Subgroups — C₂×C₁₃×#3347 #15747578

Order 3328.

1962 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	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3347	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#555	—	2	4	no	—
21	C₁₃×#555	C₂²	1	8	yes	complemented
22	C₁₃×#553	—	2	4	no	—
23	C₁₃×#553	C₂²	1	8	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#126	—	2	1	no	—
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	—	2	1	no	—
28	C₂×C₁₃×#124	—	2	1	no	—
29	C₂×C₁₃×#123	—	2	1	no	—
30	C₂×C₁₃×#121	—	2	1	no	—
31	C₂×C₁₃×#121	—	2	1	no	—
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#117	—	2	1	no	—
41	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₁₃×#501	C₂²	1	8	yes	complemented
46	C₁₃×#482	C₂²	1	8	yes	complemented
47	C₁₃×#482	C₂²	1	8	yes	complemented
48	C₁₃×#482	C₂²	1	8	yes	complemented
49	C₁₃×#480	C₂²	1	8	yes	complemented
50	C₁₃×#478	C₂²	1	8	yes	complemented
51	C₁₃×#474	C₂²	1	8	yes	complemented
52	C₁₃×#469	C₂²	1	8	yes	complemented
53	C₁₃×#466	C₂²	1	8	yes	complemented
54	C₁₃×#442	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#428	C₂²	1	8	yes	complemented
57	C₁₃×#427	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×D₈	—	2	4	no	—
91	C₂×C₁₃×D₈	C₂³	1	4	yes	—
92	C₂×C₁₃×M₁₆	—	2	4	no	—
93	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
94	C₂²×C₈×C₁₃	—	2	4	no	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×#126	—	2	8	no	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	C₂³	1	4	yes	—
105	C₁₃×#124	—	2	8	no	—
106	C₁₃×#124	—	2	8	no	—
107	C₁₃×#123	—	2	8	no	—
108	C₁₃×#121	—	2	8	no	—
109	C₁₃×#121	—	2	8	no	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	2	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	C₂³	1	4	yes	—
115	C₁₃×#121	C₂³	1	4	yes	—
116	C₁₃×#121	C₂³	1	4	yes	—
117	C₁₃×#121	C₂³	1	4	yes	—
118	C₄×D₄×C₁₃	—	2	8	no	—
119	C₄×D₄×C₁₃	—	2	2	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	D₄	1	4	yes	—
122	C₄×D₄×C₁₃	C₂³	1	4	yes	—
123	C₄×D₄×C₁₃	C₂³	1	4	yes	—
124	C₄×D₄×C₁₃	C₂³	1	4	yes	—
125	C₁₃×#117	—	2	2	no	—
126	C₁₃×#117	—	2	2	no	—
127	C₁₃×#117	—	2	2	no	—
128	C₁₃×#117	—	2	8	no	—
129	C₁₃×#117	C₂³	1	4	yes	—
130	C₁₃×#117	C₂³	1	4	yes	—
131	C₁₃×#117	C₂³	1	4	yes	—
132	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
145	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
155	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₁₃	—	2	1	no	—
157	C₂×C₄²×C₁₃	—	2	1	no	—
158	C₂×C₄²×C₁₃	—	2	1	no	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×#107	C₂³	1	4	yes	—
161	C₁₃×#107	C₂³	1	4	yes	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#107	C₂³	1	4	yes	—
164	C₁₃×#107	C₂³	1	4	yes	—
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	4	yes	—
167	C₁₃×#106	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₁₃×#102	C₂³	1	4	yes	—
171	C₁₃×#102	C₂³	1	4	yes	—
172	C₁₃×#102	C₂³	1	4	yes	—
173	C₁₃×#102	C₂³	1	4	yes	—
174	C₁₃×#102	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×#97	C₂³	1	4	yes	—
179	C₂×#3347	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂⁴×C₁₃	—	2	1	no	—
181	C₂⁴×C₁₃	—	2	1	no	—
182	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₃	—	2	4	no	—
185	C₂×Q₈×C₁₃	—	8	2	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	4	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	4	no	—
198	C₂×D₄×C₁₃	—	8	2	no	—
199	C₂×D₄×C₁₃	—	8	2	no	—
200	C₂×D₄×C₁₃	—	8	2	no	—
201	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
202	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	2	4	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	4	4	no	—
218	C₂²×C₄×C₁₃	—	8	2	no	—
219	C₂²×C₄×C₁₃	—	8	2	no	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×D₈	—	2	8	no	—
230	C₁₃×M₁₆	—	2	8	no	—
231	C₂×C₈×C₁₃	—	2	2	no	—
232	C₂×C₈×C₁₃	—	2	2	no	—
233	C₂×C₈×C₁₃	—	2	2	no	—
234	C₂×C₈×C₁₃	—	2	8	no	—
235	C₂×C₈×C₁₃	#41	1	4	yes	—
236	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
251	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
252	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
253	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
254	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
255	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
267	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃	—	2	4	no	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	C₂×D₄	1	2	yes	—
272	C₄²×C₁₃	C₂⁴	1	2	yes	—
273	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#3347	C₂×C₁₃	1	16	yes	direct product factor
276	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
284	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
286	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	4	2	no	—
298	C₂³×C₁₃	—	4	2	no	—
299	C₂³×C₁₃	—	4	2	no	—
300	C₂³×C₁₃	—	4	2	no	—
301	C₂³×C₁₃	—	4	2	no	—
302	C₂³×C₁₃	—	4	2	no	—
303	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
305	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₁₃	—	8	4	no	—
307	D₄×C₁₃	—	2	2	no	—
308	D₄×C₁₃	—	2	2	no	—
309	D₄×C₁₃	—	2	2	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	4	4	no	—
312	D₄×C₁₃	—	4	8	no	—
313	D₄×C₁₃	—	4	2	no	—
314	D₄×C₁₃	—	4	2	no	—
315	D₄×C₁₃	—	8	4	no	—
316	D₄×C₁₃	—	8	4	no	—
317	D₄×C₁₃	—	8	4	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	4	no	—
323	C₂×C₄×C₁₃	—	2	4	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	4	8	no	—
335	C₂×C₄×C₁₃	—	4	2	no	—
336	C₂×C₄×C₁₃	—	4	2	no	—
337	C₂×C₄×C₁₃	—	4	2	no	—
338	C₂×C₄×C₁₃	—	4	2	no	—
339	C₂×C₄×C₁₃	—	4	2	no	—
340	C₂×C₄×C₁₃	—	4	2	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	—	8	4	no	—
343	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
351	C₈×C₁₃	—	2	2	no	—
352	C₈×C₁₃	—	2	2	no	—
353	C₈×C₁₃	—	2	2	no	—
354	C₈×C₁₃	C₂×#41	1	4	yes	—
355	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
357	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
358	#555	—	2	4	no	—
359	#555	C₂²×C₁₃	1	8	yes	complemented
360	#553	—	2	4	no	—
361	#553	C₂²×C₁₃	1	8	yes	complemented
362	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×#126	—	2	1	no	—
364	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#124	—	2	1	no	—
366	C₂×#124	—	2	1	no	—
367	C₂×#123	—	2	1	no	—
368	C₂×#121	—	2	1	no	—
369	C₂×#121	—	2	1	no	—
370	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₄×D₄	—	2	1	no	—
375	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#117	—	2	1	no	—
379	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
383	#501	C₂²×C₁₃	1	8	yes	complemented
384	#482	C₂²×C₁₃	1	8	yes	complemented
385	#482	C₂²×C₁₃	1	8	yes	complemented
386	#482	C₂²×C₁₃	1	8	yes	complemented
387	#480	C₂²×C₁₃	1	8	yes	complemented
388	#478	C₂²×C₁₃	1	8	yes	complemented
389	#474	C₂²×C₁₃	1	8	yes	complemented
390	#469	C₂²×C₁₃	1	8	yes	complemented
391	#466	C₂²×C₁₃	1	8	yes	complemented
392	#442	C₂²×C₁₃	1	8	yes	complemented
393	#435	C₂²×C₁₃	1	8	yes	complemented
394	#428	C₂²×C₁₃	1	8	yes	complemented
395	#427	C₂²×C₁₃	1	8	yes	complemented
396	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
415	C₂²×C₁₃	—	2	2	no	—
416	C₂²×C₁₃	—	2	2	no	—
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	4	4	no	—
422	C₂²×C₁₃	—	4	4	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	8	4	no	—
430	C₂²×C₁₃	—	8	4	no	—
431	C₂²×C₁₃	#547	1	2	yes	—
432	C₂²×C₁₃	#575	1	2	yes	—
433	C₂²×C₁₃	#576	1	2	yes	—
434	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	2	2	no	—
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	2	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	#547	1	2	yes	—
446	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
447	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
448	C₂²×Q₈	—	2	1	no	—
449	C₂²×D₄	—	2	1	no	—
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×D₈	—	2	4	no	—
462	C₂×D₈	C₂³×C₁₃	1	4	yes	—
463	C₂×M₁₆	—	2	4	no	—
464	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
465	C₂²×C₈	—	2	4	no	—
466	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
468	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₄⋊Q₈	—	2	2	no	—
472	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
473	#126	—	2	8	no	—
474	#125	—	2	2	no	—
475	#125	C₂³×C₁₃	1	4	yes	—
476	#124	—	2	8	no	—
477	#124	—	2	8	no	—
478	#123	—	2	8	no	—
479	#121	—	2	8	no	—
480	#121	—	2	8	no	—
481	#121	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	C₂³×C₁₃	1	4	yes	—
486	#121	C₂³×C₁₃	1	4	yes	—
487	#121	C₂³×C₁₃	1	4	yes	—
488	#121	C₂³×C₁₃	1	4	yes	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	D₄×C₁₃	1	4	yes	—
493	C₄×D₄	C₂³×C₁₃	1	4	yes	—
494	C₄×D₄	C₂³×C₁₃	1	4	yes	—
495	C₄×D₄	C₂³×C₁₃	1	4	yes	—
496	#117	—	2	2	no	—
497	#117	—	2	2	no	—
498	#117	—	2	2	no	—
499	#117	—	2	8	no	—
500	#117	C₂³×C₁₃	1	4	yes	—
501	#117	C₂³×C₁₃	1	4	yes	—
502	#117	C₂³×C₁₃	1	4	yes	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	#107	C₂³×C₁₃	1	4	yes	—
532	#107	C₂³×C₁₃	1	4	yes	—
533	#107	C₂³×C₁₃	1	4	yes	—
534	#107	C₂³×C₁₃	1	4	yes	—
535	#107	C₂³×C₁₃	1	4	yes	—
536	#106	C₂³×C₁₃	1	4	yes	—
537	#106	C₂³×C₁₃	1	4	yes	—
538	#106	C₂³×C₁₃	1	4	yes	—
539	#106	C₂³×C₁₃	1	4	yes	—
540	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
541	#102	C₂³×C₁₃	1	4	yes	—
542	#102	C₂³×C₁₃	1	4	yes	—
543	#102	C₂³×C₁₃	1	4	yes	—
544	#102	C₂³×C₁₃	1	4	yes	—
545	#102	C₂³×C₁₃	1	4	yes	—
546	#102	C₂³×C₁₃	1	4	yes	—
547	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
548	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
549	#97	C₂³×C₁₃	1	4	yes	—
550	C₂×C₁₃	—	4	2	no	—
551	C₂×C₁₃	—	4	2	no	—
552	C₂×C₁₃	—	8	2	no	—
553	C₂×C₁₃	—	8	2	no	—
554	C₂×C₁₃	#3347	1	4	yes	direct product factor
555	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
556	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
557	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
561	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	8	2	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	8	2	no	—
577	C₂×D₄	—	8	2	no	—
578	C₂×D₄	—	8	2	no	—
579	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
580	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
581	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	8	2	no	—
597	C₂²×C₄	—	8	2	no	—
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
607	D₈	—	2	8	no	—
608	M₁₆	—	2	8	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	8	no	—
613	C₂×C₈	C₁₃×#41	1	4	yes	—
614	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
615	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
645	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	C₂×D₄×C₁₃	1	2	yes	—
650	C₄²	C₂⁴×C₁₃	1	2	yes	—
651	C₁₃	C₂×#3347	1	1	yes	characteristic, direct product factor, Sylow
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
667	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	Q₈	—	8	4	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	—	8	4	no	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
712	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
713	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
714	C₈	—	2	2	no	—
715	C₈	—	2	2	no	—
716	C₈	—	2	2	no	—
717	C₈	C₂×C₁₃×#41	1	4	yes	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	8	4	no	—
734	C₂²	C₁₃×#547	1	2	yes	—
735	C₂²	C₁₃×#575	1	2	yes	—
736	C₂²	C₁₃×#576	1	2	yes	—
737	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	C₁₃×#547	1	2	yes	—
749	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
750	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
751	C₂	—	4	2	no	—
752	C₂	—	4	2	no	—
753	C₂	—	8	2	no	—
754	C₂	—	8	2	no	—
755	C₂	C₁₃×#3347	1	4	yes	direct product factor
756	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
757	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
758	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#555	C₂	semidirect
2. C₂×C₁₃×#553	C₂	semidirect
3. C₁₃×#3347	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#482	C₂	semidirect
6. C₂×C₁₃×#482	C₂	semidirect
7. C₂×C₁₃×#482	C₂	semidirect
8. C₂×C₁₃×#480	C₂	semidirect
9. C₂×C₁₃×#478	C₂	semidirect
10. C₂×C₁₃×#474	C₂	semidirect
11. C₂×C₁₃×#469	C₂	semidirect
12. C₂×C₁₃×#466	C₂	semidirect
13. C₂×C₁₃×#442	C₂	semidirect
14. C₂×C₁₃×#435	C₂	semidirect
15. C₂×C₁₃×#428	C₂	semidirect
16. C₂×C₁₃×#427	C₂	semidirect
21. C₁₃×#555	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#482	C₂²	semidirect
47. C₁₃×#482	C₂²	semidirect
48. C₁₃×#482	C₂²	semidirect
49. C₁₃×#480	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#474	C₂²	semidirect
52. C₁₃×#469	C₂²	semidirect
53. C₁₃×#466	C₂²	semidirect
54. C₁₃×#442	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
56. C₁₃×#428	C₂²	semidirect
57. C₁₃×#427	C₂²	semidirect
179. C₂×#3347	C₁₃	direct (N × H)
273. C₂×#555	C₂×C₁₃	semidirect
274. C₂×#553	C₂×C₁₃	semidirect
275. #3347	C₂×C₁₃	direct (N × H)
276. C₂×#501	C₂×C₁₃	semidirect
277. C₂×#482	C₂×C₁₃	semidirect
278. C₂×#482	C₂×C₁₃	semidirect
279. C₂×#482	C₂×C₁₃	semidirect
280. C₂×#480	C₂×C₁₃	semidirect
281. C₂×#478	C₂×C₁₃	semidirect
282. C₂×#474	C₂×C₁₃	semidirect
283. C₂×#469	C₂×C₁₃	semidirect
284. C₂×#466	C₂×C₁₃	semidirect
285. C₂×#442	C₂×C₁₃	semidirect
286. C₂×#435	C₂×C₁₃	semidirect
287. C₂×#428	C₂×C₁₃	semidirect
288. C₂×#427	C₂×C₁₃	semidirect
359. #555	C₂²×C₁₃	semidirect
361. #553	C₂²×C₁₃	semidirect
383. #501	C₂²×C₁₃	semidirect
384. #482	C₂²×C₁₃	semidirect
385. #482	C₂²×C₁₃	semidirect
386. #482	C₂²×C₁₃	semidirect
387. #480	C₂²×C₁₃	semidirect
388. #478	C₂²×C₁₃	semidirect
389. #474	C₂²×C₁₃	semidirect
390. #469	C₂²×C₁₃	semidirect
391. #466	C₂²×C₁₃	semidirect
392. #442	C₂²×C₁₃	semidirect
393. #435	C₂²×C₁₃	semidirect
394. #428	C₂²×C₁₃	semidirect
395. #427	C₂²×C₁₃	semidirect
554. C₂×C₁₃	#3347	direct (N × H)
651. C₁₃	C₂×#3347	direct (N × H)
755. C₂	C₁₃×#3347	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#555	2
C₂×C₁₃×#553	2
C₁₃×#3347	2
C₂×C₁₃×#501	2
C₂×C₁₃×#482	2
C₂×C₁₃×#480	2
C₂×C₁₃×#478	2
C₂×C₁₃×#474	2
C₂×C₁₃×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#442	2
C₂×C₁₃×#435	2
C₂×C₁₃×#428	2
C₂×C₁₃×#427	2
C₂×#3347	13

Subgroups — C2×C13×#3347 #15747578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3347 #15747578