Subgroups — C₂×C₁₃×#3511 #15749138

Order 3328.

7758 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#555	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#553	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#548	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#533	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₂²×C₁₃×#41	C₂²	1	4	yes	—
19	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#556	C₂²	1	32	yes	complemented
21	C₁₃×#555	C₂²	1	32	yes	complemented
22	C₁₃×#554	C₂²	1	32	yes	complemented
23	C₁₃×#553	C₂²	1	64	yes	complemented
24	C₁₃×#548	C₂²	1	64	yes	complemented
25	C₁₃×#547	C₂²	1	32	yes	complemented
26	C₁₃×#542	C₂²	1	64	yes	complemented
27	C₁₃×#537	C₂²	1	32	yes	complemented
28	C₁₃×#533	C₂²	1	32	yes	complemented
29	C₁₃×#532	C₂²	1	16	yes	complemented
30	C₁₃×#532	C₂²	1	32	yes	complemented
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	16	yes	complemented
37	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#126	C₂²	1	8	yes	—
39	C₂×C₁₃×#125	C₂²	1	4	yes	—
40	C₂×C₁₃×#124	C₂²	1	2	yes	—
41	C₂×C₁₃×#124	C₂²	1	4	yes	—
42	C₂×C₁₃×#124	C₂²	1	8	yes	—
43	C₂×C₁₃×#123	C₂²	1	8	yes	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
48	C₂×C₁₃×#121	C₂²	1	4	yes	—
49	C₂×C₁₃×#121	C₂²	1	2	yes	—
50	C₂×C₁₃×#121	C₂²	1	2	yes	—
51	C₂×C₁₃×#121	C₂²	1	4	yes	—
52	C₂×C₁₃×#121	C₂²	1	4	yes	—
53	C₂×C₁₃×#121	C₂²	1	8	yes	—
54	C₁₃×#520	C₂²	1	32	yes	complemented
55	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
59	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
62	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
63	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
65	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
66	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
67	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
68	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
69	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#117	C₂²	1	2	yes	—
71	C₂×C₁₃×#117	C₂²	1	4	yes	—
72	C₂×C₁₃×#117	C₂²	1	4	yes	—
73	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
75	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
77	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
78	C₂×C₁₃×#41	—	2	8	no	—
79	C₂×C₁₃×#41	—	2	16	no	—
80	C₂×C₁₃×#41	—	4	16	no	—
81	C₂×C₁₃×#41	C₂³	1	8	yes	—
82	C₂×C₁₃×#41	C₂³	1	16	yes	—
83	C₂×C₁₃×#41	C₂³	1	32	yes	—
84	C₂²×Q₈×C₁₃	—	4	8	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
88	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	16	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
108	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
110	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
111	C₁₃×#127	C₂³	1	8	yes	—
112	C₁₃×#126	C₂³	1	64	yes	—
113	C₁₃×#125	C₂³	1	32	yes	—
114	C₁₃×#124	C₂³	1	16	yes	—
115	C₁₃×#124	C₂³	1	32	yes	—
116	C₁₃×#124	C₂³	1	64	yes	—
117	C₁₃×#123	C₂³	1	64	yes	—
118	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
119	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	—
122	C₁₃×#121	C₂³	1	32	yes	—
123	C₁₃×#121	C₂³	1	16	yes	—
124	C₁₃×#121	C₂³	1	16	yes	—
125	C₁₃×#121	C₂³	1	32	yes	—
126	C₁₃×#121	C₂³	1	32	yes	—
127	C₁₃×#121	C₂³	1	64	yes	—
128	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
129	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
132	C₄×D₄×C₁₃	C₂³	1	8	yes	—
133	C₄×D₄×C₁₃	C₂³	1	16	yes	—
134	C₄×D₄×C₁₃	C₂³	1	16	yes	—
135	C₄×D₄×C₁₃	C₂³	1	8	yes	—
136	C₄×D₄×C₁₃	C₂³	1	32	yes	—
137	C₄×D₄×C₁₃	C₂³	1	64	yes	—
138	C₄×D₄×C₁₃	C₂³	1	16	yes	—
139	C₄×D₄×C₁₃	C₂³	1	32	yes	—
140	C₄×D₄×C₁₃	C₂³	1	16	yes	—
141	C₁₃×#117	C₂³	1	8	yes	—
142	C₁₃×#117	C₂³	1	16	yes	—
143	C₁₃×#117	C₂³	1	32	yes	—
144	C₁₃×#117	C₂³	1	32	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
178	C₂×#3511	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
181	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₁₃×#41	—	2	32	no	—
183	C₁₃×#41	—	2	64	no	—
184	C₁₃×#41	—	4	64	no	—
185	C₂×Q₈×C₁₃	—	2	4	no	—
186	C₂×Q₈×C₁₃	—	2	8	no	—
187	C₂×Q₈×C₁₃	—	2	16	no	—
188	C₂×Q₈×C₁₃	—	4	8	no	—
189	C₂×Q₈×C₁₃	—	4	32	no	—
190	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
191	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
192	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
193	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	2	16	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	8	no	—
198	C₂×D₄×C₁₃	—	2	8	no	—
199	C₂×D₄×C₁₃	—	2	8	no	—
200	C₂×D₄×C₁₃	—	4	16	no	—
201	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
202	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
203	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
204	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
206	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
207	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
208	C₂²×C₄×C₁₃	—	2	16	no	—
209	C₂²×C₄×C₁₃	—	2	8	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	8	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	8	no	—
214	C₂²×C₄×C₁₃	—	4	8	no	—
215	C₂²×C₄×C₁₃	—	4	16	no	—
216	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
217	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
238	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
239	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
244	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
245	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
246	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
247	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
248	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
249	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
250	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
251	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
252	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
253	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
254	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
255	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
256	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
257	C₄²×C₁₃	C₂⁴	1	4	yes	—
258	C₄²×C₁₃	C₂⁴	1	8	yes	—
259	C₄²×C₁₃	C₂⁴	1	4	yes	—
260	C₄²×C₁₃	C₂⁴	1	8	yes	—
261	C₄²×C₁₃	C₂⁴	1	4	yes	—
262	C₄²×C₁₃	C₂⁴	1	4	yes	—
263	C₄²×C₁₃	C₂⁴	1	8	yes	—
264	C₄²×C₁₃	C₂⁴	1	32	yes	—
265	#3511	C₂×C₁₃	1	32	yes	direct product factor
266	C₂×#556	C₂×C₁₃	1	2	yes	complemented
267	C₂×#555	C₂×C₁₃	1	2	yes	complemented
268	C₂×#554	C₂×C₁₃	1	2	yes	complemented
269	C₂×#553	C₂×C₁₃	1	4	yes	complemented
270	C₂×#548	C₂×C₁₃	1	4	yes	complemented
271	C₂×#547	C₂×C₁₃	1	2	yes	complemented
272	C₂×#542	C₂×C₁₃	1	4	yes	complemented
273	C₂×#537	C₂×C₁₃	1	2	yes	complemented
274	C₂×#533	C₂×C₁₃	1	2	yes	complemented
275	C₂×#532	C₂×C₁₃	1	2	yes	complemented
276	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#520	C₂×C₁₃	1	2	yes	complemented
279	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	4	no	—
283	C₂³×C₁₃	—	2	8	no	—
284	C₂³×C₁₃	—	2	4	no	—
285	C₂³×C₁₃	—	2	8	no	—
286	C₂³×C₁₃	—	2	4	no	—
287	C₂³×C₁₃	—	2	8	no	—
288	C₂³×C₁₃	C₂×#41	1	4	yes	—
289	C₂³×C₁₃	C₂⁵	1	4	yes	—
290	C₂³×C₁₃	C₂⁵	1	8	yes	—
291	C₂³×C₁₃	C₂⁵	1	2	yes	—
292	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
293	Q₈×C₁₃	—	2	8	no	—
294	Q₈×C₁₃	—	2	16	no	—
295	Q₈×C₁₃	—	2	32	no	—
296	Q₈×C₁₃	—	4	16	no	—
297	D₄×C₁₃	—	2	16	no	—
298	D₄×C₁₃	—	2	32	no	—
299	D₄×C₁₃	—	2	8	no	—
300	D₄×C₁₃	—	2	16	no	—
301	D₄×C₁₃	—	2	16	no	—
302	D₄×C₁₃	—	2	16	no	—
303	D₄×C₁₃	—	4	32	no	—
304	C₂×C₄×C₁₃	—	2	8	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	16	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	32	no	—
312	C₂×C₄×C₁₃	—	2	16	no	—
313	C₂×C₄×C₁₃	—	2	8	no	—
314	C₂×C₄×C₁₃	—	2	16	no	—
315	C₂×C₄×C₁₃	—	2	8	no	—
316	C₂×C₄×C₁₃	—	2	16	no	—
317	C₂×C₄×C₁₃	—	4	16	no	—
318	C₂×C₄×C₁₃	—	4	32	no	—
319	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
320	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
321	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
322	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
323	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
324	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
325	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
326	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
327	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
328	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
329	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
330	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
331	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
332	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
333	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
334	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
335	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×#41	C₂²×C₁₃	1	2	yes	—
337	C₂²×#41	C₂²×C₁₃	1	4	yes	—
338	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
339	#556	C₂²×C₁₃	1	32	yes	complemented
340	#555	C₂²×C₁₃	1	32	yes	complemented
341	#554	C₂²×C₁₃	1	32	yes	complemented
342	#553	C₂²×C₁₃	1	64	yes	complemented
343	#548	C₂²×C₁₃	1	64	yes	complemented
344	#547	C₂²×C₁₃	1	32	yes	complemented
345	#542	C₂²×C₁₃	1	64	yes	complemented
346	#537	C₂²×C₁₃	1	32	yes	complemented
347	#533	C₂²×C₁₃	1	32	yes	complemented
348	#532	C₂²×C₁₃	1	16	yes	complemented
349	#532	C₂²×C₁₃	1	32	yes	complemented
350	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
351	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
352	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
353	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
354	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊Q₈	C₂²×C₁₃	1	16	yes	complemented
356	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#126	C₂²×C₁₃	1	8	yes	—
358	C₂×#125	C₂²×C₁₃	1	4	yes	—
359	C₂×#124	C₂²×C₁₃	1	2	yes	—
360	C₂×#124	C₂²×C₁₃	1	4	yes	—
361	C₂×#124	C₂²×C₁₃	1	8	yes	—
362	C₂×#123	C₂²×C₁₃	1	8	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
366	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
367	C₂×#121	C₂²×C₁₃	1	4	yes	—
368	C₂×#121	C₂²×C₁₃	1	2	yes	—
369	C₂×#121	C₂²×C₁₃	1	2	yes	—
370	C₂×#121	C₂²×C₁₃	1	4	yes	—
371	C₂×#121	C₂²×C₁₃	1	4	yes	—
372	C₂×#121	C₂²×C₁₃	1	8	yes	—
373	#520	C₂²×C₁₃	1	32	yes	complemented
374	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
375	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
378	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
379	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
381	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
384	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
385	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
387	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
388	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#117	C₂²×C₁₃	1	2	yes	—
390	C₂×#117	C₂²×C₁₃	1	4	yes	—
391	C₂×#117	C₂²×C₁₃	1	4	yes	—
392	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
393	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
394	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
395	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	2	8	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	2	8	no	—
402	C₂²×C₁₃	—	2	4	no	—
403	C₂²×C₁₃	—	2	8	no	—
404	C₂²×C₁₃	—	2	4	no	—
405	C₂²×C₁₃	—	2	8	no	—
406	C₂²×C₁₃	—	4	8	no	—
407	C₂²×C₁₃	—	4	16	no	—
408	C₂²×C₁₃	C₂²×#41	1	4	yes	—
409	C₂²×C₁₃	C₂²×#41	1	2	yes	—
410	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
411	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
412	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
413	C₄×C₁₃	—	2	8	no	—
414	C₄×C₁₃	—	2	4	no	—
415	C₄×C₁₃	—	2	4	no	—
416	C₄×C₁₃	—	2	2	no	—
417	C₄×C₁₃	—	2	16	no	—
418	C₄×C₁₃	—	2	4	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	C₂²×#41	1	4	yes	—
421	C₄×C₁₃	C₂²×#41	1	4	yes	—
422	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
423	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
424	C₂×#41	—	2	8	no	—
425	C₂×#41	—	2	16	no	—
426	C₂×#41	—	4	16	no	—
427	C₂×#41	C₂³×C₁₃	1	8	yes	—
428	C₂×#41	C₂³×C₁₃	1	16	yes	—
429	C₂×#41	C₂³×C₁₃	1	32	yes	—
430	C₂²×Q₈	—	4	8	no	—
431	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
433	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
434	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
435	C₂²×Q₈	C₂³×C₁₃	1	16	yes	—
436	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
437	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
438	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
439	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
441	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
442	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
443	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
445	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
446	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
449	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
450	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
451	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
453	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
454	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
455	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
456	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
457	#127	C₂³×C₁₃	1	8	yes	—
458	#126	C₂³×C₁₃	1	64	yes	—
459	#125	C₂³×C₁₃	1	32	yes	—
460	#124	C₂³×C₁₃	1	16	yes	—
461	#124	C₂³×C₁₃	1	32	yes	—
462	#124	C₂³×C₁₃	1	64	yes	—
463	#123	C₂³×C₁₃	1	64	yes	—
464	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
465	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
466	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
467	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	—
468	#121	C₂³×C₁₃	1	32	yes	—
469	#121	C₂³×C₁₃	1	16	yes	—
470	#121	C₂³×C₁₃	1	16	yes	—
471	#121	C₂³×C₁₃	1	32	yes	—
472	#121	C₂³×C₁₃	1	32	yes	—
473	#121	C₂³×C₁₃	1	64	yes	—
474	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
475	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
476	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
477	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
478	C₄×D₄	C₂³×C₁₃	1	8	yes	—
479	C₄×D₄	C₂³×C₁₃	1	16	yes	—
480	C₄×D₄	C₂³×C₁₃	1	16	yes	—
481	C₄×D₄	C₂³×C₁₃	1	8	yes	—
482	C₄×D₄	C₂³×C₁₃	1	32	yes	—
483	C₄×D₄	C₂³×C₁₃	1	64	yes	—
484	C₄×D₄	C₂³×C₁₃	1	16	yes	—
485	C₄×D₄	C₂³×C₁₃	1	32	yes	—
486	C₄×D₄	C₂³×C₁₃	1	16	yes	—
487	#117	C₂³×C₁₃	1	8	yes	—
488	#117	C₂³×C₁₃	1	16	yes	—
489	#117	C₂³×C₁₃	1	32	yes	—
490	#117	C₂³×C₁₃	1	32	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
514	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
516	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
522	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
523	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×C₁₃	—	2	4	no	—
525	C₂×C₁₃	—	4	4	no	—
526	C₂×C₁₃	—	4	8	no	—
527	C₂×C₁₃	#3511	1	4	yes	direct product factor
528	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
529	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
531	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
532	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
533	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
534	#41	—	2	32	no	—
535	#41	—	2	64	no	—
536	#41	—	4	64	no	—
537	C₂×Q₈	—	2	4	no	—
538	C₂×Q₈	—	2	8	no	—
539	C₂×Q₈	—	2	16	no	—
540	C₂×Q₈	—	4	8	no	—
541	C₂×Q₈	—	4	32	no	—
542	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
543	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
544	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
545	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
546	C₂×D₄	—	2	8	no	—
547	C₂×D₄	—	2	16	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	8	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	4	16	no	—
553	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
554	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
555	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
556	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
557	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
558	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
559	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
560	C₂²×C₄	—	2	16	no	—
561	C₂²×C₄	—	2	8	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	8	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	8	no	—
566	C₂²×C₄	—	4	8	no	—
567	C₂²×C₄	—	4	16	no	—
568	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
569	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
577	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
578	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
582	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
583	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
584	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
589	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
590	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
591	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
592	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
593	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
594	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
595	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
596	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
597	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
598	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
599	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
600	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
601	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
602	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
603	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
604	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
605	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
606	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
607	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
608	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
609	C₄²	C₂⁴×C₁₃	1	4	yes	—
610	C₄²	C₂⁴×C₁₃	1	8	yes	—
611	C₄²	C₂⁴×C₁₃	1	4	yes	—
612	C₄²	C₂⁴×C₁₃	1	8	yes	—
613	C₄²	C₂⁴×C₁₃	1	4	yes	—
614	C₄²	C₂⁴×C₁₃	1	4	yes	—
615	C₄²	C₂⁴×C₁₃	1	8	yes	—
616	C₄²	C₂⁴×C₁₃	1	32	yes	—
617	C₁₃	C₂×#3511	1	1	yes	characteristic, direct product factor, Sylow
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	8	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	8	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	8	no	—
626	C₂³	C₂×C₁₃×#41	1	4	yes	—
627	C₂³	C₂⁵×C₁₃	1	4	yes	—
628	C₂³	C₂⁵×C₁₃	1	8	yes	—
629	C₂³	C₂⁵×C₁₃	1	2	yes	—
630	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
631	Q₈	—	2	8	no	—
632	Q₈	—	2	16	no	—
633	Q₈	—	2	32	no	—
634	Q₈	—	4	16	no	—
635	D₄	—	2	16	no	—
636	D₄	—	2	32	no	—
637	D₄	—	2	8	no	—
638	D₄	—	2	16	no	—
639	D₄	—	2	16	no	—
640	D₄	—	2	16	no	—
641	D₄	—	4	32	no	—
642	C₂×C₄	—	2	8	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	16	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	32	no	—
650	C₂×C₄	—	2	16	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	16	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	16	no	—
655	C₂×C₄	—	4	16	no	—
656	C₂×C₄	—	4	32	no	—
657	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
658	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
659	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
660	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
661	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
662	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
663	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
664	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
665	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
666	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
667	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
668	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
669	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
670	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
671	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
672	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	8	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	8	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	8	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	4	8	no	—
683	C₂²	—	4	16	no	—
684	C₂²	C₂²×C₁₃×#41	1	4	yes	—
685	C₂²	C₂²×C₁₃×#41	1	2	yes	—
686	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
687	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
688	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
689	C₄	—	2	8	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	16	no	—
694	C₄	—	2	4	no	—
695	C₄	—	2	2	no	—
696	C₄	C₂²×C₁₃×#41	1	4	yes	—
697	C₄	C₂²×C₁₃×#41	1	4	yes	—
698	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
699	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
700	C₂	—	2	4	no	—
701	C₂	—	4	4	no	—
702	C₂	—	4	8	no	—
703	C₂	C₁₃×#3511	1	4	yes	direct product factor
704	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
705	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	direct (N × H)
2. C₂×C₁₃×#556	C₂	semidirect
3. C₂×C₁₃×#555	C₂	semidirect
4. C₂×C₁₃×#554	C₂	semidirect
5. C₂×C₁₃×#553	C₂	semidirect
6. C₂×C₁₃×#548	C₂	semidirect
7. C₂×C₁₃×#547	C₂	semidirect
8. C₂×C₁₃×#542	C₂	semidirect
9. C₂×C₁₃×#537	C₂	semidirect
10. C₂×C₁₃×#533	C₂	semidirect
11. C₂×C₁₃×#532	C₂	semidirect
12. C₂×C₁₃×#532	C₂	semidirect
13. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
14. C₂×C₁₃×#520	C₂	semidirect
15. C₂×C₄×C₁₃×#41	C₂	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#555	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
24. C₁₃×#548	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
26. C₁₃×#542	C₂²	semidirect
27. C₁₃×#537	C₂²	semidirect
28. C₁₃×#533	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
36. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
54. C₁₃×#520	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
178. C₂×#3511	C₁₃	direct (N × H)
216. C₂²×C₄×C₁₃	#41	semidirect
265. #3511	C₂×C₁₃	direct (N × H)
266. C₂×#556	C₂×C₁₃	semidirect
267. C₂×#555	C₂×C₁₃	semidirect
268. C₂×#554	C₂×C₁₃	semidirect
269. C₂×#553	C₂×C₁₃	semidirect
270. C₂×#548	C₂×C₁₃	semidirect
271. C₂×#547	C₂×C₁₃	semidirect
272. C₂×#542	C₂×C₁₃	semidirect
273. C₂×#537	C₂×C₁₃	semidirect
274. C₂×#533	C₂×C₁₃	semidirect
275. C₂×#532	C₂×C₁₃	semidirect
276. C₂×#532	C₂×C₁₃	semidirect
277. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
278. C₂×#520	C₂×C₁₃	semidirect
279. C₂×C₄×#41	C₂×C₁₃	semidirect
321. C₂×C₄×C₁₃	C₂×#41	semidirect
339. #556	C₂²×C₁₃	semidirect
340. #555	C₂²×C₁₃	semidirect
341. #554	C₂²×C₁₃	semidirect
342. #553	C₂²×C₁₃	semidirect
343. #548	C₂²×C₁₃	semidirect
344. #547	C₂²×C₁₃	semidirect
345. #542	C₂²×C₁₃	semidirect
346. #537	C₂²×C₁₃	semidirect
347. #533	C₂²×C₁₃	semidirect
348. #532	C₂²×C₁₃	semidirect
349. #532	C₂²×C₁₃	semidirect
355. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
373. #520	C₂²×C₁₃	semidirect
374. C₄×#41	C₂²×C₁₃	semidirect
527. C₂×C₁₃	#3511	direct (N × H)
568. C₂²×C₄	C₁₃×#41	semidirect
617. C₁₃	C₂×#3511	direct (N × H)
659. C₂×C₄	C₂×C₁₃×#41	semidirect
703. C₂	C₁₃×#3511	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×#3511	2
C₂×C₁₃×#556	2
C₂×C₁₃×#555	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₂×C₁₃×#542	2
C₂×C₁₃×#537	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#520	2
C₂×C₄×C₁₃×#41	2
C₂×#3511	13

Subgroups — C2×C13×#3511 #15749138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3511 #15749138