Subgroups — #62213

Order 256.

849 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	#3516	C₂	1	1	yes	maximal, characteristic, complemented
3	#3388	C₂	1	1	yes	maximal, characteristic, complemented
4	#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	#3351	C₂	1	1	yes	maximal, characteristic, complemented
8	#3346	C₂	1	1	yes	maximal, characteristic, complemented
9	#3345	C₂	1	1	yes	maximal, characteristic, complemented
10	#3339	C₂	1	1	yes	maximal, characteristic, complemented
11	#3337	C₂	1	1	yes	maximal, characteristic, complemented
12	#3335	C₂	1	1	yes	maximal, characteristic, complemented
13	#3326	C₂	1	1	yes	maximal, characteristic, complemented
14	#3320	C₂	1	1	yes	maximal, characteristic, complemented
15	#3308	C₂	1	1	yes	maximal, characteristic, complemented
16	#3301	C₂	1	1	yes	maximal, characteristic, complemented
17	#3301	C₂	1	1	yes	maximal, characteristic, complemented
18	#3298	C₂	1	1	yes	maximal, characteristic, complemented
19	#3260	C₂	1	1	yes	maximal, characteristic, complemented
20	#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	#3247	C₂	1	1	yes	maximal, characteristic, complemented
22	#3244	C₂	1	1	yes	maximal, characteristic, complemented
23	#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	#3232	C₂	1	1	yes	maximal, characteristic, complemented
25	#3126	C₂	1	1	yes	maximal, characteristic, complemented
26	#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	#3103	C₂	1	1	yes	maximal, characteristic, complemented
28	#3084	C₂	1	1	yes	maximal, characteristic, complemented
29	#3082	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#479	C₂	1	1	yes	maximal, characteristic, complemented
31	#2994	C₂	1	1	yes	maximal, characteristic, complemented
32	#563	—	2	1	no	—
33	#562	—	2	1	no	—
34	#557	C₂²	1	1	yes	characteristic
35	#556	—	2	1	no	—
36	#556	C₂²	1	1	yes	characteristic
37	#554	—	2	1	no	—
38	#554	C₂²	1	1	yes	characteristic
39	#554	C₂²	1	1	yes	characteristic
40	#554	C₂²	1	1	yes	characteristic
41	#553	—	2	1	no	—
42	#553	C₂²	1	1	yes	characteristic
43	#553	C₂²	1	1	yes	characteristic
44	#553	C₂²	1	1	yes	characteristic
45	#553	C₂²	1	1	yes	characteristic
46	#553	C₂²	1	1	yes	characteristic
47	#552	—	2	1	no	—
48	#552	C₂²	1	1	yes	characteristic
49	D₄×Q₈	C₂²	1	1	yes	characteristic
50	#548	C₂²	1	1	yes	characteristic
51	#548	C₂²	1	1	yes	characteristic
52	#547	—	2	1	no	—
53	#547	—	2	1	no	—
54	#547	C₂²	1	1	yes	characteristic
55	#547	C₂²	1	1	yes	characteristic
56	#544	C₂²	1	1	yes	characteristic
57	#544	C₂²	1	1	yes	characteristic
58	#542	—	2	1	no	—
59	#542	C₂²	1	1	yes	characteristic
60	#541	—	2	1	no	—
61	#541	C₂²	1	1	yes	characteristic
62	#540	C₂²	1	1	yes	characteristic
63	#540	C₂²	1	1	yes	characteristic
64	#539	—	2	1	no	—
65	#539	—	2	1	no	—
66	#539	—	2	1	no	—
67	#537	—	2	1	no	—
68	#532	C₂²	1	1	yes	characteristic
69	#529	—	2	1	no	—
70	#529	—	2	1	no	—
71	#529	C₂²	1	1	yes	characteristic
72	#529	C₂²	1	1	yes	characteristic
73	C₂×#125	C₂²	1	1	yes	characteristic
74	#520	C₂²	1	1	yes	characteristic
75	#519	C₂²	1	1	yes	characteristic
76	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
77	#501	C₂²	1	1	yes	characteristic
78	#501	C₂²	1	1	yes	characteristic
79	#499	C₂²	1	1	yes	characteristic
80	#499	C₂²	1	1	yes	characteristic
81	#499	C₂²	1	1	yes	characteristic
82	#498	C₂²	1	1	yes	characteristic
83	#491	C₂²	1	1	yes	characteristic
84	#489	C₂²	1	1	yes	characteristic
85	#488	C₂²	1	1	yes	characteristic
86	#488	C₂²	1	1	yes	characteristic
87	#488	C₂²	1	1	yes	characteristic
88	#487	C₂²	1	1	yes	characteristic
89	#485	C₂²	1	1	yes	characteristic
90	#485	C₂²	1	1	yes	characteristic
91	#485	C₂²	1	1	yes	characteristic
92	#484	C₂²	1	1	yes	characteristic
93	#484	C₂²	1	1	yes	characteristic
94	#483	C₂²	1	1	yes	characteristic
95	#483	C₂²	1	1	yes	characteristic
96	#483	C₂²	1	1	yes	characteristic
97	#482	C₂²	1	1	yes	characteristic
98	#482	C₂²	1	1	yes	characteristic
99	#482	C₂²	1	1	yes	characteristic
100	#481	C₂²	1	1	yes	characteristic
101	#481	C₂²	1	1	yes	characteristic
102	#481	C₂²	1	1	yes	characteristic
103	#481	C₂²	1	1	yes	characteristic
104	#481	C₂²	1	1	yes	characteristic
105	#480	C₂²	1	1	yes	characteristic
106	#480	C₂²	1	1	yes	characteristic
107	#479	C₂²	1	1	yes	characteristic
108	#479	C₂²	1	1	yes	characteristic
109	#479	C₂²	1	1	yes	characteristic
110	#479	C₂²	1	1	yes	characteristic
111	#479	C₂²	1	1	yes	characteristic
112	#479	C₂²	1	1	yes	characteristic
113	#479	C₂²	1	1	yes	characteristic
114	#479	C₂²	1	1	yes	characteristic
115	#479	C₂²	1	1	yes	characteristic
116	#479	C₂²	1	1	yes	characteristic
117	#479	C₂²	1	1	yes	characteristic
118	#479	C₂²	1	1	yes	characteristic
119	#479	C₂²	1	1	yes	characteristic
120	#478	C₂²	1	1	yes	characteristic
121	#478	C₂²	1	1	yes	characteristic
122	#478	C₂²	1	1	yes	characteristic
123	#478	C₂²	1	1	yes	characteristic
124	#478	C₂²	1	1	yes	characteristic
125	#478	C₂²	1	1	yes	characteristic
126	#478	C₂²	1	1	yes	characteristic
127	#477	C₂²	1	1	yes	characteristic
128	#477	C₂²	1	1	yes	characteristic
129	#476	C₂²	1	1	yes	characteristic
130	#476	C₂²	1	1	yes	characteristic
131	#476	C₂²	1	1	yes	characteristic
132	#475	C₂²	1	1	yes	characteristic
133	#475	C₂²	1	1	yes	characteristic
134	#475	C₂²	1	1	yes	characteristic
135	#475	C₂²	1	1	yes	characteristic
136	#474	C₂²	1	1	yes	characteristic
137	#469	C₂²	1	1	yes	characteristic
138	#468	C₂²	1	1	yes	characteristic
139	#468	C₂²	1	1	yes	characteristic
140	#468	C₂²	1	1	yes	characteristic
141	#466	C₂²	1	1	yes	characteristic
142	#466	C₂²	1	1	yes	characteristic
143	#466	C₂²	1	1	yes	characteristic
144	#465	C₂²	1	1	yes	characteristic
145	#465	C₂²	1	1	yes	characteristic
146	#465	C₂²	1	1	yes	characteristic
147	#465	C₂²	1	1	yes	characteristic
148	#465	C₂²	1	1	yes	characteristic
149	#463	C₂²	1	1	yes	characteristic
150	#463	C₂²	1	1	yes	characteristic
151	#463	C₂²	1	1	yes	characteristic
152	#463	C₂²	1	1	yes	characteristic
153	#461	C₂²	1	1	yes	characteristic
154	#461	C₂²	1	1	yes	characteristic
155	#460	C₂²	1	1	yes	characteristic
156	#460	C₂²	1	1	yes	characteristic
157	#460	C₂²	1	1	yes	characteristic
158	#459	C₂²	1	1	yes	characteristic
159	#449	C₂²	1	1	yes	characteristic
160	#449	C₂²	1	1	yes	characteristic
161	#448	C₂²	1	1	yes	characteristic
162	#448	C₂²	1	1	yes	characteristic
163	#448	C₂²	1	1	yes	characteristic
164	#448	C₂²	1	1	yes	characteristic
165	#446	C₂²	1	1	yes	characteristic
166	C₈×Q₈	C₂²	1	1	yes	characteristic
167	#442	C₂²	1	1	yes	characteristic
168	#440	C₂²	1	1	yes	characteristic
169	#440	C₂²	1	1	yes	characteristic
170	#440	C₂²	1	1	yes	characteristic
171	C₄×SD₁₆	C₂²	1	1	yes	characteristic
172	C₄×SD₁₆	C₂²	1	1	yes	characteristic
173	C₄×SD₁₆	C₂²	1	1	yes	characteristic
174	C₄×SD₁₆	C₂²	1	1	yes	characteristic
175	C₄×SD₁₆	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆	C₂²	1	1	yes	characteristic
178	C₄×D₈	C₂²	1	1	yes	characteristic
179	#436	C₂²	1	1	yes	characteristic
180	#435	C₂²	1	1	yes	characteristic
181	#435	C₂²	1	1	yes	characteristic
182	C₈×D₄	C₂²	1	1	yes	characteristic
183	C₈×D₄	C₂²	1	1	yes	characteristic
184	C₈×D₄	C₂²	1	1	yes	characteristic
185	#433	C₂²	1	1	yes	characteristic
186	#433	C₂²	1	1	yes	characteristic
187	#431	C₂²	1	1	yes	characteristic
188	#428	C₂²	1	1	yes	characteristic
189	#428	C₂²	1	1	yes	characteristic
190	#427	C₂²	1	1	yes	characteristic
191	C₂×#107	C₂²	1	1	yes	characteristic
192	C₂×#106	C₂²	1	1	yes	characteristic
193	C₂×#106	C₂²	1	1	yes	characteristic
194	#424	C₂²	1	1	yes	characteristic
195	#424	C₂²	1	1	yes	characteristic
196	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
197	#419	C₂²	1	1	yes	characteristic
198	#417	C₂²	1	1	yes	characteristic
199	#416	C₂²	1	1	yes	characteristic
200	C₂×#103	C₂²	1	1	yes	characteristic
201	C₂×#103	C₂²	1	1	yes	characteristic
202	C₂×#103	C₂²	1	1	yes	characteristic
203	C₂×#41	—	2	1	no	—
204	C₂×#41	—	2	1	no	—
205	C₂×#41	—	2	1	no	—
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂²×Q₈	C₂³	1	1	yes	characteristic
208	C₂²×Q₈	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆	C₂³	1	1	yes	characteristic
215	C₂×D₈	C₂³	1	1	yes	characteristic
216	C₂×D₈	C₂³	1	1	yes	characteristic
217	C₂×M₁₆	C₂³	1	1	yes	characteristic
218	C₂×M₁₆	C₂³	1	1	yes	characteristic
219	C₂²×C₈	C₂³	1	1	yes	characteristic
220	C₂²×C₈	C₂³	1	1	yes	characteristic
221	C₂²×C₈	C₂³	1	1	yes	characteristic
222	C₂²×C₈	C₂³	1	1	yes	characteristic
223	C₄⋊Q₈	—	2	1	no	—
224	C₄⋊Q₈	—	2	1	no	—
225	C₄⋊Q₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	C₂³	1	1	yes	characteristic
228	C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	#127	C₂³	1	1	yes	characteristic
233	#126	—	2	1	no	—
234	#126	—	2	1	no	—
235	#126	—	2	1	no	—
236	#126	—	2	1	no	—
237	#126	—	2	1	no	—
238	#126	—	2	1	no	—
239	#126	—	2	1	no	—
240	#126	—	2	1	no	—
241	#126	—	2	1	no	—
242	#126	—	2	1	no	—
243	#126	—	2	1	no	—
244	#126	—	2	1	no	—
245	#126	D₄	1	1	yes	characteristic
246	#126	D₄	1	1	yes	characteristic
247	#125	—	2	1	no	—
248	#125	—	2	1	no	—
249	#125	—	2	1	no	—
250	#125	—	2	1	no	—
251	#125	—	2	1	no	—
252	#125	—	2	1	no	—
253	#125	—	2	1	no	—
254	#125	—	2	1	no	—
255	#125	—	2	1	no	—
256	#125	—	2	1	no	—
257	#125	D₄	1	1	yes	characteristic
258	#125	C₂³	1	1	yes	characteristic
259	#125	C₂³	1	1	yes	characteristic
260	#125	C₂³	1	1	yes	characteristic
261	#125	C₂³	1	1	yes	characteristic
262	#125	C₂³	1	1	yes	characteristic
263	#125	C₂³	1	1	yes	characteristic
264	#125	C₂³	1	1	yes	characteristic
265	#125	C₂³	1	1	yes	characteristic
266	#124	—	2	1	no	—
267	#124	—	2	1	no	—
268	#124	—	2	1	no	—
269	#124	—	2	1	no	—
270	#124	D₄	1	1	yes	characteristic
271	#124	C₂³	1	1	yes	characteristic
272	#124	C₂³	1	1	yes	characteristic
273	#123	—	2	1	no	—
274	#123	—	2	1	no	—
275	#123	—	2	1	no	—
276	#123	—	2	1	no	—
277	#123	—	2	1	no	—
278	#123	—	2	1	no	—
279	#123	—	2	1	no	—
280	#123	—	2	1	no	—
281	#123	—	2	1	no	—
282	#123	—	2	1	no	—
283	#123	—	2	1	no	—
284	#123	—	2	1	no	—
285	#123	—	2	1	no	—
286	#123	—	2	1	no	—
287	#123	—	2	1	no	—
288	#123	—	2	1	no	—
289	#123	D₄	1	1	yes	characteristic
290	#123	D₄	1	1	yes	characteristic
291	C₂²⋊Q₈	—	2	1	no	—
292	C₂²⋊Q₈	—	2	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	—	2	1	no	—
311	C₂²⋊Q₈	D₄	1	1	yes	characteristic
312	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
313	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
315	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	#121	—	2	1	no	—
328	#121	D₄	1	1	yes	characteristic
329	#121	C₂³	1	1	yes	characteristic
330	#121	C₂³	1	1	yes	characteristic
331	#121	C₂³	1	1	yes	characteristic
332	#121	C₂³	1	1	yes	characteristic
333	#121	C₂³	1	1	yes	characteristic
334	#121	C₂³	1	1	yes	characteristic
335	#121	C₂³	1	1	yes	characteristic
336	#121	C₂³	1	1	yes	characteristic
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	C₂³	1	1	yes	characteristic
343	C₄×Q₈	C₂³	1	1	yes	characteristic
344	C₄×Q₈	C₂³	1	1	yes	characteristic
345	C₄×Q₈	C₂³	1	1	yes	characteristic
346	C₄×Q₈	C₂³	1	1	yes	characteristic
347	C₄×Q₈	C₂³	1	1	yes	characteristic
348	C₄×Q₈	C₂³	1	1	yes	characteristic
349	C₄×Q₈	C₂³	1	1	yes	characteristic
350	C₄×Q₈	C₂³	1	1	yes	characteristic
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂³	1	1	yes	characteristic
365	C₄×D₄	C₂³	1	1	yes	characteristic
366	C₄×D₄	C₂³	1	1	yes	characteristic
367	C₄×D₄	C₂³	1	1	yes	characteristic
368	C₄×D₄	C₂³	1	1	yes	characteristic
369	C₄×D₄	C₂³	1	1	yes	characteristic
370	C₄×D₄	C₂³	1	1	yes	characteristic
371	C₄×D₄	C₂³	1	1	yes	characteristic
372	C₄×D₄	C₂³	1	1	yes	characteristic
373	C₄×D₄	C₂³	1	1	yes	characteristic
374	C₄×D₄	C₂³	1	1	yes	characteristic
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	C₂³	1	1	yes	characteristic
382	#117	C₂³	1	1	yes	characteristic
383	#117	C₂³	1	1	yes	characteristic
384	#117	C₂³	1	1	yes	characteristic
385	#117	C₂³	1	1	yes	characteristic
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂³	1	1	yes	characteristic
400	#107	C₂³	1	1	yes	characteristic
401	#107	C₂³	1	1	yes	characteristic
402	#107	C₂³	1	1	yes	characteristic
403	#107	C₂³	1	1	yes	characteristic
404	#107	C₂³	1	1	yes	characteristic
405	#107	C₂³	1	1	yes	characteristic
406	#107	C₂³	1	1	yes	characteristic
407	#107	C₂³	1	1	yes	characteristic
408	#107	C₂³	1	1	yes	characteristic
409	#107	C₂³	1	1	yes	characteristic
410	#106	C₂³	1	1	yes	characteristic
411	#106	C₂³	1	1	yes	characteristic
412	#106	C₂³	1	1	yes	characteristic
413	#106	C₂³	1	1	yes	characteristic
414	#106	C₂³	1	1	yes	characteristic
415	#106	C₂³	1	1	yes	characteristic
416	#106	C₂³	1	1	yes	characteristic
417	#106	C₂³	1	1	yes	characteristic
418	#106	C₂³	1	1	yes	characteristic
419	#106	C₂³	1	1	yes	characteristic
420	#106	C₂³	1	1	yes	characteristic
421	#106	C₂³	1	1	yes	characteristic
422	#106	C₂³	1	1	yes	characteristic
423	#106	C₂³	1	1	yes	characteristic
424	C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₄⋊C₈	C₂³	1	1	yes	characteristic
434	#103	C₂³	1	1	yes	characteristic
435	#103	C₂³	1	1	yes	characteristic
436	#103	C₂³	1	1	yes	characteristic
437	#103	C₂³	1	1	yes	characteristic
438	#103	C₂³	1	1	yes	characteristic
439	#103	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#102	C₂³	1	1	yes	characteristic
453	#102	C₂³	1	1	yes	characteristic
454	#102	C₂³	1	1	yes	characteristic
455	#102	C₂³	1	1	yes	characteristic
456	#102	C₂³	1	1	yes	characteristic
457	#102	C₂³	1	1	yes	characteristic
458	#102	C₂³	1	1	yes	characteristic
459	#102	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	#97	C₂³	1	1	yes	characteristic
473	#97	C₂³	1	1	yes	characteristic
474	C₄×C₈	C₂³	1	1	yes	characteristic
475	C₄×C₈	C₂³	1	1	yes	characteristic
476	C₄×C₈	C₂³	1	1	yes	characteristic
477	C₄×C₈	C₂³	1	1	yes	characteristic
478	#41	—	2	2	no	—
479	#41	—	4	1	no	—
480	#41	—	8	2	no	—
481	#41	—	8	2	no	—
482	#41	—	8	2	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	4	1	no	—
492	C₂×Q₈	—	4	1	no	—
493	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
494	C₂×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	C₂×D₄	1	1	yes	characteristic
509	C₂×D₄	C₂×D₄	1	1	yes	characteristic
510	C₂×D₄	C₂×D₄	1	1	yes	characteristic
511	C₂×D₄	C₂⁴	1	1	yes	characteristic
512	C₂×D₄	C₂⁴	1	1	yes	characteristic
513	C₂×D₄	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴	1	1	yes	characteristic
536	SD₁₆	—	2	2	no	—
537	SD₁₆	—	2	2	no	—
538	SD₁₆	—	4	1	no	—
539	SD₁₆	—	4	1	no	—
540	SD₁₆	—	4	1	no	—
541	SD₁₆	—	4	1	no	—
542	D₈	—	4	1	no	—
543	D₈	—	4	1	no	—
544	M₁₆	—	4	1	no	—
545	M₁₆	—	4	1	no	—
546	C₂×C₈	—	4	1	no	—
547	C₂×C₈	—	4	1	no	—
548	C₂×C₈	—	4	1	no	—
549	C₂×C₈	—	4	1	no	—
550	C₂×C₈	C₂⁴	1	1	yes	characteristic
551	C₂×C₈	C₂⁴	1	1	yes	characteristic
552	C₂×C₈	C₂⁴	1	1	yes	characteristic
553	C₂×C₈	C₂⁴	1	1	yes	characteristic
554	C₂×C₈	C₂⁴	1	1	yes	characteristic
555	C₂×C₈	C₂⁴	1	1	yes	characteristic
556	C₂×C₈	C₂⁴	1	1	yes	characteristic
557	C₂×C₈	C₂⁴	1	1	yes	characteristic
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
648	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	C₂×D₄	1	1	yes	characteristic
667	C₄²	C₂×D₄	1	1	yes	characteristic
668	C₄²	C₂⁴	1	1	yes	characteristic
669	C₄²	C₂⁴	1	1	yes	characteristic
670	C₄²	C₂⁴	1	1	yes	characteristic
671	C₄²	C₂⁴	1	1	yes	characteristic
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	C₂²×D₄	1	1	yes	characteristic
676	C₂³	C₂²×D₄	1	1	yes	characteristic
677	C₂³	C₂²×D₄	1	1	yes	characteristic
678	Q₈	—	2	1	no	—
679	Q₈	—	2	1	no	—
680	Q₈	—	2	1	no	—
681	Q₈	—	2	1	no	—
682	Q₈	—	2	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	2	no	—
685	Q₈	—	4	2	no	—
686	Q₈	—	8	1	no	—
687	Q₈	—	8	1	no	—
688	Q₈	—	8	1	no	—
689	Q₈	—	8	1	no	—
690	Q₈	2₋¹⁺⁴	1	2	yes	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	1	no	—
694	D₄	—	2	1	no	—
695	D₄	—	2	1	no	—
696	D₄	—	2	1	no	—
697	D₄	—	2	1	no	—
698	D₄	—	2	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	2	no	—
704	D₄	—	8	1	no	—
705	D₄	—	8	1	no	—
706	D₄	—	8	1	no	—
707	D₄	—	8	1	no	—
708	D₄	—	8	1	no	—
709	D₄	—	8	1	no	—
710	D₄	—	8	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	8	1	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	1	no	—
742	C₂×C₄	—	8	1	no	—
743	C₂×C₄	—	8	1	no	—
744	C₂×C₄	—	8	1	no	—
745	C₂×C₄	—	8	1	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	—	8	1	no	—
749	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄	C₂⁵	1	1	yes	characteristic
761	C₈	—	2	1	no	—
762	C₈	—	2	1	no	—
763	C₈	—	2	1	no	—
764	C₈	—	2	1	no	—
765	C₈	—	2	1	no	—
766	C₈	—	2	1	no	—
767	C₈	—	2	1	no	—
768	C₈	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	#577	1	2	yes	—
787	C₂²	C₂³×D₄	1	1	yes	characteristic
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	2	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
813	C₄	#585	1	1	yes	characteristic
814	C₂	—	2	2	no	—
815	C₂	—	4	1	no	—
816	C₂	—	4	1	no	—
817	C₂	—	8	1	no	—
818	C₂	—	8	1	no	—
819	C₂	—	8	1	no	—
820	C₂	#3489	1	1	yes	characteristic
821	C₂	C₂×#577	1	1	yes	characteristic
822	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3559	C₂	semidirect
2. #3516	C₂	semidirect
3. #3388	C₂	semidirect
4. #3381	C₂	semidirect
5. #3376	C₂	semidirect
6. #3360	C₂	semidirect
7. #3351	C₂	semidirect
8. #3346	C₂	semidirect
9. #3345	C₂	semidirect
10. #3339	C₂	semidirect
11. #3337	C₂	semidirect
12. #3335	C₂	semidirect
13. #3326	C₂	semidirect
14. #3320	C₂	semidirect
15. #3308	C₂	semidirect
16. #3301	C₂	semidirect
17. #3301	C₂	semidirect
18. #3298	C₂	semidirect
19. #3260	C₂	semidirect
20. #3257	C₂	semidirect
21. #3247	C₂	semidirect
22. #3244	C₂	semidirect
23. #3242	C₂	semidirect
24. #3232	C₂	semidirect
25. #3126	C₂	semidirect
26. #3119	C₂	semidirect
27. #3103	C₂	semidirect
28. #3084	C₂	semidirect
29. #3082	C₂	semidirect
30. C₂×#479	C₂	semidirect
31. #2994	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3559	2
#3516	2
#3388	2
#3381	2
#3376	2
#3360	2
#3351	2
#3346	2
#3345	2
#3339	2
#3337	2
#3335	2
#3326	2
#3320	2
#3308	2
#3301	2
#3298	2
#3260	2
#3257	2
#3247	2
#3244	2
#3242	2
#3232	2
#3126	2
#3119	2
#3103	2
#3084	2
#3082	2
C₂×#479	2
#2994	2