Subgroups — C₂×C₁₃×#3554 #15749085

Order 3328.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3554	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#562	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#559	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
15	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	2	yes	—
20	C₂²×C₁₃×#41	C₂²	1	2	yes	—
21	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#562	C₂²	1	64	yes	complemented
23	C₁₃×#559	C₂²	1	32	yes	complemented
24	C₁₃×#559	C₂²	1	16	yes	complemented
25	C₁₃×#557	C₂²	1	16	yes	complemented
26	C₁₃×#554	C₂²	1	32	yes	complemented
27	C₁₃×#550	C₂²	1	16	yes	complemented
28	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
29	C₁₃×#548	C₂²	1	32	yes	complemented
30	C₁₃×#547	C₂²	1	32	yes	complemented
31	C₁₃×#542	C₂²	1	32	yes	complemented
32	C₁₃×#542	C₂²	1	32	yes	complemented
33	C₁₃×#540	C₂²	1	32	yes	complemented
34	C₁₃×#539	C₂²	1	64	yes	complemented
35	C₁₃×#536	C₂²	1	32	yes	complemented
36	C₁₃×#533	C₂²	1	16	yes	complemented
37	C₁₃×#532	C₂²	1	16	yes	complemented
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#127	C₂²	1	2	yes	—
45	C₁₃×#529	C₂²	1	16	yes	complemented
46	C₂×C₁₃×#126	C₂²	1	2	yes	—
47	C₂×C₁₃×#126	C₂²	1	4	yes	—
48	C₂×C₁₃×#125	C₂²	1	4	yes	—
49	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#125	C₂²	1	2	yes	—
51	C₂×C₁₃×#125	C₂²	1	2	yes	—
52	C₂×C₁₃×#124	C₂²	1	4	yes	—
53	C₂×C₁₃×#124	C₂²	1	4	yes	—
54	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#124	C₂²	1	2	yes	—
56	C₂×C₁₃×#124	C₂²	1	2	yes	—
57	C₂×C₁₃×#124	C₂²	1	2	yes	—
58	C₂×C₁₃×#123	C₂²	1	2	yes	—
59	C₂×C₁₃×#123	C₂²	1	4	yes	—
60	C₂×C₁₃×#123	C₂²	1	4	yes	—
61	C₂×C₁₃×#123	C₂²	1	4	yes	—
62	C₂×C₁₃×#123	C₂²	1	4	yes	—
63	C₂×C₁₃×#123	C₂²	1	4	yes	—
64	C₂×C₁₃×#123	C₂²	1	4	yes	—
65	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
67	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
68	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
69	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
73	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
74	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
75	C₂×C₁₃×#121	C₂²	1	2	yes	—
76	C₂×C₁₃×#121	C₂²	1	4	yes	—
77	C₂×C₁₃×#121	C₂²	1	4	yes	—
78	C₂×C₁₃×#121	C₂²	1	4	yes	—
79	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
80	C₂×C₁₃×#121	C₂²	1	2	yes	—
81	C₂×C₁₃×#121	C₂²	1	2	yes	—
82	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
83	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
84	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
85	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
86	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
87	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
88	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
92	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
93	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
94	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
95	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
96	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
97	C₂×C₁₃×#117	C₂²	1	2	yes	—
98	C₂×C₁₃×#117	C₂²	1	2	yes	—
99	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
100	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
101	C₂×C₁₃×#41	—	4	8	no	—
102	C₂×C₁₃×#41	—	4	8	no	—
103	C₂×C₁₃×#41	C₂³	1	16	yes	—
104	C₂×C₁₃×#41	C₂³	1	16	yes	—
105	C₂²×Q₈×C₁₃	—	4	8	no	—
106	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
112	C₂²×Q₈×C₁₃	C₂³	1	16	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
119	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
134	C₁₃×#127	C₂³	1	8	yes	—
135	C₁₃×#127	C₂³	1	16	yes	—
136	C₁₃×#126	C₂³	1	16	yes	—
137	C₁₃×#126	C₂³	1	32	yes	—
138	C₁₃×#125	C₂³	1	8	yes	—
139	C₁₃×#125	C₂³	1	16	yes	—
140	C₁₃×#125	C₂³	1	32	yes	—
141	C₁₃×#125	C₂³	1	16	yes	—
142	C₁₃×#124	C₂³	1	8	yes	—
143	C₁₃×#124	C₂³	1	16	yes	—
144	C₁₃×#124	C₂³	1	16	yes	—
145	C₁₃×#124	C₂³	1	32	yes	—
146	C₁₃×#124	C₂³	1	16	yes	—
147	C₁₃×#124	C₂³	1	32	yes	—
148	C₁₃×#123	C₂³	1	16	yes	—
149	C₁₃×#123	C₂³	1	32	yes	—
150	C₁₃×#123	C₂³	1	32	yes	—
151	C₁₃×#123	C₂³	1	32	yes	—
152	C₁₃×#123	C₂³	1	32	yes	—
153	C₁₃×#123	C₂³	1	32	yes	—
154	C₁₃×#123	C₂³	1	32	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
161	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
165	C₁₃×#121	C₂³	1	8	yes	—
166	C₁₃×#121	C₂³	1	16	yes	—
167	C₁₃×#121	C₂³	1	16	yes	—
168	C₁₃×#121	C₂³	1	32	yes	—
169	C₁₃×#121	C₂³	1	32	yes	—
170	C₁₃×#121	C₂³	1	32	yes	—
171	C₁₃×#121	C₂³	1	16	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
178	C₄×D₄×C₁₃	C₂³	1	16	yes	—
179	C₄×D₄×C₁₃	C₂³	1	8	yes	—
180	C₄×D₄×C₁₃	C₂³	1	16	yes	—
181	C₄×D₄×C₁₃	C₂³	1	16	yes	—
182	C₄×D₄×C₁₃	C₂³	1	32	yes	—
183	C₄×D₄×C₁₃	C₂³	1	16	yes	—
184	C₄×D₄×C₁₃	C₂³	1	16	yes	—
185	C₄×D₄×C₁₃	C₂³	1	16	yes	—
186	C₄×D₄×C₁₃	C₂³	1	16	yes	—
187	C₁₃×#117	C₂³	1	16	yes	—
188	C₁₃×#117	C₂³	1	16	yes	—
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	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	4	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	4	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
230	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
231	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
234	C₂×#3554	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
236	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
238	C₁₃×#41	—	4	32	no	—
239	C₁₃×#41	—	4	32	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	2	8	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	2	4	no	—
244	C₂×Q₈×C₁₃	—	4	8	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	—	4	32	no	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
252	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
253	C₂×D₄×C₁₃	—	2	8	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	8	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	4	4	no	—
258	C₂×D₄×C₁₃	—	4	8	no	—
259	C₂×D₄×C₁₃	—	4	8	no	—
260	C₂×D₄×C₁₃	—	4	8	no	—
261	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
268	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
269	C₂²×C₄×C₁₃	—	2	8	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	4	8	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	8	no	—
275	C₂²×C₄×C₁₃	—	4	8	no	—
276	C₂²×C₄×C₁₃	—	4	8	no	—
277	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	8	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	4	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
320	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
323	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₄²×C₁₃	C₂⁴	1	4	yes	—
335	C₄²×C₁₃	C₂⁴	1	4	yes	—
336	C₄²×C₁₃	C₂⁴	1	4	yes	—
337	C₄²×C₁₃	C₂⁴	1	4	yes	—
338	C₄²×C₁₃	C₂⁴	1	8	yes	—
339	C₄²×C₁₃	C₂⁴	1	8	yes	—
340	C₄²×C₁₃	C₂⁴	1	8	yes	—
341	C₄²×C₁₃	C₂⁴	1	16	yes	—
342	#3554	C₂×C₁₃	1	32	yes	direct product factor
343	C₂×#562	C₂×C₁₃	1	4	yes	complemented
344	C₂×#559	C₂×C₁₃	1	2	yes	complemented
345	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
346	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
347	C₂×#554	C₂×C₁₃	1	2	yes	complemented
348	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂×#548	C₂×C₁₃	1	2	yes	complemented
351	C₂×#547	C₂×C₁₃	1	2	yes	complemented
352	C₂×#542	C₂×C₁₃	1	2	yes	complemented
353	C₂×#542	C₂×C₁₃	1	2	yes	complemented
354	C₂×#540	C₂×C₁₃	1	2	yes	complemented
355	C₂×#539	C₂×C₁₃	1	4	yes	complemented
356	C₂×#536	C₂×C₁₃	1	2	yes	complemented
357	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂³×C₁₃	—	2	4	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	8	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	4	no	—
365	C₂³×C₁₃	—	2	8	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	8	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	C₂⁵	1	4	yes	—
370	C₂³×C₁₃	C₂⁵	1	2	yes	—
371	C₂³×C₁₃	C₂⁵	1	8	yes	—
372	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
373	Q₈×C₁₃	—	2	8	no	—
374	Q₈×C₁₃	—	2	16	no	—
375	Q₈×C₁₃	—	2	8	no	—
376	Q₈×C₁₃	—	2	8	no	—
377	Q₈×C₁₃	—	4	16	no	—
378	Q₈×C₁₃	—	4	8	no	—
379	D₄×C₁₃	—	2	16	no	—
380	D₄×C₁₃	—	2	8	no	—
381	D₄×C₁₃	—	2	16	no	—
382	D₄×C₁₃	—	4	8	no	—
383	D₄×C₁₃	—	4	8	no	—
384	D₄×C₁₃	—	4	16	no	—
385	D₄×C₁₃	—	4	16	no	—
386	D₄×C₁₃	—	4	16	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	8	no	—
391	C₂×C₄×C₁₃	—	2	4	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	4	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	16	no	—
400	C₂×C₄×C₁₃	—	2	8	no	—
401	C₂×C₄×C₁₃	—	2	8	no	—
402	C₂×C₄×C₁₃	—	4	16	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	16	no	—
405	C₂×C₄×C₁₃	—	4	16	no	—
406	C₂×C₄×C₁₃	—	4	16	no	—
407	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
409	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
410	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
411	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
412	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
414	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
423	C₂²×#41	C₂²×C₁₃	1	2	yes	—
424	C₂²×#41	C₂²×C₁₃	1	2	yes	—
425	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
426	#562	C₂²×C₁₃	1	64	yes	complemented
427	#559	C₂²×C₁₃	1	32	yes	complemented
428	#559	C₂²×C₁₃	1	16	yes	complemented
429	#557	C₂²×C₁₃	1	16	yes	complemented
430	#554	C₂²×C₁₃	1	32	yes	complemented
431	#550	C₂²×C₁₃	1	16	yes	complemented
432	D₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
433	#548	C₂²×C₁₃	1	32	yes	complemented
434	#547	C₂²×C₁₃	1	32	yes	complemented
435	#542	C₂²×C₁₃	1	32	yes	complemented
436	#542	C₂²×C₁₃	1	32	yes	complemented
437	#540	C₂²×C₁₃	1	32	yes	complemented
438	#539	C₂²×C₁₃	1	64	yes	complemented
439	#536	C₂²×C₁₃	1	32	yes	complemented
440	#533	C₂²×C₁₃	1	16	yes	complemented
441	#532	C₂²×C₁₃	1	16	yes	complemented
442	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
446	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
447	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#127	C₂²×C₁₃	1	2	yes	—
449	#529	C₂²×C₁₃	1	16	yes	complemented
450	C₂×#126	C₂²×C₁₃	1	2	yes	—
451	C₂×#126	C₂²×C₁₃	1	4	yes	—
452	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×#125	C₂²×C₁₃	1	2	yes	—
454	C₂×#125	C₂²×C₁₃	1	4	yes	—
455	C₂×#125	C₂²×C₁₃	1	2	yes	—
456	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×#124	C₂²×C₁₃	1	2	yes	—
458	C₂×#124	C₂²×C₁₃	1	2	yes	—
459	C₂×#124	C₂²×C₁₃	1	4	yes	—
460	C₂×#124	C₂²×C₁₃	1	2	yes	—
461	C₂×#124	C₂²×C₁₃	1	4	yes	—
462	C₂×#123	C₂²×C₁₃	1	2	yes	—
463	C₂×#123	C₂²×C₁₃	1	4	yes	—
464	C₂×#123	C₂²×C₁₃	1	4	yes	—
465	C₂×#123	C₂²×C₁₃	1	4	yes	—
466	C₂×#123	C₂²×C₁₃	1	4	yes	—
467	C₂×#123	C₂²×C₁₃	1	4	yes	—
468	C₂×#123	C₂²×C₁₃	1	4	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
474	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
475	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	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	—
479	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×#121	C₂²×C₁₃	1	2	yes	—
481	C₂×#121	C₂²×C₁₃	1	2	yes	—
482	C₂×#121	C₂²×C₁₃	1	4	yes	—
483	C₂×#121	C₂²×C₁₃	1	4	yes	—
484	C₂×#121	C₂²×C₁₃	1	4	yes	—
485	C₂×#121	C₂²×C₁₃	1	2	yes	—
486	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
490	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
493	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
495	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
496	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
497	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
500	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
501	C₂×#117	C₂²×C₁₃	1	2	yes	—
502	C₂×#117	C₂²×C₁₃	1	2	yes	—
503	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
504	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
505	C₂²×C₁₃	—	2	4	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	8	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	2	4	no	—
510	C₂²×C₁₃	—	2	8	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	2	8	no	—
513	C₂²×C₁₃	—	2	4	no	—
514	C₂²×C₁₃	—	4	8	no	—
515	C₂²×C₁₃	—	4	4	no	—
516	C₂²×C₁₃	—	4	16	no	—
517	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
518	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
519	C₂²×C₁₃	#585	1	2	yes	—
520	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	4	no	—
523	C₄×C₁₃	—	2	4	no	—
524	C₄×C₁₃	—	2	8	no	—
525	C₄×C₁₃	—	2	4	no	—
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	2	4	no	—
528	C₄×C₁₃	—	2	4	no	—
529	C₄×C₁₃	—	2	4	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	4	no	—
533	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
534	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
535	C₂×#41	—	4	8	no	—
536	C₂×#41	—	4	8	no	—
537	C₂×#41	C₂³×C₁₃	1	16	yes	—
538	C₂×#41	C₂³×C₁₃	1	16	yes	—
539	C₂²×Q₈	—	4	8	no	—
540	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
543	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
545	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
546	C₂²×Q₈	C₂³×C₁₃	1	16	yes	—
547	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
549	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
550	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
551	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
552	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
553	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
554	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
555	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
557	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
559	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
560	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
561	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
562	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
564	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
565	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
566	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
567	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
568	#127	C₂³×C₁₃	1	8	yes	—
569	#127	C₂³×C₁₃	1	16	yes	—
570	#126	C₂³×C₁₃	1	16	yes	—
571	#126	C₂³×C₁₃	1	32	yes	—
572	#125	C₂³×C₁₃	1	8	yes	—
573	#125	C₂³×C₁₃	1	16	yes	—
574	#125	C₂³×C₁₃	1	32	yes	—
575	#125	C₂³×C₁₃	1	16	yes	—
576	#124	C₂³×C₁₃	1	8	yes	—
577	#124	C₂³×C₁₃	1	16	yes	—
578	#124	C₂³×C₁₃	1	16	yes	—
579	#124	C₂³×C₁₃	1	32	yes	—
580	#124	C₂³×C₁₃	1	16	yes	—
581	#124	C₂³×C₁₃	1	32	yes	—
582	#123	C₂³×C₁₃	1	16	yes	—
583	#123	C₂³×C₁₃	1	32	yes	—
584	#123	C₂³×C₁₃	1	32	yes	—
585	#123	C₂³×C₁₃	1	32	yes	—
586	#123	C₂³×C₁₃	1	32	yes	—
587	#123	C₂³×C₁₃	1	32	yes	—
588	#123	C₂³×C₁₃	1	32	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
599	#121	C₂³×C₁₃	1	8	yes	—
600	#121	C₂³×C₁₃	1	16	yes	—
601	#121	C₂³×C₁₃	1	16	yes	—
602	#121	C₂³×C₁₃	1	32	yes	—
603	#121	C₂³×C₁₃	1	32	yes	—
604	#121	C₂³×C₁₃	1	32	yes	—
605	#121	C₂³×C₁₃	1	16	yes	—
606	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
607	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
608	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
609	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
610	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
611	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
612	C₄×D₄	C₂³×C₁₃	1	16	yes	—
613	C₄×D₄	C₂³×C₁₃	1	8	yes	—
614	C₄×D₄	C₂³×C₁₃	1	16	yes	—
615	C₄×D₄	C₂³×C₁₃	1	16	yes	—
616	C₄×D₄	C₂³×C₁₃	1	32	yes	—
617	C₄×D₄	C₂³×C₁₃	1	16	yes	—
618	C₄×D₄	C₂³×C₁₃	1	16	yes	—
619	C₄×D₄	C₂³×C₁₃	1	16	yes	—
620	C₄×D₄	C₂³×C₁₃	1	16	yes	—
621	#117	C₂³×C₁₃	1	16	yes	—
622	#117	C₂³×C₁₃	1	16	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
659	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
663	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
667	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
668	C₂×C₁₃	—	4	4	no	—
669	C₂×C₁₃	—	4	2	no	—
670	C₂×C₁₃	—	4	8	no	—
671	C₂×C₁₃	#3554	1	4	yes	direct product factor
672	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
674	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
675	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
676	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
678	#41	—	4	32	no	—
679	#41	—	4	32	no	—
680	C₂×Q₈	—	2	4	no	—
681	C₂×Q₈	—	2	8	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	4	8	no	—
685	C₂×Q₈	—	4	4	no	—
686	C₂×Q₈	—	4	32	no	—
687	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
688	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
689	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
690	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
691	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
692	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	4	8	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	8	no	—
701	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
702	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
703	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
704	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
705	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
706	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
707	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
708	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
709	C₂²×C₄	—	2	8	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	4	8	no	—
713	C₂²×C₄	—	4	8	no	—
714	C₂²×C₄	—	4	8	no	—
715	C₂²×C₄	—	4	8	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
732	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
742	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
743	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
744	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
745	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
747	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
759	C₄⋊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	8	yes	—
764	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
766	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
767	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
768	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
773	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
774	C₄²	C₂⁴×C₁₃	1	4	yes	—
775	C₄²	C₂⁴×C₁₃	1	4	yes	—
776	C₄²	C₂⁴×C₁₃	1	4	yes	—
777	C₄²	C₂⁴×C₁₃	1	4	yes	—
778	C₄²	C₂⁴×C₁₃	1	8	yes	—
779	C₄²	C₂⁴×C₁₃	1	8	yes	—
780	C₄²	C₂⁴×C₁₃	1	8	yes	—
781	C₄²	C₂⁴×C₁₃	1	16	yes	—
782	C₁₃	C₂×#3554	1	1	yes	characteristic, direct product factor, Sylow
783	C₂³	—	2	4	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	8	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	8	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	8	no	—
791	C₂³	—	2	4	no	—
792	C₂³	C₂⁵×C₁₃	1	4	yes	—
793	C₂³	C₂⁵×C₁₃	1	2	yes	—
794	C₂³	C₂⁵×C₁₃	1	8	yes	—
795	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
796	Q₈	—	2	8	no	—
797	Q₈	—	2	16	no	—
798	Q₈	—	2	8	no	—
799	Q₈	—	2	8	no	—
800	Q₈	—	4	16	no	—
801	Q₈	—	4	8	no	—
802	D₄	—	2	16	no	—
803	D₄	—	2	8	no	—
804	D₄	—	2	16	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	8	no	—
807	D₄	—	4	16	no	—
808	D₄	—	4	16	no	—
809	D₄	—	4	16	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	8	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	16	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	8	no	—
825	C₂×C₄	—	4	16	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	16	no	—
828	C₂×C₄	—	4	16	no	—
829	C₂×C₄	—	4	16	no	—
830	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
831	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
832	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
833	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
834	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
835	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
836	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
837	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
838	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
839	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
840	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
841	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
842	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
843	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
844	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
845	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	8	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	8	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	16	no	—
858	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
859	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
860	C₂²	C₁₃×#585	1	2	yes	—
861	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	4	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
875	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
876	C₂	—	4	4	no	—
877	C₂	—	4	2	no	—
878	C₂	—	4	8	no	—
879	C₂	C₁₃×#3554	1	4	yes	direct product factor
880	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
882	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×#3554	C₂	direct (N × H)
2. C₂×C₁₃×#562	C₂	semidirect
3. C₂×C₁₃×#559	C₂	semidirect
4. C₂×C₁₃×#559	C₂	semidirect
5. C₂×C₁₃×#557	C₂	semidirect
6. C₂×C₁₃×#554	C₂	semidirect
7. C₂×C₁₃×#550	C₂	semidirect
8. C₂×D₄×Q₈×C₁₃	C₂	semidirect
9. C₂×C₁₃×#548	C₂	semidirect
10. C₂×C₁₃×#547	C₂	semidirect
11. C₂×C₁₃×#542	C₂	semidirect
12. C₂×C₁₃×#542	C₂	semidirect
13. C₂×C₁₃×#540	C₂	semidirect
14. C₂×C₁₃×#539	C₂	semidirect
15. C₂×C₁₃×#536	C₂	semidirect
16. C₂×C₁₃×#533	C₂	semidirect
17. C₂×C₁₃×#532	C₂	semidirect
18. C₂×C₁₃×#529	C₂	semidirect
22. C₁₃×#562	C₂²	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#559	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#550	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#542	C₂²	semidirect
33. C₁₃×#540	C₂²	semidirect
34. C₁₃×#539	C₂²	semidirect
35. C₁₃×#536	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
45. C₁₃×#529	C₂²	semidirect
234. C₂×#3554	C₁₃	direct (N × H)
342. #3554	C₂×C₁₃	direct (N × H)
343. C₂×#562	C₂×C₁₃	semidirect
344. C₂×#559	C₂×C₁₃	semidirect
345. C₂×#559	C₂×C₁₃	semidirect
346. C₂×#557	C₂×C₁₃	semidirect
347. C₂×#554	C₂×C₁₃	semidirect
348. C₂×#550	C₂×C₁₃	semidirect
349. C₂×D₄×Q₈	C₂×C₁₃	semidirect
350. C₂×#548	C₂×C₁₃	semidirect
351. C₂×#547	C₂×C₁₃	semidirect
352. C₂×#542	C₂×C₁₃	semidirect
353. C₂×#542	C₂×C₁₃	semidirect
354. C₂×#540	C₂×C₁₃	semidirect
355. C₂×#539	C₂×C₁₃	semidirect
356. C₂×#536	C₂×C₁₃	semidirect
357. C₂×#533	C₂×C₁₃	semidirect
358. C₂×#532	C₂×C₁₃	semidirect
359. C₂×#529	C₂×C₁₃	semidirect
426. #562	C₂²×C₁₃	semidirect
427. #559	C₂²×C₁₃	semidirect
428. #559	C₂²×C₁₃	semidirect
429. #557	C₂²×C₁₃	semidirect
430. #554	C₂²×C₁₃	semidirect
431. #550	C₂²×C₁₃	semidirect
432. D₄×Q₈	C₂²×C₁₃	semidirect
433. #548	C₂²×C₁₃	semidirect
434. #547	C₂²×C₁₃	semidirect
435. #542	C₂²×C₁₃	semidirect
436. #542	C₂²×C₁₃	semidirect
437. #540	C₂²×C₁₃	semidirect
438. #539	C₂²×C₁₃	semidirect
439. #536	C₂²×C₁₃	semidirect
440. #533	C₂²×C₁₃	semidirect
441. #532	C₂²×C₁₃	semidirect
449. #529	C₂²×C₁₃	semidirect
671. C₂×C₁₃	#3554	direct (N × H)
782. C₁₃	C₂×#3554	direct (N × H)
879. C₂	C₁₃×#3554	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×#3554	2
C₂×C₁₃×#562	2
C₂×C₁₃×#559	2
C₂×C₁₃×#557	2
C₂×C₁₃×#554	2
C₂×C₁₃×#550	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₂×C₁₃×#542	2
C₂×C₁₃×#540	2
C₂×C₁₃×#539	2
C₂×C₁₃×#536	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×#3554	13

Subgroups — C2×C13×#3554 #15749085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3554 #15749085