Subgroups — C₂×#13116298 #15891858

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718662	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718662	C₂	1	1	yes	maximal, characteristic
4	C₂²×#88063	C₂	1	1	yes	maximal, characteristic
5	#13116298	C₂	1	8	yes	maximal, direct product factor
6	C₂×#11718125	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₅₂	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	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	C₂×#88063	—	2	2	no	—
17	C₂×#88063	—	2	2	no	—
18	C₂×#88063	C₂²	1	4	yes	—
19	#11718785	—	2	2	no	—
20	#11718785	C₂²	1	4	yes	complemented
21	C₂×#88062	—	2	2	no	—
22	#11718662	—	2	2	no	—
23	#11718662	—	2	2	no	—
24	#11718662	C₂²	1	4	yes	—
25	#11718662	C₂²	1	4	yes	—
26	C₂×#88049	—	2	2	no	—
27	C₂×#88049	—	2	2	no	—
28	C₁₃×H(3,ℤ/4)	C₂²	1	4	yes	complemented
29	#11718125	C₂²	1	4	yes	complemented
30	#11718125	C₂²	1	4	yes	complemented
31	C₂⁴×D₁₃	—	2	1	no	—
32	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²×D₅₂	—	2	1	no	—
34	C₂²×D₅₂	—	2	1	no	—
35	C₂²×D₅₂	—	2	1	no	—
36	C₂²×D₅₂	—	2	1	no	—
37	C₂²×D₅₂	—	2	1	no	—
38	C₂²×D₅₂	—	2	1	no	—
39	C₂²×D₅₂	—	2	1	no	—
40	C₂²×D₅₂	—	2	1	no	—
41	C₂²×D₅₂	—	2	1	no	—
42	C₂²×D₅₂	—	2	1	no	—
43	C₂²×D₅₂	—	2	1	no	—
44	C₂²×D₅₂	D₄	1	2	yes	—
45	C₂²×D₅₂	D₄	1	2	yes	—
46	C₂²×D₅₂	C₂³	1	2	yes	—
47	C₂×C₁₃×M₁₆	—	2	1	no	—
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₁₃×#117	—	2	1	no	—
55	C₁₃×#117	—	2	1	no	—
56	C₁₃×#117	—	2	1	no	—
57	C₁₃×#117	—	2	1	no	—
58	C₁₃×#117	—	2	1	no	—
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	C₂³	1	2	yes	—
61	C₁₃×#117	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×#6099	—	2	1	no	—
69	C₂×#6099	—	2	1	no	—
70	C₂×#6099	—	2	1	no	—
71	C₂×#6099	—	2	1	no	—
72	C₂×#6099	—	2	1	no	—
73	C₂×#6099	—	2	1	no	—
74	C₂×#6099	—	2	1	no	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
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	D₄	1	2	yes	—
83	C₂×#6099	C₂³	1	2	yes	—
84	C₂×#6099	C₂³	1	2	yes	—
85	C₂×#6099	C₂³	1	2	yes	—
86	C₂²×#1055	—	2	1	no	—
87	C₂²×#1055	—	2	1	no	—
88	C₂²×#1055	D₄	1	2	yes	—
89	#88063	—	2	8	no	—
90	#88062	—	2	8	no	—
91	#88049	—	2	8	no	—
92	#88049	—	2	8	no	—
93	C₂×#2081	—	13	1	no	maximal, Sylow
94	C₂⁴×C₁₃	#41	1	1	yes	characteristic
95	C₂³×D₁₃	—	2	2	no	—
96	C₂³×D₁₃	—	2	2	no	—
97	C₂³×D₁₃	—	2	2	no	—
98	C₂³×D₁₃	—	4	1	no	—
99	C₂³×D₁₃	—	4	1	no	—
100	C₂³×D₁₃	—	4	1	no	—
101	C₂³×D₁₃	—	4	1	no	—
102	C₂³×D₁₃	—	8	4	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×D₅₂	—	2	2	no	—
120	C₂×D₅₂	—	2	2	no	—
121	C₂×D₅₂	—	2	2	no	—
122	C₂×D₅₂	—	2	2	no	—
123	C₂×D₅₂	—	2	2	no	—
124	C₂×D₅₂	—	2	2	no	—
125	C₂×D₅₂	—	2	2	no	—
126	C₂×D₅₂	—	2	2	no	—
127	C₂×D₅₂	—	2	2	no	—
128	C₂×D₅₂	—	2	2	no	—
129	C₂×D₅₂	—	2	2	no	—
130	C₂×D₅₂	—	2	2	no	—
131	C₂×D₅₂	—	2	2	no	—
132	C₂×D₅₂	—	2	2	no	—
133	C₂×D₅₂	—	2	2	no	—
134	C₂×D₅₂	—	4	1	no	—
135	C₂×D₅₂	—	4	1	no	—
136	C₂×D₅₂	—	4	1	no	—
137	C₂×D₅₂	—	4	1	no	—
138	C₂×D₅₂	—	4	1	no	—
139	C₂×D₅₂	—	4	1	no	—
140	C₂×D₅₂	—	4	1	no	—
141	C₂×D₅₂	—	4	1	no	—
142	C₂×D₅₂	—	4	1	no	—
143	C₂×D₅₂	—	4	1	no	—
144	C₂×D₅₂	—	4	1	no	—
145	C₂×D₅₂	—	4	1	no	—
146	C₂×D₅₂	C₂×D₄	1	4	yes	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	2	no	—
149	C₁₃×M₁₆	—	4	1	no	—
150	C₁₃×M₁₆	—	4	1	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	4	1	no	—
153	C₂×C₈×C₁₃	—	4	1	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	4	1	no	—
157	C₁₃×C₄⋊C₄	—	4	1	no	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	—	4	1	no	—
161	C₁₃×C₂²⋊C₄	—	4	1	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	2	2	no	—
164	C₄²×C₁₃	—	4	1	no	—
165	C₄²×C₁₃	—	4	1	no	—
166	#6099	—	2	2	no	—
167	#6099	—	2	2	no	—
168	#6099	—	2	2	no	—
169	#6099	—	2	2	no	—
170	#6099	—	2	2	no	—
171	#6099	—	2	2	no	—
172	#6099	—	2	2	no	—
173	#6099	—	2	2	no	—
174	#6099	—	4	1	no	—
175	#6099	—	4	1	no	—
176	#6099	—	4	1	no	—
177	#6099	—	4	1	no	—
178	C₂×#1055	—	2	2	no	—
179	C₂×#1055	—	2	2	no	—
180	C₂×#1055	—	2	2	no	—
181	C₂×#1055	—	2	2	no	—
182	C₂×#1055	—	4	1	no	—
183	C₂×#1055	—	4	1	no	—
184	C₂×#1055	—	4	1	no	—
185	C₂×#1055	—	4	1	no	—
186	C₂×#1055	C₂×D₄	1	4	yes	—
187	C₂×#430	—	13	1	no	—
188	C₂×#418	—	13	1	no	—
189	C₂×#418	—	13	1	no	—
190	C₂²×#100	—	13	1	no	—
191	#2081	—	13	8	no	—
192	C₂×#344	—	13	1	no	—
193	C₂×#344	—	13	1	no	—
194	C₂×H(3,ℤ/4)	D₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	#123	1	1	yes	characteristic
197	C₂³×C₁₃	#123	1	1	yes	characteristic
198	C₂³×C₁₃	#124	1	1	yes	characteristic
199	C₂³×C₁₃	#124	1	1	yes	characteristic
200	C₂³×C₁₃	#126	1	1	yes	characteristic
201	C₂³×C₁₃	#126	1	1	yes	characteristic
202	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂²×D₁₃	—	2	4	no	—
204	C₂²×D₁₃	—	4	2	no	—
205	C₂²×D₁₃	—	4	2	no	—
206	C₂²×D₁₃	—	4	2	no	—
207	C₂²×D₁₃	—	4	2	no	—
208	C₂²×D₁₃	—	4	2	no	—
209	C₂²×D₁₃	—	4	2	no	—
210	C₂²×D₁₃	—	8	4	no	—
211	C₂²×D₁₃	—	8	4	no	—
212	C₂²×D₁₃	—	8	4	no	—
213	C₂²×D₁₃	—	8	4	no	—
214	C₂²×D₁₃	—	8	4	no	—
215	C₂²×D₁₃	—	8	4	no	—
216	C₂²×D₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	8	2	no	—
220	C₂×C₄×C₁₃	—	8	2	no	—
221	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
231	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
235	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	D₅₂	—	2	4	no	—
250	D₅₂	—	2	4	no	—
251	D₅₂	—	4	2	no	—
252	D₅₂	—	4	2	no	—
253	D₅₂	—	4	2	no	—
254	D₅₂	—	4	2	no	—
255	D₅₂	—	4	2	no	—
256	D₅₂	—	4	2	no	—
257	C₈×C₁₃	—	4	2	no	—
258	#1055	—	2	4	no	—
259	#1055	—	4	2	no	—
260	#1055	—	4	2	no	—
261	C₂³×D₄	—	13	1	no	—
262	C₂²×M₁₆	—	13	1	no	—
263	C₂²×M₁₆	—	13	1	no	—
264	C₂²×M₁₆	—	13	1	no	—
265	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
266	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
267	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
268	#430	—	13	4	no	—
269	#430	—	26	2	no	—
270	C₂×#108	—	26	2	no	—
271	#418	—	13	4	no	—
272	#418	—	13	4	no	—
273	#418	—	26	2	no	—
274	#418	—	26	2	no	—
275	C₂×#102	—	26	2	no	—
276	C₂×#102	—	26	2	no	—
277	C₂×#100	—	13	4	no	—
278	C₂×#100	—	26	2	no	—
279	C₂×#100	—	26	2	no	—
280	#344	—	13	4	no	—
281	#344	—	13	4	no	—
282	H(3,ℤ/4)	C₂×D₁₃	1	4	yes	complemented
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	4	1	no	—
287	C₂²×C₁₃	—	4	1	no	—
288	C₂²×C₁₃	—	4	1	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	#397	1	1	yes	characteristic
291	C₂²×C₁₃	#397	1	1	yes	characteristic
292	C₂²×C₁₃	#397	1	1	yes	characteristic
293	C₂²×C₁₃	#397	1	1	yes	characteristic
294	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
295	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
296	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
297	C₂×D₁₃	—	4	4	no	—
298	C₂×D₁₃	—	8	4	no	—
299	C₂×D₁₃	—	8	4	no	—
300	C₂×D₁₃	—	8	4	no	—
301	C₂×D₁₃	—	8	4	no	—
302	C₂×D₁₃	—	8	4	no	—
303	C₂×D₁₃	—	8	4	no	—
304	C₂×D₁₃	—	8	4	no	—
305	C₄×C₁₃	—	8	2	no	—
306	C₄×C₁₃	—	8	2	no	—
307	C₄×C₁₃	#397	1	1	yes	characteristic
308	C₄×C₁₃	#397	1	1	yes	characteristic
309	C₄×C₁₃	#397	1	1	yes	characteristic
310	C₄×C₁₃	#397	1	1	yes	characteristic
311	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
312	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
313	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
314	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
315	C₂⁵	—	26	1	no	—
316	C₂²×D₄	—	13	2	no	—
317	C₂²×D₄	—	13	2	no	—
318	C₂²×D₄	—	13	2	no	—
319	C₂²×D₄	—	26	1	no	—
320	C₂²×D₄	—	26	1	no	—
321	C₂²×D₄	—	26	1	no	—
322	C₂²×D₄	—	26	1	no	—
323	C₂²×D₄	—	26	1	no	—
324	C₂²×D₄	—	26	1	no	—
325	C₂²×D₄	—	26	1	no	—
326	C₂²×D₄	—	26	1	no	—
327	C₂²×D₄	—	26	1	no	—
328	C₂²×D₄	—	26	1	no	—
329	C₂²×D₄	—	26	1	no	—
330	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	13	2	no	—
337	C₂×M₁₆	—	13	2	no	—
338	C₂×M₁₆	—	13	2	no	—
339	C₂×M₁₆	—	13	2	no	—
340	C₂×M₁₆	—	26	1	no	—
341	C₂×M₁₆	—	26	1	no	—
342	C₂×M₁₆	—	26	1	no	—
343	C₂×M₁₆	—	26	1	no	—
344	C₂×M₁₆	—	26	1	no	—
345	C₂×M₁₆	—	26	1	no	—
346	C₂×M₁₆	—	26	1	no	—
347	C₂×M₁₆	—	26	1	no	—
348	C₂×M₁₆	—	26	1	no	—
349	C₂×M₁₆	—	26	1	no	—
350	C₂×M₁₆	—	26	1	no	—
351	C₂×M₁₆	—	26	1	no	—
352	C₂×M₁₆	—	26	1	no	—
353	C₂×M₁₆	—	26	1	no	—
354	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	13	2	no	—
357	C₂²×C₈	—	26	1	no	—
358	C₂²×C₈	—	26	1	no	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	C₂²×D₁₃	1	2	yes	—
366	#117	C₂²×D₁₃	1	2	yes	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	#108	—	26	8	no	—
374	#102	—	26	8	no	—
375	#102	—	26	8	no	—
376	#100	—	26	8	no	—
377	C₂×C₁₃	—	2	1	no	—
378	C₂×C₁₃	—	2	1	no	—
379	C₂×C₁₃	—	2	1	no	—
380	C₂×C₁₃	—	2	1	no	—
381	C₂×C₁₃	—	2	1	no	—
382	C₂×C₁₃	—	2	1	no	—
383	C₂×C₁₃	#2081	1	2	yes	complemented
384	C₂×C₁₃	C₂×#397	1	1	yes	characteristic
385	D₁₃	—	8	4	no	—
386	C₂⁴	—	26	2	no	—
387	C₂⁴	—	26	2	no	—
388	C₂⁴	—	26	2	no	—
389	C₂⁴	—	52	1	no	—
390	C₂⁴	—	52	1	no	—
391	C₂⁴	—	52	1	no	—
392	C₂⁴	—	52	1	no	—
393	C₂⁴	—	104	4	no	—
394	C₂⁴	#6129	1	1	yes	characteristic
395	C₂×D₄	—	13	4	no	—
396	C₂×D₄	—	26	2	no	—
397	C₂×D₄	—	26	2	no	—
398	C₂×D₄	—	26	2	no	—
399	C₂×D₄	—	26	2	no	—
400	C₂×D₄	—	26	2	no	—
401	C₂×D₄	—	26	2	no	—
402	C₂×D₄	—	26	2	no	—
403	C₂×D₄	—	26	2	no	—
404	C₂×D₄	—	26	2	no	—
405	C₂×D₄	—	26	2	no	—
406	C₂×D₄	—	26	2	no	—
407	C₂×D₄	—	26	2	no	—
408	C₂×D₄	—	26	2	no	—
409	C₂×D₄	—	26	2	no	—
410	C₂×D₄	—	26	2	no	—
411	C₂×D₄	—	52	1	no	—
412	C₂×D₄	—	52	1	no	—
413	C₂×D₄	—	52	1	no	—
414	C₂×D₄	—	52	1	no	—
415	C₂×D₄	—	52	1	no	—
416	C₂×D₄	—	52	1	no	—
417	C₂×D₄	—	52	1	no	—
418	C₂×D₄	—	52	1	no	—
419	C₂×D₄	—	52	1	no	—
420	C₂×D₄	—	52	1	no	—
421	C₂×D₄	—	52	1	no	—
422	C₂×D₄	—	52	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	#6127	1	1	yes	characteristic
426	C₂²×C₄	#6127	1	1	yes	characteristic
427	C₂²×C₄	#6127	1	1	yes	characteristic
428	C₂²×C₄	#6127	1	1	yes	characteristic
429	C₂²×C₄	#6127	1	1	yes	characteristic
430	C₂²×C₄	#6127	1	1	yes	characteristic
431	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
432	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
433	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
434	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
435	C₂²×C₄	#6129	1	1	yes	characteristic
436	C₂²×C₄	#6131	1	1	yes	characteristic
437	C₂²×C₄	#6131	1	1	yes	characteristic
438	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	26	2	no	—
444	M₁₆	—	26	2	no	—
445	M₁₆	—	26	2	no	—
446	M₁₆	—	26	2	no	—
447	M₁₆	—	26	2	no	—
448	M₁₆	—	26	2	no	—
449	M₁₆	—	26	2	no	—
450	M₁₆	—	26	2	no	—
451	M₁₆	—	52	1	no	—
452	M₁₆	—	52	1	no	—
453	M₁₆	—	52	1	no	—
454	M₁₆	—	52	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	4	1	no	—
457	C₂×C₈	—	4	1	no	—
458	C₂×C₈	—	13	4	no	—
459	C₂×C₈	—	26	2	no	—
460	C₂×C₈	—	26	2	no	—
461	C₂×C₈	—	26	2	no	—
462	C₂×C₈	—	26	2	no	—
463	C₂×C₈	—	52	1	no	—
464	C₂×C₈	—	52	1	no	—
465	C₂×C₈	—	52	1	no	—
466	C₂×C₈	—	52	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	4	1	no	—
478	C₄²	—	4	1	no	—
479	C₁₃	C₂×#2081	1	1	yes	characteristic, complemented, Sylow
480	C₂³	—	4	2	no	—
481	C₂³	—	26	4	no	—
482	C₂³	—	52	2	no	—
483	C₂³	—	52	2	no	—
484	C₂³	—	52	2	no	—
485	C₂³	—	52	2	no	—
486	C₂³	—	52	2	no	—
487	C₂³	—	52	2	no	—
488	C₂³	—	104	4	no	—
489	C₂³	—	104	4	no	—
490	C₂³	—	104	4	no	—
491	C₂³	—	104	4	no	—
492	C₂³	—	104	4	no	—
493	C₂³	—	104	4	no	—
494	C₂³	—	104	4	no	—
495	C₂³	#88137	1	1	yes	characteristic
496	C₂³	#88137	1	1	yes	characteristic
497	C₂³	#88139	1	1	yes	characteristic
498	C₂³	#88139	1	1	yes	characteristic
499	C₂³	#88152	1	1	yes	characteristic
500	C₂³	#88152	1	1	yes	characteristic
501	C₂³	C₂×#6129	1	1	yes	characteristic
502	D₄	—	26	4	no	—
503	D₄	—	26	4	no	—
504	D₄	—	52	2	no	—
505	D₄	—	52	2	no	—
506	D₄	—	52	2	no	—
507	D₄	—	52	2	no	—
508	D₄	—	52	2	no	—
509	D₄	—	52	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	#88130	1	1	yes	characteristic
515	C₂×C₄	#88130	1	1	yes	characteristic
516	C₂×C₄	#88130	1	1	yes	characteristic
517	C₂×C₄	#88130	1	1	yes	characteristic
518	C₂×C₄	#88137	1	1	yes	characteristic
519	C₂×C₄	#88137	1	1	yes	characteristic
520	C₂×C₄	#88138	1	1	yes	characteristic
521	C₂×C₄	#88138	1	1	yes	characteristic
522	C₂×C₄	#88138	1	1	yes	characteristic
523	C₂×C₄	#88138	1	1	yes	characteristic
524	C₂×C₄	#88139	1	1	yes	characteristic
525	C₂×C₄	#88139	1	1	yes	characteristic
526	C₂×C₄	#88148	1	1	yes	characteristic
527	C₂×C₄	#88148	1	1	yes	characteristic
528	C₂×C₄	#88148	1	1	yes	characteristic
529	C₂×C₄	#88148	1	1	yes	characteristic
530	C₂×C₄	#88148	1	1	yes	characteristic
531	C₂×C₄	#88148	1	1	yes	characteristic
532	C₂×C₄	#88148	1	1	yes	characteristic
533	C₂×C₄	#88148	1	1	yes	characteristic
534	C₂×C₄	#88152	1	1	yes	characteristic
535	C₂×C₄	#88152	1	1	yes	characteristic
536	C₂×C₄	C₂×#6127	1	1	yes	characteristic
537	C₂×C₄	C₂×#6127	1	1	yes	characteristic
538	C₂×C₄	C₂×#6127	1	1	yes	characteristic
539	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂×#6131	1	1	yes	characteristic
542	C₈	—	4	2	no	—
543	C₈	—	26	4	no	—
544	C₈	—	52	2	no	—
545	C₈	—	52	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	52	4	no	—
554	C₂²	—	104	4	no	—
555	C₂²	—	104	4	no	—
556	C₂²	—	104	4	no	—
557	C₂²	—	104	4	no	—
558	C₂²	—	104	4	no	—
559	C₂²	—	104	4	no	—
560	C₂²	—	104	4	no	—
561	C₂²	#11718336	1	1	yes	characteristic
562	C₂²	#11718336	1	1	yes	characteristic
563	C₂²	#11718336	1	1	yes	characteristic
564	C₂²	#11718336	1	1	yes	characteristic
565	C₂²	C₂×#88137	1	1	yes	characteristic
566	C₂²	C₂×#88139	1	1	yes	characteristic
567	C₂²	C₂×#88152	1	1	yes	characteristic
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	#11718336	1	1	yes	characteristic
571	C₄	#11718336	1	1	yes	characteristic
572	C₄	#11718336	1	1	yes	characteristic
573	C₄	#11718336	1	1	yes	characteristic
574	C₄	C₂×#88130	1	1	yes	characteristic
575	C₄	C₂×#88138	1	1	yes	characteristic
576	C₄	C₂×#88148	1	1	yes	characteristic
577	C₄	C₂×#88148	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	104	4	no	—
585	C₂	#13116298	1	2	yes	direct product factor
586	C₂	C₂×#11718336	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718336
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×H(3,ℤ/4)	C₂
socle	C₂²×C₁₃	#397
prime radical	C₂³×D₅₂	C₂²
hypercenter	C₂×H(3,ℤ/4)	D₁₃
hypocenter	C₁₃	C₂×#2081
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
1. C₂×#11718785	C₂	semidirect
5. #13116298	C₂	direct (N × H)
6. C₂×#11718125	C₂	semidirect
7. C₂×#11718125	C₂	semidirect
8. C₂×C₁₃×H(3,ℤ/4)	C₂	semidirect
20. #11718785	C₂²	semidirect
28. C₁₃×H(3,ℤ/4)	C₂²	semidirect
29. #11718125	C₂²	semidirect
30. #11718125	C₂²	semidirect
194. C₂×H(3,ℤ/4)	D₁₃	semidirect
282. H(3,ℤ/4)	C₂×D₁₃	semidirect
383. C₂×C₁₃	#2081	semidirect
479. C₁₃	C₂×#2081	semidirect
585. C₂	#13116298	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×#11718785	2
C₂×#11718662	2
C₂²×#88063	2
#13116298	2
C₂×#11718125	2
C₂×C₁₃×H(3,ℤ/4)	2
C₂×#2081	13

Subgroups — C2×#13116298 #15891858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116298 #15891858