Subgroups — C₂×#13115077 #15863817

Order 3328.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719450	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718585	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718666	C₂	1	1	yes	maximal, characteristic
5	C₂²×#88045	C₂	1	1	yes	maximal, characteristic
6	#13115077	C₂	1	8	yes	maximal, direct product factor
7	C₂×#11718125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	#11719450	—	2	2	no	—
17	#11719450	—	2	2	no	—
18	#11719450	—	2	2	no	—
19	#11719450	C₂²	1	4	yes	—
20	C₂×#88161	—	2	2	no	—
21	C₂×M₁₆×D₁₃	—	2	2	no	—
22	C₂×#88155	—	2	2	no	—
23	#11718785	—	2	2	no	—
24	#11718785	C₂²	1	4	yes	complemented
25	C₂×#88062	—	2	2	no	—
26	#11718666	—	2	2	no	—
27	#11718666	C₂²	1	4	yes	—
28	C₂×#88045	—	2	2	no	—
29	C₂×#88045	C₄	1	2	yes	complemented
30	C₂×#88045	C₄	1	2	yes	complemented
31	C₂×#88045	C₄	1	4	yes	complemented
32	C₂×#88045	C₂²	1	4	yes	—
33	#11718585	—	2	2	no	—
34	#11718585	C₂²	1	4	yes	complemented
35	C₂×C₄⋊#1055	—	2	2	no	—
36	C₁₃×#339	C₂²	1	4	yes	complemented
37	#11718125	C₂²	1	4	yes	complemented
38	C₂³×C₄×C₁₃	—	2	1	no	—
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×C₂²⋊D₁₃	—	2	1	no	—
41	C₂×#6127	—	2	1	no	—
42	C₂×#6127	—	2	1	no	—
43	C₂×#6127	—	2	1	no	—
44	C₂×#6127	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×#6127	—	2	1	no	—
47	C₂×#6127	C₂×C₄	1	2	yes	—
48	C₂×#6127	C₂×C₄	1	2	yes	—
49	C₂×#6127	D₄	1	2	yes	—
50	C₂×#6127	D₄	1	2	yes	—
51	C₂×#6127	Q₈	1	2	yes	—
52	C₂×#6127	C₂³	1	2	yes	—
53	C₂²×D₅₂	Q₈	1	1	yes	characteristic
54	C₂²×C₄×D₁₃	—	2	1	no	—
55	C₂²×Dic₂₆	Q₈	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂×C₁₃×M₁₆	—	2	1	no	—
59	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
60	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	—	2	1	no	—
63	C₁₃×#117	—	2	1	no	—
64	C₁₃×#117	—	2	1	no	—
65	C₁₃×#117	—	2	1	no	—
66	C₁₃×#117	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	—	2	1	no	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	1	no	—
87	C₂×#6099	—	2	1	no	—
88	C₂×#6099	—	2	1	no	—
89	C₂×#6099	C₂×C₄	1	2	yes	—
90	C₂×#6099	C₂×C₄	1	2	yes	—
91	C₂×#6099	D₄	1	2	yes	—
92	C₂×#6099	C₂³	1	2	yes	—
93	C₂×#6099	C₂³	1	2	yes	—
94	C₂×#6099	C₂³	1	2	yes	—
95	C₂²×#1055	—	2	1	no	—
96	C₂²×#1055	—	2	1	no	—
97	C₂²×#1055	D₄	1	2	yes	—
98	#88161	—	2	8	no	—
99	#88161	—	2	8	no	—
100	M₁₆×D₁₃	—	2	8	no	—
101	M₁₆×D₁₃	—	2	8	no	—
102	#88155	—	2	8	no	—
103	#88155	—	2	8	no	—
104	C₂×#6094	—	2	4	no	—
105	C₂×C₈×D₁₃	—	2	4	no	—
106	#88062	—	2	8	no	—
107	#88045	—	2	8	no	—
108	#88045	C₂×C₄	1	8	yes	complemented
109	#88045	C₂×C₄	1	8	yes	complemented
110	C₄⋊#1055	—	2	8	no	—
111	C₂×#1861	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	#41	1	1	yes	characteristic
113	C₂³×D₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	4	1	no	—
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	—	2	2	no	—
135	C₂×C₂²⋊D₁₃	—	2	2	no	—
136	C₂×C₂²⋊D₁₃	—	2	2	no	—
137	C₂×C₂²⋊D₁₃	—	2	2	no	—
138	C₂×C₂²⋊D₁₃	—	2	2	no	—
139	C₂×C₂²⋊D₁₃	—	2	2	no	—
140	C₂²×Dic₁₃	—	2	1	no	—
141	#6127	—	2	2	no	—
142	#6127	—	2	2	no	—
143	#6127	—	2	2	no	—
144	#6127	—	2	2	no	—
145	#6127	—	2	2	no	—
146	#6127	—	2	2	no	—
147	#6127	—	2	2	no	—
148	#6127	—	2	2	no	—
149	#6127	—	2	2	no	—
150	#6127	—	2	2	no	—
151	#6127	—	2	2	no	—
152	#6127	—	2	2	no	—
153	#6127	C₄⋊C₄	1	4	yes	—
154	#6127	C₄⋊C₄	1	4	yes	—
155	#6127	C₂²×C₄	1	4	yes	—
156	#6127	C₂×D₄	1	4	yes	—
157	C₂×D₅₂	—	2	1	no	—
158	C₂×D₅₂	—	2	1	no	—
159	C₂×D₅₂	—	2	1	no	—
160	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
161	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
162	C₂×D₅₂	C₂×Q₈	1	2	yes	—
163	C₂×C₄×D₁₃	—	2	2	no	—
164	C₂×C₄×D₁₃	—	2	2	no	—
165	C₂×C₄×D₁₃	—	2	2	no	—
166	C₂×C₄×D₁₃	—	2	2	no	—
167	C₂×C₄×D₁₃	—	2	2	no	—
168	C₂×C₄×D₁₃	—	2	2	no	—
169	C₂×Dic₂₆	—	2	1	no	—
170	C₂×Dic₂₆	—	2	1	no	—
171	C₂×Dic₂₆	—	2	1	no	—
172	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
173	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
174	C₂×Dic₂₆	C₂×Q₈	1	2	yes	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	2	2	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
179	C₂×C₈×C₁₃	—	2	2	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	4	1	no	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	4	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	2	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	2	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	4	1	no	—
192	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
193	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
194	#6099	—	2	2	no	—
195	#6099	—	2	2	no	—
196	#6099	—	2	2	no	—
197	#6099	—	2	2	no	—
198	#6099	—	2	2	no	—
199	#6099	—	2	2	no	—
200	#6099	—	2	2	no	—
201	#6099	—	2	2	no	—
202	#6099	—	2	2	no	—
203	#6099	—	4	1	no	—
204	#6099	—	4	1	no	—
205	#6099	C₂²×C₄	1	4	yes	—
206	C₂×#1055	—	2	2	no	—
207	C₂×#1055	—	2	2	no	—
208	C₂×#1055	—	2	2	no	—
209	C₂×#1055	—	2	2	no	—
210	C₂×#1055	—	2	2	no	—
211	C₂×#1055	—	2	2	no	—
212	C₂×#1055	—	4	1	no	—
213	C₂×#1055	—	4	1	no	—
214	C₂×#1055	C₂×D₄	1	4	yes	—
215	#6094	—	2	16	no	—
216	C₈×D₁₃	—	2	16	no	—
217	C₂×#568	—	13	1	no	—
218	C₂×#430	—	13	1	no	—
219	C₂×#423	—	13	1	no	—
220	C₂×#421	—	13	1	no	—
221	C₂²×#104	—	13	1	no	—
222	#1861	—	13	8	no	—
223	C₂×#344	—	13	1	no	—
224	C₂×#339	D₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
227	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
228	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂³×C₁₃	#123	1	1	yes	characteristic
231	C₂³×C₁₃	#123	1	1	yes	characteristic
232	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂²×D₁₃	—	2	2	no	—
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	—	2	2	no	—
236	C₂²×D₁₃	—	8	2	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	4	4	no	—
241	C₂×C₄×C₁₃	—	4	4	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	8	2	no	—
245	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
256	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
257	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
266	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
273	C₂²⋊D₁₃	—	2	4	no	—
274	C₂²⋊D₁₃	—	2	4	no	—
275	C₂²⋊D₁₃	—	2	4	no	—
276	C₂²⋊D₁₃	—	2	4	no	—
277	C₂×Dic₁₃	—	2	2	no	—
278	C₂×Dic₁₃	—	2	2	no	—
279	C₂×Dic₁₃	—	2	2	no	—
280	D₅₂	—	2	2	no	—
281	D₅₂	—	2	2	no	—
282	D₅₂	—	2	2	no	—
283	D₅₂	C₂×C₄⋊C₄	1	4	yes	—
284	C₄×D₁₃	—	2	4	no	—
285	C₄×D₁₃	—	2	4	no	—
286	C₄×D₁₃	—	2	4	no	—
287	C₄×D₁₃	—	2	4	no	—
288	Dic₂₆	—	2	2	no	—
289	Dic₂₆	—	2	2	no	—
290	Dic₂₆	—	2	2	no	—
291	Dic₂₆	C₂×C₄⋊C₄	1	4	yes	—
292	C₈×C₁₃	—	2	4	no	—
293	#1055	—	2	4	no	—
294	#1055	—	2	4	no	—
295	#1055	—	4	2	no	—
296	C₂²×#41	—	13	1	no	—
297	#568	—	13	4	no	—
298	#568	—	26	2	no	—
299	#568	—	26	2	no	—
300	#568	—	26	2	no	—
301	C₂×#131	—	26	2	no	—
302	C₂×#131	—	26	2	no	—
303	C₂²×M₁₆	—	13	1	no	—
304	C₂²×M₁₆	—	13	1	no	—
305	C₂²×M₁₆	—	13	1	no	—
306	C₂²×M₁₆	—	26	2	no	—
307	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
308	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
309	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
310	#430	—	13	4	no	—
311	#430	—	26	2	no	—
312	C₂×#108	—	26	2	no	—
313	#423	—	13	4	no	—
314	#423	—	26	2	no	—
315	C₂×C₄⋊C₈	—	26	2	no	—
316	#421	—	13	4	no	—
317	#421	—	26	2	no	—
318	C₂×#104	—	13	2	no	—
319	C₂×#104	—	13	4	no	—
320	C₂×#104	—	13	2	no	—
321	C₂×#104	—	13	4	no	—
322	C₂×#104	—	26	2	no	—
323	#344	—	13	4	no	—
324	#339	C₂×D₁₃	1	4	yes	complemented
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	#385	1	1	yes	characteristic
333	C₂²×C₁₃	#385	1	1	yes	characteristic
334	C₂²×C₁₃	#385	1	1	yes	characteristic
335	C₂²×C₁₃	#385	1	1	yes	characteristic
336	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
337	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
339	C₂×D₁₃	—	2	4	no	—
340	C₂×D₁₃	—	4	4	no	—
341	C₂×D₁₃	—	8	2	no	—
342	C₂×D₁₃	—	8	2	no	—
343	C₄×C₁₃	—	2	4	no	—
344	C₄×C₁₃	—	4	2	no	—
345	C₄×C₁₃	—	8	2	no	—
346	C₄×C₁₃	#385	1	1	yes	characteristic
347	C₄×C₁₃	#385	1	1	yes	characteristic
348	C₄×C₁₃	#385	1	1	yes	characteristic
349	C₄×C₁₃	#385	1	1	yes	characteristic
350	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
351	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
352	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
353	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
354	Dic₁₃	—	2	4	no	—
355	C₂×#41	—	13	2	no	—
356	C₂×#41	—	13	2	no	—
357	C₂×#41	—	13	2	no	—
358	C₂×#41	—	13	2	no	—
359	C₂×#41	—	13	2	no	—
360	C₂×#41	—	13	2	no	—
361	C₂×#41	—	26	1	no	—
362	C₂×#41	—	26	1	no	—
363	C₂×#41	—	26	1	no	—
364	C₂×#41	—	26	1	no	—
365	C₂×#41	—	26	1	no	—
366	C₂×#41	—	26	1	no	—
367	C₂²×Q₈	—	13	1	no	—
368	C₂²×D₄	—	13	1	no	—
369	C₂²×D₄	—	26	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	26	1	no	—
372	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
373	#131	—	26	8	no	—
374	#131	—	26	8	no	—
375	#131	—	26	8	no	—
376	#131	—	26	8	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	13	2	no	—
381	C₂×M₁₆	—	13	2	no	—
382	C₂×M₁₆	—	13	2	no	—
383	C₂×M₁₆	—	13	2	no	—
384	C₂×M₁₆	—	13	2	no	—
385	C₂×M₁₆	—	13	2	no	—
386	C₂×M₁₆	—	26	4	no	—
387	C₂×M₁₆	—	26	8	no	—
388	C₂×M₁₆	—	26	1	no	—
389	C₂×M₁₆	—	26	1	no	—
390	C₂×M₁₆	—	26	1	no	—
391	C₂×M₁₆	—	26	1	no	—
392	C₂×M₁₆	—	26	1	no	—
393	C₂×M₁₆	—	26	1	no	—
394	C₂×M₁₆	—	26	1	no	—
395	C₂×M₁₆	—	26	8	no	—
396	C₂×M₁₆	—	26	1	no	—
397	C₂×M₁₆	—	26	1	no	—
398	C₂×M₁₆	—	26	1	no	—
399	C₂×M₁₆	—	26	1	no	—
400	C₂×M₁₆	—	26	1	no	—
401	C₂×M₁₆	D₅₂	1	2	yes	—
402	C₂×M₁₆	D₅₂	1	2	yes	—
403	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	13	2	no	—
406	C₂²×C₈	—	26	4	no	—
407	C₂²×C₈	—	26	1	no	—
408	C₂²×C₈	—	26	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	C₂²×D₁₃	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
420	C₂×C₄²	C₄×D₁₃	1	2	yes	—
421	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
422	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
423	#108	—	26	8	no	—
424	C₄⋊C₈	—	26	8	no	—
425	#104	—	13	8	no	—
426	#104	—	13	8	no	—
427	#104	—	26	8	no	—
428	C₂×C₁₃	—	2	1	no	—
429	C₂×C₁₃	—	2	1	no	—
430	C₂×C₁₃	—	2	1	no	—
431	C₂×C₁₃	—	2	1	no	—
432	C₂×C₁₃	—	2	1	no	—
433	C₂×C₁₃	—	2	1	no	—
434	C₂×C₁₃	#1861	1	2	yes	complemented
435	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
436	D₁₃	—	4	4	no	—
437	C₂⁴	—	26	1	no	—
438	C₂⁴	#6129	1	1	yes	characteristic
439	#41	—	13	4	no	—
440	#41	—	13	4	no	—
441	#41	—	13	4	no	—
442	#41	—	13	4	no	—
443	#41	—	26	2	no	—
444	#41	—	26	2	no	—
445	#41	—	26	2	no	—
446	#41	—	26	2	no	—
447	#41	—	26	2	no	—
448	#41	—	26	2	no	—
449	#41	—	26	2	no	—
450	#41	—	26	2	no	—
451	#41	—	26	2	no	—
452	#41	—	26	2	no	—
453	#41	—	26	2	no	—
454	#41	—	26	2	no	—
455	C₂×Q₈	—	13	2	no	—
456	C₂×Q₈	—	13	2	no	—
457	C₂×Q₈	—	13	2	no	—
458	C₂×Q₈	—	26	1	no	—
459	C₂×Q₈	—	26	1	no	—
460	C₂×Q₈	—	26	1	no	—
461	C₂×D₄	—	13	2	no	—
462	C₂×D₄	—	13	2	no	—
463	C₂×D₄	—	13	2	no	—
464	C₂×D₄	—	26	2	no	—
465	C₂×D₄	—	26	2	no	—
466	C₂×D₄	—	26	2	no	—
467	C₂×D₄	—	26	2	no	—
468	C₂×D₄	—	26	2	no	—
469	C₂×D₄	—	26	2	no	—
470	C₂×D₄	—	26	1	no	—
471	C₂×D₄	—	26	1	no	—
472	C₂×D₄	—	26	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	26	1	no	—
480	C₂²×C₄	—	26	2	no	—
481	C₂²×C₄	—	26	2	no	—
482	C₂²×C₄	—	26	2	no	—
483	C₂²×C₄	—	26	2	no	—
484	C₂²×C₄	—	26	2	no	—
485	C₂²×C₄	—	26	2	no	—
486	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
490	C₂²×C₄	#6127	1	1	yes	characteristic
491	C₂²×C₄	#6127	1	1	yes	characteristic
492	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
493	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
494	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
495	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
496	C₂²×C₄	#6129	1	1	yes	characteristic
497	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
498	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
500	M₁₆	—	2	2	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	13	4	no	—
504	M₁₆	—	26	16	no	—
505	M₁₆	—	26	2	no	—
506	M₁₆	—	26	2	no	—
507	M₁₆	—	26	2	no	—
508	M₁₆	—	26	2	no	—
509	M₁₆	—	26	2	no	—
510	M₁₆	—	26	2	no	—
511	M₁₆	—	26	2	no	—
512	M₁₆	—	26	2	no	—
513	M₁₆	—	26	2	no	—
514	M₁₆	—	52	1	no	—
515	M₁₆	—	52	1	no	—
516	M₁₆	C₂×D₅₂	1	4	yes	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	13	4	no	—
521	C₂×C₈	—	26	16	no	—
522	C₂×C₈	—	26	2	no	—
523	C₂×C₈	—	26	2	no	—
524	C₂×C₈	—	26	2	no	—
525	C₂×C₈	—	26	2	no	—
526	C₂×C₈	—	26	2	no	—
527	C₂×C₈	—	26	2	no	—
528	C₂×C₈	—	52	1	no	—
529	C₂×C₈	—	52	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	4	1	no	—
540	C₄²	C₂×C₄×D₁₃	1	2	yes	—
541	C₄²	C₂×C₄×D₁₃	1	2	yes	—
542	C₁₃	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
543	C₂³	—	4	2	no	—
544	C₂³	—	26	2	no	—
545	C₂³	—	26	2	no	—
546	C₂³	—	26	2	no	—
547	C₂³	—	104	2	no	—
548	C₂³	#88135	1	1	yes	characteristic
549	C₂³	#88135	1	1	yes	characteristic
550	C₂³	#88137	1	1	yes	characteristic
551	C₂³	#88137	1	1	yes	characteristic
552	C₂³	#88151	1	1	yes	characteristic
553	C₂³	#88151	1	1	yes	characteristic
554	C₂³	C₂×#6129	1	1	yes	characteristic
555	Q₈	—	13	4	no	—
556	Q₈	—	26	2	no	—
557	Q₈	—	26	2	no	—
558	Q₈	—	26	2	no	—
559	D₄	—	13	4	no	—
560	D₄	—	26	4	no	—
561	D₄	—	26	4	no	—
562	D₄	—	26	4	no	—
563	D₄	—	26	4	no	—
564	D₄	—	26	2	no	—
565	D₄	—	26	2	no	—
566	D₄	—	26	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	8	2	no	—
575	C₂×C₄	—	26	2	no	—
576	C₂×C₄	—	26	2	no	—
577	C₂×C₄	—	26	2	no	—
578	C₂×C₄	—	26	4	no	—
579	C₂×C₄	—	26	4	no	—
580	C₂×C₄	—	26	4	no	—
581	C₂×C₄	—	26	4	no	—
582	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
583	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
584	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
585	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
586	C₂×C₄	#88135	1	1	yes	characteristic
587	C₂×C₄	#88135	1	1	yes	characteristic
588	C₂×C₄	#88136	1	1	yes	characteristic
589	C₂×C₄	#88136	1	1	yes	characteristic
590	C₂×C₄	#88136	1	1	yes	characteristic
591	C₂×C₄	#88136	1	1	yes	characteristic
592	C₂×C₄	#88137	1	1	yes	characteristic
593	C₂×C₄	#88137	1	1	yes	characteristic
594	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
595	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
596	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
597	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
598	C₂×C₄	#88150	1	1	yes	characteristic
599	C₂×C₄	#88150	1	1	yes	characteristic
600	C₂×C₄	#88150	1	1	yes	characteristic
601	C₂×C₄	#88150	1	1	yes	characteristic
602	C₂×C₄	#88151	1	1	yes	characteristic
603	C₂×C₄	#88151	1	1	yes	characteristic
604	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
606	C₂×C₄	C₂×#6127	1	1	yes	characteristic
607	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	26	4	no	—
612	C₈	—	26	4	no	—
613	C₈	—	52	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	26	4	no	—
622	C₂²	—	52	4	no	—
623	C₂²	—	104	2	no	—
624	C₂²	—	104	2	no	—
625	C₂²	#11718329	1	1	yes	characteristic
626	C₂²	#11718329	1	1	yes	characteristic
627	C₂²	#11718329	1	1	yes	characteristic
628	C₂²	#11718329	1	1	yes	characteristic
629	C₂²	C₂×#88135	1	1	yes	characteristic
630	C₂²	C₂×#88137	1	1	yes	characteristic
631	C₂²	C₂×#88151	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	4	2	no	—
634	C₄	—	8	2	no	—
635	C₄	—	26	4	no	—
636	C₄	#11718329	1	1	yes	characteristic
637	C₄	#11718329	1	1	yes	characteristic
638	C₄	#11718329	1	1	yes	characteristic
639	C₄	#11718329	1	1	yes	characteristic
640	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
641	C₄	C₂×#88136	1	1	yes	characteristic
642	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
643	C₄	C₂×#88150	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	52	4	no	—
651	C₂	#13115077	1	2	yes	direct product factor
652	C₂	C₂×#11718329	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88136
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#339	C₂
socle	C₂²×C₁₃	#385
prime radical	C₂²×#6127	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#339	D₁₃
hypocenter	C₁₃	C₂×#1861
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
2. C₂×#11718785	C₂	semidirect
3. C₂×#11718585	C₂	semidirect
6. #13115077	C₂	direct (N × H)
7. C₂×#11718125	C₂	semidirect
8. C₂×C₁₃×#339	C₂	semidirect
24. #11718785	C₂²	semidirect
29. C₂×#88045	C₄	semidirect
30. C₂×#88045	C₄	semidirect
31. C₂×#88045	C₄	semidirect
34. #11718585	C₂²	semidirect
36. C₁₃×#339	C₂²	semidirect
37. #11718125	C₂²	semidirect
108. #88045	C₂×C₄	semidirect
109. #88045	C₂×C₄	semidirect
224. C₂×#339	D₁₃	semidirect
324. #339	C₂×D₁₃	semidirect
434. C₂×C₁₃	#1861	semidirect
542. C₁₃	C₂×#1861	semidirect
651. C₂	#13115077	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×#11719450	2
C₂×#11718785	2
C₂×#11718585	2
C₂×#11718666	2
C₂²×#88045	2
#13115077	2
C₂×#11718125	2
C₂×C₁₃×#339	2
C₂×#1861	13

Subgroups — C2×#13115077 #15863817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115077 #15863817