Subgroups — #6803849

Order 512.

1087 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#33192	C₂	1	1	yes	maximal, characteristic, complemented
2	#32699	C₂	1	2	yes	maximal, complemented
3	#32696	C₂	1	2	yes	maximal, complemented
4	#31417	C₂	1	2	yes	maximal, complemented
5	#31415	C₂	1	2	yes	maximal, complemented
6	#30238	C₂	1	1	yes	maximal, characteristic, complemented
7	#30237	C₂	1	1	yes	maximal, characteristic, complemented
8	#29230	C₂	1	1	yes	maximal, characteristic, complemented
9	#28501	C₂	1	1	yes	maximal, characteristic, complemented
10	#28182	C₂	1	2	yes	maximal, complemented
11	#27987	C₂	1	2	yes	maximal, complemented
12	#25448	C₂	1	1	yes	maximal, characteristic, complemented
13	#25447	C₂	1	1	yes	maximal, characteristic
14	#24989	C₂	1	1	yes	maximal, characteristic, complemented
15	#24988	C₂	1	1	yes	maximal, characteristic, complemented
16	#24987	C₂	1	2	yes	maximal, complemented
17	#24808	C₂	1	2	yes	maximal, complemented
18	#23199	C₂	1	1	yes	maximal, characteristic, complemented
19	#22694	C₂	1	1	yes	maximal, characteristic, complemented
20	#22286	C₂	1	1	yes	maximal, characteristic, complemented
21	#22285	C₂	1	1	yes	maximal, characteristic, complemented
22	#21558	C₂	1	1	yes	maximal, characteristic, complemented
23	#20787	C₂	1	1	yes	maximal, characteristic, complemented
24	#3156	C₂²	1	1	yes	characteristic
25	#3155	C₂²	1	1	yes	characteristic
26	C₂×#495	C₂²	1	1	yes	characteristic
27	#3069	C₂²	1	2	yes	—
28	#3068	C₂²	1	2	yes	—
29	#3067	C₂²	1	1	yes	characteristic
30	C₂×#473	C₂²	1	1	yes	characteristic
31	C₂×#472	C₂²	1	1	yes	characteristic
32	C₂×#471	C₂²	1	2	yes	—
33	C₂×#471	C₂²	1	2	yes	—
34	#3057	C₂²	1	2	yes	—
35	#3040	C₂²	1	2	yes	—
36	#2957	C₂²	1	1	yes	characteristic
37	#2957	C₂²	1	1	yes	characteristic
38	#2955	C₂²	1	2	yes	—
39	C₂×#443	C₂²	1	1	yes	characteristic
40	#2950	C₂²	1	1	yes	characteristic
41	#2949	C₂²	1	2	yes	—
42	#2948	C₂²	1	1	yes	characteristic
43	#2916	C₂²	1	2	yes	—
44	C₄×#131	C₂²	1	1	yes	characteristic
45	#2102	C₂²	1	2	yes	—
46	#2102	C₂²	1	2	yes	—
47	#2082	C₂²	1	2	yes	—
48	#2082	C₂²	1	2	yes	—
49	#2082	C₂²	1	2	yes	—
50	#2082	C₂²	1	2	yes	—
51	#2081	C₂²	1	2	yes	—
52	#2081	C₂²	1	2	yes	—
53	#2081	C₂²	1	2	yes	—
54	#2081	C₂²	1	2	yes	—
55	#2070	C₂²	1	2	yes	—
56	#2069	C₂²	1	2	yes	—
57	#2049	C₂²	1	2	yes	—
58	#2049	C₂²	1	2	yes	—
59	#2048	C₂²	1	2	yes	—
60	#2048	C₂²	1	2	yes	—
61	#2009	C₂²	1	2	yes	—
62	#2008	C₂²	1	2	yes	—
63	#2004	C₂²	1	2	yes	—
64	#2003	C₂²	1	2	yes	—
65	#1979	C₂²	1	1	yes	characteristic
66	#1979	C₂²	1	1	yes	characteristic
67	#1979	C₂²	1	1	yes	characteristic
68	#1978	C₂²	1	1	yes	characteristic
69	#1978	C₂²	1	1	yes	characteristic
70	#1978	C₂²	1	1	yes	characteristic
71	#1977	C₂²	1	2	yes	—
72	#1977	C₂²	1	2	yes	—
73	#1976	C₂²	1	1	yes	characteristic
74	#1967	C₂²	1	2	yes	—
75	#1953	C₂²	1	1	yes	characteristic
76	#1953	C₂²	1	1	yes	characteristic
77	#1953	C₂²	1	1	yes	characteristic
78	#1953	C₂²	1	1	yes	characteristic
79	#1953	C₂²	1	1	yes	characteristic
80	#1953	C₂²	1	2	yes	—
81	#1932	C₂²	1	2	yes	—
82	#1915	C₂²	1	2	yes	—
83	#1914	C₂²	1	2	yes	—
84	#1912	C₂²	1	2	yes	—
85	#1911	C₂²	1	2	yes	—
86	#1910	C₂²	1	2	yes	—
87	#1909	C₂²	1	2	yes	—
88	#1906	C₂²	1	2	yes	—
89	#1905	C₂²	1	2	yes	—
90	#1905	C₂²	1	2	yes	—
91	#1904	C₂²	1	2	yes	—
92	#1904	C₂²	1	2	yes	—
93	#1903	C₂²	1	2	yes	—
94	#1902	C₂²	1	2	yes	—
95	#1888	C₂²	1	2	yes	—
96	#1885	C₂²	1	2	yes	—
97	#1861	C₂²	1	2	yes	—
98	#1861	C₂²	1	2	yes	—
99	#1848	C₂²	1	1	yes	characteristic
100	#1841	C₂²	1	1	yes	characteristic
101	#1841	C₂²	1	1	yes	characteristic
102	#1833	C₂²	1	1	yes	characteristic
103	#1833	C₂²	1	1	yes	characteristic
104	#1833	C₂²	1	2	yes	—
105	#1833	C₂²	1	1	yes	characteristic
106	#1833	C₂²	1	1	yes	characteristic
107	#1830	C₂²	1	2	yes	—
108	#1829	C₂²	1	2	yes	—
109	#1827	C₂²	1	1	yes	characteristic
110	#1827	C₂²	1	1	yes	characteristic
111	#1814	C₂²	1	2	yes	—
112	#1814	C₂²	1	1	yes	characteristic
113	#1813	C₂²	1	1	yes	characteristic
114	#1812	C₂²	1	1	yes	characteristic
115	#1772	C₂²	1	1	yes	characteristic
116	#1772	C₂²	1	1	yes	characteristic
117	#1772	C₂²	1	1	yes	characteristic
118	#1757	C₂²	1	1	yes	characteristic
119	#1757	C₂²	1	1	yes	characteristic
120	#1757	C₂²	1	2	yes	—
121	#1747	C₂²	1	1	yes	characteristic
122	#1747	C₂²	1	1	yes	characteristic
123	#575	C₂³	1	2	yes	—
124	C₂×#137	C₂³	1	2	yes	—
125	C₂×#137	C₂³	1	2	yes	—
126	C₂×AGL(1,ℤ/8)	C₂³	1	2	yes	—
127	C₂×AGL(1,ℤ/8)	C₂³	1	2	yes	—
128	C₂×#135	C₂³	1	1	yes	characteristic
129	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
130	C₂²×SD₁₆	C₂³	1	2	yes	—
131	C₂²×D₈	C₂³	1	1	yes	characteristic
132	#568	C₂³	1	2	yes	—
133	#568	C₂³	1	2	yes	—
134	C₂×#131	C₂³	1	1	yes	characteristic
135	C₂×#131	C₂³	1	1	yes	characteristic
136	C₂×#131	C₂³	1	2	yes	—
137	#536	C₂³	1	2	yes	—
138	#535	C₂³	1	2	yes	—
139	C₂×#124	C₂³	1	2	yes	—
140	#519	C₂³	1	2	yes	—
141	#518	C₂³	1	2	yes	—
142	C₄×#41	C₂³	1	1	yes	characteristic
143	#497	—	2	2	no	—
144	#496	—	2	2	no	—
145	#495	—	2	1	no	—
146	#495	—	2	1	no	—
147	#495	—	2	1	no	—
148	#495	—	2	1	no	—
149	#495	—	2	1	no	—
150	#495	—	2	1	no	—
151	#494	—	2	1	no	—
152	#493	—	2	1	no	—
153	#473	—	2	1	no	—
154	#473	—	4	2	no	—
155	#473	—	4	1	no	—
156	#473	—	4	1	no	—
157	#472	—	2	1	no	—
158	#472	—	4	2	no	—
159	#472	—	4	1	no	—
160	#472	—	4	1	no	—
161	#471	—	2	2	no	—
162	#471	—	4	2	no	—
163	#471	—	4	2	no	—
164	#471	—	4	2	no	—
165	#471	—	4	2	no	—
166	#471	—	4	2	no	—
167	#471	—	4	2	no	—
168	#468	—	4	2	no	—
169	#465	—	4	2	no	—
170	#464	—	4	2	no	—
171	#463	—	4	2	no	—
172	#444	—	4	1	no	—
173	#444	—	4	1	no	—
174	#444	—	4	2	no	—
175	#443	—	2	1	no	—
176	#443	—	2	1	no	—
177	#443	—	2	1	no	—
178	#443	—	2	1	no	—
179	#443	—	4	1	no	—
180	#443	—	4	1	no	—
181	#443	—	4	2	no	—
182	#442	—	4	1	no	—
183	#441	—	4	1	no	—
184	#440	—	4	2	no	—
185	C₄×Q₁₆	—	4	1	no	—
186	C₄×SD₁₆	—	4	2	no	—
187	C₄×D₈	—	4	1	no	—
188	#430	—	4	2	no	—
189	#430	C₂³	1	2	yes	—
190	#430	C₂³	1	2	yes	—
191	#430	C₂³	1	2	yes	—
192	#430	C₂³	1	2	yes	—
193	#430	C₂³	1	2	yes	—
194	C₂×#108	—	4	2	no	—
195	C₂×#108	C₂³	1	1	yes	characteristic
196	C₂×#108	C₂³	1	1	yes	characteristic
197	C₂×#108	C₂³	1	2	yes	—
198	C₂×#108	C₂³	1	1	yes	characteristic
199	C₂×#108	C₂³	1	1	yes	characteristic
200	C₂×#108	C₂³	1	1	yes	characteristic
201	C₂×#108	C₂³	1	1	yes	characteristic
202	#427	C₂³	1	1	yes	characteristic
203	#427	C₂³	1	1	yes	characteristic
204	#427	C₂³	1	1	yes	characteristic
205	#423	C₂³	1	2	yes	—
206	#421	C₂³	1	2	yes	—
207	#421	C₂³	1	2	yes	—
208	#421	C₂³	1	2	yes	—
209	#421	C₂³	1	2	yes	—
210	C₂×#104	C₂³	1	2	yes	—
211	#419	C₂³	1	2	yes	—
212	#419	C₂³	1	2	yes	—
213	#419	C₂³	1	2	yes	—
214	#419	C₂³	1	2	yes	—
215	#418	C₂³	1	2	yes	—
216	#418	C₂³	1	2	yes	—
217	#418	C₂³	1	2	yes	—
218	#418	C₂³	1	2	yes	—
219	#413	C₂³	1	1	yes	characteristic
220	#413	C₂³	1	2	yes	—
221	#413	C₂³	1	1	yes	characteristic
222	C₂×#101	C₂³	1	2	yes	—
223	C₂×#101	C₂³	1	2	yes	—
224	C₂×#101	C₂³	1	2	yes	—
225	C₂×#101	C₂³	1	2	yes	—
226	C₂×#100	C₂³	1	2	yes	—
227	C₂×#100	C₂³	1	2	yes	—
228	C₂×#100	C₂³	1	2	yes	—
229	C₂×#100	C₂³	1	2	yes	—
230	#410	C₂³	1	1	yes	characteristic
231	#410	C₂³	1	1	yes	characteristic
232	#410	C₂³	1	2	yes	—
233	#405	—	2	1	no	—
234	#405	—	2	1	no	—
235	#405	C₂³	1	1	yes	characteristic
236	#405	C₂³	1	1	yes	characteristic
237	#405	C₂³	1	1	yes	characteristic
238	#405	C₂³	1	2	yes	—
239	#405	C₂³	1	1	yes	characteristic
240	#405	C₂³	1	1	yes	characteristic
241	#405	C₂³	1	1	yes	characteristic
242	C₄×M₁₆	—	2	1	no	—
243	C₄×M₁₆	C₂³	1	1	yes	characteristic
244	C₂×C₄×C₈	—	2	1	no	—
245	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
246	#344	C₂³	1	1	yes	characteristic
247	#344	C₂³	1	2	yes	—
248	#344	C₂³	1	1	yes	characteristic
249	#344	C₂³	1	2	yes	—
250	#344	C₂³	1	2	yes	—
251	#344	C₂³	1	2	yes	—
252	#344	C₂³	1	2	yes	—
253	#344	C₂³	1	2	yes	—
254	#344	C₂³	1	1	yes	characteristic
255	#344	C₂³	1	2	yes	—
256	#344	C₂³	1	1	yes	characteristic
257	#344	C₂³	1	2	yes	—
258	#339	C₂³	1	1	yes	characteristic
259	#339	C₂³	1	1	yes	characteristic
260	#339	C₂³	1	1	yes	characteristic
261	#339	C₂³	1	1	yes	characteristic
262	#339	C₂³	1	2	yes	—
263	#338	C₂³	1	1	yes	characteristic
264	#338	C₂³	1	1	yes	characteristic
265	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
266	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
267	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
268	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
269	H(3,ℤ/4)	C₂³	1	2	yes	—
270	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
271	H(3,ℤ/4)	C₂³	1	1	yes	characteristic
272	H(3,ℤ/4)	C₂³	1	2	yes	—
273	C₂×#41	C₂⁴	1	2	yes	—
274	C₂×#41	C₂⁴	1	1	yes	characteristic
275	C₂²×Q₈	C₂⁴	1	2	yes	—
276	C₂²×D₄	C₂⁴	1	2	yes	—
277	#137	—	2	2	no	—
278	#137	—	2	2	no	—
279	#137	—	4	2	no	—
280	#137	—	4	2	no	—
281	#137	—	4	2	no	—
282	#137	—	4	2	no	—
283	AGL(1,ℤ/8)	—	2	2	no	—
284	AGL(1,ℤ/8)	—	2	2	no	—
285	AGL(1,ℤ/8)	—	4	2	no	—
286	AGL(1,ℤ/8)	—	4	2	no	—
287	AGL(1,ℤ/8)	—	4	2	no	—
288	AGL(1,ℤ/8)	—	4	2	no	—
289	#135	—	2	1	no	—
290	#135	—	2	1	no	—
291	#135	—	2	1	no	—
292	#135	—	2	1	no	—
293	#135	—	4	2	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	—	2	2	no	—
296	C₂×Q₁₆	—	2	1	no	—
297	C₂×Q₁₆	—	2	1	no	—
298	C₂×Q₁₆	—	2	1	no	—
299	C₂×Q₁₆	—	2	1	no	—
300	C₂×Q₁₆	—	2	1	no	—
301	C₂×Q₁₆	—	2	1	no	—
302	C₂×Q₁₆	#41	1	1	yes	characteristic
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×SD₁₆	—	2	2	no	—
311	C₂×SD₁₆	—	2	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	#41	1	2	yes	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	2	no	—
316	C₂×D₈	—	2	1	no	—
317	C₂×D₈	—	2	1	no	—
318	C₂×D₈	—	2	1	no	—
319	C₂×D₈	—	2	1	no	—
320	C₂×D₈	—	2	1	no	—
321	C₂×D₈	—	2	1	no	—
322	C₂×D₈	#41	1	1	yes	characteristic
323	#131	—	2	2	no	—
324	#131	—	2	2	no	—
325	#131	—	2	1	no	—
326	#131	—	2	1	no	—
327	#131	—	2	1	no	—
328	#131	—	2	2	no	—
329	#131	—	2	1	no	—
330	#131	—	2	2	no	—
331	#131	—	2	1	no	—
332	#131	—	2	1	no	—
333	#131	—	2	1	no	—
334	#131	—	2	1	no	—
335	#131	—	4	2	no	—
336	#131	—	4	2	no	—
337	#131	—	4	2	no	—
338	#131	—	4	2	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂×M₁₆	—	4	2	no	—
343	C₂×M₁₆	—	4	2	no	—
344	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
345	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
346	C₂×M₁₆	C₂⁴	1	2	yes	—
347	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
348	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
349	C₂×M₁₆	C₂⁴	1	2	yes	—
350	C₂×M₁₆	C₂⁴	1	2	yes	—
351	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
352	C₂×M₁₆	C₂⁴	1	1	yes	characteristic
353	C₂×M₁₆	C₂⁴	1	2	yes	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	2	no	—
357	C₂²×C₈	C₂⁴	1	1	yes	characteristic
358	C₂²×C₈	C₂⁴	1	1	yes	characteristic
359	C₄⋊Q₈	—	2	2	no	—
360	#127	—	2	2	no	—
361	#124	—	2	2	no	—
362	#124	—	2	2	no	—
363	#124	—	2	2	no	—
364	#124	—	2	2	no	—
365	#124	—	4	2	no	—
366	#123	—	4	2	no	—
367	C₂²⋊Q₈	—	4	2	no	—
368	#121	—	4	2	no	—
369	#120	—	4	2	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	4	2	no	—
372	C₄×Q₈	—	4	2	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	4	2	no	—
375	C₄×D₄	—	4	2	no	—
376	C₄×D₄	—	4	1	no	—
377	#117	—	2	1	no	—
378	#117	—	4	2	no	—
379	#117	C₂⁴	1	1	yes	characteristic
380	#117	C₂⁴	1	1	yes	characteristic
381	#117	C₂⁴	1	2	yes	—
382	#117	C₂⁴	1	1	yes	characteristic
383	#117	C₂⁴	1	1	yes	characteristic
384	#117	C₂⁴	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	—	4	2	no	—
386	C₂×C₂²⋊C₄	—	4	2	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	C₂⁴	1	1	yes	characteristic
389	#108	—	2	1	no	—
390	#108	—	2	1	no	—
391	#108	—	2	1	no	—
392	#108	—	2	1	no	—
393	#108	—	2	1	no	—
394	#108	—	2	2	no	—
395	#108	—	2	1	no	—
396	#108	—	2	2	no	—
397	#108	—	2	1	no	—
398	#108	—	2	1	no	—
399	#108	—	2	1	no	—
400	#108	—	2	1	no	—
401	#108	—	2	1	no	—
402	#108	—	2	1	no	—
403	#108	—	4	2	no	—
404	#108	—	4	2	no	—
405	#108	—	4	2	no	—
406	#108	—	4	2	no	—
407	#108	—	4	2	no	—
408	#107	—	2	1	no	—
409	#107	—	2	1	no	—
410	#107	—	2	1	no	—
411	#106	—	2	1	no	—
412	#106	—	2	1	no	—
413	#106	—	2	1	no	—
414	C₄⋊C₈	—	4	2	no	—
415	#104	—	2	2	no	—
416	#104	—	2	2	no	—
417	#104	—	4	2	no	—
418	#104	—	4	2	no	—
419	#104	—	4	2	no	—
420	#104	—	4	2	no	—
421	#103	—	4	2	no	—
422	#103	—	4	2	no	—
423	#103	—	4	2	no	—
424	#103	—	4	2	no	—
425	#102	—	4	2	no	—
426	#102	—	4	2	no	—
427	#102	—	4	2	no	—
428	#102	—	4	2	no	—
429	#101	—	2	2	no	—
430	#101	—	2	1	no	—
431	#101	—	2	1	no	—
432	#101	—	4	2	no	—
433	#101	—	4	2	no	—
434	#101	—	4	2	no	—
435	#101	—	4	2	no	—
436	#100	—	2	2	no	—
437	#100	—	2	1	no	—
438	#100	—	2	1	no	—
439	#100	—	4	2	no	—
440	#100	—	4	2	no	—
441	#100	—	4	2	no	—
442	#100	—	4	2	no	—
443	#99	—	4	2	no	—
444	#99	—	4	1	no	—
445	#99	—	4	1	no	—
446	#97	—	2	1	no	—
447	#97	—	2	1	no	—
448	#97	—	2	1	no	—
449	#97	—	2	1	no	—
450	#97	—	2	2	no	—
451	#97	—	2	1	no	—
452	#97	—	2	1	no	—
453	#97	—	2	1	no	—
454	C₄×C₈	—	2	1	no	—
455	C₄×C₈	—	2	1	no	—
456	C₄×C₈	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	—	2	1	no	—
459	C₄×C₈	—	2	2	no	—
460	C₄×C₈	—	2	1	no	—
461	C₄×C₈	—	2	1	no	—
462	C₄×C₈	#41	1	1	yes	characteristic
463	C₄×C₈	#41	1	1	yes	characteristic
464	C₄×C₈	#41	1	1	yes	characteristic
465	C₄×C₈	#41	1	1	yes	characteristic
466	C₂⁴	—	2	2	no	—
467	#41	—	2	2	no	—
468	#41	—	2	1	no	—
469	#41	—	2	1	no	—
470	#41	—	2	2	no	—
471	#41	—	2	2	no	—
472	#41	—	2	1	no	—
473	#41	—	2	1	no	—
474	#41	—	2	2	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	C₂×#41	1	2	yes	—
482	C₂×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	8	2	no	—
492	C₂×D₄	C₂×#41	1	2	yes	—
493	C₂×D₄	H(5,𝔽₂)	1	1	yes	characteristic
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	8	2	no	—
500	C₂²×C₄	C₂⁵	1	1	yes	characteristic
501	Q₁₆	—	2	1	no	—
502	Q₁₆	—	2	1	no	—
503	Q₁₆	—	4	2	no	—
504	Q₁₆	—	4	1	no	—
505	Q₁₆	—	4	1	no	—
506	Q₁₆	—	4	1	no	—
507	Q₁₆	—	4	1	no	—
508	Q₁₆	—	8	2	no	—
509	Q₁₆	—	8	2	no	—
510	SD₁₆	—	2	2	no	—
511	SD₁₆	—	2	2	no	—
512	SD₁₆	—	4	2	no	—
513	SD₁₆	—	4	2	no	—
514	SD₁₆	—	4	2	no	—
515	SD₁₆	—	4	2	no	—
516	SD₁₆	—	4	2	no	—
517	SD₁₆	—	4	2	no	—
518	SD₁₆	—	8	2	no	—
519	SD₁₆	—	8	2	no	—
520	SD₁₆	—	8	2	no	—
521	SD₁₆	—	8	2	no	—
522	D₈	—	2	1	no	—
523	D₈	—	2	1	no	—
524	D₈	—	4	2	no	—
525	D₈	—	4	1	no	—
526	D₈	—	4	1	no	—
527	D₈	—	4	1	no	—
528	D₈	—	4	1	no	—
529	D₈	—	8	2	no	—
530	D₈	—	8	2	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	2	no	—
542	M₁₆	—	2	2	no	—
543	M₁₆	—	2	2	no	—
544	M₁₆	—	2	2	no	—
545	M₁₆	—	2	1	no	—
546	M₁₆	—	2	2	no	—
547	M₁₆	—	2	2	no	—
548	M₁₆	—	2	1	no	—
549	M₁₆	—	2	1	no	—
550	M₁₆	—	2	1	no	—
551	M₁₆	—	4	1	no	—
552	M₁₆	—	4	2	no	—
553	M₁₆	—	4	1	no	—
554	M₁₆	—	4	2	no	—
555	M₁₆	—	4	1	no	—
556	M₁₆	—	4	1	no	—
557	M₁₆	—	8	2	no	—
558	M₁₆	—	8	2	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	2	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	2	no	—
567	C₂×C₈	—	2	2	no	—
568	C₂×C₈	—	2	2	no	—
569	C₂×C₈	—	4	1	no	—
570	C₂×C₈	—	4	2	no	—
571	C₂×C₈	—	4	2	no	—
572	C₂×C₈	—	4	1	no	—
573	C₂×C₈	—	4	1	no	—
574	C₂×C₈	—	4	1	no	—
575	C₂×C₈	—	8	2	no	—
576	C₂×C₈	—	8	2	no	—
577	C₂×C₈	C₂×#41	1	1	yes	characteristic
578	C₂×C₈	C₂×#41	1	1	yes	characteristic
579	C₂×C₈	C₂×#41	1	1	yes	characteristic
580	C₂×C₈	C₂×#41	1	1	yes	characteristic
581	C₂×C₈	C₂×#41	1	1	yes	characteristic
582	C₂×C₈	C₂×#41	1	1	yes	characteristic
583	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
584	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
587	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
588	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	—	8	2	no	—
597	C₄⋊C₄	—	8	2	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	8	2	no	—
606	C₂²⋊C₄	—	8	2	no	—
607	C₂²⋊C₄	—	8	2	no	—
608	C₂²⋊C₄	—	8	2	no	—
609	C₂²⋊C₄	—	8	2	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	4	1	no	—
618	C₄²	—	8	2	no	—
619	C₄²	C₂×#41	1	1	yes	characteristic
620	C₄²	C₂×#41	1	1	yes	characteristic
621	C₂³	—	2	1	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	4	2	no	—
624	C₂³	—	4	2	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	16	2	no	—
627	C₂³	#585	1	1	yes	characteristic
628	Q₈	—	2	2	no	—
629	Q₈	—	2	1	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	1	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	4	2	no	—
634	Q₈	—	4	2	no	—
635	Q₈	—	4	2	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	1	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	1	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	2	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	32	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	—	32	2	no	—
669	C₂×C₄	C₂²×#41	1	1	yes	characteristic
670	C₂×C₄	C₂²×#41	1	1	yes	characteristic
671	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
675	C₈	—	4	1	no	—
676	C₈	—	4	2	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	2	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₈	—	4	1	no	—
683	C₈	—	4	2	no	—
684	C₈	—	4	2	no	—
685	C₈	#540	1	1	yes	characteristic
686	C₈	#540	1	1	yes	characteristic
687	C₈	#540	1	1	yes	characteristic
688	C₈	#540	1	1	yes	characteristic
689	C₈	#553	1	1	yes	characteristic
690	C₈	#553	1	1	yes	characteristic
691	C₈	#553	1	1	yes	characteristic
692	C₈	#553	1	1	yes	characteristic
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	2	no	—
698	C₂²	—	8	2	no	—
699	C₂²	—	16	2	no	—
700	C₂²	—	16	2	no	—
701	C₂²	—	16	2	no	—
702	C₂²	#3494	1	1	yes	characteristic
703	C₂²	#3514	1	1	yes	characteristic
704	C₂²	#3546	1	1	yes	characteristic
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	2	no	—
709	C₄	—	8	1	no	—
710	C₄	—	8	1	no	—
711	C₄	—	8	1	no	—
712	C₄	—	8	2	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	—	8	2	no	—
716	C₄	C₂×#540	1	1	yes	characteristic
717	C₄	C₂×#553	1	1	yes	characteristic
718	C₄	#3519	1	1	yes	characteristic
719	C₄	#3543	1	1	yes	characteristic
720	C₂	—	2	1	no	—
721	C₂	—	2	1	no	—
722	C₂	—	2	1	no	—
723	C₂	—	8	1	no	—
724	C₂	—	8	2	no	—
725	C₂	—	16	2	no	—
726	C₂	#39148	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#39148
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#25447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #33192	C₂	semidirect
2. #32699	C₂	semidirect
3. #32696	C₂	semidirect
4. #31417	C₂	semidirect
5. #31415	C₂	semidirect
6. #30238	C₂	semidirect
7. #30237	C₂	semidirect
8. #29230	C₂	semidirect
9. #28501	C₂	semidirect
10. #28182	C₂	semidirect
11. #27987	C₂	semidirect
12. #25448	C₂	semidirect
14. #24989	C₂	semidirect
15. #24988	C₂	semidirect
16. #24987	C₂	semidirect
17. #24808	C₂	semidirect
18. #23199	C₂	semidirect
19. #22694	C₂	semidirect
20. #22286	C₂	semidirect
21. #22285	C₂	semidirect
22. #21558	C₂	semidirect
23. #20787	C₂	semidirect

Maximal subgroups

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

subgroup	index
#33192	2
#32699	2
#32696	2
#31417	2
#31415	2
#30238	2
#30237	2
#29230	2
#28501	2
#28182	2
#27987	2
#25448	2
#25447	2
#24989	2
#24988	2
#24987	2
#24808	2
#23199	2
#22694	2
#22286	2
#22285	2
#21558	2
#20787	2