Subgroups — #60979

Order 256.

898 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	#3260	C₂	1	2	yes	maximal, complemented
4	#3257	C₂	1	2	yes	maximal, complemented
5	#3241	C₂	1	2	yes	maximal, complemented
6	#3236	C₂	1	1	yes	maximal, characteristic, complemented
7	#3232	C₂	1	1	yes	maximal, characteristic, complemented
8	#3221	C₂	1	2	yes	maximal, complemented
9	#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	#3208	C₂	1	1	yes	maximal, characteristic, complemented
11	#3194	C₂	1	1	yes	maximal, characteristic, complemented
12	#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	#3188	C₂	1	1	yes	maximal, characteristic, complemented
14	#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	#3179	C₂	1	2	yes	maximal, complemented
16	#3174	C₂	1	2	yes	maximal, complemented
17	#3126	C₂	1	2	yes	maximal, complemented
18	#3119	C₂	1	2	yes	maximal, complemented
19	#3114	C₂	1	1	yes	maximal, characteristic, complemented
20	#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#556	—	2	1	no	—
25	#554	—	2	1	no	—
26	#552	—	2	1	no	—
27	#552	—	2	1	no	—
28	#552	—	2	1	no	—
29	#552	—	2	1	no	—
30	#551	—	2	1	no	—
31	#551	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic, complemented
33	#542	C₂²	1	1	yes	characteristic, complemented
34	#542	C₂²	1	1	yes	characteristic, complemented
35	#541	C₂²	1	1	yes	characteristic, complemented
36	#541	C₂²	1	1	yes	characteristic, complemented
37	#540	—	2	1	no	—
38	#540	—	2	1	no	—
39	#540	—	2	1	no	—
40	#540	—	2	1	no	—
41	#540	C₂²	1	2	yes	—
42	#540	C₂²	1	2	yes	—
43	#540	C₂²	1	2	yes	—
44	#540	C₂²	1	2	yes	—
45	#536	C₂²	1	1	yes	characteristic, complemented
46	#533	C₂²	1	1	yes	characteristic
47	#533	C₂²	1	1	yes	characteristic
48	C₂×#127	C₂²	1	1	yes	characteristic
49	#529	C₂²	1	1	yes	characteristic
50	#529	C₂²	1	1	yes	characteristic
51	C₂×#125	C₂²	1	1	yes	characteristic
52	#525	C₂²	1	1	yes	characteristic
53	C₂×#123	—	2	1	no	—
54	C₂×#123	—	2	1	no	—
55	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×#121	—	2	1	no	—
57	C₂×#121	—	2	1	no	—
58	C₂×#121	C₂²	1	1	yes	characteristic
59	C₂×#121	C₂²	1	1	yes	characteristic
60	#520	C₂²	1	1	yes	characteristic, complemented
61	#519	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
64	C₂×#117	C₂²	1	1	yes	characteristic
65	#501	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#496	C₂²	1	2	yes	complemented
68	#492	C₂²	1	2	yes	complemented
69	#491	C₂²	1	2	yes	complemented
70	#490	C₂²	1	2	yes	complemented
71	#488	C₂²	1	2	yes	complemented
72	#486	C₂²	1	2	yes	complemented
73	#484	C₂²	1	1	yes	characteristic
74	#484	C₂²	1	1	yes	characteristic
75	#484	C₂²	1	1	yes	characteristic
76	#483	C₂²	1	1	yes	characteristic
77	#483	C₂²	1	1	yes	characteristic
78	#483	C₂²	1	1	yes	characteristic
79	#482	C₂²	1	2	yes	complemented
80	#482	C₂²	1	2	yes	complemented
81	#481	C₂²	1	1	yes	characteristic
82	#481	C₂²	1	2	yes	complemented
83	#480	C₂²	1	1	yes	characteristic
84	#480	C₂²	1	2	yes	complemented
85	#479	C₂²	1	2	yes	complemented
86	#479	C₂²	1	2	yes	complemented
87	#479	C₂²	1	2	yes	complemented
88	#478	C₂²	1	2	yes	complemented
89	#478	C₂²	1	2	yes	complemented
90	#478	C₂²	1	2	yes	complemented
91	#476	C₂²	1	2	yes	complemented
92	#474	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	#468	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	#465	C₂²	1	2	yes	complemented
101	#463	C₂²	1	2	yes	complemented
102	#463	C₂²	1	2	yes	complemented
103	#461	C₂²	1	2	yes	complemented
104	#461	C₂²	1	2	yes	complemented
105	#460	C₂²	1	2	yes	complemented
106	#460	C₂²	1	2	yes	complemented
107	#460	C₂²	1	2	yes	complemented
108	#459	C₂²	1	2	yes	complemented
109	#450	C₂²	1	1	yes	characteristic
110	#450	C₂²	1	1	yes	characteristic
111	#450	C₂²	1	1	yes	characteristic
112	#450	C₂²	1	1	yes	characteristic
113	#450	C₂²	1	1	yes	characteristic
114	#450	C₂²	1	1	yes	characteristic
115	#449	C₂²	1	2	yes	complemented
116	#449	C₂²	1	2	yes	complemented
117	#448	C₂²	1	2	yes	complemented
118	#448	C₂²	1	2	yes	complemented
119	#447	C₂²	1	1	yes	characteristic
120	#447	C₂²	1	1	yes	characteristic
121	#442	C₂²	1	2	yes	complemented
122	#440	C₂²	1	2	yes	complemented
123	#440	C₂²	1	2	yes	complemented
124	#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆	C₂²	1	2	yes	complemented
126	C₄×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×SD₁₆	C₂²	1	2	yes	complemented
128	C₄×D₈	C₂²	1	2	yes	complemented
129	#433	C₂²	1	2	yes	complemented
130	#433	C₂²	1	2	yes	complemented
131	#432	C₂²	1	1	yes	characteristic
132	#432	C₂²	1	1	yes	characteristic
133	#431	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic
135	#424	C₂²	1	2	yes	complemented
136	#407	C₂²	1	1	yes	characteristic
137	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	#405	C₂²	1	2	yes	complemented
139	C₂×#41	C₂³	1	1	yes	characteristic
140	C₂²×Q₈	C₂³	1	1	yes	characteristic
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	C₂³	1	1	yes	characteristic
146	C₂²×D₄	C₂³	1	1	yes	characteristic
147	C₂³×C₄	—	2	1	no	—
148	C₂³×C₄	—	2	1	no	—
149	C₂³×C₄	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×D₈	C₂³	1	2	yes	—
157	C₂×D₈	C₂³	1	2	yes	—
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	#127	—	2	1	no	—
166	#127	—	2	1	no	—
167	#127	C₂³	1	2	yes	—
168	#127	C₂³	1	2	yes	—
169	#126	—	2	1	no	—
170	#126	—	2	1	no	—
171	#126	—	2	1	no	—
172	#126	—	2	1	no	—
173	#126	—	2	1	no	—
174	#126	—	2	1	no	—
175	#126	—	2	1	no	—
176	#126	—	2	1	no	—
177	#125	—	2	1	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	—	2	1	no	—
181	#125	—	2	1	no	—
182	#125	—	2	1	no	—
183	#125	—	2	1	no	—
184	#125	—	2	1	no	—
185	#125	—	2	1	no	—
186	#125	C₂³	1	2	yes	—
187	#125	C₂³	1	2	yes	—
188	#125	C₂³	1	1	yes	characteristic
189	#125	C₂³	1	1	yes	characteristic
190	#124	—	2	1	no	—
191	#124	—	2	1	no	—
192	#124	C₂³	1	1	yes	characteristic
193	#124	C₂³	1	1	yes	characteristic
194	#123	—	2	1	no	—
195	#123	—	2	1	no	—
196	#123	—	2	1	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	#123	—	2	2	no	—
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	—	2	1	no	—
206	#123	—	2	1	no	—
207	#123	—	2	1	no	—
208	#123	—	2	1	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	1	no	—
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	—	2	1	no	—
213	C₂²⋊Q₈	—	2	1	no	—
214	C₂²⋊Q₈	—	2	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	C₂²⋊Q₈	—	2	1	no	—
218	C₂²⋊Q₈	—	2	1	no	—
219	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	#121	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	—	2	2	no	—
230	#121	—	2	2	no	—
231	#121	—	2	2	no	—
232	#121	—	2	2	no	—
233	#121	—	2	2	no	—
234	#121	—	2	2	no	—
235	#121	—	2	2	no	—
236	#121	—	2	2	no	—
237	#121	C₂³	1	2	yes	—
238	#121	C₂³	1	2	yes	—
239	#121	C₂³	1	2	yes	—
240	#121	C₂³	1	2	yes	—
241	#121	C₂³	1	1	yes	characteristic
242	#121	C₂³	1	1	yes	characteristic
243	#120	—	2	1	no	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₄×Q₈	C₂³	1	1	yes	characteristic
253	C₄×Q₈	C₂³	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	C₂³	1	2	yes	—
265	C₄×D₄	C₂³	1	2	yes	—
266	C₄×D₄	C₂³	1	2	yes	—
267	C₄×D₄	C₂³	1	2	yes	—
268	C₄×D₄	C₂³	1	1	yes	characteristic
269	C₄×D₄	C₂³	1	1	yes	characteristic
270	#117	—	2	1	no	—
271	#117	—	2	1	no	—
272	#117	—	2	1	no	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	—	2	1	no	—
276	#117	—	2	1	no	—
277	#117	D₄	1	1	yes	characteristic
278	#117	D₄	1	1	yes	characteristic
279	#117	D₄	1	1	yes	characteristic
280	#117	D₄	1	1	yes	characteristic
281	#117	C₂³	1	1	yes	characteristic
282	#117	C₂³	1	1	yes	characteristic
283	#117	C₂³	1	1	yes	characteristic
284	#117	C₂³	1	1	yes	characteristic
285	#117	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
291	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	1	yes	characteristic
304	#107	C₂³	1	2	yes	—
305	#107	C₂³	1	2	yes	—
306	#107	C₂³	1	2	yes	—
307	#107	C₂³	1	2	yes	—
308	#106	C₂³	1	2	yes	—
309	#106	C₂³	1	2	yes	—
310	#106	C₂³	1	2	yes	—
311	#106	C₂³	1	2	yes	—
312	C₄⋊C₈	C₂³	1	2	yes	—
313	C₄⋊C₈	C₂³	1	2	yes	—
314	C₄⋊C₈	C₂³	1	2	yes	—
315	C₄⋊C₈	C₂³	1	2	yes	—
316	#103	C₂³	1	2	yes	—
317	#103	C₂³	1	2	yes	—
318	#103	C₂³	1	2	yes	—
319	#103	C₂³	1	2	yes	—
320	#103	C₂³	1	2	yes	—
321	#103	C₂³	1	2	yes	—
322	#102	C₂³	1	2	yes	—
323	#102	C₂³	1	2	yes	—
324	#102	C₂³	1	2	yes	—
325	#102	C₂³	1	2	yes	—
326	#102	C₂³	1	2	yes	—
327	#102	C₂³	1	2	yes	—
328	#102	C₂³	1	2	yes	—
329	#102	C₂³	1	2	yes	—
330	#102	C₂³	1	2	yes	—
331	#102	C₂³	1	2	yes	—
332	C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈	C₂³	1	2	yes	—
338	#97	C₂³	1	2	yes	—
339	#97	C₂³	1	2	yes	—
340	C₄×C₈	C₂³	1	2	yes	—
341	C₄×C₈	C₂³	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	—	2	1	no	—
344	C₂⁴	C₂×D₄	1	1	yes	characteristic
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	C₂⁴	1	1	yes	characteristic
351	C₂×Q₈	C₂⁴	1	1	yes	characteristic
352	C₂×Q₈	C₂⁴	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	—	8	2	no	—
370	C₂×D₄	—	8	2	no	—
371	C₂×D₄	—	8	2	no	—
372	C₂×D₄	C₂⁴	1	1	yes	characteristic
373	C₂×D₄	C₂⁴	1	2	yes	—
374	C₂×D₄	C₂⁴	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	8	2	no	—
388	C₂²×C₄	—	8	2	no	—
389	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴	1	1	yes	characteristic
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	SD₁₆	—	4	2	no	—
402	SD₁₆	—	4	2	no	—
403	SD₁₆	—	4	2	no	—
404	SD₁₆	—	4	2	no	—
405	D₈	—	4	2	no	—
406	D₈	—	4	2	no	—
407	M₁₆	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	C₂⁴	1	2	yes	—
410	C₂×C₈	C₂⁴	1	2	yes	—
411	C₂×C₈	C₂⁴	1	2	yes	—
412	C₂×C₈	C₂⁴	1	2	yes	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
446	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
452	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
453	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄	C₂⁴	1	2	yes	—
455	C₄⋊C₄	C₂⁴	1	2	yes	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
484	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
485	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	C₂×D₄	1	1	yes	characteristic
495	C₄²	C₂×D₄	1	1	yes	characteristic
496	C₄²	C₂×D₄	1	1	yes	characteristic
497	C₄²	C₂×D₄	1	1	yes	characteristic
498	C₄²	C₂⁴	1	1	yes	characteristic
499	C₄²	C₂⁴	1	1	yes	characteristic
500	C₄²	C₂⁴	1	1	yes	characteristic
501	C₄²	C₂⁴	1	1	yes	characteristic
502	C₂³	—	2	2	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	C₂²×D₄	1	1	yes	characteristic
515	C₂³	C₂²×D₄	1	1	yes	characteristic
516	C₂³	C₂²×D₄	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	8	1	no	—
522	Q₈	—	8	1	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	8	2	no	—
533	D₄	—	8	2	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	2	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	2	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	8	1	no	—
565	C₂×C₄	—	8	1	no	—
566	C₂×C₄	—	8	2	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	1	no	—
571	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄	C₂⁵	1	1	yes	characteristic
583	C₈	—	2	2	no	—
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	2	2	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	4	no	—
606	C₂²	—	8	4	no	—
607	C₂²	#577	1	2	yes	—
608	C₂²	C₂³×D₄	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	1	no	—
629	C₄	#585	1	2	yes	—
630	C₂	—	2	2	no	—
631	C₂	—	4	1	no	—
632	C₂	—	4	1	no	—
633	C₂	—	8	1	no	—
634	C₂	—	8	2	no	—
635	C₂	—	8	2	no	—
636	C₂	#3449	1	1	yes	characteristic
637	C₂	C₂×#577	1	1	yes	characteristic
638	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3495	C₂	semidirect
2. C₂×#540	C₂	semidirect
3. #3260	C₂	semidirect
4. #3257	C₂	semidirect
5. #3241	C₂	semidirect
6. #3236	C₂	semidirect
7. #3232	C₂	semidirect
8. #3221	C₂	semidirect
9. #3217	C₂	semidirect
10. #3208	C₂	semidirect
11. #3194	C₂	semidirect
12. #3193	C₂	semidirect
13. #3188	C₂	semidirect
14. #3187	C₂	semidirect
15. #3179	C₂	semidirect
16. #3174	C₂	semidirect
17. #3126	C₂	semidirect
18. #3119	C₂	semidirect
19. #3114	C₂	semidirect
20. #3110	C₂	semidirect
21. #3105	C₂	semidirect
22. #3101	C₂	semidirect
23. #2924	C₂	semidirect
32. #544	C₂²	semidirect
33. #542	C₂²	semidirect
34. #542	C₂²	semidirect
35. #541	C₂²	semidirect
36. #541	C₂²	semidirect
45. #536	C₂²	semidirect
60. #520	C₂²	semidirect
61. #519	C₂²	semidirect
65. #501	C₂²	semidirect
66. #499	C₂²	semidirect
67. #496	C₂²	semidirect
68. #492	C₂²	semidirect
69. #491	C₂²	semidirect
70. #490	C₂²	semidirect
71. #488	C₂²	semidirect
72. #486	C₂²	semidirect
79. #482	C₂²	semidirect
80. #482	C₂²	semidirect
82. #481	C₂²	semidirect
84. #480	C₂²	semidirect
85. #479	C₂²	semidirect
86. #479	C₂²	semidirect
87. #479	C₂²	semidirect
88. #478	C₂²	semidirect
89. #478	C₂²	semidirect
90. #478	C₂²	semidirect
91. #476	C₂²	semidirect
92. #474	C₂²	semidirect
93. #469	C₂²	semidirect
94. #468	C₂²	semidirect
95. #468	C₂²	semidirect
96. #468	C₂²	semidirect
97. #466	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #465	C₂²	semidirect
101. #463	C₂²	semidirect
102. #463	C₂²	semidirect
103. #461	C₂²	semidirect
104. #461	C₂²	semidirect
105. #460	C₂²	semidirect
106. #460	C₂²	semidirect
107. #460	C₂²	semidirect
108. #459	C₂²	semidirect
115. #449	C₂²	semidirect
116. #449	C₂²	semidirect
117. #448	C₂²	semidirect
118. #448	C₂²	semidirect
121. #442	C₂²	semidirect
122. #440	C₂²	semidirect
123. #440	C₂²	semidirect
124. #440	C₂²	semidirect
125. C₄×SD₁₆	C₂²	semidirect
126. C₄×SD₁₆	C₂²	semidirect
127. C₄×SD₁₆	C₂²	semidirect
128. C₄×D₈	C₂²	semidirect
129. #433	C₂²	semidirect
130. #433	C₂²	semidirect
135. #424	C₂²	semidirect
138. #405	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3495	2
C₂×#540	2
#3260	2
#3257	2
#3241	2
#3236	2
#3232	2
#3221	2
#3217	2
#3208	2
#3194	2
#3193	2
#3188	2
#3187	2
#3179	2
#3174	2
#3126	2
#3119	2
#3114	2
#3110	2
#3105	2
#3101	2
#2924	2