Subgroups — #60587

Order 256.

1042 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	#3126	C₂	1	2	yes	maximal, complemented
4	#3122	C₂	1	2	yes	maximal, complemented
5	#3121	C₂	1	2	yes	maximal, complemented
6	#3118	C₂	1	2	yes	maximal, complemented
7	#3115	C₂	1	2	yes	maximal, complemented
8	#3111	C₂	1	2	yes	maximal, complemented
9	#3106	C₂	1	2	yes	maximal, complemented
10	#3102	C₂	1	2	yes	maximal, complemented
11	#3093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#482	C₂	1	1	yes	maximal, characteristic, complemented
13	#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	#3006	C₂	1	1	yes	maximal, characteristic, complemented
18	#3002	C₂	1	1	yes	maximal, characteristic, complemented
19	#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	#2946	C₂	1	1	yes	maximal, characteristic, complemented
22	#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×#135	C₂²	1	1	yes	characteristic
28	C₂×#135	C₂²	1	1	yes	characteristic
29	#555	—	2	1	no	—
30	#553	—	2	1	no	—
31	#553	—	2	1	no	—
32	#551	—	2	2	no	—
33	#547	—	2	1	no	—
34	#546	—	2	2	no	—
35	#544	C₂²	1	1	yes	characteristic, complemented
36	#542	C₂²	1	2	yes	—
37	#540	C₂²	1	2	yes	—
38	#535	C₂²	1	1	yes	characteristic, complemented
39	#532	C₂²	1	2	yes	complemented
40	#529	C₂²	1	2	yes	complemented
41	#525	C₂²	1	1	yes	characteristic
42	C₂×#121	C₂²	1	1	yes	characteristic
43	#520	—	2	1	no	—
44	#520	—	2	1	no	—
45	#520	C₂²	1	1	yes	characteristic
46	#520	C₂²	1	1	yes	characteristic
47	#520	C₂²	1	1	yes	characteristic
48	#520	C₂²	1	1	yes	characteristic
49	#520	C₂²	1	1	yes	characteristic, complemented
50	#519	C₂²	1	2	yes	complemented
51	#518	—	2	2	no	—
52	#518	C₂²	1	2	yes	complemented
53	#518	C₂²	1	1	yes	characteristic, complemented
54	C₄×#41	—	2	2	no	—
55	C₄×#41	C₂²	1	2	yes	complemented
56	C₄×#41	C₂²	1	2	yes	complemented
57	C₂×#117	—	2	1	no	—
58	C₂×#117	—	2	1	no	—
59	C₂×#117	C₂²	1	1	yes	characteristic
60	C₂×#117	C₂²	1	1	yes	characteristic
61	#485	C₂²	1	2	yes	complemented
62	#485	C₂²	1	2	yes	complemented
63	#482	C₂²	1	2	yes	—
64	#482	C₂²	1	2	yes	—
65	#482	C₂²	1	2	yes	complemented
66	#482	C₂²	1	2	yes	complemented
67	#482	C₂²	1	2	yes	complemented
68	#482	C₂²	1	2	yes	complemented
69	#479	C₂²	1	2	yes	complemented
70	#479	C₂²	1	2	yes	complemented
71	#478	C₂²	1	2	yes	complemented
72	#478	C₂²	1	2	yes	complemented
73	#477	C₂²	1	2	yes	complemented
74	#476	C₂²	1	2	yes	complemented
75	#475	C₂²	1	2	yes	complemented
76	#474	C₂²	1	2	yes	complemented
77	#464	C₂²	1	2	yes	complemented
78	#464	C₂²	1	2	yes	complemented
79	#463	C₂²	1	2	yes	complemented
80	#463	C₂²	1	2	yes	complemented
81	#460	C₂²	1	2	yes	complemented
82	#460	C₂²	1	2	yes	complemented
83	#459	C₂²	1	2	yes	complemented
84	#459	C₂²	1	2	yes	complemented
85	#452	C₂²	1	1	yes	characteristic, complemented
86	#452	C₂²	1	1	yes	characteristic, complemented
87	#451	C₂²	1	1	yes	characteristic, complemented
88	#450	C₂²	1	1	yes	characteristic, complemented
89	#449	C₂²	1	2	yes	—
90	#449	C₂²	1	2	yes	—
91	#449	C₂²	1	1	yes	characteristic, complemented
92	#449	C₂²	1	1	yes	characteristic, complemented
93	#448	C₂²	1	2	yes	—
94	#448	C₂²	1	1	yes	characteristic, complemented
95	#447	C₂²	1	2	yes	—
96	#447	C₂²	1	1	yes	characteristic, complemented
97	#442	C₂²	1	2	yes	complemented
98	#442	C₂²	1	2	yes	complemented
99	#442	C₂²	1	2	yes	complemented
100	#441	C₂²	1	2	yes	complemented
101	#440	C₂²	1	2	yes	complemented
102	#440	C₂²	1	2	yes	complemented
103	#440	C₂²	1	2	yes	complemented
104	#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆	C₂²	1	2	yes	complemented
106	C₄×SD₁₆	C₂²	1	2	yes	complemented
107	C₄×SD₁₆	C₂²	1	2	yes	complemented
108	C₄×SD₁₆	C₂²	1	2	yes	complemented
109	C₄×SD₁₆	C₂²	1	2	yes	complemented
110	C₄×D₈	C₂²	1	2	yes	complemented
111	C₄×D₈	C₂²	1	2	yes	complemented
112	C₄×D₈	C₂²	1	2	yes	complemented
113	#433	C₂²	1	2	yes	complemented
114	#433	C₂²	1	2	yes	complemented
115	#432	C₂²	1	2	yes	complemented
116	#431	C₂²	1	2	yes	complemented
117	#428	C₂²	1	1	yes	characteristic, complemented
118	#428	C₂²	1	1	yes	characteristic, complemented
119	C₂×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×#106	C₂²	1	1	yes	characteristic, complemented
121	#424	C₂²	1	1	yes	characteristic, complemented
122	#424	C₂²	1	1	yes	characteristic, complemented
123	#417	C₂²	1	1	yes	characteristic
124	#417	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic, complemented
126	#417	C₂²	1	1	yes	characteristic, complemented
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	C₂×#102	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102	C₂²	1	1	yes	characteristic, complemented
131	#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic, complemented
134	#405	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	4	no	—
136	C₂×#41	—	2	4	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	—	2	2	no	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂×#41	C₂³	1	1	yes	characteristic
143	C₂×#41	C₂³	1	1	yes	characteristic
144	C₂×#41	C₂³	1	1	yes	characteristic
145	C₂²×Q₈	C₂³	1	1	yes	characteristic
146	C₂²×D₄	—	2	1	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	C₂³	1	1	yes	characteristic
149	C₂²×D₄	C₂³	1	1	yes	characteristic
150	C₂³×C₄	—	2	1	no	—
151	C₂³×C₄	C₂³	1	1	yes	characteristic
152	AGL(1,ℤ/8)	—	2	4	no	—
153	AGL(1,ℤ/8)	—	2	4	no	—
154	#135	—	2	4	no	—
155	#135	—	2	4	no	—
156	C₂×Q₁₆	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆	C₂³	1	2	yes	—
163	C₂×SD₁₆	C₂³	1	2	yes	—
164	C₂×D₈	C₂³	1	1	yes	characteristic
165	C₂×D₈	C₂³	1	1	yes	characteristic
166	C₂×D₈	C₂³	1	2	yes	—
167	C₂×D₈	C₂³	1	2	yes	—
168	C₂×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×M₁₆	C₂³	1	1	yes	characteristic
170	C₂²×C₈	C₂³	1	1	yes	characteristic
171	C₂²×C₈	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈	—	2	1	no	—
173	C₄⋊Q₈	C₂³	1	2	yes	—
174	#127	C₂³	1	2	yes	—
175	#126	—	2	2	no	—
176	#126	—	2	2	no	—
177	#125	—	2	1	no	—
178	#125	C₂³	1	2	yes	—
179	#124	—	2	2	no	—
180	#124	—	2	2	no	—
181	#124	C₂³	1	2	yes	—
182	#123	—	2	1	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	C₂²⋊Q₈	—	2	2	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	#121	—	2	1	no	—
192	#121	—	2	1	no	—
193	#121	—	2	2	no	—
194	#121	—	2	1	no	—
195	#121	—	2	1	no	—
196	#121	—	2	2	no	—
197	#121	—	2	2	no	—
198	#121	C₂³	1	2	yes	—
199	#121	C₂³	1	2	yes	—
200	#121	C₂³	1	1	yes	characteristic
201	#121	C₂³	1	1	yes	characteristic
202	#120	—	2	1	no	—
203	#120	—	2	2	no	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	C₂³	1	2	yes	—
207	C₄×Q₈	C₂³	1	2	yes	—
208	C₄×Q₈	C₂³	1	2	yes	—
209	C₄×Q₈	C₂³	1	2	yes	—
210	C₄×Q₈	C₂³	1	2	yes	—
211	C₄×D₄	—	2	2	no	—
212	C₄×D₄	—	2	2	no	—
213	C₄×D₄	—	2	2	no	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	1	no	—
216	C₄×D₄	—	2	1	no	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	C₂³	1	2	yes	—
229	C₄×D₄	C₂³	1	2	yes	—
230	C₄×D₄	C₂³	1	2	yes	—
231	C₄×D₄	C₂³	1	2	yes	—
232	C₄×D₄	C₂³	1	2	yes	—
233	C₄×D₄	C₂³	1	2	yes	—
234	C₄×D₄	C₂³	1	2	yes	—
235	#117	—	2	1	no	—
236	#117	—	2	1	no	—
237	#117	—	2	1	no	—
238	#117	—	2	1	no	—
239	#117	—	2	1	no	—
240	#117	—	2	1	no	—
241	#117	—	2	1	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	D₄	1	1	yes	characteristic
248	#117	D₄	1	1	yes	characteristic
249	#117	D₄	1	2	yes	—
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	1	yes	characteristic
253	#117	C₂³	1	2	yes	—
254	#117	C₂³	1	1	yes	characteristic
255	#117	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
262	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	D₄	1	2	yes	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	C₂³	1	2	yes	—
276	#107	C₂³	1	2	yes	—
277	#107	C₂³	1	2	yes	—
278	#107	C₂³	1	2	yes	—
279	#107	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	2	yes	—
282	#106	C₂³	1	2	yes	—
283	#106	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	2	yes	—
287	C₄⋊C₈	C₂³	1	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	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	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂²⋊C₈	C₂³	1	2	yes	—
314	#97	C₂³	1	2	yes	—
315	#97	C₂³	1	2	yes	—
316	C₄×C₈	C₂³	1	2	yes	—
317	C₄×C₈	C₂³	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	C₂×D₄	1	1	yes	characteristic
321	#41	—	2	8	no	—
322	#41	—	2	8	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	8	4	no	—
332	#41	#41	1	4	yes	complemented
333	#41	#41	1	4	yes	complemented
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈	C₂⁴	1	1	yes	characteristic
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂×D₄	C₂⁴	1	2	yes	—
361	C₂×D₄	C₂⁴	1	1	yes	characteristic
362	C₂×D₄	C₂⁴	1	1	yes	characteristic
363	C₂×D₄	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄	1	2	yes	—
387	C₂²×C₄	C₂×D₄	1	2	yes	—
388	C₂²×C₄	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴	1	1	yes	characteristic
391	Q₁₆	—	2	2	no	—
392	Q₁₆	—	2	2	no	—
393	SD₁₆	—	2	2	no	—
394	SD₁₆	—	2	2	no	—
395	SD₁₆	—	2	4	no	—
396	SD₁₆	—	2	4	no	—
397	SD₁₆	—	2	2	no	—
398	SD₁₆	—	2	2	no	—
399	D₈	—	2	2	no	—
400	D₈	—	2	2	no	—
401	D₈	—	2	4	no	—
402	D₈	—	2	4	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₈	C₂⁴	1	2	yes	—
410	C₂×C₈	C₂⁴	1	2	yes	—
411	C₂×C₈	C₂⁴	1	1	yes	characteristic
412	C₂×C₈	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
427	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
429	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
430	C₄⋊C₄	C₂×D₄	1	2	yes	—
431	C₄⋊C₄	C₂×D₄	1	2	yes	—
432	C₄⋊C₄	C₂⁴	1	2	yes	—
433	C₄⋊C₄	C₂⁴	1	2	yes	—
434	C₄⋊C₄	C₂⁴	1	2	yes	—
435	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄	C₂×D₄	1	2	yes	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	1	no	—
467	C₄²	C₂×D₄	1	2	yes	—
468	C₄²	C₂×D₄	1	2	yes	—
469	C₄²	C₂⁴	1	2	yes	—
470	C₄²	C₂⁴	1	2	yes	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	8	1	no	—
481	C₂³	—	8	1	no	—
482	C₂³	—	8	1	no	—
483	C₂³	—	8	1	no	—
484	C₂³	C₂²×D₄	1	1	yes	characteristic
485	C₂³	C₂²×D₄	1	1	yes	characteristic
486	C₂³	C₂²×D₄	1	1	yes	characteristic
487	Q₈	—	2	4	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	8	2	no	—
493	Q₈	C₂×#41	1	2	yes	—
494	Q₈	C₂×#41	1	2	yes	—
495	D₄	—	2	4	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	4	no	—
500	D₄	—	2	1	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	1	no	—
513	D₄	—	8	2	no	—
514	D₄	C₂×#41	1	2	yes	—
515	D₄	C₂×#41	1	2	yes	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	2	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	—	8	1	no	—
549	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄	1	2	yes	—
551	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄	1	2	yes	—
553	C₂×C₄	C₂²×D₄	1	2	yes	—
554	C₂×C₄	C₂²×D₄	1	2	yes	—
555	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄	C₂×#41	1	2	yes	—
557	C₂×C₄	C₂×#41	1	2	yes	—
558	C₂×C₄	C₂⁵	1	1	yes	characteristic
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	8	2	no	—
586	C₂²	—	8	4	no	—
587	C₂²	—	16	2	no	—
588	C₂²	#525	1	2	yes	—
589	C₂²	C₂³×D₄	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	#525	1	2	yes	—
605	C₄	C₂²×#41	1	1	yes	characteristic
606	C₄	C₂²×#41	1	1	yes	characteristic
607	C₂	—	2	2	no	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	2	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	1	no	—
613	C₂	—	8	2	no	—
614	C₂	C₂×#525	1	1	yes	characteristic
615	C₂	#3584	1	1	yes	characteristic
616	C₂	#3585	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. #3494	C₂	semidirect
2. #3428	C₂	semidirect
3. #3126	C₂	semidirect
4. #3122	C₂	semidirect
5. #3121	C₂	semidirect
6. #3118	C₂	semidirect
7. #3115	C₂	semidirect
8. #3111	C₂	semidirect
9. #3106	C₂	semidirect
10. #3102	C₂	semidirect
11. #3093	C₂	semidirect
12. C₂×#482	C₂	semidirect
13. #3084	C₂	semidirect
14. #3083	C₂	semidirect
15. #3045	C₂	semidirect
16. #3045	C₂	semidirect
17. #3006	C₂	semidirect
18. #3002	C₂	semidirect
19. #2952	C₂	semidirect
20. #2951	C₂	semidirect
21. #2946	C₂	semidirect
22. #2946	C₂	semidirect
23. #2924	C₂	semidirect
35. #544	C₂²	semidirect
38. #535	C₂²	semidirect
39. #532	C₂²	semidirect
40. #529	C₂²	semidirect
49. #520	C₂²	semidirect
50. #519	C₂²	semidirect
52. #518	C₂²	semidirect
53. #518	C₂²	semidirect
55. C₄×#41	C₂²	semidirect
56. C₄×#41	C₂²	semidirect
61. #485	C₂²	semidirect
62. #485	C₂²	semidirect
65. #482	C₂²	semidirect
66. #482	C₂²	semidirect
67. #482	C₂²	semidirect
68. #482	C₂²	semidirect
69. #479	C₂²	semidirect
70. #479	C₂²	semidirect
71. #478	C₂²	semidirect
72. #478	C₂²	semidirect
73. #477	C₂²	semidirect
74. #476	C₂²	semidirect
75. #475	C₂²	semidirect
76. #474	C₂²	semidirect
77. #464	C₂²	semidirect
78. #464	C₂²	semidirect
79. #463	C₂²	semidirect
80. #463	C₂²	semidirect
81. #460	C₂²	semidirect
82. #460	C₂²	semidirect
83. #459	C₂²	semidirect
84. #459	C₂²	semidirect
85. #452	C₂²	semidirect
86. #452	C₂²	semidirect
87. #451	C₂²	semidirect
88. #450	C₂²	semidirect
91. #449	C₂²	semidirect
92. #449	C₂²	semidirect
94. #448	C₂²	semidirect
96. #447	C₂²	semidirect
97. #442	C₂²	semidirect
98. #442	C₂²	semidirect
99. #442	C₂²	semidirect
100. #441	C₂²	semidirect
101. #440	C₂²	semidirect
102. #440	C₂²	semidirect
103. #440	C₂²	semidirect
104. #440	C₂²	semidirect
105. C₄×Q₁₆	C₂²	semidirect
106. C₄×SD₁₆	C₂²	semidirect
107. C₄×SD₁₆	C₂²	semidirect
108. C₄×SD₁₆	C₂²	semidirect
109. C₄×SD₁₆	C₂²	semidirect
110. C₄×D₈	C₂²	semidirect
111. C₄×D₈	C₂²	semidirect
112. C₄×D₈	C₂²	semidirect
113. #433	C₂²	semidirect
114. #433	C₂²	semidirect
115. #432	C₂²	semidirect
116. #431	C₂²	semidirect
117. #428	C₂²	semidirect
118. #428	C₂²	semidirect
119. C₂×#107	C₂²	semidirect
120. C₂×#106	C₂²	semidirect
121. #424	C₂²	semidirect
122. #424	C₂²	semidirect
125. #417	C₂²	semidirect
126. #417	C₂²	semidirect
129. C₂×#102	C₂²	semidirect
130. C₂×#102	C₂²	semidirect
133. #405	C₂²	semidirect
134. #405	C₂²	semidirect
332. #41	#41	semidirect
333. #41	#41	semidirect

Maximal subgroups

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

subgroup	index
#3494	2
#3428	2
#3126	2
#3122	2
#3121	2
#3118	2
#3115	2
#3111	2
#3106	2
#3102	2
#3093	2
C₂×#482	2
#3084	2
#3083	2
#3045	2
#3006	2
#3002	2
#2952	2
#2951	2
#2946	2
#2924	2