Subgroups — #61918

Order 256.

830 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	#3402	C₂	1	1	yes	maximal, characteristic, complemented
5	#3401	C₂	1	1	yes	maximal, characteristic, complemented
6	#3401	C₂	1	1	yes	maximal, characteristic, complemented
7	#3400	C₂	1	1	yes	maximal, characteristic, complemented
8	#3398	C₂	1	1	yes	maximal, characteristic, complemented
9	#3394	C₂	1	1	yes	maximal, characteristic, complemented
10	#3393	C₂	1	1	yes	maximal, characteristic, complemented
11	#3377	C₂	1	1	yes	maximal, characteristic, complemented
12	#3376	C₂	1	1	yes	maximal, characteristic, complemented
13	#3374	C₂	1	1	yes	maximal, characteristic, complemented
14	#3372	C₂	1	1	yes	maximal, characteristic, complemented
15	#3371	C₂	1	1	yes	maximal, characteristic, complemented
16	#3370	C₂	1	1	yes	maximal, characteristic, complemented
17	#3364	C₂	1	1	yes	maximal, characteristic, complemented
18	#3360	C₂	1	1	yes	maximal, characteristic, complemented
19	#3225	C₂	1	1	yes	maximal, characteristic, complemented
20	#3225	C₂	1	1	yes	maximal, characteristic, complemented
21	#3223	C₂	1	1	yes	maximal, characteristic, complemented
22	#3221	C₂	1	1	yes	maximal, characteristic, complemented
23	#3219	C₂	1	1	yes	maximal, characteristic, complemented
24	#3212	C₂	1	1	yes	maximal, characteristic, complemented
25	#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	#3124	C₂	1	1	yes	maximal, characteristic, complemented
27	#3120	C₂	1	1	yes	maximal, characteristic, complemented
28	#3119	C₂	1	1	yes	maximal, characteristic, complemented
29	#3117	C₂	1	1	yes	maximal, characteristic, complemented
30	#3108	C₂	1	1	yes	maximal, characteristic, complemented
31	#2985	C₂	1	1	yes	maximal, characteristic, complemented
32	#563	—	2	1	no	—
33	#563	—	2	1	no	—
34	#559	C₂²	1	1	yes	characteristic
35	#559	C₂²	1	1	yes	characteristic
36	#559	C₂²	1	1	yes	characteristic
37	#559	C₂²	1	1	yes	characteristic
38	#557	C₂²	1	1	yes	characteristic
39	#557	C₂²	1	1	yes	characteristic
40	#557	C₂²	1	1	yes	characteristic
41	#557	C₂²	1	1	yes	characteristic
42	#556	—	2	1	no	—
43	#556	C₂²	1	1	yes	characteristic
44	#556	C₂²	1	1	yes	characteristic
45	#556	C₂²	1	1	yes	characteristic
46	#556	C₂²	1	1	yes	characteristic
47	#556	C₂²	1	1	yes	characteristic
48	#556	C₂²	1	1	yes	characteristic
49	#554	—	2	1	no	—
50	#554	C₂²	1	1	yes	characteristic
51	#554	C₂²	1	1	yes	characteristic
52	#552	—	2	1	no	—
53	#552	—	2	1	no	—
54	#552	—	2	1	no	—
55	#552	—	2	1	no	—
56	#542	—	2	1	no	—
57	#542	—	2	1	no	—
58	#542	C₂²	1	1	yes	characteristic
59	#542	C₂²	1	1	yes	characteristic
60	#541	C₂²	1	1	yes	characteristic
61	#540	C₂²	1	1	yes	characteristic
62	#539	—	2	1	no	—
63	#539	—	2	1	no	—
64	#539	—	2	1	no	—
65	#539	—	2	1	no	—
66	#536	C₂²	1	1	yes	characteristic
67	#536	C₂²	1	1	yes	characteristic
68	#533	C₂²	1	1	yes	characteristic
69	#532	C₂²	1	1	yes	characteristic
70	#529	—	2	1	no	—
71	#529	—	2	1	no	—
72	#529	C₂²	1	1	yes	characteristic
73	#529	C₂²	1	1	yes	characteristic
74	#520	C₂²	1	1	yes	characteristic
75	#520	C₂²	1	1	yes	characteristic
76	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
77	#497	C₂²	1	1	yes	characteristic
78	#497	C₂²	1	1	yes	characteristic
79	#497	C₂²	1	1	yes	characteristic
80	#497	C₂²	1	1	yes	characteristic
81	#496	C₂²	1	1	yes	characteristic
82	#496	C₂²	1	1	yes	characteristic
83	#495	C₂²	1	1	yes	characteristic
84	#495	C₂²	1	1	yes	characteristic
85	#495	C₂²	1	1	yes	characteristic
86	#495	C₂²	1	1	yes	characteristic
87	#494	C₂²	1	1	yes	characteristic
88	#492	C₂²	1	1	yes	characteristic
89	#491	C₂²	1	1	yes	characteristic
90	#491	C₂²	1	1	yes	characteristic
91	#491	C₂²	1	1	yes	characteristic
92	#490	C₂²	1	1	yes	characteristic
93	#489	C₂²	1	1	yes	characteristic
94	#489	C₂²	1	1	yes	characteristic
95	#488	C₂²	1	1	yes	characteristic
96	#488	C₂²	1	1	yes	characteristic
97	#488	C₂²	1	1	yes	characteristic
98	#488	C₂²	1	1	yes	characteristic
99	#487	C₂²	1	1	yes	characteristic
100	#487	C₂²	1	1	yes	characteristic
101	#484	C₂²	1	1	yes	characteristic
102	#483	C₂²	1	1	yes	characteristic
103	#481	C₂²	1	1	yes	characteristic
104	#480	C₂²	1	1	yes	characteristic
105	#479	C₂²	1	1	yes	characteristic
106	#479	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	#478	C₂²	1	1	yes	characteristic
112	#478	C₂²	1	1	yes	characteristic
113	#477	C₂²	1	1	yes	characteristic
114	#476	C₂²	1	1	yes	characteristic
115	#475	C₂²	1	1	yes	characteristic
116	#474	C₂²	1	1	yes	characteristic
117	#464	C₂²	1	1	yes	characteristic
118	#464	C₂²	1	1	yes	characteristic
119	#464	C₂²	1	1	yes	characteristic
120	#464	C₂²	1	1	yes	characteristic
121	#464	C₂²	1	1	yes	characteristic
122	#464	C₂²	1	1	yes	characteristic
123	#464	C₂²	1	1	yes	characteristic
124	#464	C₂²	1	1	yes	characteristic
125	#464	C₂²	1	1	yes	characteristic
126	#464	C₂²	1	1	yes	characteristic
127	#464	C₂²	1	1	yes	characteristic
128	#464	C₂²	1	1	yes	characteristic
129	#463	C₂²	1	1	yes	characteristic
130	#463	C₂²	1	1	yes	characteristic
131	#463	C₂²	1	1	yes	characteristic
132	#463	C₂²	1	1	yes	characteristic
133	#463	C₂²	1	1	yes	characteristic
134	#463	C₂²	1	1	yes	characteristic
135	#463	C₂²	1	1	yes	characteristic
136	#463	C₂²	1	1	yes	characteristic
137	#462	C₂²	1	1	yes	characteristic
138	#462	C₂²	1	1	yes	characteristic
139	#462	C₂²	1	1	yes	characteristic
140	#462	C₂²	1	1	yes	characteristic
141	#462	C₂²	1	1	yes	characteristic
142	#462	C₂²	1	1	yes	characteristic
143	#461	C₂²	1	1	yes	characteristic
144	#461	C₂²	1	1	yes	characteristic
145	#461	C₂²	1	1	yes	characteristic
146	#461	C₂²	1	1	yes	characteristic
147	#461	C₂²	1	1	yes	characteristic
148	#461	C₂²	1	1	yes	characteristic
149	#460	C₂²	1	1	yes	characteristic
150	#460	C₂²	1	1	yes	characteristic
151	#459	C₂²	1	1	yes	characteristic
152	#459	C₂²	1	1	yes	characteristic
153	#452	C₂²	1	1	yes	characteristic
154	#452	C₂²	1	1	yes	characteristic
155	#452	C₂²	1	1	yes	characteristic
156	#452	C₂²	1	1	yes	characteristic
157	#451	C₂²	1	1	yes	characteristic
158	#451	C₂²	1	1	yes	characteristic
159	#449	C₂²	1	1	yes	characteristic
160	#449	C₂²	1	1	yes	characteristic
161	#449	C₂²	1	1	yes	characteristic
162	#449	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	#446	C₂²	1	1	yes	characteristic
167	#446	C₂²	1	1	yes	characteristic
168	#446	C₂²	1	1	yes	characteristic
169	#446	C₂²	1	1	yes	characteristic
170	#446	C₂²	1	1	yes	characteristic
171	C₈×Q₈	C₂²	1	1	yes	characteristic
172	C₈×Q₈	C₂²	1	1	yes	characteristic
173	#442	C₂²	1	1	yes	characteristic
174	#442	C₂²	1	1	yes	characteristic
175	#441	C₂²	1	1	yes	characteristic
176	#441	C₂²	1	1	yes	characteristic
177	#441	C₂²	1	1	yes	characteristic
178	#441	C₂²	1	1	yes	characteristic
179	#440	C₂²	1	1	yes	characteristic
180	#440	C₂²	1	1	yes	characteristic
181	#440	C₂²	1	1	yes	characteristic
182	#440	C₂²	1	1	yes	characteristic
183	#440	C₂²	1	1	yes	characteristic
184	#440	C₂²	1	1	yes	characteristic
185	C₄×Q₁₆	C₂²	1	1	yes	characteristic
186	C₄×Q₁₆	C₂²	1	1	yes	characteristic
187	C₄×Q₁₆	C₂²	1	1	yes	characteristic
188	C₄×Q₁₆	C₂²	1	1	yes	characteristic
189	C₄×SD₁₆	C₂²	1	1	yes	characteristic
190	C₄×SD₁₆	C₂²	1	1	yes	characteristic
191	C₄×SD₁₆	C₂²	1	1	yes	characteristic
192	C₄×SD₁₆	C₂²	1	1	yes	characteristic
193	C₄×SD₁₆	C₂²	1	1	yes	characteristic
194	C₄×SD₁₆	C₂²	1	1	yes	characteristic
195	C₄×D₈	C₂²	1	1	yes	characteristic
196	C₄×D₈	C₂²	1	1	yes	characteristic
197	#433	C₂²	1	1	yes	characteristic
198	#433	C₂²	1	1	yes	characteristic
199	#433	C₂²	1	1	yes	characteristic
200	#433	C₂²	1	1	yes	characteristic
201	#432	C₂²	1	1	yes	characteristic
202	#431	C₂²	1	1	yes	characteristic
203	C₂×#41	C₂³	1	1	yes	characteristic
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂²×Q₈	C₂³	1	1	yes	characteristic
206	C₂×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂×Q₁₆	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆	C₂³	1	1	yes	characteristic
226	C₂×D₈	C₂³	1	1	yes	characteristic
227	C₂×D₈	C₂³	1	1	yes	characteristic
228	C₂×D₈	C₂³	1	1	yes	characteristic
229	C₂×D₈	C₂³	1	1	yes	characteristic
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	D₄	1	1	yes	characteristic
233	C₄⋊Q₈	D₄	1	1	yes	characteristic
234	C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₄⋊Q₈	C₂³	1	1	yes	characteristic
236	C₄⋊Q₈	C₂³	1	1	yes	characteristic
237	C₄⋊Q₈	C₂³	1	1	yes	characteristic
238	C₄⋊Q₈	C₂³	1	1	yes	characteristic
239	C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³	1	1	yes	characteristic
242	#127	C₂³	1	1	yes	characteristic
243	#127	C₂³	1	1	yes	characteristic
244	#126	—	2	1	no	—
245	#126	—	2	1	no	—
246	#126	—	2	1	no	—
247	#126	—	2	1	no	—
248	#126	—	2	1	no	—
249	#126	—	2	1	no	—
250	#126	—	2	1	no	—
251	#126	—	2	1	no	—
252	#126	—	2	1	no	—
253	#126	—	2	1	no	—
254	#126	—	2	1	no	—
255	#126	—	2	1	no	—
256	#126	—	2	1	no	—
257	#126	—	2	1	no	—
258	#126	—	2	1	no	—
259	#126	—	2	1	no	—
260	#126	—	2	1	no	—
261	#126	—	2	1	no	—
262	#125	—	2	1	no	—
263	#125	—	2	1	no	—
264	#125	—	2	1	no	—
265	#125	—	2	1	no	—
266	#125	—	2	1	no	—
267	#125	—	2	1	no	—
268	#125	—	2	1	no	—
269	#125	—	2	1	no	—
270	#125	—	2	1	no	—
271	#125	—	2	1	no	—
272	#125	—	2	1	no	—
273	#125	—	2	1	no	—
274	#125	D₄	1	1	yes	characteristic
275	#125	D₄	1	1	yes	characteristic
276	#125	C₂³	1	1	yes	characteristic
277	#125	C₂³	1	1	yes	characteristic
278	#125	C₂³	1	1	yes	characteristic
279	#125	C₂³	1	1	yes	characteristic
280	#124	—	2	1	no	—
281	#124	—	2	1	no	—
282	#124	—	2	1	no	—
283	#124	—	2	1	no	—
284	#124	—	2	1	no	—
285	#124	—	2	1	no	—
286	#124	C₂³	1	1	yes	characteristic
287	#124	C₂³	1	1	yes	characteristic
288	#124	C₂³	1	1	yes	characteristic
289	#124	C₂³	1	1	yes	characteristic
290	#124	C₂³	1	1	yes	characteristic
291	#124	C₂³	1	1	yes	characteristic
292	#124	C₂³	1	1	yes	characteristic
293	#124	C₂³	1	1	yes	characteristic
294	#124	C₂³	1	1	yes	characteristic
295	#124	C₂³	1	1	yes	characteristic
296	#123	—	2	1	no	—
297	#123	—	2	1	no	—
298	#123	—	2	1	no	—
299	#123	—	2	1	no	—
300	#123	—	2	1	no	—
301	#123	—	2	1	no	—
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	—	2	1	no	—
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	#123	—	2	1	no	—
311	#123	—	2	1	no	—
312	#123	—	2	1	no	—
313	#123	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	D₄	1	1	yes	characteristic
333	C₂²⋊Q₈	D₄	1	1	yes	characteristic
334	C₂²⋊Q₈	D₄	1	1	yes	characteristic
335	C₂²⋊Q₈	D₄	1	1	yes	characteristic
336	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
337	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	#121	C₂³	1	1	yes	characteristic
343	#121	C₂³	1	1	yes	characteristic
344	C₄×Q₈	—	2	1	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	C₂³	1	1	yes	characteristic
351	C₄×Q₈	C₂³	1	1	yes	characteristic
352	C₄×Q₈	C₂³	1	1	yes	characteristic
353	C₄×Q₈	C₂³	1	1	yes	characteristic
354	C₄×Q₈	C₂³	1	1	yes	characteristic
355	C₄×Q₈	C₂³	1	1	yes	characteristic
356	C₄×Q₈	C₂³	1	1	yes	characteristic
357	C₄×Q₈	C₂³	1	1	yes	characteristic
358	C₄×Q₈	C₂³	1	1	yes	characteristic
359	C₄×Q₈	C₂³	1	1	yes	characteristic
360	C₄×Q₈	C₂³	1	1	yes	characteristic
361	C₄×Q₈	C₂³	1	1	yes	characteristic
362	C₄×Q₈	C₂³	1	1	yes	characteristic
363	C₄×Q₈	C₂³	1	1	yes	characteristic
364	C₄×Q₈	C₂³	1	1	yes	characteristic
365	C₄×Q₈	C₂³	1	1	yes	characteristic
366	C₄×Q₈	C₂³	1	1	yes	characteristic
367	C₄×Q₈	C₂³	1	1	yes	characteristic
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂³	1	1	yes	characteristic
381	C₄×D₄	C₂³	1	1	yes	characteristic
382	C₄×D₄	C₂³	1	1	yes	characteristic
383	C₄×D₄	C₂³	1	1	yes	characteristic
384	C₄×D₄	C₂³	1	1	yes	characteristic
385	C₄×D₄	C₂³	1	1	yes	characteristic
386	C₄×D₄	C₂³	1	1	yes	characteristic
387	C₄×D₄	C₂³	1	1	yes	characteristic
388	C₄×D₄	C₂³	1	1	yes	characteristic
389	C₄×D₄	C₂³	1	1	yes	characteristic
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	C₂³	1	1	yes	characteristic
401	#117	C₂³	1	1	yes	characteristic
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	C₂³	1	1	yes	characteristic
410	#107	C₂³	1	1	yes	characteristic
411	#107	C₂³	1	1	yes	characteristic
412	#107	C₂³	1	1	yes	characteristic
413	#107	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	C₄⋊C₈	C₂³	1	1	yes	characteristic
419	C₄⋊C₈	C₂³	1	1	yes	characteristic
420	C₄⋊C₈	C₂³	1	1	yes	characteristic
421	C₄⋊C₈	C₂³	1	1	yes	characteristic
422	C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₄⋊C₈	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	#103	C₂³	1	1	yes	characteristic
431	#103	C₂³	1	1	yes	characteristic
432	#103	C₂³	1	1	yes	characteristic
433	#103	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	#102	C₂³	1	1	yes	characteristic
451	#102	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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	#97	C₂³	1	1	yes	characteristic
467	#97	C₂³	1	1	yes	characteristic
468	#97	C₂³	1	1	yes	characteristic
469	#97	C₂³	1	1	yes	characteristic
470	#97	C₂³	1	1	yes	characteristic
471	#97	C₂³	1	1	yes	characteristic
472	C₄×C₈	C₂³	1	1	yes	characteristic
473	C₄×C₈	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	—	4	1	no	—
479	#41	—	4	1	no	—
480	#41	—	4	1	no	—
481	#41	—	4	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	4	1	no	—
486	C₂×Q₈	—	4	1	no	—
487	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
488	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
489	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
490	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
491	C₂×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈	C₂⁴	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	C₂⁴	1	1	yes	characteristic
506	C₂×D₄	C₂⁴	1	1	yes	characteristic
507	C₂×D₄	C₂⁴	1	1	yes	characteristic
508	C₂×D₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴	1	1	yes	characteristic
526	Q₁₆	—	4	1	no	—
527	Q₁₆	—	4	1	no	—
528	Q₁₆	—	4	1	no	—
529	Q₁₆	—	4	1	no	—
530	Q₁₆	—	4	1	no	—
531	Q₁₆	—	4	1	no	—
532	Q₁₆	—	4	1	no	—
533	Q₁₆	—	4	1	no	—
534	SD₁₆	—	4	1	no	—
535	SD₁₆	—	4	1	no	—
536	SD₁₆	—	4	1	no	—
537	SD₁₆	—	4	1	no	—
538	SD₁₆	—	4	1	no	—
539	SD₁₆	—	4	1	no	—
540	SD₁₆	—	4	1	no	—
541	SD₁₆	—	4	1	no	—
542	SD₁₆	—	4	1	no	—
543	SD₁₆	—	4	1	no	—
544	SD₁₆	—	4	1	no	—
545	SD₁₆	—	4	1	no	—
546	D₈	—	4	1	no	—
547	D₈	—	4	1	no	—
548	D₈	—	4	1	no	—
549	D₈	—	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	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄	C₂×D₄	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	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	C₂×D₄	1	1	yes	characteristic
672	C₄²	C₂×D₄	1	1	yes	characteristic
673	C₄²	C₂⁴	1	1	yes	characteristic
674	C₄²	C₂⁴	1	1	yes	characteristic
675	C₄²	C₂⁴	1	1	yes	characteristic
676	C₄²	C₂⁴	1	1	yes	characteristic
677	C₄²	C₂⁴	1	1	yes	characteristic
678	C₄²	C₂⁴	1	1	yes	characteristic
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	C₂²×D₄	1	1	yes	characteristic
684	Q₈	—	2	1	no	—
685	Q₈	—	2	1	no	—
686	Q₈	—	2	1	no	—
687	Q₈	—	2	1	no	—
688	Q₈	—	2	1	no	—
689	Q₈	—	2	1	no	—
690	Q₈	—	2	1	no	—
691	Q₈	—	2	1	no	—
692	Q₈	—	2	1	no	—
693	Q₈	—	2	1	no	—
694	Q₈	—	2	1	no	—
695	Q₈	—	2	1	no	—
696	Q₈	—	4	1	no	—
697	Q₈	—	4	1	no	—
698	Q₈	—	4	1	no	—
699	Q₈	—	4	1	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	8	1	no	—
702	Q₈	—	8	1	no	—
703	D₄	—	2	1	no	—
704	D₄	—	2	1	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	1	no	—
708	D₄	—	2	1	no	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	2	no	—
714	D₄	—	8	1	no	—
715	D₄	—	8	1	no	—
716	D₄	—	8	1	no	—
717	D₄	—	8	1	no	—
718	D₄	—	8	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	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄	C₂⁵	1	1	yes	characteristic
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	C₈	—	2	1	no	—
770	C₈	—	2	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	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	C₂³×D₄	1	1	yes	characteristic
787	C₄	—	2	1	no	—
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	1	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	#585	1	1	yes	characteristic
813	C₄	#585	1	1	yes	characteristic
814	C₂	—	4	1	no	—
815	C₂	—	8	1	no	—
816	C₂	—	8	1	no	—
817	C₂	—	8	1	no	—
818	C₂	—	8	1	no	—
819	C₂	#3487	1	1	yes	characteristic
820	C₂	#3584	1	1	yes	characteristic
821	C₂	#3586	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 ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3557	C₂	semidirect
2. #3507	C₂	semidirect
3. #3403	C₂	semidirect
4. #3402	C₂	semidirect
5. #3401	C₂	semidirect
6. #3401	C₂	semidirect
7. #3400	C₂	semidirect
8. #3398	C₂	semidirect
9. #3394	C₂	semidirect
10. #3393	C₂	semidirect
11. #3377	C₂	semidirect
12. #3376	C₂	semidirect
13. #3374	C₂	semidirect
14. #3372	C₂	semidirect
15. #3371	C₂	semidirect
16. #3370	C₂	semidirect
17. #3364	C₂	semidirect
18. #3360	C₂	semidirect
19. #3225	C₂	semidirect
20. #3225	C₂	semidirect
21. #3223	C₂	semidirect
22. #3221	C₂	semidirect
23. #3219	C₂	semidirect
24. #3212	C₂	semidirect
25. #3125	C₂	semidirect
26. #3124	C₂	semidirect
27. #3120	C₂	semidirect
28. #3119	C₂	semidirect
29. #3117	C₂	semidirect
30. #3108	C₂	semidirect
31. #2985	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3557	2
#3507	2
#3403	2
#3402	2
#3401	2
#3400	2
#3398	2
#3394	2
#3393	2
#3377	2
#3376	2
#3374	2
#3372	2
#3371	2
#3370	2
#3364	2
#3360	2
#3225	2
#3223	2
#3221	2
#3219	2
#3212	2
#3125	2
#3124	2
#3120	2
#3119	2
#3117	2
#3108	2
#2985	2