Subgroups — #60324

Order 256.

947 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3481	C₂	1	1	yes	maximal, characteristic
2	#2995	C₂	1	2	yes	maximal, complemented
3	#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	#2978	C₂	1	2	yes	maximal, complemented
9	#2976	C₂	1	2	yes	maximal, complemented
10	#2975	C₂	1	1	yes	maximal, characteristic, complemented
11	#2974	C₂	1	1	yes	maximal, characteristic, complemented
12	#2973	C₂	1	2	yes	maximal, complemented
13	#2971	C₂	1	1	yes	maximal, characteristic, complemented
14	#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	#2967	C₂	1	2	yes	maximal, complemented
16	#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×M₁₆	C₂	1	2	yes	maximal, complemented
20	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
21	#2933	C₂	1	2	yes	maximal, complemented
22	#2930	C₂	1	2	yes	maximal, complemented
23	C₂×#436	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#131	C₂²	1	2	yes	complemented
25	C₂²×M₁₆	C₂²	1	2	yes	complemented
26	C₂²×M₁₆	C₂²	1	2	yes	complemented
27	#559	C₄	1	1	yes	characteristic
28	#554	C₄	1	1	yes	characteristic
29	#554	C₄	1	1	yes	characteristic
30	#553	C₄	1	1	yes	characteristic
31	#553	C₄	1	1	yes	characteristic
32	#553	C₄	1	2	yes	—
33	#551	C₄	1	2	yes	—
34	#551	C₄	1	2	yes	—
35	#546	C₄	1	2	yes	—
36	#546	C₄	1	1	yes	characteristic
37	#546	C₄	1	1	yes	characteristic
38	D₄²	C₄	1	1	yes	characteristic
39	#532	C₂²	1	1	yes	characteristic
40	#529	C₂²	1	1	yes	characteristic
41	#529	C₂²	1	2	yes	—
42	#529	C₂²	1	1	yes	characteristic
43	#525	C₂²	1	2	yes	—
44	#525	C₂²	1	2	yes	—
45	C₄×#41	C₂²	1	1	yes	characteristic
46	C₄×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄	C₂²	1	2	yes	—
49	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
50	#446	C₂²	1	1	yes	characteristic, complemented
51	#446	C₂²	1	1	yes	characteristic, complemented
52	#446	C₂²	1	1	yes	characteristic, complemented
53	#446	C₂²	1	2	yes	complemented
54	#446	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
57	#436	C₂²	1	1	yes	characteristic
58	#436	C₂²	1	1	yes	characteristic
59	#436	C₂²	1	1	yes	characteristic
60	#436	C₂²	1	1	yes	characteristic
61	#436	C₂²	1	2	yes	complemented
62	#436	C₂²	1	1	yes	characteristic, complemented
63	#436	C₂²	1	2	yes	complemented
64	#436	C₂²	1	1	yes	characteristic, complemented
65	#436	C₂²	1	1	yes	characteristic, complemented
66	#436	C₂²	1	2	yes	complemented
67	#436	C₂²	1	2	yes	complemented
68	#436	C₂²	1	2	yes	complemented
69	#436	C₂²	1	2	yes	complemented
70	#436	C₂²	1	1	yes	characteristic, complemented
71	#436	C₂²	1	1	yes	characteristic, complemented
72	#436	C₂²	1	1	yes	characteristic, complemented
73	#436	C₂²	1	2	yes	complemented
74	#436	C₂²	1	2	yes	complemented
75	#435	C₂²	1	1	yes	characteristic
76	#435	C₂²	1	2	yes	—
77	#435	C₂²	1	1	yes	characteristic
78	#435	C₂²	1	2	yes	complemented
79	#435	C₂²	1	2	yes	complemented
80	#435	C₂²	1	2	yes	complemented
81	#435	C₂²	1	2	yes	complemented
82	#435	C₂²	1	1	yes	characteristic, complemented
83	#435	C₂²	1	2	yes	complemented
84	#435	C₂²	1	2	yes	complemented
85	#435	C₂²	1	2	yes	complemented
86	#435	C₂²	1	2	yes	complemented
87	#435	C₂²	1	2	yes	complemented
88	#435	C₂²	1	2	yes	complemented
89	#435	C₂²	1	2	yes	complemented
90	#435	C₂²	1	1	yes	characteristic, complemented
91	#435	C₂²	1	2	yes	complemented
92	#435	C₂²	1	2	yes	complemented
93	#435	C₂²	1	2	yes	complemented
94	#435	C₂²	1	2	yes	complemented
95	C₈×D₄	C₂²	1	2	yes	complemented
96	C₈×D₄	C₂²	1	2	yes	complemented
97	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
98	C₈×D₄	C₂²	1	2	yes	complemented
99	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
100	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
101	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
102	#433	C₂²	1	2	yes	complemented
103	#433	C₂²	1	2	yes	complemented
104	#433	C₂²	1	2	yes	complemented
105	#433	C₂²	1	2	yes	complemented
106	#432	C₂²	1	1	yes	characteristic, complemented
107	#432	C₂²	1	2	yes	complemented
108	#432	C₂²	1	2	yes	complemented
109	#432	C₂²	1	1	yes	characteristic, complemented
110	#431	C₂²	1	1	yes	characteristic, complemented
111	#431	C₂²	1	1	yes	characteristic, complemented
112	#431	C₂²	1	1	yes	characteristic, complemented
113	#431	C₂²	1	1	yes	characteristic, complemented
114	#424	C₂²	1	2	yes	complemented
115	#424	C₂²	1	2	yes	complemented
116	#423	C₂²	1	2	yes	complemented
117	#423	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
120	#408	C₂²	1	2	yes	complemented
121	#408	C₂²	1	2	yes	complemented
122	#408	C₂²	1	2	yes	complemented
123	#407	C₂²	1	2	yes	complemented
124	#407	C₂²	1	2	yes	complemented
125	#407	C₂²	1	2	yes	complemented
126	#407	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
128	C₂×C₂²⋊C₈	C₂²	1	2	yes	complemented
129	#405	C₂²	1	2	yes	complemented
130	#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
132	C₄×M₁₆	C₂²	1	2	yes	complemented
133	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	C₂×C₄	1	1	yes	characteristic
136	C₂×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×#41	C₂³	1	2	yes	—
138	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
139	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
140	C₂²×D₄	C₂×C₄	1	2	yes	—
141	C₂³×C₄	C₂³	1	2	yes	—
142	C₂³×C₄	C₂³	1	2	yes	—
143	#131	—	4	4	no	—
144	C₂×M₁₆	—	4	4	no	—
145	C₂×M₁₆	—	4	4	no	—
146	C₂×M₁₆	C₂³	1	1	yes	characteristic
147	C₂×M₁₆	C₂³	1	2	yes	—
148	C₂×M₁₆	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	1	yes	characteristic
150	C₂×M₁₆	C₂³	1	2	yes	—
151	C₂×M₁₆	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	2	yes	—
153	C₂×M₁₆	C₂³	1	2	yes	—
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂²×C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	2	yes	—
163	C₂²×C₈	C₂³	1	2	yes	—
164	C₂²×C₈	C₂³	1	2	yes	—
165	C₂²×C₈	C₂³	1	1	yes	characteristic
166	C₂²×C₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
168	#127	C₂×C₄	1	1	yes	characteristic
169	#126	C₂×C₄	1	2	yes	—
170	#126	C₂×C₄	1	2	yes	—
171	#126	C₂×C₄	1	2	yes	—
172	#126	C₂×C₄	1	2	yes	—
173	#125	C₂×C₄	1	1	yes	characteristic
174	#125	C₂×C₄	1	2	yes	—
175	#125	C₂×C₄	1	1	yes	characteristic
176	#124	C₂×C₄	1	1	yes	characteristic
177	#124	C₂×C₄	1	1	yes	characteristic
178	#124	C₂×C₄	1	2	yes	—
179	#124	C₂×C₄	1	2	yes	—
180	#123	C₂×C₄	1	2	yes	—
181	#123	C₂×C₄	1	2	yes	—
182	#123	C₂×C₄	1	2	yes	—
183	#123	C₂×C₄	1	2	yes	—
184	#123	C₂×C₄	1	2	yes	—
185	#123	C₂×C₄	1	2	yes	—
186	#123	C₂×C₄	1	2	yes	—
187	#123	C₂×C₄	1	2	yes	—
188	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
193	C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	#121	C₂×C₄	1	2	yes	—
196	#121	C₂×C₄	1	2	yes	—
197	#121	C₂×C₄	1	2	yes	—
198	#121	C₂×C₄	1	2	yes	—
199	#121	C₂×C₄	1	1	yes	characteristic
200	#121	C₂×C₄	1	1	yes	characteristic
201	#121	C₂×C₄	1	2	yes	—
202	#121	C₂×C₄	1	1	yes	characteristic
203	#121	C₂×C₄	1	1	yes	characteristic
204	#121	C₂×C₄	1	2	yes	—
205	#120	C₂×C₄	1	2	yes	—
206	#120	C₂×C₄	1	2	yes	—
207	#120	C₂×C₄	1	2	yes	—
208	#120	C₂×C₄	1	2	yes	—
209	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
210	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
211	C₄×Q₈	C₂³	1	1	yes	characteristic
212	C₄×Q₈	C₂³	1	1	yes	characteristic
213	C₄×D₄	C₂×C₄	1	1	yes	characteristic
214	C₄×D₄	C₂×C₄	1	2	yes	—
215	C₄×D₄	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄	C₂×C₄	1	2	yes	—
217	C₄×D₄	C₂×C₄	1	2	yes	—
218	C₄×D₄	C₂×C₄	1	2	yes	—
219	C₄×D₄	C₂×C₄	1	2	yes	—
220	C₄×D₄	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄	C₂×C₄	1	1	yes	characteristic
222	C₄×D₄	C₂×C₄	1	2	yes	—
223	C₄×D₄	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄	C₂×C₄	1	1	yes	characteristic
225	C₄×D₄	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄	C₂×C₄	1	2	yes	—
228	C₄×D₄	C₂³	1	1	yes	characteristic
229	C₄×D₄	C₂³	1	1	yes	characteristic
230	C₄×D₄	C₂³	1	2	yes	—
231	C₄×D₄	C₂³	1	2	yes	—
232	C₄×D₄	C₂³	1	2	yes	—
233	C₄×D₄	C₂³	1	2	yes	—
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	1	yes	characteristic
236	C₄×D₄	C₂³	1	2	yes	—
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	2	yes	—
240	#117	C₂×C₄	1	1	yes	characteristic
241	#117	C₂×C₄	1	1	yes	characteristic
242	#117	C₂×C₄	1	2	yes	—
243	#117	C₂×C₄	1	1	yes	characteristic
244	#117	C₂×C₄	1	1	yes	characteristic
245	#117	C₂³	1	2	yes	—
246	#117	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
254	C₂×C₄²	C₂³	1	1	yes	characteristic
255	C₂×C₄²	C₂³	1	1	yes	characteristic
256	C₂×C₄²	C₂³	1	2	yes	—
257	C₂×C₄²	C₂³	1	1	yes	characteristic
258	C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₄⋊C₈	C₂³	1	2	yes	—
262	C₄⋊C₈	C₂³	1	2	yes	—
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	2	yes	—
265	C₄⋊C₈	C₂³	1	2	yes	—
266	C₄⋊C₈	C₂³	1	2	yes	—
267	C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₄⋊C₈	C₂³	1	2	yes	—
270	C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₄⋊C₈	C₂³	1	2	yes	—
275	C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂²⋊C₈	C₂³	1	2	yes	—
279	C₂²⋊C₈	C₂³	1	2	yes	—
280	C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂²⋊C₈	C₂³	1	2	yes	—
289	C₂²⋊C₈	C₂³	1	2	yes	—
290	C₂²⋊C₈	C₂³	1	2	yes	—
291	C₂²⋊C₈	C₂³	1	2	yes	—
292	C₂²⋊C₈	C₂³	1	2	yes	—
293	C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈	C₂³	1	2	yes	—
296	#97	C₂³	1	1	yes	characteristic
297	#97	C₂³	1	1	yes	characteristic
298	#97	C₂³	1	2	yes	—
299	#97	C₂³	1	1	yes	characteristic
300	#97	C₂³	1	1	yes	characteristic
301	#97	C₂³	1	2	yes	—
302	#97	C₂³	1	2	yes	—
303	#97	C₂³	1	2	yes	—
304	C₄×C₈	C₂³	1	1	yes	characteristic
305	C₄×C₈	C₂³	1	1	yes	characteristic
306	C₄×C₈	C₂³	1	1	yes	characteristic
307	C₄×C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	2	yes	—
313	C₂⁴	C₂²×C₄	1	2	yes	—
314	C₂⁴	C₂²×C₄	1	2	yes	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
320	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈	C₂²×C₄	1	2	yes	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄	C₂²×C₄	1	2	yes	—
329	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
331	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₄	C₂²×C₄	1	2	yes	—
333	C₂×D₄	C₂²×C₄	1	2	yes	—
334	C₂×D₄	C₂²×C₄	1	2	yes	—
335	C₂×D₄	C₂²×C₄	1	2	yes	—
336	C₂×D₄	C₂²×C₄	1	2	yes	—
337	C₂×D₄	C₂²×C₄	1	2	yes	—
338	C₂×D₄	C₂²×C₄	1	2	yes	—
339	C₂×D₄	C₂²×C₄	1	2	yes	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄	1	2	yes	—
350	C₂²×C₄	C₂²×C₄	1	2	yes	—
351	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄	1	2	yes	—
353	C₂²×C₄	C₂²×C₄	1	2	yes	—
354	C₂²×C₄	C₂²×C₄	1	2	yes	—
355	C₂²×C₄	C₂²×C₄	1	2	yes	—
356	C₂²×C₄	C₂²×C₄	1	2	yes	—
357	C₂²×C₄	C₂²×C₄	1	2	yes	—
358	C₂²×C₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴	1	2	yes	—
361	C₂²×C₄	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴	1	2	yes	—
363	C₂²×C₄	C₂⁴	1	2	yes	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	2	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	4	1	no	—
373	M₁₆	—	4	2	no	—
374	M₁₆	—	4	2	no	—
375	M₁₆	—	4	1	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	4	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	—	4	1	no	—
381	C₂×C₈	—	4	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	—	4	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	2	yes	—
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₈	C₂⁴	1	2	yes	—
394	C₂×C₈	C₂⁴	1	2	yes	—
395	C₂×C₈	C₂⁴	1	2	yes	—
396	C₂×C₈	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊C₄	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
419	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
437	C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
438	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
443	C₄²	C₂²×C₄	1	1	yes	characteristic
444	C₄²	C₂²×C₄	1	1	yes	characteristic
445	C₄²	C₂²×C₄	1	1	yes	characteristic
446	C₄²	C₂²×C₄	1	2	yes	—
447	C₄²	C₂²×C₄	1	2	yes	—
448	C₄²	C₂²×C₄	1	1	yes	characteristic
449	C₄²	C₂²×C₄	1	1	yes	characteristic
450	C₄²	C₂²×C₄	1	1	yes	characteristic
451	C₄²	C₂⁴	1	1	yes	characteristic
452	C₄²	C₂⁴	1	1	yes	characteristic
453	C₄²	C₂⁴	1	2	yes	—
454	C₄²	C₂⁴	1	1	yes	characteristic
455	C₄²	C₂⁴	1	1	yes	characteristic
456	C₂³	—	2	4	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	C₂³×C₄	1	2	yes	—
463	C₂³	C₂³×C₄	1	2	yes	—
464	C₂³	C₂³×C₄	1	1	yes	characteristic
465	C₂³	C₂³×C₄	1	2	yes	—
466	C₂³	C₂³×C₄	1	1	yes	characteristic
467	C₂³	C₂³×C₄	1	1	yes	characteristic
468	Q₈	—	2	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	1	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
513	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₄	1	2	yes	—
518	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
519	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
520	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄	C₂³×C₄	1	2	yes	—
522	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄	C₂³×C₄	1	2	yes	—
525	C₂×C₄	C₂³×C₄	1	2	yes	—
526	C₂×C₄	C₂³×C₄	1	2	yes	—
527	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
528	C₂×C₄	C₂⁵	1	1	yes	characteristic
529	C₈	—	2	2	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	2	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	2	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	H(5,𝔽₂)	1	2	yes	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	#568	1	2	yes	—
561	C₂²	C₂⁴×C₄	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	#568	1	2	yes	—
578	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₄	#585	1	1	yes	characteristic
580	C₂	—	2	2	no	—
581	C₂	—	4	1	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	1	no	—
585	C₂	—	4	2	no	—
586	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂	C₂×#568	1	1	yes	characteristic
588	C₂	C₂×#568	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3481	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2995	C₂	semidirect
3. #2994	C₂	semidirect
4. #2993	C₂	semidirect
5. #2990	C₂	semidirect
6. #2989	C₂	semidirect
7. #2981	C₂	semidirect
8. #2978	C₂	semidirect
9. #2976	C₂	semidirect
10. #2975	C₂	semidirect
11. #2974	C₂	semidirect
12. #2973	C₂	semidirect
13. #2971	C₂	semidirect
14. #2969	C₂	semidirect
15. #2967	C₂	semidirect
16. #2966	C₂	semidirect
17. #2965	C₂	semidirect
18. #2935	C₂	semidirect
19. D₄×M₁₆	C₂	semidirect
20. D₄×M₁₆	C₂	semidirect
21. #2933	C₂	semidirect
22. #2930	C₂	semidirect
23. C₂×#436	C₂	semidirect
24. C₂×#131	C₂²	semidirect
25. C₂²×M₁₆	C₂²	semidirect
26. C₂²×M₁₆	C₂²	semidirect
50. #446	C₂²	semidirect
51. #446	C₂²	semidirect
52. #446	C₂²	semidirect
53. #446	C₂²	semidirect
54. #446	C₂²	semidirect
55. C₈×Q₈	C₂²	semidirect
56. C₈×Q₈	C₂²	semidirect
61. #436	C₂²	semidirect
62. #436	C₂²	semidirect
63. #436	C₂²	semidirect
64. #436	C₂²	semidirect
65. #436	C₂²	semidirect
66. #436	C₂²	semidirect
67. #436	C₂²	semidirect
68. #436	C₂²	semidirect
69. #436	C₂²	semidirect
70. #436	C₂²	semidirect
71. #436	C₂²	semidirect
72. #436	C₂²	semidirect
73. #436	C₂²	semidirect
74. #436	C₂²	semidirect
78. #435	C₂²	semidirect
79. #435	C₂²	semidirect
80. #435	C₂²	semidirect
81. #435	C₂²	semidirect
82. #435	C₂²	semidirect
83. #435	C₂²	semidirect
84. #435	C₂²	semidirect
85. #435	C₂²	semidirect
86. #435	C₂²	semidirect
87. #435	C₂²	semidirect
88. #435	C₂²	semidirect
89. #435	C₂²	semidirect
90. #435	C₂²	semidirect
91. #435	C₂²	semidirect
92. #435	C₂²	semidirect
93. #435	C₂²	semidirect
94. #435	C₂²	semidirect
95. C₈×D₄	C₂²	semidirect
96. C₈×D₄	C₂²	semidirect
97. C₈×D₄	C₂²	semidirect
98. C₈×D₄	C₂²	semidirect
99. C₈×D₄	C₂²	semidirect
100. C₈×D₄	C₂²	semidirect
101. C₈×D₄	C₂²	semidirect
102. #433	C₂²	semidirect
103. #433	C₂²	semidirect
104. #433	C₂²	semidirect
105. #433	C₂²	semidirect
106. #432	C₂²	semidirect
107. #432	C₂²	semidirect
108. #432	C₂²	semidirect
109. #432	C₂²	semidirect
110. #431	C₂²	semidirect
111. #431	C₂²	semidirect
112. #431	C₂²	semidirect
113. #431	C₂²	semidirect
114. #424	C₂²	semidirect
115. #424	C₂²	semidirect
116. #423	C₂²	semidirect
117. #423	C₂²	semidirect
118. C₂×C₄⋊C₈	C₂²	semidirect
119. C₂×C₄⋊C₈	C₂²	semidirect
120. #408	C₂²	semidirect
121. #408	C₂²	semidirect
122. #408	C₂²	semidirect
123. #407	C₂²	semidirect
124. #407	C₂²	semidirect
125. #407	C₂²	semidirect
126. #407	C₂²	semidirect
127. C₂×C₂²⋊C₈	C₂²	semidirect
128. C₂×C₂²⋊C₈	C₂²	semidirect
129. #405	C₂²	semidirect
130. #405	C₂²	semidirect
131. C₄×M₁₆	C₂²	semidirect
132. C₄×M₁₆	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3481	2
#2995	2
#2994	2
#2993	2
#2990	2
#2989	2
#2981	2
#2978	2
#2976	2
#2975	2
#2974	2
#2973	2
#2971	2
#2969	2
#2967	2
#2966	2
#2965	2
#2935	2
D₄×M₁₆	2
#2933	2
#2930	2
C₂×#436	2