yes	complemented
142	C₁₃×#123	C₂³	1	32	yes	complemented
143	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
148	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
149	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
150	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
152	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₁₃×#121	C₂³	1	8	yes	—
155	C₁₃×#121	C₂³	1	16	yes	—
156	C₁₃×#121	C₂³	1	32	yes	—
157	C₁₃×#121	C₂³	1	32	yes	complemented
158	C₁₃×#120	C₂³	1	32	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
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×D₄×C₁₃	C₂³	1	16	yes	—
164	C₄×D₄×C₁₃	C₂³	1	32	yes	—
165	C₄×D₄×C₁₃	C₂³	1	16	yes	—
166	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
167	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
168	C₁₃×#117	C₂³	1	16	yes	—
169	C₁₃×#117	C₂³	1	16	yes	complemented
170	C₁₃×#117	C₂³	1	32	yes	complemented
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
199	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
210	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
211	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
213	C₂×#3561	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	8	no	—
215	C₂⁴×C₁₃	—	4	4	no	—
216	C₂⁴×C₁₃	—	4	4	no	—
217	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
218	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
219	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
221	C₁₃×#41	—	4	32	no	—
222	C₂×Q₈×C₁₃	—	2	8	no	—
223	C₂×Q₈×C₁₃	—	2	8	no	—
224	C₂×Q₈×C₁₃	—	4	8	no	—
225	C₂×Q₈×C₁₃	—	4	4	no	—
226	C₂×Q₈×C₁₃	—	4	2	no	—
227	C₂×Q₈×C₁₃	—	4	4	no	—
228	C₂×Q₈×C₁₃	—	4	16	no	—
229	C₂×Q₈×C₁₃	—	4	32	no	—
230	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
234	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
235	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
236	C₂×D₄×C₁₃	—	2	8	no	—
237	C₂×D₄×C₁₃	—	2	8	no	—
238	C₂×D₄×C₁₃	—	4	16	no	—
239	C₂×D₄×C₁₃	—	4	4	no	—
240	C₂×D₄×C₁₃	—	4	8	no	—
241	C₂×D₄×C₁₃	—	4	2	no	—
242	C₂×D₄×C₁₃	—	4	8	no	—
243	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
245	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
246	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	8	no	—
252	C₂²×C₄×C₁₃	—	4	8	no	—
253	C₂²×C₄×C₁₃	—	4	2	no	—
254	C₂²×C₄×C₁₃	—	4	8	no	—
255	C₂²×C₄×C₁₃	—	4	4	no	—
256	C₂²×C₄×C₁₃	—	4	8	no	—
257	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
299	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
300	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
303	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
304	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
305	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
307	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
308	C₄²×C₁₃	C₂⁴	1	4	yes	—
309	C₄²×C₁₃	C₂⁴	1	4	yes	—
310	C₄²×C₁₃	C₂⁴	1	4	yes	—
311	C₄²×C₁₃	C₂⁴	1	4	yes	—
312	C₄²×C₁₃	C₂⁴	1	16	yes	—
313	C₄²×C₁₃	C₂⁴	1	8	yes	—
314	C₄²×C₁₃	C₂⁴	1	16	yes	—
315	#3561	C₂×C₁₃	1	32	yes	direct product factor
316	C₂×#563	C₂×C₁₃	1	2	yes	complemented
317	C₂×#562	C₂×C₁₃	1	2	yes	complemented
318	C₂×#556	C₂×C₁₃	1	2	yes	complemented
319	C₂×#551	C₂×C₁₃	1	4	yes	complemented
320	C₂×D₄×Q₈	C₂×C₁₃	1	2	yes	complemented
321	C₂×#548	C₂×C₁₃	1	2	yes	complemented
322	C₂×#546	C₂×C₁₃	1	2	yes	complemented
323	C₂×#543	C₂×C₁₃	1	2	yes	complemented
324	C₂×#542	C₂×C₁₃	1	2	yes	complemented
325	C₂×#542	C₂×C₁₃	1	4	yes	complemented
326	C₂×#538	C₂×C₁₃	1	2	yes	complemented
327	C₂×#536	C₂×C₁₃	1	2	yes	complemented
328	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	4	no	—
334	C₂³×C₁₃	—	2	8	no	—
335	C₂³×C₁₃	—	2	4	no	—
336	C₂³×C₁₃	—	2	8	no	—
337	C₂³×C₁₃	—	2	8	no	—
338	C₂³×C₁₃	—	2	4	no	—
339	C₂³×C₁₃	—	2	16	no	—
340	C₂³×C₁₃	—	4	8	no	—
341	C₂³×C₁₃	—	4	8	no	—
342	C₂³×C₁₃	—	8	16	no	—
343	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
344	C₂³×C₁₃	C₂⁵	1	8	yes	—
345	C₂³×C₁₃	C₂⁵	1	4	yes	—
346	C₂³×C₁₃	C₂⁵	1	2	yes	—
347	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
348	Q₈×C₁₃	—	2	16	no	—
349	Q₈×C₁₃	—	2	16	no	—
350	Q₈×C₁₃	—	4	16	no	—
351	Q₈×C₁₃	—	4	8	no	—
352	Q₈×C₁₃	—	4	4	no	—
353	Q₈×C₁₃	—	4	8	no	—
354	D₄×C₁₃	—	2	16	no	—
355	D₄×C₁₃	—	2	16	no	—
356	D₄×C₁₃	—	4	8	no	—
357	D₄×C₁₃	—	4	16	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	4	16	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	8	no	—
363	C₂×C₄×C₁₃	—	2	8	no	—
364	C₂×C₄×C₁₃	—	2	8	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	4	no	—
368	C₂×C₄×C₁₃	—	2	4	no	—
369	C₂×C₄×C₁₃	—	2	8	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	8	no	—
373	C₂×C₄×C₁₃	—	2	16	no	—
374	C₂×C₄×C₁₃	—	4	16	no	—
375	C₂×C₄×C₁₃	—	4	4	no	—
376	C₂×C₄×C₁₃	—	4	16	no	—
377	C₂×C₄×C₁₃	—	4	8	no	—
378	C₂×C₄×C₁₃	—	4	16	no	—
379	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
380	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
382	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
383	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
384	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
386	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
387	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
388	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
389	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
390	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
391	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
392	C₂²×#41	C₂²×C₁₃	1	2	yes	—
393	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
395	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
396	#563	C₂²×C₁₃	1	32	yes	complemented
397	#562	C₂²×C₁₃	1	32	yes	complemented
398	#556	C₂²×C₁₃	1	32	yes	complemented
399	#551	C₂²×C₁₃	1	64	yes	complemented
400	D₄×Q₈	C₂²×C₁₃	1	32	yes	complemented
401	#548	C₂²×C₁₃	1	32	yes	complemented
402	#546	C₂²×C₁₃	1	32	yes	complemented
403	#543	C₂²×C₁₃	1	32	yes	complemented
404	#542	C₂²×C₁₃	1	32	yes	complemented
405	#542	C₂²×C₁₃	1	64	yes	complemented
406	#538	C₂²×C₁₃	1	32	yes	complemented
407	#536	C₂²×C₁₃	1	32	yes	complemented
408	#533	C₂²×C₁₃	1	16	yes	complemented
409	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
412	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
413	#529	C₂²×C₁₃	1	16	yes	complemented
414	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
415	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
416	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
417	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
418	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
420	C₂×#124	C₂²×C₁₃	1	2	yes	—
421	C₂×#124	C₂²×C₁₃	1	2	yes	—
422	C₂×#124	C₂²×C₁₃	1	2	yes	—
423	C₂×#124	C₂²×C₁₃	1	2	yes	—
424	C₂×#124	C₂²×C₁₃	1	2	yes	—
425	C₂×#124	C₂²×C₁₃	1	16	yes	complemented
426	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
428	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
429	C₂×#123	C₂²×C₁₃	1	2	yes	—
430	C₂×#123	C₂²×C₁₃	1	4	yes	—
431	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
432	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
433	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
434	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
436	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
437	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
438	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
439	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
440	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
441	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
442	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
443	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
444	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
445	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#121	C₂²×C₁₃	1	2	yes	—
447	C₂×#121	C₂²×C₁₃	1	4	yes	—
448	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
449	C₂×#120	C₂²×C₁₃	1	4	yes	—
450	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
452	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
453	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
454	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
455	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
456	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
457	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
459	C₂×#117	C₂²×C₁₃	1	2	yes	—
460	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
461	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
462	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
463	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
464	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
465	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×C₁₃	—	2	2	no	—
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	8	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	2	8	no	—
471	C₂²×C₁₃	—	2	4	no	—
472	C₂²×C₁₃	—	2	8	no	—
473	C₂²×C₁₃	—	2	8	no	—
474	C₂²×C₁₃	—	2	4	no	—
475	C₂²×C₁₃	—	4	8	no	—
476	C₂²×C₁₃	—	4	16	no	—
477	C₂²×C₁₃	—	8	16	no	—
478	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
479	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
480	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
481	C₂²×C₁₃	#585	1	2	yes	—
482	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
483	C₄×C₁₃	—	2	4	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	8	no	—
486	C₄×C₁₃	—	2	8	no	—
487	C₄×C₁₃	—	2	2	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	2	4	no	—
490	C₄×C₁₃	—	2	4	no	—
491	C₄×C₁₃	—	2	8	no	—
492	C₄×C₁₃	—	2	2	no	—
493	C₄×C₁₃	—	2	2	no	—
494	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
495	C₂⁵	C₂³×C₁₃	1	2	yes	—
496	C₂×#41	—	4	8	no	—
497	C₂×#41	C₂³×C₁₃	1	16	yes	—
498	C₂²×Q₈	—	4	4	no	—
499	C₂²×Q₈	—	4	8	no	—
500	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
501	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
502	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
504	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
505	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
506	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
507	C₂²×Q₈	C₂³×C₁₃	1	16	yes	complemented
508	C₂²×D₄	—	4	4	no	—
509	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
510	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
511	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
512	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
514	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
515	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
516	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
520	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
522	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
523	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
524	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
525	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
526	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
527	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
528	#126	C₂³×C₁₃	1	16	yes	complemented
529	#126	C₂³×C₁₃	1	32	yes	complemented
530	#126	C₂³×C₁₃	1	32	yes	complemented
531	#126	C₂³×C₁₃	1	32	yes	complemented
532	#125	C₂³×C₁₃	1	8	yes	complemented
533	#125	C₂³×C₁₃	1	16	yes	complemented
534	#124	C₂³×C₁₃	1	16	yes	—
535	#124	C₂³×C₁₃	1	16	yes	—
536	#124	C₂³×C₁₃	1	16	yes	—
537	#124	C₂³×C₁₃	1	16	yes	—
538	#124	C₂³×C₁₃	1	16	yes	—
539	#124	C₂³×C₁₃	1	8	yes	complemented
540	#124	C₂³×C₁₃	1	32	yes	complemented
541	#124	C₂³×C₁₃	1	32	yes	complemented
542	#123	C₂³×C₁₃	1	16	yes	—
543	#123	C₂³×C₁₃	1	32	yes	—
544	#123	C₂³×C₁₃	1	32	yes	complemented
545	#123	C₂³×C₁₃	1	32	yes	complemented
546	#123	C₂³×C₁₃	1	32	yes	complemented
547	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
548	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
549	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
550	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
551	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
552	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
553	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
554	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
555	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
556	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
557	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
558	#121	C₂³×C₁₃	1	8	yes	—
559	#121	C₂³×C₁₃	1	16	yes	—
560	#121	C₂³×C₁₃	1	32	yes	—
561	#121	C₂³×C₁₃	1	32	yes	complemented
562	#120	C₂³×C₁₃	1	32	yes	—
563	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
564	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
565	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
566	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
567	C₄×D₄	C₂³×C₁₃	1	16	yes	—
568	C₄×D₄	C₂³×C₁₃	1	32	yes	—
569	C₄×D₄	C₂³×C₁₃	1	16	yes	—
570	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
571	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
572	#117	C₂³×C₁₃	1	16	yes	—
573	#117	C₂³×C₁₃	1	16	yes	complemented
574	#117	C₂³×C₁₃	1	32	yes	complemented
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
610	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
617	C₂×C₁₃	—	2	4	no	—
618	C₂×C₁₃	—	4	4	no	—
619	C₂×C₁₃	—	4	8	no	—
620	C₂×C₁₃	#3561	1	4	yes	direct product factor
621	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
623	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
624	C₂⁴	—	2	8	no	—
625	C₂⁴	—	4	4	no	—
626	C₂⁴	—	4	4	no	—
627	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
628	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
629	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
631	#41	—	4	32	no	—
632	C₂×Q₈	—	2	8	no	—
633	C₂×Q₈	—	2	8	no	—
634	C₂×Q₈	—	4	8	no	—
635	C₂×Q₈	—	4	4	no	—
636	C₂×Q₈	—	4	2	no	—
637	C₂×Q₈	—	4	4	no	—
638	C₂×Q₈	—	4	16	no	—
639	C₂×Q₈	—	4	32	no	—
640	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
641	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
642	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
643	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
644	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
645	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
646	C₂×D₄	—	2	8	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	4	16	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	8	no	—
651	C₂×D₄	—	4	8	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
654	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
655	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
656	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
657	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
658	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	8	no	—
662	C₂²×C₄	—	4	8	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	4	8	no	—
665	C₂²×C₄	—	4	8	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
687	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
688	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
689	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
691	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
692	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
693	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
694	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
695	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
696	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
697	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
698	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
699	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
700	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
701	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
702	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
703	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
704	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
705	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
706	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
707	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
708	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
709	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
710	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
711	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
712	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
713	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
714	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
715	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
716	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
717	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
718	C₄²	C₂⁴×C₁₃	1	4	yes	—
719	C₄²	C₂⁴×C₁₃	1	4	yes	—
720	C₄²	C₂⁴×C₁₃	1	4	yes	—
721	C₄²	C₂⁴×C₁₃	1	4	yes	—
722	C₄²	C₂⁴×C₁₃	1	16	yes	—
723	C₄²	C₂⁴×C₁₃	1	8	yes	—
724	C₄²	C₂⁴×C₁₃	1	16	yes	—
725	C₁₃	C₂×#3561	1	1	yes	characteristic, direct product factor, Sylow
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	8	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	8	no	—
732	C₂³	—	2	8	no	—
733	C₂³	—	2	4	no	—
734	C₂³	—	2	16	no	—
735	C₂³	—	4	8	no	—
736	C₂³	—	4	8	no	—
737	C₂³	—	8	16	no	—
738	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
739	C₂³	C₂⁵×C₁₃	1	8	yes	—
740	C₂³	C₂⁵×C₁₃	1	4	yes	—
741	C₂³	C₂⁵×C₁₃	1	2	yes	—
742	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
743	Q₈	—	2	16	no	—
744	Q₈	—	2	16	no	—
745	Q₈	—	4	16	no	—
746	Q₈	—	4	8	no	—
747	Q₈	—	4	4	no	—
748	Q₈	—	4	8	no	—
749	D₄	—	2	16	no	—
750	D₄	—	2	16	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	16	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	16	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	8	no	—
759	C₂×C₄	—	2	8	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	8	no	—
768	C₂×C₄	—	2	16	no	—
769	C₂×C₄	—	4	16	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	16	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	16	no	—
774	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
775	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
776	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
777	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
778	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
779	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
780	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
781	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
782	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
783	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
784	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
785	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
786	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
787	C₂²	—	2	8	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	4	no	—
791	C₂²	—	2	8	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	8	no	—
794	C₂²	—	2	8	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	4	8	no	—
797	C₂²	—	4	16	no	—
798	C₂²	—	8	16	no	—
799	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
800	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
801	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
802	C₂²	C₁₃×#585	1	2	yes	—
803	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
804	C₄	—	2	4	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	8	no	—
807	C₄	—	2	8	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	8	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	4	8	no	—
818	C₂	—	4	4	no	—
819	C₂	C₁₃×#3561	1	4	yes	direct product factor
820	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
822	C₂	C₂×C₁₃×#585	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×#3561	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#562	C₂	semidirect
4. C₂×C₁₃×#556	C₂	semidirect
5. C₂×C₁₃×#551	C₂	semidirect
6. C₂×D₄×Q₈×C₁₃	C₂	semidirect
7. C₂×C₁₃×#548	C₂	semidirect
8. C₂×C₁₃×#546	C₂	semidirect
9. C₂×C₁₃×#543	C₂	semidirect
10. C₂×C₁₃×#542	C₂	semidirect
11. C₂×C₁₃×#542	C₂	semidirect
12. C₂×C₁₃×#538	C₂	semidirect
13. C₂×C₁₃×#536	C₂	semidirect
14. C₂×C₁₃×#533	C₂	semidirect
15. C₂×C₁₃×#529	C₂	semidirect
16. C₂²×C₁₃×#124	C₂	semidirect
19. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₁₃×#563	C₂²	semidirect
22. C₁₃×#562	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#551	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#548	C₂²	semidirect
27. C₁₃×#546	C₂²	semidirect
28. C₁₃×#543	C₂²	semidirect
29. C₁₃×#542	C₂²	semidirect
30. C₁₃×#542	C₂²	semidirect
31. C₁₃×#538	C₂²	semidirect
32. C₁₃×#536	C₂²	semidirect
33. C₁₃×#533	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
38. C₁₃×#529	C₂²	semidirect
39. C₂×C₁₃×#126	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
50. C₂×C₁₃×#124	C₂²	semidirect
51. C₂×C₁₃×#124	C₂²	semidirect
52. C₂×C₁₃×#124	C₂²	semidirect
53. C₂×C₁₃×#124	C₂²	semidirect
56. C₂×C₁₃×#123	C₂²	semidirect
57. C₂×C₁₃×#123	C₂²	semidirect
58. C₂×C₁₃×#123	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
67. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
69. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
73. C₂×C₁₃×#121	C₂²	semidirect
75. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
76. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
77. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
78. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
82. C₂×C₄×D₄×C₁₃	C₂²	semidirect
83. C₂×C₄×D₄×C₁₃	C₂²	semidirect
85. C₂×C₁₃×#117	C₂²	semidirect
86. C₂×C₁₃×#117	C₂²	semidirect
103. C₂²×Q₈×C₁₃	C₂³	semidirect
120. C₁₃×C₄⋊Q₈	C₂³	semidirect
121. C₁₃×C₄⋊Q₈	C₂³	semidirect
122. C₁₃×C₄⋊Q₈	C₂³	semidirect
123. C₁₃×C₄⋊Q₈	C₂³	semidirect
124. C₁₃×#126	C₂³	semidirect
125. C₁₃×#126	C₂³	semidirect
126. C₁₃×#126	C₂³	semidirect
127. C₁₃×#126	C₂³	semidirect
128. C₁₃×#125	C₂³	semidirect
129. C₁₃×#125	C₂³	semidirect
135. C₁₃×#124	C₂³	semidirect
136. C₁₃×#124	C₂³	semidirect
137. C₁₃×#124	C₂³	semidirect
140. C₁₃×#123	C₂³	semidirect
141. C₁₃×#123	C₂³	semidirect
142. C₁₃×#123	C₂³	semidirect
147. C₁₃×C₂²⋊Q₈	C₂³	semidirect
148. C₁₃×C₂²⋊Q₈	C₂³	semidirect
149. C₁₃×C₂²⋊Q₈	C₂³	semidirect
150. C₁₃×C₂²⋊Q₈	C₂³	semidirect
151. C₁₃×C₂²⋊Q₈	C₂³	semidirect
152. C₁₃×C₂²⋊Q₈	C₂³	semidirect
153. C₁₃×C₂²⋊Q₈	C₂³	semidirect
157. C₁₃×#121	C₂³	semidirect
159. C₄×Q₈×C₁₃	C₂³	semidirect
160. C₄×Q₈×C₁₃	C₂³	semidirect
161. C₄×Q₈×C₁₃	C₂³	semidirect
162. C₄×Q₈×C₁₃	C₂³	semidirect
166. C₄×D₄×C₁₃	C₂³	semidirect
167. C₄×D₄×C₁₃	C₂³	semidirect
169. C₁₃×#117	C₂³	semidirect
170. C₁₃×#117	C₂³	semidirect
213. C₂×#3561	C₁₃	direct (N × H)
315. #3561	C₂×C₁₃	direct (N × H)
316. C₂×#563	C₂×C₁₃	semidirect
317. C₂×#562	C₂×C₁₃	semidirect
318. C₂×#556	C₂×C₁₃	semidirect
319. C₂×#551	C₂×C₁₃	semidirect
320. C₂×D₄×Q₈	C₂×C₁₃	semidirect
321. C₂×#548	C₂×C₁₃	semidirect
322. C₂×#546	C₂×C₁₃	semidirect
323. C₂×#543	C₂×C₁₃	semidirect
324. C₂×#542	C₂×C₁₃	semidirect
325. C₂×#542	C₂×C₁₃	semidirect
326. C₂×#538	C₂×C₁₃	semidirect
327. C₂×#536	C₂×C₁₃	semidirect
328. C₂×#533	C₂×C₁₃	semidirect
329. C₂×#529	C₂×C₁₃	semidirect
330. C₂²×#124	C₂×C₁₃	semidirect
394. C₂³×Q₈	C₂²×C₁₃	semidirect
396. #563	C₂²×C₁₃	semidirect
397. #562	C₂²×C₁₃	semidirect
398. #556	C₂²×C₁₃	semidirect
399. #551	C₂²×C₁₃	semidirect
400. D₄×Q₈	C₂²×C₁₃	semidirect
401. #548	C₂²×C₁₃	semidirect
402. #546	C₂²×C₁₃	semidirect
403. #543	C₂²×C₁₃	semidirect
404. #542	C₂²×C₁₃	semidirect
405. #542	C₂²×C₁₃	semidirect
406. #538	C₂²×C₁₃	semidirect
407. #536	C₂²×C₁₃	semidirect
408. #533	C₂²×C₁₃	semidirect
409. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
410. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
411. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
412. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
413. #529	C₂²×C₁₃	semidirect
414. C₂×#126	C₂²×C₁₃	semidirect
415. C₂×#126	C₂²×C₁₃	semidirect
416. C₂×#126	C₂²×C₁₃	semidirect
417. C₂×#126	C₂²×C₁₃	semidirect
418. C₂×#125	C₂²×C₁₃	semidirect
419. C₂×#125	C₂²×C₁₃	semidirect
425. C₂×#124	C₂²×C₁₃	semidirect
426. C₂×#124	C₂²×C₁₃	semidirect
427. C₂×#124	C₂²×C₁₃	semidirect
428. C₂×#124	C₂²×C₁₃	semidirect
431. C₂×#123	C₂²×C₁₃	semidirect
432. C₂×#123	C₂²×C₁₃	semidirect
433. C₂×#123	C₂²×C₁₃	semidirect
438. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
439. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
440. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
441. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
442. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
443. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
444. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
448. C₂×#121	C₂²×C₁₃	semidirect
450. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
451. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
452. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
453. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
457. C₂×C₄×D₄	C₂²×C₁₃	semidirect
458. C₂×C₄×D₄	C₂²×C₁₃	semidirect
460. C₂×#117	C₂²×C₁₃	semidirect
461. C₂×#117	C₂²×C₁₃	semidirect
507. C₂²×Q₈	C₂³×C₁₃	semidirect
524. C₄⋊Q₈	C₂³×C₁₃	semidirect
525. C₄⋊Q₈	C₂³×C₁₃	semidirect
526. C₄⋊Q₈	C₂³×C₁₃	semidirect
527. C₄⋊Q₈	C₂³×C₁₃	semidirect
528. #126	C₂³×C₁₃	semidirect
529. #126	C₂³×C₁₃	semidirect
530. #126	C₂³×C₁₃	semidirect
531. #126	C₂³×C₁₃	semidirect
532. #125	C₂³×C₁₃	semidirect
533. #125	C₂³×C₁₃	semidirect
539. #124	C₂³×C₁₃	semidirect
540. #124	C₂³×C₁₃	semidirect
541. #124	C₂³×C₁₃	semidirect
544. #123	C₂³×C₁₃	semidirect
545. #123	C₂³×C₁₃	semidirect
546. #123	C₂³×C₁₃	semidirect
551. C₂²⋊Q₈	C₂³×C₁₃	semidirect
552. C₂²⋊Q₈	C₂³×C₁₃	semidirect
553. C₂²⋊Q₈	C₂³×C₁₃	semidirect
554. C₂²⋊Q₈	C₂³×C₁₃	semidirect
555. C₂²⋊Q₈	C₂³×C₁₃	semidirect
556. C₂²⋊Q₈	C₂³×C₁₃	semidirect
557. C₂²⋊Q₈	C₂³×C₁₃	semidirect
561. #121	C₂³×C₁₃	semidirect
563. C₄×Q₈	C₂³×C₁₃	semidirect
564. C₄×Q₈	C₂³×C₁₃	semidirect
565. C₄×Q₈	C₂³×C₁₃	semidirect
566. C₄×Q₈	C₂³×C₁₃	semidirect
570. C₄×D₄	C₂³×C₁₃	semidirect
571. C₄×D₄	C₂³×C₁₃	semidirect
573. #117	C₂³×C₁₃	semidirect
574. #117	C₂³×C₁₃	semidirect
620. C₂×C₁₃	#3561	direct (N × H)
725. C₁₃	C₂×#3561	direct (N × H)
819. C₂	C₁₃×#3561	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×#3561	2
C₂×C₁₃×#563	2
C₂×C₁₃×#562	2
C₂×C₁₃×#556	2
C₂×C₁₃×#551	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#546	2
C₂×C₁₃×#543	2
C₂×C₁₃×#542	2
C₂×C₁₃×#538	2
C₂×C₁₃×#536	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#124	2
C₂×#3561	13

Subgroups — C2×C13×#3561 #15749070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3561 #15749070