Subgroups — #61733

Order 256.

1015 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	#3354	C₂	1	1	yes	maximal, characteristic, complemented
4	#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	#3345	C₂	1	2	yes	maximal, complemented
6	#3343	C₂	1	2	yes	maximal, complemented
7	#3335	C₂	1	1	yes	maximal, characteristic, complemented
8	#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	#3318	C₂	1	2	yes	maximal, complemented
12	#3310	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	#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	#3194	C₂	1	2	yes	maximal, complemented
18	#3188	C₂	1	2	yes	maximal, complemented
19	#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	#3094	C₂	1	2	yes	maximal, complemented
22	C₂×#482	C₂	1	2	yes	maximal, complemented
23	#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)	—	2	1	no	—
25	#556	C₂²	1	1	yes	characteristic, complemented
26	#555	C₂²	1	1	yes	characteristic, complemented
27	#554	C₂²	1	1	yes	characteristic, complemented
28	#553	C₂²	1	2	yes	complemented
29	#552	—	2	1	no	—
30	#552	C₂²	1	2	yes	complemented
31	#551	—	2	2	no	—
32	#547	C₂²	1	1	yes	characteristic
33	#547	C₂²	1	2	yes	—
34	#547	C₂²	1	1	yes	characteristic
35	#547	C₂²	1	1	yes	characteristic, complemented
36	#546	—	2	1	no	—
37	#546	—	2	1	no	—
38	#546	—	2	2	no	—
39	#546	—	2	1	no	—
40	D₄²	C₂²	1	1	yes	characteristic
41	D₄²	C₂²	1	2	yes	—
42	D₄²	C₂²	1	1	yes	characteristic
43	#537	—	2	1	no	—
44	#534	—	2	2	no	—
45	#533	C₂²	1	1	yes	characteristic, complemented
46	#532	C₂²	1	1	yes	characteristic
47	#532	C₂²	1	1	yes	characteristic
48	#529	—	2	2	no	—
49	#529	—	2	1	no	—
50	#525	C₂²	1	2	yes	complemented
51	C₂×#121	C₂²	1	2	yes	—
52	C₂×#121	C₂²	1	2	yes	—
53	C₄×#41	—	2	1	no	—
54	C₄×#41	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×#117	C₂²	1	2	yes	complemented
57	#501	C₂²	1	2	yes	complemented
58	#500	C₂²	1	1	yes	characteristic, complemented
59	#498	C₂²	1	1	yes	characteristic, complemented
60	#490	C₂²	1	2	yes	complemented
61	#486	C₂²	1	1	yes	characteristic, complemented
62	#486	C₂²	1	1	yes	characteristic, complemented
63	#484	C₂²	1	2	yes	complemented
64	#483	C₂²	1	2	yes	complemented
65	#482	C₂²	1	1	yes	characteristic, complemented
66	#482	C₂²	1	2	yes	complemented
67	#482	C₂²	1	2	yes	complemented
68	#482	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#482	C₂²	1	2	yes	complemented
73	#482	C₂²	1	1	yes	characteristic, complemented
74	#482	C₂²	1	2	yes	complemented
75	#482	C₂²	1	2	yes	complemented
76	#481	C₂²	1	2	yes	complemented
77	#481	C₂²	1	2	yes	complemented
78	#481	C₂²	1	2	yes	complemented
79	#480	C₂²	1	2	yes	complemented
80	#480	C₂²	1	2	yes	complemented
81	#480	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#478	C₂²	1	2	yes	complemented
84	#477	C₂²	1	1	yes	characteristic, complemented
85	#476	C₂²	1	1	yes	characteristic, complemented
86	#476	C₂²	1	1	yes	characteristic, complemented
87	#476	C₂²	1	1	yes	characteristic, complemented
88	#475	C₂²	1	1	yes	characteristic, complemented
89	#474	C₂²	1	1	yes	characteristic, complemented
90	#474	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic, complemented
92	#469	C₂²	1	2	yes	complemented
93	#469	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	complemented
95	#468	C₂²	1	2	yes	complemented
96	#466	C₂²	1	2	yes	complemented
97	#466	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#460	C₂²	1	1	yes	characteristic, complemented
101	#460	C₂²	1	1	yes	characteristic, complemented
102	#459	C₂²	1	1	yes	characteristic, complemented
103	#459	C₂²	1	1	yes	characteristic, complemented
104	#450	C₂²	1	2	yes	complemented
105	#450	C₂²	1	2	yes	complemented
106	#449	C₂²	1	1	yes	characteristic, complemented
107	#449	C₂²	1	1	yes	characteristic, complemented
108	#449	C₂²	1	2	yes	complemented
109	#447	C₂²	1	2	yes	complemented
110	#447	C₂²	1	2	yes	complemented
111	#442	C₂²	1	2	yes	complemented
112	#440	C₂²	1	2	yes	complemented
113	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
117	#436	C₂²	1	1	yes	characteristic, complemented
118	#436	C₂²	1	1	yes	characteristic, complemented
119	#435	C₂²	1	2	yes	complemented
120	#435	C₂²	1	2	yes	complemented
121	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
123	#432	C₂²	1	1	yes	characteristic, complemented
124	#431	C₂²	1	1	yes	characteristic, complemented
125	#428	C₂²	1	2	yes	complemented
126	#428	C₂²	1	2	yes	complemented
127	C₂×#107	C₂²	1	2	yes	complemented
128	C₂×#106	C₂²	1	2	yes	complemented
129	#418	C₂²	1	2	yes	complemented
130	#418	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	#407	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)	—	4	8	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	2	1	no	—
142	C₂×#41	C₂³	1	1	yes	characteristic
143	C₂²×D₄	—	2	2	no	—
144	C₂²×D₄	—	2	2	no	—
145	C₂²×D₄	—	2	2	no	—
146	C₂²×D₄	—	2	1	no	—
147	C₂²×D₄	—	2	1	no	—
148	C₂²×D₄	D₄	1	1	yes	characteristic
149	C₂²×D₄	C₂³	1	2	yes	—
150	C₂²×D₄	C₂³	1	2	yes	—
151	C₂³×C₄	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×D₈	C₂³	1	1	yes	characteristic
156	C₂×D₈	C₂³	1	1	yes	characteristic
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	#127	C₂³	1	1	yes	characteristic
167	#127	C₂³	1	1	yes	characteristic
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	1	no	—
173	#125	C₂³	1	2	yes	—
174	#124	—	2	1	no	—
175	#124	—	2	2	no	—
176	#124	—	2	1	no	—
177	#124	—	2	1	no	—
178	#123	—	2	2	no	—
179	#123	—	2	2	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	#121	—	2	2	no	—
196	#121	—	2	1	no	—
197	#121	—	2	2	no	—
198	#121	—	2	2	no	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	—	2	1	no	—
202	#121	—	2	1	no	—
203	#121	—	2	1	no	—
204	#121	—	2	1	no	—
205	#121	—	2	2	no	—
206	#121	C₂³	1	1	yes	characteristic
207	#121	C₂³	1	2	yes	—
208	#121	C₂³	1	1	yes	characteristic
209	#121	C₂³	1	2	yes	—
210	#121	C₂³	1	2	yes	—
211	#121	C₂³	1	2	yes	—
212	#121	C₂³	1	2	yes	—
213	#121	C₂³	1	2	yes	—
214	#121	C₂³	1	2	yes	—
215	#120	—	2	2	no	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	#120	—	2	2	no	—
219	#120	—	2	2	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	D₄	1	1	yes	characteristic
234	C₄×D₄	D₄	1	1	yes	characteristic
235	C₄×D₄	D₄	1	2	yes	—
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	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	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	2	2	no	—
248	#117	—	2	1	no	—
249	#117	C₂³	1	1	yes	characteristic
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	D₄	1	2	yes	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	2	yes	—
278	#106	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	#103	C₂³	1	1	yes	characteristic
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	2	yes	—
286	#102	C₂³	1	1	yes	characteristic
287	#102	C₂³	1	1	yes	characteristic
288	#102	C₂³	1	2	yes	—
289	#102	C₂³	1	2	yes	—
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	1	yes	characteristic
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	2	yes	—
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂×D₄	1	2	yes	—
316	#41	—	4	1	no	—
317	#41	—	4	1	no	—
318	#41	—	4	4	no	—
319	#41	—	4	4	no	—
320	#41	—	4	8	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂×D₄	1	2	yes	—
356	C₂×D₄	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄	C₂⁴	1	1	yes	characteristic
359	C₂×D₄	C₂⁴	1	2	yes	—
360	C₂×D₄	C₂⁴	1	1	yes	characteristic
361	C₂×D₄	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄	1	2	yes	—
376	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄	1	2	yes	—
378	C₂²×C₄	C₂×D₄	1	2	yes	—
379	C₂²×C₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴	1	2	yes	—
381	C₂²×C₄	C₂⁴	1	2	yes	—
382	SD₁₆	—	4	1	no	—
383	SD₁₆	—	4	2	no	—
384	SD₁₆	—	4	1	no	—
385	D₈	—	4	1	no	—
386	D₈	—	4	2	no	—
387	D₈	—	4	1	no	—
388	M₁₆	—	4	2	no	—
389	M₁₆	—	4	2	no	—
390	C₂×C₈	—	4	2	no	—
391	C₂×C₈	—	4	2	no	—
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₈	C₂⁴	1	1	yes	characteristic
394	C₂×C₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₈	C₂⁴	1	1	yes	characteristic
396	C₂×C₈	C₂⁴	1	2	yes	—
397	C₂×C₈	C₂⁴	1	2	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	2	yes	—
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	C₂×D₄	1	1	yes	characteristic
453	C₄²	C₂×D₄	1	1	yes	characteristic
454	C₄²	C₂⁴	1	1	yes	characteristic
455	C₄²	C₂⁴	1	1	yes	characteristic
456	C₂³	—	2	4	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	8	2	no	—
466	C₂³	—	8	2	no	—
467	C₂³	—	8	2	no	—
468	C₂³	—	8	2	no	—
469	C₂³	C₂²×D₄	1	2	yes	—
470	C₂³	C₂²×D₄	1	1	yes	characteristic
471	C₂³	C₂²×D₄	1	2	yes	—
472	Q₈	—	2	1	no	—
473	Q₈	—	2	1	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	1	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	1	no	—
481	D₄	—	2	1	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	2	no	—
499	D₄	—	8	1	no	—
500	D₄	—	8	1	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	D₄	AGL(1,ℤ/8)	1	4	yes	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	8	1	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄	1	2	yes	—
536	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄	1	2	yes	—
540	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂⁵	1	1	yes	characteristic
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	8	4	no	—
569	C₂²	—	16	4	no	—
570	C₂²	—	16	4	no	—
571	C₂²	C₂×AGL(1,ℤ/8)	1	4	yes	—
572	C₂²	C₂³×D₄	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
588	C₄	#585	1	1	yes	characteristic
589	C₄	#585	1	1	yes	characteristic
590	C₂	—	2	4	no	—
591	C₂	—	4	1	no	—
592	C₂	—	4	2	no	—
593	C₂	—	8	1	no	—
594	C₂	—	8	1	no	—
595	C₂	—	8	2	no	—
596	C₂	—	8	1	no	—
597	C₂	#3485	1	1	yes	characteristic
598	C₂	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
599	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×C₄×D₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3496	C₂	semidirect
2. #3475	C₂	semidirect
3. #3354	C₂	semidirect
4. #3353	C₂	semidirect
5. #3345	C₂	semidirect
6. #3343	C₂	semidirect
7. #3335	C₂	semidirect
8. #3334	C₂	semidirect
9. #3325	C₂	semidirect
10. #3324	C₂	semidirect
11. #3318	C₂	semidirect
12. #3310	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3235	C₂	semidirect
16. #3228	C₂	semidirect
17. #3194	C₂	semidirect
18. #3188	C₂	semidirect
19. #3115	C₂	semidirect
20. #3106	C₂	semidirect
21. #3094	C₂	semidirect
22. C₂×#482	C₂	semidirect
23. #2974	C₂	semidirect
25. #556	C₂²	semidirect
26. #555	C₂²	semidirect
27. #554	C₂²	semidirect
28. #553	C₂²	semidirect
30. #552	C₂²	semidirect
35. #547	C₂²	semidirect
45. #533	C₂²	semidirect
50. #525	C₂²	semidirect
54. C₄×#41	C₂²	semidirect
56. C₂×#117	C₂²	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
59. #498	C₂²	semidirect
60. #490	C₂²	semidirect
61. #486	C₂²	semidirect
62. #486	C₂²	semidirect
63. #484	C₂²	semidirect
64. #483	C₂²	semidirect
65. #482	C₂²	semidirect
66. #482	C₂²	semidirect
67. #482	C₂²	semidirect
68. #482	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #482	C₂²	semidirect
73. #482	C₂²	semidirect
74. #482	C₂²	semidirect
75. #482	C₂²	semidirect
76. #481	C₂²	semidirect
77. #481	C₂²	semidirect
78. #481	C₂²	semidirect
79. #480	C₂²	semidirect
80. #480	C₂²	semidirect
81. #480	C₂²	semidirect
82. #478	C₂²	semidirect
83. #478	C₂²	semidirect
84. #477	C₂²	semidirect
85. #476	C₂²	semidirect
86. #476	C₂²	semidirect
87. #476	C₂²	semidirect
88. #475	C₂²	semidirect
89. #474	C₂²	semidirect
90. #474	C₂²	semidirect
91. #474	C₂²	semidirect
92. #469	C₂²	semidirect
93. #469	C₂²	semidirect
94. #468	C₂²	semidirect
95. #468	C₂²	semidirect
96. #466	C₂²	semidirect
97. #466	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #460	C₂²	semidirect
101. #460	C₂²	semidirect
102. #459	C₂²	semidirect
103. #459	C₂²	semidirect
104. #450	C₂²	semidirect
105. #450	C₂²	semidirect
106. #449	C₂²	semidirect
107. #449	C₂²	semidirect
108. #449	C₂²	semidirect
109. #447	C₂²	semidirect
110. #447	C₂²	semidirect
111. #442	C₂²	semidirect
112. #440	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
117. #436	C₂²	semidirect
118. #436	C₂²	semidirect
119. #435	C₂²	semidirect
120. #435	C₂²	semidirect
121. C₈×D₄	C₂²	semidirect
122. C₈×D₄	C₂²	semidirect
123. #432	C₂²	semidirect
124. #431	C₂²	semidirect
125. #428	C₂²	semidirect
126. #428	C₂²	semidirect
127. C₂×#107	C₂²	semidirect
128. C₂×#106	C₂²	semidirect
129. #418	C₂²	semidirect
130. #418	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. #407	C₂²	semidirect
134. C₂×C₂²⋊C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3496	2
#3475	2
#3354	2
#3353	2
#3345	2
#3343	2
#3335	2
#3334	2
#3325	2
#3324	2
#3318	2
#3310	2
#3295	2
#3294	2
#3235	2
#3228	2
#3194	2
#3188	2
#3115	2
#3106	2
#3094	2
C₂×#482	2
#2974	2