Subgroups — #60935

Order 256.

916 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	#3494	C₂	1	1	yes	maximal, characteristic, complemented
3	#3263	C₂	1	2	yes	maximal, complemented
4	#3260	C₂	1	2	yes	maximal, complemented
5	#3258	C₂	1	2	yes	maximal, complemented
6	#3257	C₂	1	2	yes	maximal, complemented
7	#3250	C₂	1	2	yes	maximal, complemented
8	#3248	C₂	1	2	yes	maximal, complemented
9	#3247	C₂	1	2	yes	maximal, complemented
10	#3246	C₂	1	2	yes	maximal, complemented
11	#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	#3084	C₂	1	1	yes	maximal, characteristic, complemented
13	#3082	C₂	1	1	yes	maximal, characteristic, complemented
14	#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	#3050	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#465	C₂	1	1	yes	maximal, characteristic, complemented
19	#3046	C₂	1	1	yes	maximal, characteristic, complemented
20	#3045	C₂	1	1	yes	maximal, characteristic, complemented
21	#3043	C₂	1	1	yes	maximal, characteristic, complemented
22	#3042	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#424	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×#135	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆	C₂²	1	1	yes	characteristic
29	C₂³×C₈	C₂²	1	1	yes	characteristic
30	#556	—	2	1	no	—
31	#555	—	2	1	no	—
32	#554	—	2	1	no	—
33	#553	—	2	1	no	—
34	#553	—	2	1	no	—
35	#552	—	2	2	no	—
36	#552	—	2	1	no	—
37	#552	—	2	1	no	—
38	#551	—	2	2	no	—
39	#551	—	2	2	no	—
40	#547	—	2	1	no	—
41	#546	—	2	2	no	—
42	#544	C₂²	1	1	yes	characteristic
43	#544	C₂²	1	1	yes	characteristic
44	#542	C₂²	1	2	yes	—
45	#542	C₂²	1	2	yes	complemented
46	#541	C₂²	1	2	yes	complemented
47	#540	C₂²	1	2	yes	—
48	#536	C₂²	1	1	yes	characteristic
49	#535	C₂²	1	1	yes	characteristic
50	#533	C₂²	1	2	yes	complemented
51	#532	C₂²	1	2	yes	—
52	#529	C₂²	1	2	yes	—
53	#529	C₂²	1	2	yes	complemented
54	#525	C₂²	1	1	yes	characteristic
55	#525	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×#121	C₂²	1	1	yes	characteristic
58	#520	C₂²	1	1	yes	characteristic
59	#520	C₂²	1	1	yes	characteristic
60	#519	C₂²	1	1	yes	characteristic
61	#518	C₂²	1	1	yes	characteristic
62	C₂×#117	C₂²	1	1	yes	characteristic
63	#479	C₂²	1	2	yes	complemented
64	#479	C₂²	1	2	yes	complemented
65	#479	C₂²	1	2	yes	complemented
66	#479	C₂²	1	2	yes	complemented
67	#478	C₂²	1	2	yes	complemented
68	#478	C₂²	1	2	yes	complemented
69	#478	C₂²	1	2	yes	complemented
70	#478	C₂²	1	2	yes	complemented
71	#477	C₂²	1	2	yes	complemented
72	#476	C₂²	1	2	yes	complemented
73	#476	C₂²	1	2	yes	complemented
74	#476	C₂²	1	2	yes	complemented
75	#475	C₂²	1	2	yes	complemented
76	#475	C₂²	1	2	yes	complemented
77	#475	C₂²	1	2	yes	complemented
78	#474	C₂²	1	2	yes	complemented
79	#470	C₂²	1	2	yes	complemented
80	#469	C₂²	1	2	yes	—
81	#468	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	complemented
83	#467	C₂²	1	1	yes	characteristic, complemented
84	#467	C₂²	1	2	yes	complemented
85	#467	C₂²	1	1	yes	characteristic, complemented
86	#466	C₂²	1	2	yes	—
87	#466	C₂²	1	1	yes	characteristic, complemented
88	#466	C₂²	1	1	yes	characteristic, complemented
89	#465	C₂²	1	2	yes	—
90	#465	C₂²	1	2	yes	—
91	#465	C₂²	1	2	yes	—
92	#465	C₂²	1	2	yes	—
93	#465	C₂²	1	2	yes	—
94	#465	C₂²	1	1	yes	characteristic, complemented
95	#465	C₂²	1	2	yes	complemented
96	#465	C₂²	1	1	yes	characteristic, complemented
97	#465	C₂²	1	1	yes	characteristic, complemented
98	#465	C₂²	1	1	yes	characteristic, complemented
99	#464	C₂²	1	2	yes	complemented
100	#464	C₂²	1	2	yes	complemented
101	#464	C₂²	1	2	yes	complemented
102	#464	C₂²	1	2	yes	complemented
103	#463	C₂²	1	2	yes	complemented
104	#463	C₂²	1	2	yes	complemented
105	#463	C₂²	1	2	yes	complemented
106	#463	C₂²	1	2	yes	complemented
107	#462	C₂²	1	2	yes	complemented
108	#461	C₂²	1	2	yes	complemented
109	#461	C₂²	1	2	yes	complemented
110	#461	C₂²	1	2	yes	complemented
111	#460	C₂²	1	2	yes	complemented
112	#460	C₂²	1	2	yes	complemented
113	#460	C₂²	1	2	yes	complemented
114	#459	C₂²	1	2	yes	complemented
115	#428	C₂²	1	1	yes	characteristic
116	#428	C₂²	1	1	yes	characteristic
117	#427	C₂²	1	1	yes	characteristic
118	C₂×#106	C₂²	1	1	yes	characteristic
119	#424	C₂²	1	1	yes	characteristic
120	#424	C₂²	1	1	yes	characteristic
121	#424	C₂²	1	1	yes	characteristic
122	#424	C₂²	1	1	yes	characteristic
123	#424	C₂²	1	2	yes	complemented
124	#424	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
126	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
127	#419	C₂²	1	1	yes	characteristic
128	#418	C₂²	1	1	yes	characteristic
129	#417	C₂²	1	1	yes	characteristic
130	#417	C₂²	1	1	yes	characteristic
131	#416	C₂²	1	1	yes	characteristic
132	#416	C₂²	1	1	yes	characteristic
133	C₂×#103	C₂²	1	1	yes	characteristic
134	C₂×#102	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×D₄	—	2	1	no	—
140	C₂²×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄	C₂³	1	1	yes	characteristic
142	#137	—	4	2	no	—
143	AGL(1,ℤ/8)	—	4	2	no	—
144	#135	—	4	2	no	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×SD₁₆	—	4	2	no	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	1	yes	characteristic
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×M₁₆	—	4	2	no	—
157	C₂×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×M₁₆	C₂³	1	1	yes	characteristic
159	C₂×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₈	—	4	2	no	—
161	C₂²×C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₈	C₂³	1	1	yes	characteristic
164	C₂²×C₈	C₂³	1	1	yes	characteristic
165	C₂²×C₈	C₂³	1	1	yes	characteristic
166	C₂²×C₈	C₂³	1	1	yes	characteristic
167	C₂²×C₈	C₂³	1	2	yes	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	C₄⋊Q₈	C₂³	1	2	yes	—
172	C₄⋊Q₈	C₂³	1	2	yes	—
173	#127	C₂³	1	2	yes	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#126	—	2	2	no	—
179	#126	—	2	2	no	—
180	#125	—	2	2	no	—
181	#125	—	2	2	no	—
182	#125	—	2	1	no	—
183	#125	—	2	1	no	—
184	#125	—	2	2	no	—
185	#125	C₂³	1	2	yes	—
186	#125	C₂³	1	2	yes	—
187	#124	—	2	2	no	—
188	#124	—	2	2	no	—
189	#124	—	2	2	no	—
190	#124	C₂³	1	2	yes	—
191	#124	C₂³	1	2	yes	—
192	#123	—	2	1	no	—
193	#123	—	2	1	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	#121	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	2	no	—
219	#121	—	2	1	no	—
220	#121	—	2	1	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	C₂³	1	2	yes	—
224	#121	C₂³	1	2	yes	—
225	#121	C₂³	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#121	C₂³	1	1	yes	characteristic
228	#121	C₂³	1	1	yes	characteristic
229	#120	—	2	1	no	—
230	#120	—	2	1	no	—
231	#120	—	2	2	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	C₂³	1	2	yes	—
236	C₄×Q₈	C₂³	1	2	yes	—
237	C₄×Q₈	C₂³	1	2	yes	—
238	C₄×Q₈	C₂³	1	2	yes	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³	1	2	yes	—
251	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	2	yes	—
254	#117	—	2	2	no	—
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	D₄	1	2	yes	—
261	#117	D₄	1	1	yes	characteristic
262	#117	D₄	1	1	yes	characteristic
263	#117	C₂³	1	1	yes	characteristic
264	#117	C₂³	1	1	yes	characteristic
265	#117	C₂³	1	1	yes	characteristic
266	#117	C₂³	1	1	yes	characteristic
267	#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	D₄	1	2	yes	—
279	C₂×C₄²	C₂³	1	2	yes	—
280	#107	C₂³	1	1	yes	characteristic
281	#107	C₂³	1	1	yes	characteristic
282	#107	C₂³	1	2	yes	—
283	#107	C₂³	1	2	yes	—
284	#106	C₂³	1	2	yes	—
285	#106	C₂³	1	2	yes	—
286	#106	C₂³	1	1	yes	characteristic
287	#106	C₂³	1	1	yes	characteristic
288	#106	C₂³	1	2	yes	—
289	#106	C₂³	1	2	yes	—
290	C₄⋊C₈	C₂³	1	2	yes	—
291	C₄⋊C₈	C₂³	1	2	yes	—
292	C₄⋊C₈	C₂³	1	2	yes	—
293	C₄⋊C₈	C₂³	1	2	yes	—
294	C₄⋊C₈	C₂³	1	2	yes	—
295	C₄⋊C₈	C₂³	1	2	yes	—
296	C₄⋊C₈	C₂³	1	2	yes	—
297	C₄⋊C₈	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	1	yes	characteristic
301	#103	C₂³	1	1	yes	characteristic
302	#103	C₂³	1	1	yes	characteristic
303	#103	C₂³	1	1	yes	characteristic
304	#103	C₂³	1	2	yes	—
305	#103	C₂³	1	2	yes	—
306	#103	C₂³	1	2	yes	—
307	#103	C₂³	1	2	yes	—
308	#102	C₂³	1	2	yes	—
309	#102	C₂³	1	2	yes	—
310	#102	C₂³	1	1	yes	characteristic
311	#102	C₂³	1	1	yes	characteristic
312	#102	C₂³	1	1	yes	characteristic
313	#102	C₂³	1	1	yes	characteristic
314	#102	C₂³	1	2	yes	—
315	#102	C₂³	1	2	yes	—
316	#102	C₂³	1	2	yes	—
317	#102	C₂³	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	C₂×D₄	1	1	yes	characteristic
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	8	4	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	2	yes	—
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂×D₄	C₂⁴	1	2	yes	—
349	C₂×D₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₂×D₄	1	2	yes	—
362	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄	1	2	yes	—
366	C₂²×C₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴	1	1	yes	characteristic
369	Q₁₆	—	4	1	no	—
370	Q₁₆	—	4	2	no	—
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	1	no	—
374	SD₁₆	—	4	1	no	—
375	SD₁₆	—	4	2	no	—
376	SD₁₆	—	4	2	no	—
377	D₈	—	4	1	no	—
378	D₈	—	4	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	4	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	1	no	—
385	C₂×C₈	—	4	1	no	—
386	C₂×C₈	—	4	1	no	—
387	C₂×C₈	—	4	1	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	C₂⁴	1	2	yes	—
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₈	C₂⁴	1	1	yes	characteristic
394	C₂×C₈	C₂⁴	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	1	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	C₂×D₄	1	2	yes	—
460	C₄²	C₂×D₄	1	2	yes	—
461	C₄²	C₂⁴	1	2	yes	—
462	C₄²	C₂⁴	1	2	yes	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	8	1	no	—
471	C₂³	—	8	1	no	—
472	C₂³	C₂²×D₄	1	1	yes	characteristic
473	C₂³	C₂²×D₄	1	1	yes	characteristic
474	C₂³	C₂²×D₄	1	1	yes	characteristic
475	Q₈	—	2	2	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	8	2	no	—
483	Q₈	—	8	2	no	—
484	D₄	—	2	1	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	—	2	1	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	1	no	—
499	D₄	—	8	1	no	—
500	D₄	—	8	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	C₂²×D₄	1	2	yes	—
529	C₂×C₄	C₂²×D₄	1	2	yes	—
530	C₂×C₄	C₂²×D₄	1	2	yes	—
531	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄	1	2	yes	—
533	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
537	C₂×C₄	C₂⁵	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	16	2	no	—
562	C₂²	#537	1	2	yes	—
563	C₂²	#577	1	2	yes	—
564	C₂²	C₂³×D₄	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	#537	1	2	yes	—
581	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
582	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	8	1	no	—
587	C₂	—	8	1	no	—
588	C₂	—	8	2	no	—
589	C₂	C₂×#537	1	1	yes	characteristic
590	C₂	C₂×#577	1	1	yes	characteristic
591	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3495	C₂	semidirect
2. #3494	C₂	semidirect
3. #3263	C₂	semidirect
4. #3260	C₂	semidirect
5. #3258	C₂	semidirect
6. #3257	C₂	semidirect
7. #3250	C₂	semidirect
8. #3248	C₂	semidirect
9. #3247	C₂	semidirect
10. #3246	C₂	semidirect
11. #3084	C₂	semidirect
12. #3084	C₂	semidirect
13. #3082	C₂	semidirect
14. #3081	C₂	semidirect
15. #3056	C₂	semidirect
16. #3055	C₂	semidirect
17. #3050	C₂	semidirect
18. C₂×#465	C₂	semidirect
19. #3046	C₂	semidirect
20. #3045	C₂	semidirect
21. #3043	C₂	semidirect
22. #3042	C₂	semidirect
23. C₂×#424	C₂	semidirect
45. #542	C₂²	semidirect
46. #541	C₂²	semidirect
50. #533	C₂²	semidirect
53. #529	C₂²	semidirect
63. #479	C₂²	semidirect
64. #479	C₂²	semidirect
65. #479	C₂²	semidirect
66. #479	C₂²	semidirect
67. #478	C₂²	semidirect
68. #478	C₂²	semidirect
69. #478	C₂²	semidirect
70. #478	C₂²	semidirect
71. #477	C₂²	semidirect
72. #476	C₂²	semidirect
73. #476	C₂²	semidirect
74. #476	C₂²	semidirect
75. #475	C₂²	semidirect
76. #475	C₂²	semidirect
77. #475	C₂²	semidirect
78. #474	C₂²	semidirect
79. #470	C₂²	semidirect
82. #468	C₂²	semidirect
83. #467	C₂²	semidirect
84. #467	C₂²	semidirect
85. #467	C₂²	semidirect
87. #466	C₂²	semidirect
88. #466	C₂²	semidirect
94. #465	C₂²	semidirect
95. #465	C₂²	semidirect
96. #465	C₂²	semidirect
97. #465	C₂²	semidirect
98. #465	C₂²	semidirect
99. #464	C₂²	semidirect
100. #464	C₂²	semidirect
101. #464	C₂²	semidirect
102. #464	C₂²	semidirect
103. #463	C₂²	semidirect
104. #463	C₂²	semidirect
105. #463	C₂²	semidirect
106. #463	C₂²	semidirect
107. #462	C₂²	semidirect
108. #461	C₂²	semidirect
109. #461	C₂²	semidirect
110. #461	C₂²	semidirect
111. #460	C₂²	semidirect
112. #460	C₂²	semidirect
113. #460	C₂²	semidirect
114. #459	C₂²	semidirect
123. #424	C₂²	semidirect
124. #424	C₂²	semidirect
125. C₂×C₄⋊C₈	C₂²	semidirect
126. C₂×C₄⋊C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3495	2
#3494	2
#3263	2
#3260	2
#3258	2
#3257	2
#3250	2
#3248	2
#3247	2
#3246	2
#3084	2
#3082	2
#3081	2
#3056	2
#3055	2
#3050	2
C₂×#465	2
#3046	2
#3045	2
#3043	2
#3042	2
C₂×#424	2