Subgroups — #62533

Order 256.

886 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3365	C₂	1	1	yes	maximal, characteristic, complemented
4	#3364	C₂	1	1	yes	maximal, characteristic, complemented
5	#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	#3301	C₂	1	2	yes	maximal, complemented
8	#3300	C₂	1	2	yes	maximal, complemented
9	#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	#3297	C₂	1	2	yes	maximal, complemented
12	#3296	C₂	1	2	yes	maximal, complemented
13	#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	#3232	C₂	1	2	yes	maximal, complemented
17	#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	#3211	C₂	1	2	yes	maximal, complemented
19	#3168	C₂	1	1	yes	maximal, characteristic, complemented
20	#3168	C₂	1	2	yes	maximal, complemented
21	#3131	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#488	C₂	1	2	yes	maximal, complemented
23	C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	C₂²	1	1	yes	characteristic
25	#557	C₂²	1	1	yes	characteristic, complemented
26	#556	C₂²	1	1	yes	characteristic
27	#555	—	2	1	no	—
28	#554	C₂²	1	1	yes	characteristic
29	#554	C₂²	1	1	yes	characteristic, complemented
30	#553	C₂²	1	2	yes	complemented
31	#552	—	2	2	no	—
32	#552	—	2	1	no	—
33	#552	C₂²	1	2	yes	complemented
34	#551	—	2	2	no	—
35	D₄×Q₈	C₂²	1	1	yes	characteristic
36	#548	C₂²	1	2	yes	—
37	#547	—	2	1	no	—
38	#547	C₂²	1	1	yes	characteristic
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#542	—	2	1	no	—
43	#541	—	2	1	no	—
44	#539	—	2	2	no	—
45	#538	—	2	2	no	—
46	#533	C₂²	1	1	yes	characteristic, complemented
47	#532	C₂²	1	1	yes	characteristic
48	#529	C₂²	1	2	yes	—
49	#529	C₂²	1	1	yes	characteristic
50	#529	C₂²	1	2	yes	complemented
51	#529	C₂²	1	1	yes	characteristic, complemented
52	C₂×#125	C₂²	1	2	yes	complemented
53	C₂×#124	C₂²	1	2	yes	—
54	#520	—	2	1	no	—
55	#518	—	2	1	no	—
56	C₄×#41	C₂²	1	1	yes	characteristic
57	#499	C₂²	1	1	yes	characteristic, complemented
58	#499	C₂²	1	2	yes	complemented
59	#495	C₂²	1	1	yes	characteristic
60	#495	C₂²	1	2	yes	complemented
61	#488	C₂²	1	2	yes	—
62	#488	C₂²	1	2	yes	—
63	#488	C₂²	1	1	yes	characteristic
64	#488	C₂²	1	2	yes	—
65	#488	C₂²	1	2	yes	complemented
66	#488	C₂²	1	2	yes	complemented
67	#488	C₂²	1	2	yes	complemented
68	#488	C₂²	1	2	yes	complemented
69	#488	C₂²	1	2	yes	complemented
70	#488	C₂²	1	1	yes	characteristic, complemented
71	#487	C₂²	1	1	yes	characteristic, complemented
72	#487	C₂²	1	1	yes	characteristic, complemented
73	#486	C₂²	1	1	yes	characteristic
74	#486	C₂²	1	1	yes	characteristic
75	#485	C₂²	1	2	yes	complemented
76	#484	C₂²	1	2	yes	complemented
77	#483	C₂²	1	2	yes	complemented
78	#482	C₂²	1	2	yes	—
79	#481	C₂²	1	2	yes	—
80	#480	C₂²	1	2	yes	—
81	#479	C₂²	1	2	yes	complemented
82	#479	C₂²	1	2	yes	complemented
83	#478	C₂²	1	2	yes	complemented
84	#478	C₂²	1	2	yes	complemented
85	#477	C₂²	1	1	yes	characteristic, complemented
86	#476	C₂²	1	1	yes	characteristic
87	#475	C₂²	1	1	yes	characteristic, complemented
88	#474	C₂²	1	1	yes	characteristic
89	#467	C₂²	1	2	yes	complemented
90	#467	C₂²	1	1	yes	characteristic, complemented
91	#466	C₂²	1	2	yes	—
92	#466	C₂²	1	1	yes	characteristic
93	#465	C₂²	1	2	yes	—
94	#465	C₂²	1	1	yes	characteristic
95	#465	C₂²	1	2	yes	complemented
96	#465	C₂²	1	1	yes	characteristic, complemented
97	#464	C₂²	1	2	yes	—
98	#464	C₂²	1	2	yes	complemented
99	#463	C₂²	1	2	yes	—
100	#463	C₂²	1	2	yes	complemented
101	#462	C₂²	1	1	yes	characteristic, complemented
102	#461	C₂²	1	1	yes	characteristic, complemented
103	#460	C₂²	1	1	yes	characteristic
104	#459	C₂²	1	1	yes	characteristic
105	#452	C₂²	1	2	yes	complemented
106	#451	C₂²	1	2	yes	complemented
107	#450	C₂²	1	2	yes	—
108	#449	C₂²	1	2	yes	complemented
109	#448	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	—
111	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆	C₂²	1	2	yes	complemented
114	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆	C₂²	1	2	yes	complemented
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	2	yes	complemented
121	C₈×D₄	C₂²	1	1	yes	characteristic
122	C₈×D₄	C₂²	1	1	yes	characteristic
123	C₈×D₄	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#431	C₂²	1	2	yes	complemented
126	#431	C₂²	1	1	yes	characteristic, complemented
127	#416	C₂²	1	2	yes	complemented
128	#416	C₂²	1	2	yes	complemented
129	C₂×#103	C₂²	1	2	yes	complemented
130	C₂×#103	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	2	yes	—
132	C₂×#102	C₂²	1	2	yes	—
133	C₂×C₄×C₈	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	D₄	1	1	yes	characteristic
137	C₂×#41	C₂³	1	2	yes	—
138	C₂²×Q₈	C₂³	1	2	yes	—
139	C₂²×D₄	—	2	1	no	—
140	C₂²×D₄	C₂³	1	2	yes	—
141	C₂×Q₁₆	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆	C₂³	1	2	yes	—
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	C₂³	1	2	yes	—
147	C₂×D₈	C₂³	1	1	yes	characteristic
148	C₂×D₈	C₂³	1	2	yes	—
149	C₂²×C₈	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	#127	C₂³	1	1	yes	characteristic
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	1	no	—
164	#126	—	2	2	no	—
165	#126	—	2	1	no	—
166	#125	—	2	2	no	—
167	#125	—	2	2	no	—
168	#125	—	2	1	no	—
169	#125	—	2	2	no	—
170	#125	—	2	2	no	—
171	#125	C₂³	1	1	yes	characteristic
172	#125	C₂³	1	2	yes	—
173	#125	C₂³	1	2	yes	—
174	#125	C₂³	1	2	yes	—
175	#125	C₂³	1	1	yes	characteristic
176	#124	—	2	1	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	—	2	2	no	—
180	#124	C₂³	1	1	yes	characteristic
181	#124	C₂³	1	2	yes	—
182	#124	C₂³	1	2	yes	—
183	#124	C₂³	1	2	yes	—
184	#124	C₂³	1	1	yes	characteristic
185	#123	—	2	2	no	—
186	#123	—	2	1	no	—
187	#123	—	2	2	no	—
188	#123	—	2	1	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₂²⋊Q₈	C₂³	1	2	yes	—
207	#121	—	2	2	no	—
208	#121	—	2	2	no	—
209	#121	—	2	1	no	—
210	#121	—	2	1	no	—
211	#121	—	2	1	no	—
212	#121	—	2	2	no	—
213	#121	C₂³	1	2	yes	—
214	#121	C₂³	1	1	yes	characteristic
215	#121	C₂³	1	2	yes	—
216	#121	C₂³	1	1	yes	characteristic
217	#120	—	2	2	no	—
218	#120	—	2	2	no	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	D₄	1	1	yes	characteristic
223	C₄×Q₈	C₂³	1	2	yes	—
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	2	yes	—
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	D₄	1	1	yes	characteristic
240	C₄×D₄	D₄	1	2	yes	—
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	2	yes	—
243	C₄×D₄	C₂³	1	1	yes	characteristic
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	2	yes	—
247	#117	—	2	1	no	—
248	#117	—	2	2	no	—
249	#117	—	2	1	no	—
250	#117	—	2	1	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	D₄	1	2	yes	—
254	#117	D₄	1	1	yes	characteristic
255	#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₄²	C₂³	1	2	yes	—
265	C₂×C₄²	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	1	yes	characteristic
270	#106	C₂³	1	1	yes	characteristic
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	2	yes	—
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	2	yes	—
278	#103	C₂³	1	1	yes	characteristic
279	#103	C₂³	1	1	yes	characteristic
280	#103	C₂³	1	2	yes	—
281	#103	C₂³	1	2	yes	—
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	1	yes	characteristic
291	#102	C₂³	1	1	yes	characteristic
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₄×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₈	C₂³	1	2	yes	—
307	C₄×C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	2	no	—
313	#41	—	2	4	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	4	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈	C₂⁴	1	2	yes	—
325	C₂×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	C₂×D₄	1	2	yes	—
338	C₂×D₄	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄	C₂⁴	1	1	yes	characteristic
340	C₂×D₄	C₂⁴	1	2	yes	—
341	C₂×D₄	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	C₂×D₄	1	2	yes	—
351	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄	1	2	yes	—
353	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴	1	2	yes	—
355	C₂²×C₄	C₂⁴	1	1	yes	characteristic
356	Q₁₆	—	4	1	no	—
357	Q₁₆	—	4	2	no	—
358	SD₁₆	—	4	1	no	—
359	SD₁₆	—	4	2	no	—
360	SD₁₆	—	4	1	no	—
361	SD₁₆	—	4	2	no	—
362	D₈	—	4	2	no	—
363	D₈	—	4	1	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₈	C₂⁴	1	1	yes	characteristic
370	C₂×C₈	C₂⁴	1	2	yes	—
371	C₂×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₈	C₂⁴	1	2	yes	—
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	C₂×D₄	1	2	yes	—
440	C₄²	C₂×D₄	1	1	yes	characteristic
441	C₄²	C₂×D₄	1	1	yes	characteristic
442	C₄²	C₂×D₄	1	2	yes	—
443	C₄²	C₂⁴	1	1	yes	characteristic
444	C₄²	C₂⁴	1	2	yes	—
445	C₄²	C₂⁴	1	1	yes	characteristic
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	8	2	no	—
451	C₂³	—	8	2	no	—
452	C₂³	C₂²×D₄	1	1	yes	characteristic
453	C₂³	C₂²×D₄	1	2	yes	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	2	1	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	8	1	no	—
463	Q₈	—	8	2	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	4	4	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	2	no	—
474	D₄	—	8	1	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	1	no	—
477	D₄	—	8	1	no	—
478	D₄	—	8	2	no	—
479	D₄	#135	1	4	yes	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄	1	2	yes	—
507	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄	1	2	yes	—
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂⁵	1	1	yes	characteristic
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	16	4	no	—
535	C₂²	C₂×#135	1	4	yes	—
536	C₂²	C₂³×D₄	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	C₂×#135	1	2	yes	—
554	C₄	#585	1	1	yes	characteristic
555	C₄	#585	1	1	yes	characteristic
556	C₂	—	2	4	no	—
557	C₂	—	4	1	no	—
558	C₂	—	8	1	no	—
559	C₂	—	8	2	no	—
560	C₂	—	8	1	no	—
561	C₂	#3500	1	1	yes	characteristic
562	C₂	C₂²×#135	1	1	yes	characteristic
563	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 ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3515	C₂	semidirect
2. #3514	C₂	semidirect
3. #3365	C₂	semidirect
4. #3364	C₂	semidirect
5. #3361	C₂	semidirect
6. #3360	C₂	semidirect
7. #3301	C₂	semidirect
8. #3300	C₂	semidirect
9. #3299	C₂	semidirect
10. #3298	C₂	semidirect
11. #3297	C₂	semidirect
12. #3296	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3233	C₂	semidirect
16. #3232	C₂	semidirect
17. #3212	C₂	semidirect
18. #3211	C₂	semidirect
19. #3168	C₂	semidirect
20. #3168	C₂	semidirect
21. #3131	C₂	semidirect
22. C₂×#488	C₂	semidirect
23. C₈×#41	C₂	semidirect
25. #557	C₂²	semidirect
29. #554	C₂²	semidirect
30. #553	C₂²	semidirect
33. #552	C₂²	semidirect
46. #533	C₂²	semidirect
50. #529	C₂²	semidirect
51. #529	C₂²	semidirect
52. C₂×#125	C₂²	semidirect
57. #499	C₂²	semidirect
58. #499	C₂²	semidirect
60. #495	C₂²	semidirect
65. #488	C₂²	semidirect
66. #488	C₂²	semidirect
67. #488	C₂²	semidirect
68. #488	C₂²	semidirect
69. #488	C₂²	semidirect
70. #488	C₂²	semidirect
71. #487	C₂²	semidirect
72. #487	C₂²	semidirect
75. #485	C₂²	semidirect
76. #484	C₂²	semidirect
77. #483	C₂²	semidirect
81. #479	C₂²	semidirect
82. #479	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #477	C₂²	semidirect
87. #475	C₂²	semidirect
89. #467	C₂²	semidirect
90. #467	C₂²	semidirect
95. #465	C₂²	semidirect
96. #465	C₂²	semidirect
98. #464	C₂²	semidirect
100. #463	C₂²	semidirect
101. #462	C₂²	semidirect
102. #461	C₂²	semidirect
105. #452	C₂²	semidirect
106. #451	C₂²	semidirect
108. #449	C₂²	semidirect
109. #448	C₂²	semidirect
111. C₈×Q₈	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. C₄×Q₁₆	C₂²	semidirect
114. C₄×Q₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
123. C₈×D₄	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #431	C₂²	semidirect
126. #431	C₂²	semidirect
127. #416	C₂²	semidirect
128. #416	C₂²	semidirect
129. C₂×#103	C₂²	semidirect
130. C₂×#103	C₂²	semidirect
133. C₂×C₄×C₈	C₂²	semidirect
134. 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
#3515	2
#3514	2
#3365	2
#3364	2
#3361	2
#3360	2
#3301	2
#3300	2
#3299	2
#3298	2
#3297	2
#3296	2
#3295	2
#3294	2
#3233	2
#3232	2
#3212	2
#3211	2
#3168	2
#3131	2
C₂×#488	2
C₈×#41	2