Subgroups — #6345752

Order 512.

1579 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60676	C₂	1	1	yes	maximal, characteristic
2	#60295	C₂	1	1	yes	maximal, characteristic, complemented
3	#60266	C₂	1	1	yes	maximal, characteristic, complemented
4	#18079	C₂	1	2	yes	maximal, complemented
5	#18078	C₂	1	2	yes	maximal, complemented
6	#18077	C₂	1	2	yes	maximal, complemented
7	#18076	C₂	1	2	yes	maximal, complemented
8	#18065	C₂	1	1	yes	maximal, characteristic, complemented
9	#18063	C₂	1	1	yes	maximal, characteristic, complemented
10	#18061	C₂	1	1	yes	maximal, characteristic, complemented
11	#18061	C₂	1	1	yes	maximal, characteristic, complemented
12	#18059	C₂	1	1	yes	maximal, characteristic, complemented
13	#18057	C₂	1	1	yes	maximal, characteristic, complemented
14	#18057	C₂	1	1	yes	maximal, characteristic, complemented
15	#18055	C₂	1	1	yes	maximal, characteristic, complemented
16	#17988	C₂	1	2	yes	maximal, complemented
17	#17987	C₂	1	2	yes	maximal, complemented
18	#17969	C₂	1	2	yes	maximal, complemented
19	#17968	C₂	1	2	yes	maximal, complemented
20	#17796	C₂	1	1	yes	maximal, characteristic, complemented
21	#17504	C₂	1	1	yes	maximal, characteristic, complemented
22	#17503	C₂	1	1	yes	maximal, characteristic, complemented
23	M₁₆²	C₂	1	1	yes	maximal, characteristic, complemented
24	#3444	C₂²	1	1	yes	characteristic
25	#3444	C₂²	1	1	yes	characteristic
26	#3172	C₄	1	1	yes	characteristic
27	#3172	C₄	1	1	yes	characteristic
28	#3172	C₄	1	1	yes	characteristic
29	#3172	C₄	1	1	yes	characteristic
30	#3172	C₂²	1	1	yes	characteristic
31	#3172	C₂²	1	1	yes	characteristic
32	#3172	C₂²	1	1	yes	characteristic
33	#3172	C₂²	1	1	yes	characteristic
34	#3171	C₄	1	1	yes	characteristic
35	#3171	C₄	1	1	yes	characteristic
36	#3171	C₄	1	1	yes	characteristic
37	#3171	C₄	1	1	yes	characteristic
38	#3171	C₂²	1	1	yes	characteristic
39	#3171	C₂²	1	1	yes	characteristic
40	#3171	C₂²	1	1	yes	characteristic
41	#3171	C₂²	1	1	yes	characteristic
42	#3162	C₄	1	1	yes	characteristic
43	#3150	C₄	1	1	yes	characteristic
44	#3135	C₄	1	1	yes	characteristic
45	#3135	C₄	1	1	yes	characteristic
46	#3054	C₄	1	1	yes	characteristic
47	#3054	C₄	1	1	yes	characteristic
48	#3054	C₄	1	1	yes	characteristic
49	#3054	C₄	1	1	yes	characteristic
50	#2995	—	2	2	no	—
51	#2993	C₂²	1	2	yes	—
52	#2993	C₂²	1	2	yes	—
53	#2991	C₂²	1	1	yes	characteristic
54	#2991	C₂²	1	1	yes	characteristic
55	#2991	C₂²	1	1	yes	characteristic
56	#2991	C₂²	1	1	yes	characteristic
57	#2990	C₂²	1	1	yes	characteristic
58	#2990	C₂²	1	1	yes	characteristic
59	#2990	C₂²	1	1	yes	characteristic
60	#2990	C₂²	1	1	yes	characteristic
61	#2989	—	2	1	no	—
62	#2989	—	2	1	no	—
63	#2989	—	2	1	no	—
64	#2989	—	2	1	no	—
65	#2985	C₂²	1	2	yes	—
66	#2981	C₂²	1	2	yes	—
67	#2978	—	2	2	no	—
68	#2969	C₂²	1	2	yes	—
69	#2969	C₂²	1	2	yes	—
70	#2967	—	2	2	no	—
71	#2962	C₂²	1	2	yes	—
72	C₄×#135	C₂²	1	1	yes	characteristic
73	C₄×#135	C₂²	1	1	yes	characteristic
74	C₄×#135	C₂²	1	1	yes	characteristic
75	C₄×#135	C₂²	1	1	yes	characteristic
76	#2935	C₂²	1	2	yes	—
77	#2930	—	2	2	no	—
78	#2925	—	2	1	no	—
79	#2925	—	2	1	no	—
80	#2925	—	2	1	no	—
81	#2920	C₂²	1	1	yes	characteristic
82	#2920	C₂²	1	1	yes	characteristic
83	#2906	—	2	1	no	—
84	C₂×#423	C₂²	1	1	yes	characteristic
85	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
86	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
87	#1594	C₂²	1	2	yes	complemented
88	#1593	C₂²	1	2	yes	complemented
89	#1592	C₂²	1	2	yes	complemented
90	#1592	C₂²	1	2	yes	complemented
91	#1591	C₂²	1	2	yes	complemented
92	#1590	C₂²	1	2	yes	complemented
93	#1590	C₂²	1	2	yes	complemented
94	#1589	C₂²	1	2	yes	complemented
95	#1588	C₂²	1	2	yes	complemented
96	#1588	C₂²	1	2	yes	complemented
97	#1587	C₂²	1	2	yes	complemented
98	#1587	C₂²	1	2	yes	complemented
99	#1586	C₂²	1	2	yes	complemented
100	#1586	C₂²	1	2	yes	complemented
101	#1585	C₂²	1	2	yes	complemented
102	#1585	C₂²	1	2	yes	complemented
103	#1584	C₂²	1	2	yes	complemented
104	#1584	C₂²	1	2	yes	complemented
105	#1583	C₂²	1	2	yes	complemented
106	#1583	C₂²	1	2	yes	complemented
107	#1582	C₂²	1	2	yes	complemented
108	#1582	C₂²	1	2	yes	complemented
109	#1581	C₂²	1	2	yes	complemented
110	#1581	C₂²	1	2	yes	complemented
111	#1580	C₂²	1	2	yes	complemented
112	#1579	C₂²	1	2	yes	complemented
113	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
114	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
115	C₈×Q₁₆	C₂²	1	2	yes	complemented
116	C₈×SD₁₆	C₂²	1	2	yes	complemented
117	C₈×SD₁₆	C₂²	1	2	yes	complemented
118	C₈×D₈	C₂²	1	2	yes	complemented
119	#1569	C₂²	1	2	yes	—
120	#1569	C₂²	1	2	yes	—
121	#1567	C₂²	1	1	yes	characteristic
122	#1567	C₂²	1	1	yes	characteristic
123	#1566	C₂²	1	1	yes	characteristic
124	#1566	C₂²	1	1	yes	characteristic
125	#1565	C₂²	1	2	yes	—
126	#1565	C₂²	1	2	yes	—
127	#1494	C₂²	1	2	yes	—
128	#1494	C₂²	1	2	yes	—
129	#1493	C₂²	1	2	yes	—
130	#1492	C₂²	1	2	yes	—
131	#1489	C₂²	1	1	yes	characteristic
132	#1489	C₂²	1	1	yes	characteristic
133	#1489	C₂²	1	1	yes	characteristic
134	#1489	C₂²	1	1	yes	characteristic
135	#1489	C₂²	1	1	yes	characteristic
136	#1489	C₂²	1	1	yes	characteristic
137	#1489	C₂²	1	1	yes	characteristic
138	#1489	C₂²	1	1	yes	characteristic
139	#1485	C₂²	1	2	yes	—
140	#1484	C₂²	1	2	yes	—
141	#1483	C₂²	1	2	yes	—
142	#1483	C₂²	1	2	yes	—
143	#1455	C₂²	1	2	yes	—
144	#1455	C₂²	1	2	yes	—
145	#1451	C₂²	1	2	yes	—
146	#1451	C₂²	1	1	yes	characteristic
147	#1451	C₂²	1	1	yes	characteristic
148	C₈×M₁₆	C₂²	1	2	yes	—
149	C₈×M₁₆	C₂²	1	1	yes	characteristic
150	C₈×M₁₆	C₂²	1	1	yes	characteristic
151	C₂×#135	C₂×C₄	1	1	yes	characteristic
152	C₂×#135	C₂×C₄	1	1	yes	characteristic
153	C₂×#135	C₂×C₄	1	1	yes	characteristic
154	C₂×#135	C₂×C₄	1	1	yes	characteristic
155	C₂×#131	—	2	2	no	—
156	C₂²×M₁₆	—	2	1	no	—
157	C₂²×M₁₆	—	2	1	no	—
158	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
159	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
160	#533	C₂×C₄	1	1	yes	characteristic
161	#533	C₂×C₄	1	1	yes	characteristic
162	#533	C₂×C₄	1	1	yes	characteristic
163	#533	C₂×C₄	1	1	yes	characteristic
164	#533	C₂³	1	1	yes	characteristic
165	#533	C₂³	1	1	yes	characteristic
166	#532	C₂×C₄	1	1	yes	characteristic
167	#532	C₂×C₄	1	1	yes	characteristic
168	#532	C₂×C₄	1	1	yes	characteristic
169	#532	C₂×C₄	1	1	yes	characteristic
170	#532	C₂³	1	1	yes	characteristic
171	#532	C₂³	1	1	yes	characteristic
172	#529	—	2	1	no	—
173	#529	—	2	1	no	—
174	#529	—	2	1	no	—
175	#529	—	2	1	no	—
176	#529	—	2	1	no	—
177	#529	—	2	1	no	—
178	#529	—	2	1	no	—
179	#529	—	2	1	no	—
180	#529	C₂×C₄	1	1	yes	characteristic
181	#529	C₂×C₄	1	1	yes	characteristic
182	#529	C₂×C₄	1	1	yes	characteristic
183	#529	C₂×C₄	1	1	yes	characteristic
184	#529	C₂³	1	1	yes	characteristic
185	#529	C₂³	1	1	yes	characteristic
186	#529	C₂³	1	1	yes	characteristic
187	#529	C₂³	1	1	yes	characteristic
188	#525	—	2	1	no	—
189	#525	—	2	1	no	—
190	#525	—	2	1	no	—
191	#525	—	2	1	no	—
192	#525	C₂×C₄	1	1	yes	characteristic
193	#525	C₂×C₄	1	1	yes	characteristic
194	#525	C₂×C₄	1	1	yes	characteristic
195	#525	C₂×C₄	1	1	yes	characteristic
196	C₄×#41	—	2	1	no	—
197	C₄×#41	—	2	1	no	—
198	C₄×#41	—	2	1	no	—
199	C₄×#41	—	2	1	no	—
200	C₄×#41	C₂³	1	1	yes	characteristic
201	C₄×#41	C₂³	1	1	yes	characteristic
202	C₄×#41	C₂³	1	1	yes	characteristic
203	C₄×#41	C₂³	1	1	yes	characteristic
204	C₂²×C₄²	C₂³	1	1	yes	characteristic
205	#501	C₂×C₄	1	1	yes	characteristic
206	#501	C₂×C₄	1	1	yes	characteristic
207	#501	C₂×C₄	1	1	yes	characteristic
208	#501	C₂×C₄	1	1	yes	characteristic
209	#501	C₂×C₄	1	1	yes	characteristic
210	#501	C₂×C₄	1	1	yes	characteristic
211	#501	C₂×C₄	1	1	yes	characteristic
212	#501	C₂×C₄	1	1	yes	characteristic
213	#497	C₂×C₄	1	1	yes	characteristic
214	#497	C₂×C₄	1	1	yes	characteristic
215	#497	C₂×C₄	1	1	yes	characteristic
216	#497	C₂×C₄	1	1	yes	characteristic
217	#496	C₂×C₄	1	1	yes	characteristic
218	#496	C₂×C₄	1	1	yes	characteristic
219	#496	C₂×C₄	1	1	yes	characteristic
220	#496	C₂×C₄	1	1	yes	characteristic
221	#491	C₂×C₄	1	1	yes	characteristic
222	#491	C₂×C₄	1	1	yes	characteristic
223	#491	C₂×C₄	1	1	yes	characteristic
224	#491	C₂×C₄	1	1	yes	characteristic
225	#490	C₂×C₄	1	1	yes	characteristic
226	#490	C₂×C₄	1	1	yes	characteristic
227	#490	C₂×C₄	1	1	yes	characteristic
228	#490	C₂×C₄	1	1	yes	characteristic
229	#489	C₂×C₄	1	1	yes	characteristic
230	#489	C₂×C₄	1	1	yes	characteristic
231	#489	C₂×C₄	1	1	yes	characteristic
232	#489	C₂×C₄	1	1	yes	characteristic
233	#489	C₂×C₄	1	1	yes	characteristic
234	#489	C₂×C₄	1	1	yes	characteristic
235	#489	C₂×C₄	1	1	yes	characteristic
236	#489	C₂×C₄	1	1	yes	characteristic
237	#470	C₂×C₄	1	1	yes	characteristic
238	#470	C₂×C₄	1	1	yes	characteristic
239	#470	C₂×C₄	1	1	yes	characteristic
240	#470	C₂×C₄	1	1	yes	characteristic
241	#470	C₂×C₄	1	1	yes	characteristic
242	#470	C₂×C₄	1	1	yes	characteristic
243	#470	C₂×C₄	1	1	yes	characteristic
244	#470	C₂×C₄	1	1	yes	characteristic
245	#469	C₂×C₄	1	1	yes	characteristic
246	#469	C₂×C₄	1	1	yes	characteristic
247	#469	C₂×C₄	1	1	yes	characteristic
248	#469	C₂×C₄	1	1	yes	characteristic
249	#469	C₂×C₄	1	1	yes	characteristic
250	#469	C₂×C₄	1	1	yes	characteristic
251	#469	C₂×C₄	1	1	yes	characteristic
252	#469	C₂×C₄	1	1	yes	characteristic
253	#468	C₂×C₄	1	1	yes	characteristic
254	#468	C₂×C₄	1	1	yes	characteristic
255	#468	C₂×C₄	1	1	yes	characteristic
256	#468	C₂×C₄	1	1	yes	characteristic
257	#468	C₂×C₄	1	1	yes	characteristic
258	#468	C₂×C₄	1	1	yes	characteristic
259	#468	C₂×C₄	1	1	yes	characteristic
260	#468	C₂×C₄	1	1	yes	characteristic
261	#468	C₂×C₄	1	1	yes	characteristic
262	#468	C₂×C₄	1	1	yes	characteristic
263	#468	C₂×C₄	1	1	yes	characteristic
264	#468	C₂×C₄	1	1	yes	characteristic
265	#468	C₂×C₄	1	1	yes	characteristic
266	#468	C₂×C₄	1	1	yes	characteristic
267	#468	C₂×C₄	1	1	yes	characteristic
268	#468	C₂×C₄	1	1	yes	characteristic
269	#446	—	2	2	no	—
270	#446	—	2	2	no	—
271	#446	—	2	2	no	—
272	#446	—	2	2	no	—
273	#446	C₂³	1	2	yes	—
274	#446	C₂³	1	2	yes	—
275	#446	C₂³	1	2	yes	—
276	#446	C₂³	1	2	yes	—
277	C₈×Q₈	C₂³	1	2	yes	—
278	C₈×Q₈	C₂³	1	2	yes	—
279	C₈×Q₈	C₂³	1	2	yes	—
280	C₈×Q₈	C₂³	1	2	yes	—
281	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
282	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
283	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
284	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
285	C₄×Q₁₆	C₂³	1	1	yes	characteristic
286	C₄×Q₁₆	C₂³	1	1	yes	characteristic
287	C₄×Q₁₆	C₂³	1	1	yes	characteristic
288	C₄×Q₁₆	C₂³	1	1	yes	characteristic
289	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
290	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
291	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
292	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
293	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
294	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
295	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
296	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
297	C₄×SD₁₆	C₂³	1	1	yes	characteristic
298	C₄×SD₁₆	C₂³	1	1	yes	characteristic
299	C₄×SD₁₆	C₂³	1	1	yes	characteristic
300	C₄×SD₁₆	C₂³	1	1	yes	characteristic
301	C₄×SD₁₆	C₂³	1	1	yes	characteristic
302	C₄×SD₁₆	C₂³	1	1	yes	characteristic
303	C₄×SD₁₆	C₂³	1	1	yes	characteristic
304	C₄×SD₁₆	C₂³	1	1	yes	characteristic
305	C₄×D₈	C₂×C₄	1	1	yes	characteristic
306	C₄×D₈	C₂×C₄	1	1	yes	characteristic
307	C₄×D₈	C₂×C₄	1	1	yes	characteristic
308	C₄×D₈	C₂×C₄	1	1	yes	characteristic
309	C₄×D₈	C₂³	1	1	yes	characteristic
310	C₄×D₈	C₂³	1	1	yes	characteristic
311	C₄×D₈	C₂³	1	1	yes	characteristic
312	C₄×D₈	C₂³	1	1	yes	characteristic
313	#436	—	2	2	no	—
314	#436	—	2	2	no	—
315	#436	—	2	2	no	—
316	#436	—	2	2	no	—
317	#436	—	2	2	no	—
318	#436	—	2	2	no	—
319	#436	—	2	2	no	—
320	#436	—	2	2	no	—
321	#436	C₂³	1	2	yes	—
322	#436	C₂³	1	2	yes	—
323	#436	C₂³	1	2	yes	—
324	#436	C₂³	1	2	yes	—
325	#435	—	2	2	no	—
326	#435	—	2	2	no	—
327	#435	—	2	2	no	—
328	#435	—	2	2	no	—
329	#435	—	2	2	no	—
330	#435	—	2	2	no	—
331	#435	—	2	2	no	—
332	#435	—	2	2	no	—
333	#435	—	2	2	no	—
334	#435	—	2	2	no	—
335	#435	—	2	2	no	—
336	#435	—	2	2	no	—
337	C₈×D₄	C₂³	1	2	yes	—
338	C₈×D₄	C₂³	1	2	yes	—
339	C₈×D₄	C₂³	1	2	yes	—
340	C₈×D₄	C₂³	1	2	yes	—
341	#433	—	2	2	no	—
342	#433	—	2	2	no	—
343	#433	—	2	2	no	—
344	#433	—	2	2	no	—
345	#433	—	2	2	no	—
346	#433	—	2	2	no	—
347	#432	—	2	1	no	—
348	#432	—	2	1	no	—
349	#432	—	2	1	no	—
350	#432	—	2	1	no	—
351	#432	—	2	1	no	—
352	#432	D₄	1	1	yes	characteristic
353	#432	D₄	1	1	yes	characteristic
354	#432	D₄	1	2	yes	—
355	#432	C₂³	1	2	yes	—
356	#431	—	2	1	no	—
357	#431	—	2	1	no	—
358	#431	—	2	1	no	—
359	#431	—	2	1	no	—
360	#431	—	2	1	no	—
361	#431	C₂³	1	2	yes	—
362	#431	C₂³	1	2	yes	—
363	#431	C₂³	1	1	yes	characteristic
364	#431	C₂³	1	1	yes	characteristic
365	#427	C₂×C₄	1	1	yes	characteristic
366	#427	C₂×C₄	1	1	yes	characteristic
367	#427	C₂×C₄	1	1	yes	characteristic
368	#427	C₂×C₄	1	1	yes	characteristic
369	#424	—	2	2	no	—
370	#424	—	2	2	no	—
371	#424	—	2	2	no	—
372	#423	—	2	1	no	—
373	#423	—	2	1	no	—
374	#423	—	2	1	no	—
375	#423	—	2	1	no	—
376	#423	—	2	1	no	—
377	#423	—	2	1	no	—
378	#423	D₄	1	1	yes	characteristic
379	#423	D₄	1	1	yes	characteristic
380	#423	C₂³	1	1	yes	characteristic
381	#423	C₂³	1	1	yes	characteristic
382	#423	C₂³	1	1	yes	characteristic
383	#423	C₂³	1	1	yes	characteristic
384	#423	C₂³	1	2	yes	—
385	C₂×C₄⋊C₈	—	2	1	no	—
386	C₂×C₄⋊C₈	—	2	1	no	—
387	C₂×C₄⋊C₈	—	2	1	no	—
388	C₂×C₄⋊C₈	—	2	1	no	—
389	C₂×C₄⋊C₈	—	2	1	no	—
390	C₂×C₄⋊C₈	C₂³	1	2	yes	—
391	#416	C₂×C₄	1	1	yes	characteristic
392	#416	C₂×C₄	1	1	yes	characteristic
393	#416	C₂×C₄	1	1	yes	characteristic
394	#416	C₂×C₄	1	1	yes	characteristic
395	#416	C₂×C₄	1	1	yes	characteristic
396	#416	C₂×C₄	1	1	yes	characteristic
397	#416	C₂×C₄	1	1	yes	characteristic
398	#416	C₂×C₄	1	1	yes	characteristic
399	#408	—	2	2	no	—
400	#408	—	2	2	no	—
401	#408	—	2	2	no	—
402	#407	—	2	1	no	—
403	#407	D₄	1	2	yes	—
404	#405	—	2	2	no	—
405	#405	—	2	2	no	—
406	#405	—	2	2	no	—
407	C₄×M₁₆	—	2	1	no	—
408	C₄×M₁₆	—	2	1	no	—
409	C₄×M₁₆	—	2	1	no	—
410	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
411	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
412	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
413	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
414	C₄×M₁₆	C₂³	1	1	yes	characteristic
415	C₄×M₁₆	C₂³	1	1	yes	characteristic
416	C₄×M₁₆	C₂³	1	2	yes	—
417	C₄×M₁₆	C₂³	1	1	yes	characteristic
418	C₄×M₁₆	C₂³	1	1	yes	characteristic
419	C₄×M₁₆	C₂³	1	1	yes	characteristic
420	C₄×M₁₆	C₂³	1	1	yes	characteristic
421	C₄×M₁₆	C₂³	1	2	yes	—
422	C₂×#97	—	2	1	no	—
423	C₂×#97	C₂×C₄	1	1	yes	characteristic
424	C₂×#97	C₂×C₄	1	1	yes	characteristic
425	C₂×C₄×C₈	C₂³	1	2	yes	—
426	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
428	#335	C₂³	1	2	yes	—
429	#335	C₂³	1	2	yes	—
430	#335	C₂³	1	2	yes	—
431	#335	C₂³	1	2	yes	—
432	#334	C₂³	1	2	yes	—
433	#334	C₂³	1	2	yes	—
434	#334	C₂³	1	2	yes	—
435	#334	C₂³	1	2	yes	—
436	Q₈⋊C₈	C₂³	1	2	yes	—
437	Q₈⋊C₈	C₂³	1	2	yes	—
438	Q₈⋊C₈	C₂³	1	2	yes	—
439	Q₈⋊C₈	C₂³	1	2	yes	—
440	Q₈⋊C₈	C₂³	1	2	yes	—
441	Q₈⋊C₈	C₂³	1	2	yes	—
442	Q₈⋊C₈	C₂³	1	2	yes	—
443	Q₈⋊C₈	C₂³	1	2	yes	—
444	D₄⋊C₈	C₂³	1	2	yes	—
445	D₄⋊C₈	C₂³	1	2	yes	—
446	D₄⋊C₈	C₂³	1	2	yes	—
447	D₄⋊C₈	C₂³	1	2	yes	—
448	D₄⋊C₈	C₂³	1	2	yes	—
449	D₄⋊C₈	C₂³	1	2	yes	—
450	D₄⋊C₈	C₂³	1	2	yes	—
451	D₄⋊C₈	C₂³	1	2	yes	—
452	#322	C₂³	1	2	yes	—
453	#322	C₂³	1	2	yes	—
454	#322	C₂³	1	2	yes	—
455	#322	C₂³	1	2	yes	—
456	#322	C₂³	1	2	yes	—
457	#322	C₂³	1	2	yes	—
458	C₈²	C₂³	1	2	yes	—
459	C₈²	C₂³	1	2	yes	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	C₂²×C₄	1	1	yes	characteristic
465	C₂×#41	C₂²×C₄	1	1	yes	characteristic
466	C₂×#41	C₂²×C₄	1	1	yes	characteristic
467	C₂×#41	C₂²×C₄	1	1	yes	characteristic
468	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
469	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
470	C₂³×C₄	#41	1	1	yes	characteristic
471	#135	—	4	2	no	—
472	#135	—	4	2	no	—
473	#135	—	4	2	no	—
474	#135	—	4	2	no	—
475	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
476	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
477	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
478	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
479	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
480	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
481	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
482	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
483	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
484	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
485	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
486	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
487	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
488	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
489	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
490	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
491	#131	—	8	4	no	—
492	C₂×M₁₆	—	2	1	no	—
493	C₂×M₁₆	—	2	2	no	—
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	1	no	—
496	C₂×M₁₆	—	2	2	no	—
497	C₂×M₁₆	—	2	1	no	—
498	C₂×M₁₆	—	2	1	no	—
499	C₂×M₁₆	—	2	1	no	—
500	C₂×M₁₆	—	2	2	no	—
501	C₂×M₁₆	—	2	2	no	—
502	C₂×M₁₆	—	2	2	no	—
503	C₂×M₁₆	—	2	2	no	—
504	C₂×M₁₆	—	4	2	no	—
505	C₂×M₁₆	—	4	2	no	—
506	C₂×M₁₆	—	4	4	no	—
507	C₂×M₁₆	—	8	2	no	—
508	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
509	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
510	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
511	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
512	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
513	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
514	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
515	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
516	C₂×M₁₆	C₂×D₄	1	2	yes	—
517	C₂×M₁₆	C₂×D₄	1	2	yes	—
518	C₂²×C₈	—	2	2	no	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	2	2	no	—
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	2	2	no	—
523	C₂²×C₈	—	2	2	no	—
524	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
525	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
526	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
527	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
528	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
529	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
530	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
531	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
532	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
533	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
534	#127	C₂²×C₄	1	1	yes	characteristic
535	#127	C₂²×C₄	1	1	yes	characteristic
536	#126	—	2	1	no	—
537	#126	—	2	1	no	—
538	#126	—	2	1	no	—
539	#126	—	2	1	no	—
540	#126	—	2	1	no	—
541	#126	—	2	1	no	—
542	#126	—	2	1	no	—
543	#126	—	2	1	no	—
544	#125	—	2	1	no	—
545	#125	—	2	1	no	—
546	#125	—	2	1	no	—
547	#125	—	2	1	no	—
548	#125	C₂²×C₄	1	1	yes	characteristic
549	#125	C₂²×C₄	1	1	yes	characteristic
550	#125	C₂²×C₄	1	1	yes	characteristic
551	#125	C₂²×C₄	1	1	yes	characteristic
552	#124	—	2	1	no	—
553	#124	—	2	1	no	—
554	#124	—	2	1	no	—
555	#124	—	2	1	no	—
556	#124	C₂²×C₄	1	1	yes	characteristic
557	#124	C₂²×C₄	1	1	yes	characteristic
558	#124	C₂²×C₄	1	1	yes	characteristic
559	#124	C₂²×C₄	1	1	yes	characteristic
560	#123	—	2	1	no	—
561	#123	—	2	1	no	—
562	#123	—	2	1	no	—
563	#123	—	2	1	no	—
564	#123	—	2	1	no	—
565	#123	—	2	1	no	—
566	#123	—	2	1	no	—
567	#123	—	2	1	no	—
568	#123	—	2	1	no	—
569	#123	—	2	1	no	—
570	#123	—	2	1	no	—
571	#123	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
581	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
582	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
583	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
584	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
585	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
586	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
587	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
588	#121	—	2	1	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	—	2	1	no	—
596	#121	C₂²×C₄	1	1	yes	characteristic
597	#121	C₂²×C₄	1	1	yes	characteristic
598	#121	C₂²×C₄	1	1	yes	characteristic
599	#121	C₂²×C₄	1	1	yes	characteristic
600	#121	C₂²×C₄	1	1	yes	characteristic
601	#121	C₂²×C₄	1	1	yes	characteristic
602	#121	C₂²×C₄	1	1	yes	characteristic
603	#121	C₂²×C₄	1	1	yes	characteristic
604	#120	—	2	1	no	—
605	#120	—	2	1	no	—
606	#120	—	2	1	no	—
607	#120	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
617	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
618	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
619	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
620	C₄×Q₈	C₂⁴	1	1	yes	characteristic
621	C₄×Q₈	C₂⁴	1	1	yes	characteristic
622	C₄×Q₈	C₂⁴	1	1	yes	characteristic
623	C₄×Q₈	C₂⁴	1	1	yes	characteristic
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
657	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
658	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
659	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
660	C₄×D₄	C₂⁴	1	1	yes	characteristic
661	C₄×D₄	C₂⁴	1	1	yes	characteristic
662	C₄×D₄	C₂⁴	1	1	yes	characteristic
663	C₄×D₄	C₂⁴	1	1	yes	characteristic
664	#117	—	2	1	no	—
665	#117	—	2	1	no	—
666	#117	—	2	1	no	—
667	#117	—	2	1	no	—
668	#117	—	2	1	no	—
669	#117	—	2	1	no	—
670	#117	—	2	1	no	—
671	#117	—	2	1	no	—
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	—	2	1	no	—
675	#117	—	2	1	no	—
676	#117	—	2	1	no	—
677	#117	—	2	1	no	—
678	#117	—	2	1	no	—
679	#117	—	2	1	no	—
680	#117	C₂²×C₄	1	1	yes	characteristic
681	#117	C₂²×C₄	1	1	yes	characteristic
682	#117	C₂²×C₄	1	1	yes	characteristic
683	#117	C₂²×C₄	1	1	yes	characteristic
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
689	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
690	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
691	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
692	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
693	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
694	C₂×C₄²	#41	1	1	yes	characteristic
695	C₂×C₄²	#41	1	1	yes	characteristic
696	C₂×C₄²	#41	1	1	yes	characteristic
697	C₂×C₄²	C₂⁴	1	1	yes	characteristic
698	C₂×C₄²	C₂⁴	1	1	yes	characteristic
699	C₂×C₄²	C₂⁴	1	1	yes	characteristic
700	#107	C₂²×C₄	1	1	yes	characteristic
701	#107	C₂²×C₄	1	1	yes	characteristic
702	#107	C₂²×C₄	1	1	yes	characteristic
703	#107	C₂²×C₄	1	1	yes	characteristic
704	#107	C₂²×C₄	1	1	yes	characteristic
705	#107	C₂²×C₄	1	1	yes	characteristic
706	#107	C₂²×C₄	1	1	yes	characteristic
707	#107	C₂²×C₄	1	1	yes	characteristic
708	#106	C₂²×C₄	1	1	yes	characteristic
709	#106	C₂²×C₄	1	1	yes	characteristic
710	#106	C₂²×C₄	1	1	yes	characteristic
711	#106	C₂²×C₄	1	1	yes	characteristic
712	#106	C₂²×C₄	1	1	yes	characteristic
713	#106	C₂²×C₄	1	1	yes	characteristic
714	#106	C₂²×C₄	1	1	yes	characteristic
715	#106	C₂²×C₄	1	1	yes	characteristic
716	C₄⋊C₈	—	2	2	no	—
717	C₄⋊C₈	—	2	2	no	—
718	C₄⋊C₈	—	2	2	no	—
719	C₄⋊C₈	—	2	2	no	—
720	C₄⋊C₈	—	2	2	no	—
721	C₄⋊C₈	—	2	2	no	—
722	C₄⋊C₈	—	2	2	no	—
723	C₄⋊C₈	—	2	2	no	—
724	C₄⋊C₈	—	2	1	no	—
725	C₄⋊C₈	—	2	1	no	—
726	C₄⋊C₈	—	2	2	no	—
727	C₄⋊C₈	—	2	1	no	—
728	C₄⋊C₈	—	2	1	no	—
729	C₄⋊C₈	—	2	2	no	—
730	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
731	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
732	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
733	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
734	C₄⋊C₈	C₂×D₄	1	2	yes	—
735	C₄⋊C₈	C₂×D₄	1	2	yes	—
736	C₄⋊C₈	C₂⁴	1	2	yes	—
737	C₄⋊C₈	C₂⁴	1	2	yes	—
738	C₄⋊C₈	C₂⁴	1	2	yes	—
739	C₄⋊C₈	C₂⁴	1	2	yes	—
740	#103	C₂²×C₄	1	1	yes	characteristic
741	#103	C₂²×C₄	1	1	yes	characteristic
742	#103	C₂²×C₄	1	1	yes	characteristic
743	#103	C₂²×C₄	1	1	yes	characteristic
744	#103	C₂²×C₄	1	1	yes	characteristic
745	#103	C₂²×C₄	1	1	yes	characteristic
746	#103	C₂²×C₄	1	1	yes	characteristic
747	#103	C₂²×C₄	1	1	yes	characteristic
748	#103	C₂²×C₄	1	1	yes	characteristic
749	#103	C₂²×C₄	1	1	yes	characteristic
750	#103	C₂²×C₄	1	1	yes	characteristic
751	#103	C₂²×C₄	1	1	yes	characteristic
752	#103	C₂²×C₄	1	1	yes	characteristic
753	#103	C₂²×C₄	1	1	yes	characteristic
754	#103	C₂²×C₄	1	1	yes	characteristic
755	#103	C₂²×C₄	1	1	yes	characteristic
756	#102	C₂²×C₄	1	1	yes	characteristic
757	#102	C₂²×C₄	1	1	yes	characteristic
758	#102	C₂²×C₄	1	1	yes	characteristic
759	#102	C₂²×C₄	1	1	yes	characteristic
760	#102	C₂²×C₄	1	1	yes	characteristic
761	#102	C₂²×C₄	1	1	yes	characteristic
762	#102	C₂²×C₄	1	1	yes	characteristic
763	#102	C₂²×C₄	1	1	yes	characteristic
764	#102	C₂²×C₄	1	1	yes	characteristic
765	#102	C₂²×C₄	1	1	yes	characteristic
766	#102	C₂²×C₄	1	1	yes	characteristic
767	#102	C₂²×C₄	1	1	yes	characteristic
768	#102	C₂²×C₄	1	1	yes	characteristic
769	#102	C₂²×C₄	1	1	yes	characteristic
770	#102	C₂²×C₄	1	1	yes	characteristic
771	#102	C₂²×C₄	1	1	yes	characteristic
772	C₂²⋊C₈	—	2	2	no	—
773	C₂²⋊C₈	—	2	2	no	—
774	C₂²⋊C₈	—	2	2	no	—
775	C₂²⋊C₈	—	2	2	no	—
776	C₂²⋊C₈	—	2	2	no	—
777	C₂²⋊C₈	—	2	2	no	—
778	C₂²⋊C₈	—	2	2	no	—
779	C₂²⋊C₈	—	2	2	no	—
780	C₂²⋊C₈	—	2	2	no	—
781	C₂²⋊C₈	—	2	2	no	—
782	C₂²⋊C₈	C₂×D₄	1	2	yes	—
783	C₂²⋊C₈	C₂×D₄	1	2	yes	—
784	C₂²⋊C₈	C₂×D₄	1	2	yes	—
785	C₂²⋊C₈	C₂×D₄	1	2	yes	—
786	#97	—	2	2	no	—
787	#97	—	2	2	no	—
788	#97	—	2	2	no	—
789	#97	—	2	2	no	—
790	#97	—	2	2	no	—
791	#97	—	2	1	no	—
792	#97	—	2	1	no	—
793	#97	—	2	2	no	—
794	#97	C₂²×C₄	1	1	yes	characteristic
795	#97	C₂²×C₄	1	1	yes	characteristic
796	#97	C₂²×C₄	1	1	yes	characteristic
797	#97	C₂²×C₄	1	1	yes	characteristic
798	#97	C₂²×C₄	1	1	yes	characteristic
799	#97	C₂²×C₄	1	1	yes	characteristic
800	#97	C₂²×C₄	1	1	yes	characteristic
801	#97	C₂²×C₄	1	1	yes	characteristic
802	#97	C₂×D₄	1	2	yes	—
803	#97	C₂×D₄	1	2	yes	—
804	C₄×C₈	—	2	2	no	—
805	C₄×C₈	—	2	2	no	—
806	C₄×C₈	—	2	2	no	—
807	C₄×C₈	—	2	2	no	—
808	C₄×C₈	—	2	2	no	—
809	C₄×C₈	—	2	2	no	—
810	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
811	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
812	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
813	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
814	C₄×C₈	C₂⁴	1	2	yes	—
815	C₄×C₈	C₂⁴	1	2	yes	—
816	C₄×C₈	C₂⁴	1	1	yes	characteristic
817	C₄×C₈	C₂⁴	1	1	yes	characteristic
818	C₄×C₈	C₂⁴	1	1	yes	characteristic
819	C₄×C₈	C₂⁴	1	1	yes	characteristic
820	C₄×C₈	C₂⁴	1	2	yes	—
821	C₄×C₈	C₂⁴	1	2	yes	—
822	C₂⁴	C₄×D₄	1	1	yes	characteristic
823	#41	—	4	2	no	—
824	#41	—	4	2	no	—
825	#41	—	4	1	no	—
826	#41	—	4	1	no	—
827	#41	—	4	1	no	—
828	#41	—	4	1	no	—
829	#41	—	4	1	no	—
830	#41	—	4	1	no	—
831	#41	—	4	1	no	—
832	#41	—	4	1	no	—
833	#41	—	8	1	no	—
834	#41	—	8	1	no	—
835	#41	—	8	2	no	—
836	#41	—	8	2	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
842	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
843	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
844	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	2	1	no	—
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	1	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	1	no	—
860	C₂×D₄	—	2	1	no	—
861	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
862	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
863	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
864	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	4	1	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	1	no	—
881	C₂²×C₄	—	4	1	no	—
882	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
888	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
892	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
893	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂×#41	1	1	yes	characteristic
898	C₂²×C₄	C₂×#41	1	1	yes	characteristic
899	C₂²×C₄	C₂×#41	1	1	yes	characteristic
900	Q₁₆	—	2	2	no	—
901	Q₁₆	—	2	2	no	—
902	Q₁₆	—	4	1	no	—
903	Q₁₆	—	4	1	no	—
904	SD₁₆	—	2	2	no	—
905	SD₁₆	—	2	2	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	2	no	—
908	SD₁₆	—	4	1	no	—
909	SD₁₆	—	4	1	no	—
910	SD₁₆	—	4	1	no	—
911	SD₁₆	—	4	1	no	—
912	D₈	—	2	2	no	—
913	D₈	—	2	2	no	—
914	D₈	—	4	1	no	—
915	D₈	—	4	1	no	—
916	M₁₆	—	2	4	no	—
917	M₁₆	—	2	2	no	—
918	M₁₆	—	2	2	no	—
919	M₁₆	—	2	2	no	—
920	M₁₆	—	2	2	no	—
921	M₁₆	—	4	1	no	—
922	M₁₆	—	4	1	no	—
923	M₁₆	—	4	1	no	—
924	M₁₆	—	4	1	no	—
925	M₁₆	—	4	2	no	—
926	M₁₆	—	4	2	no	—
927	M₁₆	—	4	4	no	—
928	M₁₆	—	4	2	no	—
929	M₁₆	—	8	2	no	—
930	M₁₆	—	8	2	no	—
931	M₁₆	—	8	2	no	—
932	M₁₆	—	8	2	no	—
933	M₁₆	—	8	1	no	—
934	M₁₆	—	8	1	no	—
935	M₁₆	—	8	1	no	—
936	M₁₆	—	8	2	no	—
937	M₁₆	—	8	1	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	2	no	—
942	C₂×C₈	—	2	2	no	—
943	C₂×C₈	—	2	2	no	—
944	C₂×C₈	—	2	2	no	—
945	C₂×C₈	—	2	2	no	—
946	C₂×C₈	—	4	1	no	—
947	C₂×C₈	—	4	1	no	—
948	C₂×C₈	—	4	4	no	—
949	C₂×C₈	—	4	4	no	—
950	C₂×C₈	—	8	2	no	—
951	C₂×C₈	—	8	2	no	—
952	C₂×C₈	—	8	2	no	—
953	C₂×C₈	—	8	2	no	—
954	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
955	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
956	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
957	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
958	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
959	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
960	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
961	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
962	C₂×C₈	C₂²×D₄	1	2	yes	—
963	C₂×C₈	C₂²×D₄	1	2	yes	—
964	C₂×C₈	C₂²×D₄	1	2	yes	—
965	C₂×C₈	C₂²×D₄	1	2	yes	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1000	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1001	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1002	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1003	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1004	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1005	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	C₄×D₄	1	1	yes	characteristic
1055	C₄²	C₄×D₄	1	1	yes	characteristic
1056	C₄²	C₄×D₄	1	1	yes	characteristic
1057	C₄²	C₄×D₄	1	1	yes	characteristic
1058	C₄²	C₄×D₄	1	1	yes	characteristic
1059	C₄²	C₄×D₄	1	1	yes	characteristic
1060	C₄²	C₂³×C₄	1	1	yes	characteristic
1061	C₄²	C₂³×C₄	1	1	yes	characteristic
1062	C₄²	C₂³×C₄	1	1	yes	characteristic
1063	C₄²	C₂²×D₄	1	1	yes	characteristic
1064	C₄²	C₂²×D₄	1	1	yes	characteristic
1065	C₄²	C₂²×D₄	1	1	yes	characteristic
1066	C₄²	C₂×#41	1	1	yes	characteristic
1067	C₄²	C₂×#41	1	1	yes	characteristic
1068	C₄²	C₂×#41	1	1	yes	characteristic
1069	C₄²	C₂⁵	1	1	yes	characteristic
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	4	1	no	—
1077	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1078	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1079	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1080	Q₈	—	2	1	no	—
1081	Q₈	—	2	1	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	1	no	—
1084	Q₈	—	2	1	no	—
1085	Q₈	—	2	1	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	4	2	no	—
1089	Q₈	—	8	1	no	—
1090	Q₈	—	8	1	no	—
1091	Q₈	—	8	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	2	1	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	4	2	no	—
1102	D₄	—	4	2	no	—
1103	D₄	—	8	1	no	—
1104	D₄	—	8	1	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	1	no	—
1107	D₄	—	8	1	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	1	no	—
1110	D₄	—	8	1	no	—
1111	D₄	—	8	1	no	—
1112	D₄	—	8	1	no	—
1113	D₄	—	8	1	no	—
1114	D₄	—	8	1	no	—
1115	D₄	—	8	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	—	8	1	no	—
1167	C₂×C₄	—	8	1	no	—
1168	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1169	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1170	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1171	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1172	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1173	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1174	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1175	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1176	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1177	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1178	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1179	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1180	C₈	—	2	4	no	—
1181	C₈	—	2	2	no	—
1182	C₈	—	2	2	no	—
1183	C₈	—	2	2	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	2	1	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	1	no	—
1191	C₈	—	4	2	no	—
1192	C₈	—	4	2	no	—
1193	C₈	—	4	2	no	—
1194	C₈	—	4	2	no	—
1195	C₈	—	4	2	no	—
1196	C₈	#568	1	2	yes	—
1197	C₈	#568	1	2	yes	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	8	2	no	—
1220	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1221	C₄	—	2	1	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	#2956	1	2	yes	—
1243	C₄	C₂×#568	1	1	yes	characteristic
1244	C₄	C₂×#568	1	1	yes	characteristic
1245	C₄	#3585	1	1	yes	characteristic
1246	C₄	#3586	1	1	yes	characteristic
1247	C₂	—	4	1	no	—
1248	C₂	—	4	1	no	—
1249	C₂	—	4	1	no	—
1250	C₂	—	8	1	no	—
1251	C₂	—	8	1	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	#60144	1	1	yes	characteristic
1255	C₂	#60170	1	1	yes	characteristic
1256	C₂	C₂×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂²×C₄×D₄
prime radical	#60676	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #2920 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #60295	C₂	semidirect
3. #60266	C₂	semidirect
4. #18079	C₂	semidirect
5. #18078	C₂	semidirect
6. #18077	C₂	semidirect
7. #18076	C₂	semidirect
8. #18065	C₂	semidirect
9. #18063	C₂	semidirect
10. #18061	C₂	semidirect
11. #18061	C₂	semidirect
12. #18059	C₂	semidirect
13. #18057	C₂	semidirect
14. #18057	C₂	semidirect
15. #18055	C₂	semidirect
16. #17988	C₂	semidirect
17. #17987	C₂	semidirect
18. #17969	C₂	semidirect
19. #17968	C₂	semidirect
20. #17796	C₂	semidirect
21. #17504	C₂	semidirect
22. #17503	C₂	semidirect
23. M₁₆²	C₂	semidirect
87. #1594	C₂²	semidirect
88. #1593	C₂²	semidirect
89. #1592	C₂²	semidirect
90. #1592	C₂²	semidirect
91. #1591	C₂²	semidirect
92. #1590	C₂²	semidirect
93. #1590	C₂²	semidirect
94. #1589	C₂²	semidirect
95. #1588	C₂²	semidirect
96. #1588	C₂²	semidirect
97. #1587	C₂²	semidirect
98. #1587	C₂²	semidirect
99. #1586	C₂²	semidirect
100. #1586	C₂²	semidirect
101. #1585	C₂²	semidirect
102. #1585	C₂²	semidirect
103. #1584	C₂²	semidirect
104. #1584	C₂²	semidirect
105. #1583	C₂²	semidirect
106. #1583	C₂²	semidirect
107. #1582	C₂²	semidirect
108. #1582	C₂²	semidirect
109. #1581	C₂²	semidirect
110. #1581	C₂²	semidirect
111. #1580	C₂²	semidirect
112. #1579	C₂²	semidirect
113. SD₁₆⋊C₈	C₂²	semidirect
114. SD₁₆⋊C₈	C₂²	semidirect
115. C₈×Q₁₆	C₂²	semidirect
116. C₈×SD₁₆	C₂²	semidirect
117. C₈×SD₁₆	C₂²	semidirect
118. C₈×D₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#60676	2
#60295	2
#60266	2
#18079	2
#18078	2
#18077	2
#18076	2
#18065	2
#18063	2
#18061	2
#18059	2
#18057	2
#18055	2
#17988	2
#17987	2
#17969	2
#17968	2
#17796	2
#17504	2
#17503	2
M₁₆²	2