Subgroups — C₂×C₁₃×#3545 #15749092

Order 3328.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3545	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#555	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#551	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#551	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#546	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#534	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
14	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
19	C₁₃×#563	C₂²	1	16	yes	complemented
20	C₁₃×#562	C₂²	1	32	yes	complemented
21	C₁₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
22	C₁₃×#555	C₂²	1	32	yes	complemented
23	C₁₃×#551	C₂²	1	32	yes	complemented
24	C₁₃×#551	C₂²	1	64	yes	complemented
25	C₁₃×#546	C₂²	1	64	yes	complemented
26	C₁₃×#542	C₂²	1	64	yes	complemented
27	C₁₃×#538	C₂²	1	64	yes	complemented
28	C₁₃×#536	C₂²	1	32	yes	complemented
29	C₁₃×#534	C₂²	1	32	yes	complemented
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₁₃×#529	C₂²	1	32	yes	complemented
33	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
44	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
46	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
47	C₂×C₁₃×#124	C₂²	1	16	yes	complemented
48	C₂×C₁₃×#123	C₂²	1	2	yes	—
49	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
50	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
51	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
52	C₂×C₁₃×#123	C₂²	1	2	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	4	yes	complemented
56	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
58	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₁₃×#121	C₂²	1	2	yes	—
61	C₂×C₁₃×#121	C₂²	1	4	yes	—
62	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
63	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
64	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
65	C₂×C₁₃×#120	C₂²	1	2	yes	—
66	C₂×C₁₃×#120	C₂²	1	4	yes	—
67	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
68	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
69	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
70	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
72	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
73	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
74	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
75	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
76	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
77	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
78	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
79	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₂⁵×C₁₃	C₂³	1	2	yes	—
82	C₂⁵×C₁₃	C₂³	1	2	yes	—
83	C₂×C₁₃×#41	—	4	8	no	—
84	C₂×C₁₃×#41	C₂³	1	16	yes	—
85	C₂²×Q₈×C₁₃	—	4	4	no	—
86	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
92	C₂²×D₄×C₁₃	—	4	4	no	—
93	C₂²×D₄×C₁₃	—	4	8	no	—
94	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
113	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
114	C₁₃×#126	C₂³	1	32	yes	complemented
115	C₁₃×#126	C₂³	1	32	yes	complemented
116	C₁₃×#126	C₂³	1	32	yes	complemented
117	C₁₃×#125	C₂³	1	16	yes	complemented
118	C₁₃×#124	C₂³	1	8	yes	—
119	C₁₃×#124	C₂³	1	8	yes	—
120	C₁₃×#124	C₂³	1	32	yes	complemented
121	C₁₃×#124	C₂³	1	8	yes	complemented
122	C₁₃×#124	C₂³	1	8	yes	complemented
123	C₁₃×#124	C₂³	1	16	yes	complemented
124	C₁₃×#124	C₂³	1	16	yes	complemented
125	C₁₃×#124	C₂³	1	16	yes	complemented
126	C₁₃×#124	C₂³	1	32	yes	complemented
127	C₁₃×#124	C₂³	1	32	yes	complemented
128	C₁₃×#123	C₂³	1	16	yes	—
129	C₁₃×#123	C₂³	1	32	yes	complemented
130	C₁₃×#123	C₂³	1	16	yes	complemented
131	C₁₃×#123	C₂³	1	32	yes	complemented
132	C₁₃×#123	C₂³	1	32	yes	complemented
133	C₁₃×#123	C₂³	1	32	yes	complemented
134	C₁₃×#123	C₂³	1	32	yes	complemented
135	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
136	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
137	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
138	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
139	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
140	C₁₃×#121	C₂³	1	16	yes	—
141	C₁₃×#121	C₂³	1	32	yes	—
142	C₁₃×#121	C₂³	1	32	yes	complemented
143	C₁₃×#121	C₂³	1	32	yes	complemented
144	C₁₃×#121	C₂³	1	32	yes	complemented
145	C₁₃×#120	C₂³	1	32	yes	—
146	C₁₃×#120	C₂³	1	16	yes	—
147	C₁₃×#120	C₂³	1	16	yes	complemented
148	C₁₃×#120	C₂³	1	32	yes	complemented
149	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
150	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
151	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
152	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
153	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
154	C₁₃×#117	C₂³	1	32	yes	complemented
155	C₁₃×#117	C₂³	1	16	yes	complemented
156	C₁₃×#117	C₂³	1	32	yes	complemented
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
191	C₂×#3545	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂⁴×C₁₃	—	2	8	no	—
193	C₂⁴×C₁₃	—	4	4	no	—
194	C₂⁴×C₁₃	—	4	8	no	—
195	C₂⁴×C₁₃	—	4	8	no	—
196	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
197	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
198	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
199	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
201	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
202	C₁₃×#41	—	4	32	no	—
203	C₂×Q₈×C₁₃	—	4	2	no	—
204	C₂×Q₈×C₁₃	—	4	4	no	—
205	C₂×Q₈×C₁₃	—	4	2	no	—
206	C₂×Q₈×C₁₃	—	4	16	no	—
207	C₂×Q₈×C₁₃	—	4	4	no	—
208	C₂×Q₈×C₁₃	—	4	4	no	—
209	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
211	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
212	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
213	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
214	C₂×D₄×C₁₃	—	2	16	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	2	no	—
218	C₂×D₄×C₁₃	—	4	16	no	—
219	C₂×D₄×C₁₃	—	4	8	no	—
220	C₂×D₄×C₁₃	—	4	8	no	—
221	C₂×D₄×C₁₃	—	4	8	no	—
222	C₂×D₄×C₁₃	—	4	4	no	—
223	C₂×D₄×C₁₃	—	4	4	no	—
224	C₂×D₄×C₁₃	—	4	32	no	—
225	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
228	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
229	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
230	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
231	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
232	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
233	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	8	no	—
236	C₂²×C₄×C₁₃	—	4	8	no	—
237	C₂²×C₄×C₁₃	—	4	4	no	—
238	C₂²×C₄×C₁₃	—	4	8	no	—
239	C₂²×C₄×C₁₃	—	4	4	no	—
240	C₂²×C₄×C₁₃	—	4	8	no	—
241	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
257	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
258	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
266	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
267	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
268	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
269	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
270	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
271	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
272	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
273	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
274	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
275	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
276	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
277	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
278	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
279	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
280	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
281	C₄²×C₁₃	C₂⁴	1	4	yes	—
282	C₄²×C₁₃	C₂⁴	1	8	yes	—
283	C₄²×C₁₃	C₂⁴	1	4	yes	—
284	C₄²×C₁₃	C₂⁴	1	8	yes	—
285	C₄²×C₁₃	C₂⁴	1	16	yes	—
286	C₄²×C₁₃	C₂⁴	1	8	yes	—
287	#3545	C₂×C₁₃	1	32	yes	direct product factor
288	C₂×#563	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#562	C₂×C₁₃	1	2	yes	complemented
290	C₂×H(3,𝔽₄)	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂×#555	C₂×C₁₃	1	2	yes	complemented
292	C₂×#551	C₂×C₁₃	1	2	yes	complemented
293	C₂×#551	C₂×C₁₃	1	4	yes	complemented
294	C₂×#546	C₂×C₁₃	1	4	yes	complemented
295	C₂×#542	C₂×C₁₃	1	4	yes	complemented
296	C₂×#538	C₂×C₁₃	1	4	yes	complemented
297	C₂×#536	C₂×C₁₃	1	2	yes	complemented
298	C₂×#534	C₂×C₁₃	1	2	yes	complemented
299	C₂×#529	C₂×C₁₃	1	2	yes	complemented
300	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂³×C₁₃	—	2	4	no	—
302	C₂³×C₁₃	—	2	8	no	—
303	C₂³×C₁₃	—	2	4	no	—
304	C₂³×C₁₃	—	2	4	no	—
305	C₂³×C₁₃	—	2	8	no	—
306	C₂³×C₁₃	—	2	8	no	—
307	C₂³×C₁₃	—	2	8	no	—
308	C₂³×C₁₃	—	2	8	no	—
309	C₂³×C₁₃	—	2	16	no	—
310	C₂³×C₁₃	—	4	8	no	—
311	C₂³×C₁₃	—	4	16	no	—
312	C₂³×C₁₃	—	4	16	no	—
313	C₂³×C₁₃	—	8	16	no	—
314	C₂³×C₁₃	—	8	16	no	—
315	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
316	C₂³×C₁₃	C₂⁵	1	4	yes	—
317	C₂³×C₁₃	C₂⁵	1	8	yes	—
318	C₂³×C₁₃	C₂⁵	1	4	yes	—
319	C₂³×C₁₃	C₂⁵	1	2	yes	—
320	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
321	Q₈×C₁₃	—	4	4	no	—
322	Q₈×C₁₃	—	4	8	no	—
323	Q₈×C₁₃	—	4	4	no	—
324	Q₈×C₁₃	—	4	8	no	—
325	Q₈×C₁₃	—	4	8	no	—
326	D₄×C₁₃	—	2	32	no	—
327	D₄×C₁₃	—	4	4	no	—
328	D₄×C₁₃	—	4	8	no	—
329	D₄×C₁₃	—	4	4	no	—
330	D₄×C₁₃	—	4	16	no	—
331	D₄×C₁₃	—	4	16	no	—
332	D₄×C₁₃	—	4	16	no	—
333	D₄×C₁₃	—	4	8	no	—
334	D₄×C₁₃	—	4	8	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	8	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	16	no	—
341	C₂×C₄×C₁₃	—	2	8	no	—
342	C₂×C₄×C₁₃	—	2	4	no	—
343	C₂×C₄×C₁₃	—	2	8	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	8	no	—
346	C₂×C₄×C₁₃	—	4	16	no	—
347	C₂×C₄×C₁₃	—	4	8	no	—
348	C₂×C₄×C₁₃	—	4	16	no	—
349	C₂×C₄×C₁₃	—	4	8	no	—
350	C₂×C₄×C₁₃	—	4	16	no	—
351	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
352	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
353	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
354	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
355	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
356	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
357	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
358	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
359	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
360	C₂²×#41	C₂²×C₁₃	1	2	yes	—
361	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
363	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
364	#563	C₂²×C₁₃	1	16	yes	complemented
365	#562	C₂²×C₁₃	1	32	yes	complemented
366	H(3,𝔽₄)	C₂²×C₁₃	1	16	yes	complemented
367	#555	C₂²×C₁₃	1	32	yes	complemented
368	#551	C₂²×C₁₃	1	32	yes	complemented
369	#551	C₂²×C₁₃	1	64	yes	complemented
370	#546	C₂²×C₁₃	1	64	yes	complemented
371	#542	C₂²×C₁₃	1	64	yes	complemented
372	#538	C₂²×C₁₃	1	64	yes	complemented
373	#536	C₂²×C₁₃	1	32	yes	complemented
374	#534	C₂²×C₁₃	1	32	yes	complemented
375	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
376	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
377	#529	C₂²×C₁₃	1	32	yes	complemented
378	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
379	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
380	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
381	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
382	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
385	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
388	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
389	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
390	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
391	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
392	C₂×#124	C₂²×C₁₃	1	16	yes	complemented
393	C₂×#123	C₂²×C₁₃	1	2	yes	—
394	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
395	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
396	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
397	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
398	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
399	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
400	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
401	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
402	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
403	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
404	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
405	C₂×#121	C₂²×C₁₃	1	2	yes	—
406	C₂×#121	C₂²×C₁₃	1	4	yes	—
407	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
408	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
409	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
410	C₂×#120	C₂²×C₁₃	1	4	yes	—
411	C₂×#120	C₂²×C₁₃	1	2	yes	—
412	C₂×#120	C₂²×C₁₃	1	2	yes	complemented
413	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
414	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
415	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
416	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
417	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
418	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
419	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
420	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
421	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
422	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
423	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
424	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
425	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₂²×C₁₃	—	2	4	no	—
427	C₂²×C₁₃	—	2	8	no	—
428	C₂²×C₁₃	—	2	8	no	—
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	2	4	no	—
431	C₂²×C₁₃	—	2	8	no	—
432	C₂²×C₁₃	—	2	8	no	—
433	C₂²×C₁₃	—	2	8	no	—
434	C₂²×C₁₃	—	2	8	no	—
435	C₂²×C₁₃	—	4	16	no	—
436	C₂²×C₁₃	—	4	8	no	—
437	C₂²×C₁₃	—	4	8	no	—
438	C₂²×C₁₃	—	8	16	no	—
439	C₂²×C₁₃	—	8	16	no	—
440	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
441	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
442	C₂²×C₁₃	#585	1	4	yes	—
443	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
444	C₄×C₁₃	—	2	4	no	—
445	C₄×C₁₃	—	2	2	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	4	no	—
448	C₄×C₁₃	—	2	8	no	—
449	C₄×C₁₃	—	2	4	no	—
450	C₄×C₁₃	—	2	8	no	—
451	C₄×C₁₃	—	2	4	no	—
452	C₄×C₁₃	—	2	8	no	—
453	C₂⁵	C₂³×C₁₃	1	2	yes	—
454	C₂⁵	C₂³×C₁₃	1	2	yes	—
455	C₂×#41	—	4	8	no	—
456	C₂×#41	C₂³×C₁₃	1	16	yes	—
457	C₂²×Q₈	—	4	4	no	—
458	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
459	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
460	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
461	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
462	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
464	C₂²×D₄	—	4	4	no	—
465	C₂²×D₄	—	4	8	no	—
466	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
467	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
468	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
469	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
470	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
472	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
473	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
474	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
476	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
477	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
478	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
481	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
482	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
483	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
484	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
485	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
486	#126	C₂³×C₁₃	1	32	yes	complemented
487	#126	C₂³×C₁₃	1	32	yes	complemented
488	#126	C₂³×C₁₃	1	32	yes	complemented
489	#125	C₂³×C₁₃	1	16	yes	complemented
490	#124	C₂³×C₁₃	1	8	yes	—
491	#124	C₂³×C₁₃	1	8	yes	—
492	#124	C₂³×C₁₃	1	32	yes	complemented
493	#124	C₂³×C₁₃	1	8	yes	complemented
494	#124	C₂³×C₁₃	1	8	yes	complemented
495	#124	C₂³×C₁₃	1	16	yes	complemented
496	#124	C₂³×C₁₃	1	16	yes	complemented
497	#124	C₂³×C₁₃	1	16	yes	complemented
498	#124	C₂³×C₁₃	1	32	yes	complemented
499	#124	C₂³×C₁₃	1	32	yes	complemented
500	#123	C₂³×C₁₃	1	16	yes	—
501	#123	C₂³×C₁₃	1	32	yes	complemented
502	#123	C₂³×C₁₃	1	16	yes	complemented
503	#123	C₂³×C₁₃	1	32	yes	complemented
504	#123	C₂³×C₁₃	1	32	yes	complemented
505	#123	C₂³×C₁₃	1	32	yes	complemented
506	#123	C₂³×C₁₃	1	32	yes	complemented
507	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
508	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
509	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
510	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
511	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
512	#121	C₂³×C₁₃	1	16	yes	—
513	#121	C₂³×C₁₃	1	32	yes	—
514	#121	C₂³×C₁₃	1	32	yes	complemented
515	#121	C₂³×C₁₃	1	32	yes	complemented
516	#121	C₂³×C₁₃	1	32	yes	complemented
517	#120	C₂³×C₁₃	1	32	yes	—
518	#120	C₂³×C₁₃	1	16	yes	—
519	#120	C₂³×C₁₃	1	16	yes	complemented
520	#120	C₂³×C₁₃	1	32	yes	complemented
521	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
522	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
523	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
524	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
525	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
526	#117	C₂³×C₁₃	1	32	yes	complemented
527	#117	C₂³×C₁₃	1	16	yes	complemented
528	#117	C₂³×C₁₃	1	32	yes	complemented
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
555	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
556	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
559	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
563	C₂×C₁₃	—	2	4	no	—
564	C₂×C₁₃	—	4	8	no	—
565	C₂×C₁₃	—	4	4	no	—
566	C₂×C₁₃	—	4	4	no	—
567	C₂×C₁₃	#3545	1	4	yes	direct product factor
568	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₁₃	C₂×#585	1	2	yes	—
570	C₂⁴	—	2	8	no	—
571	C₂⁴	—	4	4	no	—
572	C₂⁴	—	4	8	no	—
573	C₂⁴	—	4	8	no	—
574	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
575	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
576	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
577	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
578	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
579	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
580	#41	—	4	32	no	—
581	C₂×Q₈	—	4	2	no	—
582	C₂×Q₈	—	4	4	no	—
583	C₂×Q₈	—	4	2	no	—
584	C₂×Q₈	—	4	16	no	—
585	C₂×Q₈	—	4	4	no	—
586	C₂×Q₈	—	4	4	no	—
587	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
588	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
589	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
590	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
591	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
592	C₂×D₄	—	2	16	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	16	no	—
597	C₂×D₄	—	4	8	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	4	8	no	—
600	C₂×D₄	—	4	8	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	—	4	32	no	—
603	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
604	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
605	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
606	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
607	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
608	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
609	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
610	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
611	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	4	4	no	—
615	C₂²×C₄	—	4	8	no	—
616	C₂²×C₄	—	4	8	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	8	no	—
619	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
621	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
628	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
630	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
631	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
635	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
636	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
637	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
638	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
639	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
640	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
641	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
642	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
643	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
644	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
645	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
646	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
647	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
648	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
649	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
650	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
651	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
652	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
653	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
656	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
657	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
658	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
659	C₄²	C₂⁴×C₁₃	1	4	yes	—
660	C₄²	C₂⁴×C₁₃	1	8	yes	—
661	C₄²	C₂⁴×C₁₃	1	4	yes	—
662	C₄²	C₂⁴×C₁₃	1	8	yes	—
663	C₄²	C₂⁴×C₁₃	1	16	yes	—
664	C₄²	C₂⁴×C₁₃	1	8	yes	—
665	C₁₃	C₂×#3545	1	1	yes	characteristic, direct product factor, Sylow
666	C₂³	—	2	4	no	—
667	C₂³	—	2	8	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	8	no	—
673	C₂³	—	2	8	no	—
674	C₂³	—	2	16	no	—
675	C₂³	—	4	8	no	—
676	C₂³	—	4	16	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	8	16	no	—
679	C₂³	—	8	16	no	—
680	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
681	C₂³	C₂⁵×C₁₃	1	4	yes	—
682	C₂³	C₂⁵×C₁₃	1	8	yes	—
683	C₂³	C₂⁵×C₁₃	1	4	yes	—
684	C₂³	C₂⁵×C₁₃	1	2	yes	—
685	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	4	no	—
689	Q₈	—	4	8	no	—
690	Q₈	—	4	8	no	—
691	D₄	—	2	32	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	8	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	16	no	—
696	D₄	—	4	16	no	—
697	D₄	—	4	16	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	8	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	16	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	16	no	—
715	C₂×C₄	—	4	16	no	—
716	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
717	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
718	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
719	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
720	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
721	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
722	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
723	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
724	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
725	C₂²	—	2	8	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	8	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	2	8	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	2	8	no	—
734	C₂²	—	4	16	no	—
735	C₂²	—	4	8	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	8	16	no	—
738	C₂²	—	8	16	no	—
739	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
740	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
741	C₂²	C₁₃×#585	1	4	yes	—
742	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	8	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	8	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	8	no	—
752	C₂	—	2	4	no	—
753	C₂	—	4	4	no	—
754	C₂	—	4	8	no	—
755	C₂	—	4	4	no	—
756	C₂	C₁₃×#3545	1	4	yes	direct product factor
757	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
758	C₂	C₂×C₁₃×#585	1	2	yes	—

	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×#3545	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#562	C₂	semidirect
4. C₂×C₁₃×H(3,𝔽₄)	C₂	semidirect
5. C₂×C₁₃×#555	C₂	semidirect
6. C₂×C₁₃×#551	C₂	semidirect
7. C₂×C₁₃×#551	C₂	semidirect
8. C₂×C₁₃×#546	C₂	semidirect
9. C₂×C₁₃×#542	C₂	semidirect
10. C₂×C₁₃×#538	C₂	semidirect
11. C₂×C₁₃×#536	C₂	semidirect
12. C₂×C₁₃×#534	C₂	semidirect
13. C₂×C₁₃×#529	C₂	semidirect
14. C₂²×C₁₃×#124	C₂	semidirect
16. C₂³×Q₈×C₁₃	C₂²	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₁₃×#563	C₂²	semidirect
20. C₁₃×#562	C₂²	semidirect
21. C₁₃×H(3,𝔽₄)	C₂²	semidirect
22. C₁₃×#555	C₂²	semidirect
23. C₁₃×#551	C₂²	semidirect
24. C₁₃×#551	C₂²	semidirect
25. C₁₃×#546	C₂²	semidirect
26. C₁₃×#542	C₂²	semidirect
27. C₁₃×#538	C₂²	semidirect
28. C₁₃×#536	C₂²	semidirect
29. C₁₃×#534	C₂²	semidirect
30. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₁₃×#529	C₂²	semidirect
33. C₂×C₁₃×#126	C₂²	semidirect
34. C₂×C₁₃×#126	C₂²	semidirect
35. C₂×C₁₃×#126	C₂²	semidirect
36. C₂×C₁₃×#125	C₂²	semidirect
39. C₂×C₁₃×#124	C₂²	semidirect
40. C₂×C₁₃×#124	C₂²	semidirect
41. C₂×C₁₃×#124	C₂²	semidirect
42. C₂×C₁₃×#124	C₂²	semidirect
43. C₂×C₁₃×#124	C₂²	semidirect
44. C₂×C₁₃×#124	C₂²	semidirect
45. C₂×C₁₃×#124	C₂²	semidirect
46. C₂×C₁₃×#124	C₂²	semidirect
47. C₂×C₁₃×#124	C₂²	semidirect
49. C₂×C₁₃×#123	C₂²	semidirect
50. C₂×C₁₃×#123	C₂²	semidirect
51. C₂×C₁₃×#123	C₂²	semidirect
52. C₂×C₁₃×#123	C₂²	semidirect
53. C₂×C₁₃×#123	C₂²	semidirect
54. C₂×C₁₃×#123	C₂²	semidirect
55. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
57. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₁₃×#121	C₂²	semidirect
63. C₂×C₁₃×#121	C₂²	semidirect
64. C₂×C₁₃×#121	C₂²	semidirect
67. C₂×C₁₃×#120	C₂²	semidirect
68. C₂×C₁₃×#120	C₂²	semidirect
69. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
70. C₂×C₄×D₄×C₁₃	C₂²	semidirect
71. C₂×C₄×D₄×C₁₃	C₂²	semidirect
72. C₂×C₄×D₄×C₁₃	C₂²	semidirect
73. C₂×C₄×D₄×C₁₃	C₂²	semidirect
74. C₂×C₁₃×#117	C₂²	semidirect
75. C₂×C₁₃×#117	C₂²	semidirect
76. C₂×C₁₃×#117	C₂²	semidirect
77. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
78. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
79. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
80. C₂²×C₄²×C₁₃	C₂²	semidirect
91. C₂²×Q₈×C₁₃	C₂³	semidirect
104. C₂²×D₄×C₁₃	C₂³	semidirect
112. C₁₃×C₄⋊Q₈	C₂³	semidirect
113. C₁₃×C₄⋊Q₈	C₂³	semidirect
114. C₁₃×#126	C₂³	semidirect
115. C₁₃×#126	C₂³	semidirect
116. C₁₃×#126	C₂³	semidirect
117. C₁₃×#125	C₂³	semidirect
120. C₁₃×#124	C₂³	semidirect
121. C₁₃×#124	C₂³	semidirect
122. C₁₃×#124	C₂³	semidirect
123. C₁₃×#124	C₂³	semidirect
124. C₁₃×#124	C₂³	semidirect
125. C₁₃×#124	C₂³	semidirect
126. C₁₃×#124	C₂³	semidirect
127. C₁₃×#124	C₂³	semidirect
129. C₁₃×#123	C₂³	semidirect
130. C₁₃×#123	C₂³	semidirect
131. C₁₃×#123	C₂³	semidirect
132. C₁₃×#123	C₂³	semidirect
133. C₁₃×#123	C₂³	semidirect
134. C₁₃×#123	C₂³	semidirect
135. C₁₃×C₂²⋊Q₈	C₂³	semidirect
136. C₁₃×C₂²⋊Q₈	C₂³	semidirect
137. C₁₃×C₂²⋊Q₈	C₂³	semidirect
138. C₁₃×C₂²⋊Q₈	C₂³	semidirect
139. C₁₃×C₂²⋊Q₈	C₂³	semidirect
142. C₁₃×#121	C₂³	semidirect
143. C₁₃×#121	C₂³	semidirect
144. C₁₃×#121	C₂³	semidirect
147. C₁₃×#120	C₂³	semidirect
148. C₁₃×#120	C₂³	semidirect
149. C₄×Q₈×C₁₃	C₂³	semidirect
150. C₄×D₄×C₁₃	C₂³	semidirect
151. C₄×D₄×C₁₃	C₂³	semidirect
152. C₄×D₄×C₁₃	C₂³	semidirect
153. C₄×D₄×C₁₃	C₂³	semidirect
154. C₁₃×#117	C₂³	semidirect
155. C₁₃×#117	C₂³	semidirect
156. C₁₃×#117	C₂³	semidirect
181. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
182. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
183. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
190. C₂×C₄²×C₁₃	C₂³	semidirect
191. C₂×#3545	C₁₃	direct (N × H)
287. #3545	C₂×C₁₃	direct (N × H)
288. C₂×#563	C₂×C₁₃	semidirect
289. C₂×#562	C₂×C₁₃	semidirect
290. C₂×H(3,𝔽₄)	C₂×C₁₃	semidirect
291. C₂×#555	C₂×C₁₃	semidirect
292. C₂×#551	C₂×C₁₃	semidirect
293. C₂×#551	C₂×C₁₃	semidirect
294. C₂×#546	C₂×C₁₃	semidirect
295. C₂×#542	C₂×C₁₃	semidirect
296. C₂×#538	C₂×C₁₃	semidirect
297. C₂×#536	C₂×C₁₃	semidirect
298. C₂×#534	C₂×C₁₃	semidirect
299. C₂×#529	C₂×C₁₃	semidirect
300. C₂²×#124	C₂×C₁₃	semidirect
361. C₂³×Q₈	C₂²×C₁₃	semidirect
363. C₂³×D₄	C₂²×C₁₃	semidirect
364. #563	C₂²×C₁₃	semidirect
365. #562	C₂²×C₁₃	semidirect
366. H(3,𝔽₄)	C₂²×C₁₃	semidirect
367. #555	C₂²×C₁₃	semidirect
368. #551	C₂²×C₁₃	semidirect
369. #551	C₂²×C₁₃	semidirect
370. #546	C₂²×C₁₃	semidirect
371. #542	C₂²×C₁₃	semidirect
372. #538	C₂²×C₁₃	semidirect
373. #536	C₂²×C₁₃	semidirect
374. #534	C₂²×C₁₃	semidirect
375. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
376. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
377. #529	C₂²×C₁₃	semidirect
378. C₂×#126	C₂²×C₁₃	semidirect
379. C₂×#126	C₂²×C₁₃	semidirect
380. C₂×#126	C₂²×C₁₃	semidirect
381. C₂×#125	C₂²×C₁₃	semidirect
384. C₂×#124	C₂²×C₁₃	semidirect
385. C₂×#124	C₂²×C₁₃	semidirect
386. C₂×#124	C₂²×C₁₃	semidirect
387. C₂×#124	C₂²×C₁₃	semidirect
388. C₂×#124	C₂²×C₁₃	semidirect
389. C₂×#124	C₂²×C₁₃	semidirect
390. C₂×#124	C₂²×C₁₃	semidirect
391. C₂×#124	C₂²×C₁₃	semidirect
392. C₂×#124	C₂²×C₁₃	semidirect
394. C₂×#123	C₂²×C₁₃	semidirect
395. C₂×#123	C₂²×C₁₃	semidirect
396. C₂×#123	C₂²×C₁₃	semidirect
397. C₂×#123	C₂²×C₁₃	semidirect
398. C₂×#123	C₂²×C₁₃	semidirect
399. C₂×#123	C₂²×C₁₃	semidirect
400. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
401. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
402. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
403. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
404. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
407. C₂×#121	C₂²×C₁₃	semidirect
408. C₂×#121	C₂²×C₁₃	semidirect
409. C₂×#121	C₂²×C₁₃	semidirect
412. C₂×#120	C₂²×C₁₃	semidirect
413. C₂×#120	C₂²×C₁₃	semidirect
414. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
415. C₂×C₄×D₄	C₂²×C₁₃	semidirect
416. C₂×C₄×D₄	C₂²×C₁₃	semidirect
417. C₂×C₄×D₄	C₂²×C₁₃	semidirect
418. C₂×C₄×D₄	C₂²×C₁₃	semidirect
419. C₂×#117	C₂²×C₁₃	semidirect
420. C₂×#117	C₂²×C₁₃	semidirect
421. C₂×#117	C₂²×C₁₃	semidirect
422. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
423. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
424. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
425. C₂²×C₄²	C₂²×C₁₃	semidirect
463. C₂²×Q₈	C₂³×C₁₃	semidirect
476. C₂²×D₄	C₂³×C₁₃	semidirect
484. C₄⋊Q₈	C₂³×C₁₃	semidirect
485. C₄⋊Q₈	C₂³×C₁₃	semidirect
486. #126	C₂³×C₁₃	semidirect
487. #126	C₂³×C₁₃	semidirect
488. #126	C₂³×C₁₃	semidirect
489. #125	C₂³×C₁₃	semidirect
492. #124	C₂³×C₁₃	semidirect
493. #124	C₂³×C₁₃	semidirect
494. #124	C₂³×C₁₃	semidirect
495. #124	C₂³×C₁₃	semidirect
496. #124	C₂³×C₁₃	semidirect
497. #124	C₂³×C₁₃	semidirect
498. #124	C₂³×C₁₃	semidirect
499. #124	C₂³×C₁₃	semidirect
501. #123	C₂³×C₁₃	semidirect
502. #123	C₂³×C₁₃	semidirect
503. #123	C₂³×C₁₃	semidirect
504. #123	C₂³×C₁₃	semidirect
505. #123	C₂³×C₁₃	semidirect
506. #123	C₂³×C₁₃	semidirect
507. C₂²⋊Q₈	C₂³×C₁₃	semidirect
508. C₂²⋊Q₈	C₂³×C₁₃	semidirect
509. C₂²⋊Q₈	C₂³×C₁₃	semidirect
510. C₂²⋊Q₈	C₂³×C₁₃	semidirect
511. C₂²⋊Q₈	C₂³×C₁₃	semidirect
514. #121	C₂³×C₁₃	semidirect
515. #121	C₂³×C₁₃	semidirect
516. #121	C₂³×C₁₃	semidirect
519. #120	C₂³×C₁₃	semidirect
520. #120	C₂³×C₁₃	semidirect
521. C₄×Q₈	C₂³×C₁₃	semidirect
522. C₄×D₄	C₂³×C₁₃	semidirect
523. C₄×D₄	C₂³×C₁₃	semidirect
524. C₄×D₄	C₂³×C₁₃	semidirect
525. C₄×D₄	C₂³×C₁₃	semidirect
526. #117	C₂³×C₁₃	semidirect
527. #117	C₂³×C₁₃	semidirect
528. #117	C₂³×C₁₃	semidirect
553. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
554. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
555. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
562. C₂×C₄²	C₂³×C₁₃	semidirect
567. C₂×C₁₃	#3545	direct (N × H)
665. C₁₃	C₂×#3545	direct (N × H)
756. C₂	C₁₃×#3545	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×#3545	2
C₂×C₁₃×#563	2
C₂×C₁₃×#562	2
C₂×C₁₃×H(3,𝔽₄)	2
C₂×C₁₃×#555	2
C₂×C₁₃×#551	2
C₂×C₁₃×#546	2
C₂×C₁₃×#542	2
C₂×C₁₃×#538	2
C₂×C₁₃×#536	2
C₂×C₁₃×#534	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#124	2
C₂×#3545	13

Subgroups — C2×C13×#3545 #15749092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3545 #15749092