Subgroups — #62302

Order 256.

932 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	#3505	C₂	1	1	yes	maximal, characteristic, complemented
3	#3352	C₂	1	1	yes	maximal, characteristic, complemented
4	#3349	C₂	1	1	yes	maximal, characteristic, complemented
5	#3345	C₂	1	1	yes	maximal, characteristic, complemented
6	#3337	C₂	1	1	yes	maximal, characteristic, complemented
7	#3327	C₂	1	1	yes	maximal, characteristic, complemented
8	#3323	C₂	1	1	yes	maximal, characteristic, complemented
9	#3320	C₂	1	1	yes	maximal, characteristic, complemented
10	#3315	C₂	1	1	yes	maximal, characteristic, complemented
11	#3311	C₂	1	1	yes	maximal, characteristic, complemented
12	#3308	C₂	1	1	yes	maximal, characteristic, complemented
13	#3301	C₂	1	1	yes	maximal, characteristic, complemented
14	#3300	C₂	1	1	yes	maximal, characteristic, complemented
15	#3285	C₂	1	1	yes	maximal, characteristic, complemented
16	#3275	C₂	1	1	yes	maximal, characteristic, complemented
17	#3270	C₂	1	1	yes	maximal, characteristic, complemented
18	#3267	C₂	1	1	yes	maximal, characteristic, complemented
19	#3256	C₂	1	1	yes	maximal, characteristic, complemented
20	#3252	C₂	1	1	yes	maximal, characteristic, complemented
21	#3197	C₂	1	1	yes	maximal, characteristic, complemented
22	#3196	C₂	1	1	yes	maximal, characteristic, complemented
23	#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	#3193	C₂	1	1	yes	maximal, characteristic, complemented
25	#3183	C₂	1	1	yes	maximal, characteristic, complemented
26	#3172	C₂	1	1	yes	maximal, characteristic, complemented
27	#3056	C₂	1	1	yes	maximal, characteristic, complemented
28	#3055	C₂	1	1	yes	maximal, characteristic, complemented
29	#3054	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#470	C₂	1	1	yes	maximal, characteristic, complemented
31	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
34	C₂×#135	C₂²	1	1	yes	characteristic, complemented
35	C₂²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂²×M₁₆	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
38	#556	C₂²	1	1	yes	characteristic
39	#554	—	2	1	no	—
40	#553	—	2	1	no	—
41	#553	—	2	1	no	—
42	#553	C₂²	1	1	yes	characteristic
43	#553	C₂²	1	1	yes	characteristic
44	#552	C₂²	1	1	yes	characteristic
45	#552	C₂²	1	1	yes	characteristic
46	#552	C₂²	1	1	yes	characteristic
47	#552	C₂²	1	1	yes	characteristic, complemented
48	#551	—	2	1	no	—
49	#551	—	2	1	no	—
50	#551	—	2	1	no	—
51	#551	—	2	1	no	—
52	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
53	#548	C₂²	1	1	yes	characteristic
54	#548	C₂²	1	1	yes	characteristic
55	#548	C₂²	1	1	yes	characteristic
56	#548	C₂²	1	1	yes	characteristic, complemented
57	#547	C₂²	1	1	yes	characteristic
58	#547	C₂²	1	1	yes	characteristic, complemented
59	#546	—	2	1	no	—
60	#546	C₂²	1	1	yes	characteristic
61	#546	C₂²	1	1	yes	characteristic
62	#542	—	2	1	no	—
63	#539	—	2	1	no	—
64	#539	—	2	1	no	—
65	#539	—	2	1	no	—
66	#538	—	2	1	no	—
67	#534	—	2	1	no	—
68	#533	C₂²	1	1	yes	characteristic, complemented
69	#529	C₂²	1	1	yes	characteristic
70	#529	C₂²	1	1	yes	characteristic
71	#529	C₂²	1	1	yes	characteristic, complemented
72	#525	C₂²	1	1	yes	characteristic
73	#525	C₂²	1	1	yes	characteristic
74	#525	C₂²	1	1	yes	characteristic
75	#525	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
78	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
79	C₂×#121	C₂²	1	1	yes	characteristic
80	#520	—	2	1	no	—
81	#518	—	2	1	no	—
82	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
83	#501	C₂²	1	1	yes	characteristic, complemented
84	#499	C₂²	1	1	yes	characteristic, complemented
85	#497	C₂²	1	1	yes	characteristic, complemented
86	#495	C₂²	1	1	yes	characteristic, complemented
87	#491	C₂²	1	1	yes	characteristic, complemented
88	#489	C₂²	1	1	yes	characteristic, complemented
89	#488	C₂²	1	1	yes	characteristic, complemented
90	#488	C₂²	1	1	yes	characteristic, complemented
91	#485	C₂²	1	1	yes	characteristic, complemented
92	#485	C₂²	1	1	yes	characteristic, complemented
93	#485	C₂²	1	1	yes	characteristic, complemented
94	#485	C₂²	1	1	yes	characteristic, complemented
95	#485	C₂²	1	1	yes	characteristic, complemented
96	#485	C₂²	1	1	yes	characteristic, complemented
97	#484	C₂²	1	1	yes	characteristic, complemented
98	#484	C₂²	1	1	yes	characteristic, complemented
99	#484	C₂²	1	1	yes	characteristic, complemented
100	#484	C₂²	1	1	yes	characteristic, complemented
101	#482	C₂²	1	1	yes	characteristic, complemented
102	#482	C₂²	1	1	yes	characteristic, complemented
103	#481	C₂²	1	1	yes	characteristic, complemented
104	#481	C₂²	1	1	yes	characteristic, complemented
105	#480	C₂²	1	1	yes	characteristic, complemented
106	#480	C₂²	1	1	yes	characteristic, complemented
107	#479	C₂²	1	1	yes	characteristic, complemented
108	#479	C₂²	1	1	yes	characteristic, complemented
109	#479	C₂²	1	1	yes	characteristic, complemented
110	#479	C₂²	1	1	yes	characteristic, complemented
111	#478	C₂²	1	1	yes	characteristic, complemented
112	#478	C₂²	1	1	yes	characteristic, complemented
113	#477	C₂²	1	1	yes	characteristic, complemented
114	#476	C₂²	1	1	yes	characteristic, complemented
115	#470	C₂²	1	1	yes	characteristic, complemented
116	#470	C₂²	1	1	yes	characteristic, complemented
117	#470	C₂²	1	1	yes	characteristic, complemented
118	#470	C₂²	1	1	yes	characteristic, complemented
119	#470	C₂²	1	1	yes	characteristic, complemented
120	#470	C₂²	1	1	yes	characteristic, complemented
121	#470	C₂²	1	1	yes	characteristic, complemented
122	#470	C₂²	1	1	yes	characteristic, complemented
123	#470	C₂²	1	1	yes	characteristic, complemented
124	#470	C₂²	1	1	yes	characteristic, complemented
125	#470	C₂²	1	1	yes	characteristic, complemented
126	#469	C₂²	1	1	yes	characteristic
127	#469	C₂²	1	1	yes	characteristic
128	#469	C₂²	1	1	yes	characteristic, complemented
129	#468	C₂²	1	1	yes	characteristic
130	#468	C₂²	1	1	yes	characteristic
131	#468	C₂²	1	1	yes	characteristic
132	#468	C₂²	1	1	yes	characteristic
133	#468	C₂²	1	1	yes	characteristic
134	#468	C₂²	1	1	yes	characteristic
135	#468	C₂²	1	1	yes	characteristic, complemented
136	#468	C₂²	1	1	yes	characteristic, complemented
137	#468	C₂²	1	1	yes	characteristic, complemented
138	#468	C₂²	1	1	yes	characteristic, complemented
139	#467	C₂²	1	1	yes	characteristic, complemented
140	#467	C₂²	1	1	yes	characteristic, complemented
141	#466	C₂²	1	1	yes	characteristic, complemented
142	#466	C₂²	1	1	yes	characteristic, complemented
143	#465	C₂²	1	1	yes	characteristic, complemented
144	#465	C₂²	1	1	yes	characteristic, complemented
145	#465	C₂²	1	1	yes	characteristic, complemented
146	#465	C₂²	1	1	yes	characteristic, complemented
147	#464	C₂²	1	1	yes	characteristic, complemented
148	#464	C₂²	1	1	yes	characteristic, complemented
149	#464	C₂²	1	1	yes	characteristic, complemented
150	#464	C₂²	1	1	yes	characteristic, complemented
151	#463	C₂²	1	1	yes	characteristic, complemented
152	#463	C₂²	1	1	yes	characteristic, complemented
153	#462	C₂²	1	1	yes	characteristic, complemented
154	#461	C₂²	1	1	yes	characteristic, complemented
155	#452	C₂²	1	1	yes	characteristic, complemented
156	#452	C₂²	1	1	yes	characteristic, complemented
157	#452	C₂²	1	1	yes	characteristic, complemented
158	#452	C₂²	1	1	yes	characteristic, complemented
159	#452	C₂²	1	1	yes	characteristic, complemented
160	#452	C₂²	1	1	yes	characteristic, complemented
161	#451	C₂²	1	1	yes	characteristic, complemented
162	#451	C₂²	1	1	yes	characteristic, complemented
163	#450	C₂²	1	1	yes	characteristic, complemented
164	#450	C₂²	1	1	yes	characteristic, complemented
165	#449	C₂²	1	1	yes	characteristic, complemented
166	#449	C₂²	1	1	yes	characteristic, complemented
167	#448	C₂²	1	1	yes	characteristic, complemented
168	#448	C₂²	1	1	yes	characteristic, complemented
169	#448	C₂²	1	1	yes	characteristic, complemented
170	#448	C₂²	1	1	yes	characteristic, complemented
171	#442	C₂²	1	1	yes	characteristic, complemented
172	#441	C₂²	1	1	yes	characteristic, complemented
173	#440	C₂²	1	1	yes	characteristic, complemented
174	#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
176	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
177	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
179	#436	C₂²	1	1	yes	characteristic
180	#436	C₂²	1	1	yes	characteristic
181	#435	C₂²	1	1	yes	characteristic
182	#435	C₂²	1	1	yes	characteristic
183	#435	C₂²	1	1	yes	characteristic, complemented
184	#435	C₂²	1	1	yes	characteristic, complemented
185	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
186	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
187	#428	C₂²	1	1	yes	characteristic, complemented
188	#428	C₂²	1	1	yes	characteristic, complemented
189	#427	C₂²	1	1	yes	characteristic, complemented
190	C₂×#106	C₂²	1	1	yes	characteristic, complemented
191	#423	C₂²	1	1	yes	characteristic, complemented
192	#419	C₂²	1	1	yes	characteristic, complemented
193	#418	C₂²	1	1	yes	characteristic, complemented
194	#417	C₂²	1	1	yes	characteristic, complemented
195	#417	C₂²	1	1	yes	characteristic, complemented
196	#416	C₂²	1	1	yes	characteristic, complemented
197	#416	C₂²	1	1	yes	characteristic, complemented
198	C₂×#103	C₂²	1	1	yes	characteristic, complemented
199	C₂×#103	C₂²	1	1	yes	characteristic, complemented
200	#407	C₂²	1	1	yes	characteristic
201	#407	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41	—	2	1	no	—
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂×#41	C₂³	1	1	yes	characteristic
208	C₂²×Q₈	C₂³	1	1	yes	characteristic
209	C₂²×Q₈	C₂³	1	1	yes	characteristic
210	C₂²×Q₈	C₂³	1	1	yes	characteristic
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	D₄	1	1	yes	characteristic
213	C₂²×D₄	C₂³	1	1	yes	characteristic
214	C₂³×C₄	C₂³	1	1	yes	characteristic
215	C₂³×C₄	C₂³	1	1	yes	characteristic
216	#137	—	4	2	no	—
217	AGL(1,ℤ/8)	—	4	2	no	—
218	#135	—	4	2	no	—
219	C₂×Q₁₆	—	4	2	no	—
220	C₂×Q₁₆	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆	C₂³	1	1	yes	characteristic
234	C₂×D₈	C₂³	1	1	yes	characteristic
235	C₂×D₈	C₂³	1	1	yes	characteristic
236	C₂×M₁₆	—	4	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂×M₁₆	C₂³	1	1	yes	characteristic
239	C₂×M₁₆	C₂³	1	1	yes	characteristic
240	C₂×M₁₆	C₂³	1	1	yes	characteristic
241	C₂×M₁₆	C₂³	1	1	yes	characteristic
242	C₂×M₁₆	C₂³	1	1	yes	characteristic
243	C₂×M₁₆	C₂³	1	1	yes	characteristic
244	C₂×M₁₆	C₂³	1	1	yes	characteristic
245	C₂×M₁₆	C₂³	1	1	yes	characteristic
246	C₂²×C₈	C₂³	1	1	yes	characteristic
247	C₂²×C₈	C₂³	1	1	yes	characteristic
248	C₂²×C₈	C₂³	1	1	yes	characteristic
249	C₂²×C₈	C₂³	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	#126	—	2	1	no	—
263	#126	—	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	C₂³	1	1	yes	characteristic
270	#125	C₂³	1	1	yes	characteristic
271	#125	C₂³	1	1	yes	characteristic
272	#124	—	2	1	no	—
273	#124	—	2	1	no	—
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	—	2	1	no	—
277	#124	C₂³	1	1	yes	characteristic
278	#124	C₂³	1	1	yes	characteristic
279	#124	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
290	#123	—	2	1	no	—
291	#123	—	2	1	no	—
292	#123	—	2	1	no	—
293	#123	—	2	1	no	—
294	#123	—	2	1	no	—
295	#123	—	2	1	no	—
296	#123	—	2	1	no	—
297	#123	—	2	1	no	—
298	#123	—	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	—	2	1	no	—
312	C₂²⋊Q₈	—	2	1	no	—
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	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
317	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
318	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
319	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
320	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
321	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
326	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
327	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
328	#121	—	2	1	no	—
329	#121	—	2	1	no	—
330	#121	—	2	1	no	—
331	#121	—	2	1	no	—
332	#121	—	2	1	no	—
333	#121	—	2	1	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	C₂³	1	1	yes	characteristic
340	#121	C₂³	1	1	yes	characteristic
341	#121	C₂³	1	1	yes	characteristic
342	#121	C₂³	1	1	yes	characteristic
343	#121	C₂³	1	1	yes	characteristic
344	#121	C₂³	1	1	yes	characteristic
345	#121	C₂³	1	1	yes	characteristic
346	#121	C₂³	1	1	yes	characteristic
347	#121	C₂³	1	1	yes	characteristic
348	#120	—	2	1	no	—
349	#120	—	2	1	no	—
350	#120	—	2	1	no	—
351	#120	—	2	1	no	—
352	#120	—	2	1	no	—
353	#120	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
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×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
380	C₄×D₄	D₄	1	1	yes	characteristic
381	C₄×D₄	D₄	1	1	yes	characteristic
382	C₄×D₄	D₄	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	C₂³	1	1	yes	characteristic
399	#117	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
419	C₂×C₄²	C₂³	1	1	yes	characteristic
420	#107	C₂³	1	1	yes	characteristic
421	#107	C₂³	1	1	yes	characteristic
422	#107	C₂³	1	1	yes	characteristic
423	#107	C₂³	1	1	yes	characteristic
424	#107	C₂³	1	1	yes	characteristic
425	#107	C₂³	1	1	yes	characteristic
426	#107	C₂³	1	1	yes	characteristic
427	#107	C₂³	1	1	yes	characteristic
428	#106	C₂³	1	1	yes	characteristic
429	#106	C₂³	1	1	yes	characteristic
430	#106	C₂³	1	1	yes	characteristic
431	#106	C₂³	1	1	yes	characteristic
432	#106	C₂³	1	1	yes	characteristic
433	#106	C₂³	1	1	yes	characteristic
434	#106	C₂³	1	1	yes	characteristic
435	#106	C₂³	1	1	yes	characteristic
436	C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₄⋊C₈	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	#103	C₂³	1	1	yes	characteristic
453	#103	C₂³	1	1	yes	characteristic
454	#103	C₂³	1	1	yes	characteristic
455	#103	C₂³	1	1	yes	characteristic
456	#103	C₂³	1	1	yes	characteristic
457	#103	C₂³	1	1	yes	characteristic
458	#103	C₂³	1	1	yes	characteristic
459	#103	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	#102	C₂³	1	1	yes	characteristic
467	#102	C₂³	1	1	yes	characteristic
468	#102	C₂³	1	1	yes	characteristic
469	#102	C₂³	1	1	yes	characteristic
470	#102	C₂³	1	1	yes	characteristic
471	#102	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈	C₂³	1	1	yes	characteristic
480	#97	C₂³	1	1	yes	characteristic
481	#97	C₂³	1	1	yes	characteristic
482	C₄×C₈	C₂³	1	1	yes	characteristic
483	C₄×C₈	C₂³	1	1	yes	characteristic
484	C₂⁴	—	2	1	no	—
485	C₂⁴	C₂×D₄	1	1	yes	characteristic
486	C₂⁴	C₂×D₄	1	1	yes	characteristic
487	#41	—	4	1	no	—
488	#41	—	4	1	no	—
489	#41	—	4	1	no	—
490	#41	—	4	1	no	—
491	#41	—	4	1	no	—
492	#41	—	4	1	no	—
493	#41	—	4	1	no	—
494	#41	—	4	1	no	—
495	#41	—	4	4	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	—	4	1	no	—
503	C₂×Q₈	—	4	1	no	—
504	C₂×Q₈	—	4	1	no	—
505	C₂×Q₈	—	4	1	no	—
506	C₂×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂×Q₈	C₂⁴	1	1	yes	characteristic
508	C₂×Q₈	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈	C₂⁴	1	1	yes	characteristic
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	4	1	no	—
526	C₂×D₄	—	4	1	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	C₂×D₄	1	1	yes	characteristic
530	C₂×D₄	C₂×D₄	1	1	yes	characteristic
531	C₂×D₄	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄	C₂⁴	1	1	yes	characteristic
534	C₂×D₄	C₂⁴	1	1	yes	characteristic
535	C₂×D₄	C₂⁴	1	1	yes	characteristic
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	4	1	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴	1	1	yes	characteristic
567	Q₁₆	—	2	2	no	—
568	Q₁₆	—	2	2	no	—
569	Q₁₆	—	4	1	no	—
570	Q₁₆	—	4	1	no	—
571	Q₁₆	—	4	1	no	—
572	Q₁₆	—	4	1	no	—
573	SD₁₆	—	2	2	no	—
574	SD₁₆	—	4	1	no	—
575	SD₁₆	—	4	1	no	—
576	SD₁₆	—	4	1	no	—
577	SD₁₆	—	4	1	no	—
578	SD₁₆	—	4	1	no	—
579	SD₁₆	—	4	1	no	—
580	SD₁₆	—	4	1	no	—
581	D₈	—	2	2	no	—
582	D₈	—	4	1	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	2	no	—
585	M₁₆	—	2	2	no	—
586	M₁₆	—	4	1	no	—
587	M₁₆	—	4	1	no	—
588	M₁₆	—	4	1	no	—
589	M₁₆	—	4	1	no	—
590	M₁₆	—	4	1	no	—
591	C₂×C₈	—	2	2	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	4	1	no	—
594	C₂×C₈	—	4	1	no	—
595	C₂×C₈	C₂⁴	1	1	yes	characteristic
596	C₂×C₈	C₂⁴	1	1	yes	characteristic
597	C₂×C₈	C₂⁴	1	1	yes	characteristic
598	C₂×C₈	C₂⁴	1	1	yes	characteristic
599	C₂×C₈	C₂⁴	1	1	yes	characteristic
600	C₂×C₈	C₂⁴	1	1	yes	characteristic
601	C₂×C₈	C₂⁴	1	1	yes	characteristic
602	C₂×C₈	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
686	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
687	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
688	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
689	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
690	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
691	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
692	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
693	C₄²	—	2	1	no	—
694	C₄²	—	2	1	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	C₂×D₄	1	1	yes	characteristic
703	C₄²	C₂×D₄	1	1	yes	characteristic
704	C₄²	C₂⁴	1	1	yes	characteristic
705	C₄²	C₂⁴	1	1	yes	characteristic
706	C₂³	—	2	2	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	2	no	—
716	C₂³	—	8	1	no	—
717	C₂³	—	8	1	no	—
718	C₂³	C₂²×D₄	1	1	yes	characteristic
719	C₂³	C₂²×D₄	1	1	yes	characteristic
720	C₂³	C₂²×D₄	1	1	yes	characteristic
721	C₂³	C₂²×D₄	1	1	yes	characteristic
722	C₂³	C₂²×D₄	1	1	yes	characteristic
723	Q₈	—	2	1	no	—
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	2	1	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	2	1	no	—
733	Q₈	—	4	2	no	—
734	Q₈	—	8	1	no	—
735	Q₈	—	8	1	no	—
736	Q₈	—	8	1	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	1	no	—
740	D₄	—	2	1	no	—
741	D₄	—	2	1	no	—
742	D₄	—	2	1	no	—
743	D₄	—	2	1	no	—
744	D₄	—	2	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	2	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	1	no	—
755	D₄	—	8	1	no	—
756	D₄	—	8	1	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	1	no	—
760	D₄	—	8	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	8	1	no	—
797	C₂×C₄	—	8	1	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	—	8	1	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	—	8	1	no	—
802	C₂×C₄	—	8	1	no	—
803	C₂×C₄	—	8	1	no	—
804	C₂×C₄	—	8	1	no	—
805	C₂×C₄	—	8	1	no	—
806	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
811	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
815	C₂×C₄	C₂⁵	1	1	yes	characteristic
816	C₈	—	2	1	no	—
817	C₈	—	2	1	no	—
818	C₈	—	2	1	no	—
819	C₈	—	2	1	no	—
820	C₈	—	2	1	no	—
821	C₈	—	2	1	no	—
822	C₈	—	2	1	no	—
823	C₈	H(5,𝔽₂)	1	2	yes	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	8	2	no	—
848	C₂²	—	8	2	no	—
849	C₂²	—	16	2	no	—
850	C₂²	#575	1	2	yes	—
851	C₂²	C₂³×D₄	1	1	yes	characteristic
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
875	C₄	#585	1	1	yes	characteristic
876	C₂	—	2	2	no	—
877	C₂	—	4	1	no	—
878	C₂	—	4	1	no	—
879	C₂	—	4	1	no	—
880	C₂	—	4	1	no	—
881	C₂	—	8	1	no	—
882	C₂	—	8	1	no	—
883	C₂	—	8	1	no	—
884	C₂	#3496	1	1	yes	characteristic
885	C₂	C₂×#575	1	1	yes	characteristic
886	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 ◁ 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. #3520	C₂	semidirect
2. #3505	C₂	semidirect
3. #3352	C₂	semidirect
4. #3349	C₂	semidirect
5. #3345	C₂	semidirect
6. #3337	C₂	semidirect
7. #3327	C₂	semidirect
8. #3323	C₂	semidirect
9. #3320	C₂	semidirect
10. #3315	C₂	semidirect
11. #3311	C₂	semidirect
12. #3308	C₂	semidirect
13. #3301	C₂	semidirect
14. #3300	C₂	semidirect
15. #3285	C₂	semidirect
16. #3275	C₂	semidirect
17. #3270	C₂	semidirect
18. #3267	C₂	semidirect
19. #3256	C₂	semidirect
20. #3252	C₂	semidirect
21. #3197	C₂	semidirect
22. #3196	C₂	semidirect
23. #3196	C₂	semidirect
24. #3193	C₂	semidirect
25. #3183	C₂	semidirect
26. #3172	C₂	semidirect
27. #3056	C₂	semidirect
28. #3055	C₂	semidirect
29. #3054	C₂	semidirect
30. C₂×#470	C₂	semidirect
31. D₄×M₁₆	C₂	semidirect
32. C₂×#137	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×#135	C₂²	semidirect
35. C₂²×Q₁₆	C₂²	semidirect
37. C₂²×M₁₆	C₂²	semidirect
47. #552	C₂²	semidirect
52. D₄×Q₈	C₂²	semidirect
56. #548	C₂²	semidirect
58. #547	C₂²	semidirect
68. #533	C₂²	semidirect
71. #529	C₂²	semidirect
75. #525	C₂²	semidirect
78. C₂×C₂²⋊Q₈	C₂²	semidirect
83. #501	C₂²	semidirect
84. #499	C₂²	semidirect
85. #497	C₂²	semidirect
86. #495	C₂²	semidirect
87. #491	C₂²	semidirect
88. #489	C₂²	semidirect
89. #488	C₂²	semidirect
90. #488	C₂²	semidirect
91. #485	C₂²	semidirect
92. #485	C₂²	semidirect
93. #485	C₂²	semidirect
94. #485	C₂²	semidirect
95. #485	C₂²	semidirect
96. #485	C₂²	semidirect
97. #484	C₂²	semidirect
98. #484	C₂²	semidirect
99. #484	C₂²	semidirect
100. #484	C₂²	semidirect
101. #482	C₂²	semidirect
102. #482	C₂²	semidirect
103. #481	C₂²	semidirect
104. #481	C₂²	semidirect
105. #480	C₂²	semidirect
106. #480	C₂²	semidirect
107. #479	C₂²	semidirect
108. #479	C₂²	semidirect
109. #479	C₂²	semidirect
110. #479	C₂²	semidirect
111. #478	C₂²	semidirect
112. #478	C₂²	semidirect
113. #477	C₂²	semidirect
114. #476	C₂²	semidirect
115. #470	C₂²	semidirect
116. #470	C₂²	semidirect
117. #470	C₂²	semidirect
118. #470	C₂²	semidirect
119. #470	C₂²	semidirect
120. #470	C₂²	semidirect
121. #470	C₂²	semidirect
122. #470	C₂²	semidirect
123. #470	C₂²	semidirect
124. #470	C₂²	semidirect
125. #470	C₂²	semidirect
128. #469	C₂²	semidirect
135. #468	C₂²	semidirect
136. #468	C₂²	semidirect
137. #468	C₂²	semidirect
138. #468	C₂²	semidirect
139. #467	C₂²	semidirect
140. #467	C₂²	semidirect
141. #466	C₂²	semidirect
142. #466	C₂²	semidirect
143. #465	C₂²	semidirect
144. #465	C₂²	semidirect
145. #465	C₂²	semidirect
146. #465	C₂²	semidirect
147. #464	C₂²	semidirect
148. #464	C₂²	semidirect
149. #464	C₂²	semidirect
150. #464	C₂²	semidirect
151. #463	C₂²	semidirect
152. #463	C₂²	semidirect
153. #462	C₂²	semidirect
154. #461	C₂²	semidirect
155. #452	C₂²	semidirect
156. #452	C₂²	semidirect
157. #452	C₂²	semidirect
158. #452	C₂²	semidirect
159. #452	C₂²	semidirect
160. #452	C₂²	semidirect
161. #451	C₂²	semidirect
162. #451	C₂²	semidirect
163. #450	C₂²	semidirect
164. #450	C₂²	semidirect
165. #449	C₂²	semidirect
166. #449	C₂²	semidirect
167. #448	C₂²	semidirect
168. #448	C₂²	semidirect
169. #448	C₂²	semidirect
170. #448	C₂²	semidirect
171. #442	C₂²	semidirect
172. #441	C₂²	semidirect
173. #440	C₂²	semidirect
174. #440	C₂²	semidirect
175. C₄×Q₁₆	C₂²	semidirect
176. C₄×Q₁₆	C₂²	semidirect
177. C₄×SD₁₆	C₂²	semidirect
178. C₄×SD₁₆	C₂²	semidirect
183. #435	C₂²	semidirect
184. #435	C₂²	semidirect
185. C₈×D₄	C₂²	semidirect
186. C₈×D₄	C₂²	semidirect
187. #428	C₂²	semidirect
188. #428	C₂²	semidirect
189. #427	C₂²	semidirect
190. C₂×#106	C₂²	semidirect
191. #423	C₂²	semidirect
192. #419	C₂²	semidirect
193. #418	C₂²	semidirect
194. #417	C₂²	semidirect
195. #417	C₂²	semidirect
196. #416	C₂²	semidirect
197. #416	C₂²	semidirect
198. C₂×#103	C₂²	semidirect
199. C₂×#103	C₂²	semidirect
201. #407	C₂²	semidirect
202. C₄×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3520	2
#3505	2
#3352	2
#3349	2
#3345	2
#3337	2
#3327	2
#3323	2
#3320	2
#3315	2
#3311	2
#3308	2
#3301	2
#3300	2
#3285	2
#3275	2
#3270	2
#3267	2
#3256	2
#3252	2
#3197	2
#3196	2
#3193	2
#3183	2
#3172	2
#3056	2
#3055	2
#3054	2
C₂×#470	2
D₄×M₁₆	2