Subgroups — #6344397

Order 512.

1571 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60294	C₂	1	1	yes	maximal, characteristic
2	#60265	C₂	1	1	yes	maximal, characteristic
3	#60210	C₂	1	1	yes	maximal, characteristic
4	#17840	C₂	1	2	yes	maximal, complemented
5	#17838	C₂	1	2	yes	maximal, complemented
6	#17836	C₂	1	2	yes	maximal, complemented
7	#17834	C₂	1	2	yes	maximal, complemented
8	#17833	C₂	1	2	yes	maximal, complemented
9	#17832	C₂	1	2	yes	maximal, complemented
10	#17831	C₂	1	2	yes	maximal, complemented
11	#17830	C₂	1	2	yes	maximal, complemented
12	#17812	C₂	1	1	yes	maximal, characteristic, complemented
13	#17812	C₂	1	1	yes	maximal, characteristic, complemented
14	#17811	C₂	1	1	yes	maximal, characteristic, complemented
15	#17811	C₂	1	1	yes	maximal, characteristic, complemented
16	#17806	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#1573	C₂	1	1	yes	maximal, characteristic, complemented
18	#17799	C₂	1	1	yes	maximal, characteristic, complemented
19	#17798	C₂	1	1	yes	maximal, characteristic, complemented
20	#17797	C₂	1	1	yes	maximal, characteristic, complemented
21	#17789	C₂	1	1	yes	maximal, characteristic, complemented
22	#17788	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#1565	C₂	1	1	yes	maximal, characteristic, complemented
24	#3444	C₂²	1	1	yes	characteristic
25	#2994	—	2	1	no	—
26	#2994	—	2	1	no	—
27	#2992	—	2	2	no	—
28	#2990	C₂²	1	2	yes	—
29	#2990	C₂²	1	2	yes	—
30	#2990	C₂²	1	2	yes	—
31	#2990	C₂²	1	2	yes	—
32	#2989	C₂²	1	1	yes	characteristic
33	#2989	C₂²	1	1	yes	characteristic
34	#2989	C₂²	1	1	yes	characteristic
35	#2989	C₂²	1	1	yes	characteristic
36	#2988	C₂²	1	1	yes	characteristic
37	#2988	C₂²	1	1	yes	characteristic
38	#2988	C₂²	1	1	yes	characteristic
39	#2988	C₂²	1	1	yes	characteristic
40	#2985	—	2	1	no	—
41	#2981	—	2	1	no	—
42	#2977	—	2	2	no	—
43	#2969	C₄	1	2	yes	—
44	#2969	C₄	1	2	yes	—
45	#2968	—	2	2	no	—
46	#2968	C₄	1	2	yes	—
47	#2968	C₄	1	2	yes	—
48	#2966	—	2	1	no	—
49	#2966	—	2	1	no	—
50	#2965	C₂²	1	2	yes	—
51	#2965	C₂²	1	2	yes	—
52	#2965	C₂²	1	2	yes	—
53	C₈×#41	C₂²	1	2	yes	—
54	#2962	—	2	1	no	—
55	#2962	C₄	1	1	yes	characteristic
56	#2962	C₄	1	1	yes	characteristic
57	#2935	—	2	1	no	—
58	#2935	C₄	1	1	yes	characteristic
59	#2935	C₄	1	1	yes	characteristic
60	#2933	C₄	1	1	yes	characteristic
61	#2933	C₄	1	1	yes	characteristic
62	#2933	C₄	1	1	yes	characteristic
63	#2933	C₄	1	1	yes	characteristic
64	#2929	—	2	2	no	—
65	#2925	C₂²	1	2	yes	—
66	#2925	C₂²	1	2	yes	—
67	#2925	C₂²	1	2	yes	—
68	#2922	C₂²	1	1	yes	characteristic
69	#2922	C₂²	1	1	yes	characteristic
70	#2920	C₂²	1	1	yes	characteristic
71	C₂×#432	C₂²	1	1	yes	characteristic
72	C₂×#431	C₂²	1	1	yes	characteristic
73	C₂×#431	C₂²	1	1	yes	characteristic
74	#2906	C₂²	1	2	yes	—
75	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
76	C₄×#131	C₂²	1	1	yes	characteristic
77	C₄×#131	C₂²	1	1	yes	characteristic
78	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
79	#1574	C₂²	1	1	yes	characteristic
80	#1574	C₂²	1	1	yes	characteristic
81	#1574	C₂²	1	1	yes	characteristic
82	#1574	C₂²	1	1	yes	characteristic
83	#1574	C₂²	1	2	yes	complemented
84	#1574	C₂²	1	2	yes	complemented
85	#1574	C₂²	1	2	yes	complemented
86	#1574	C₂²	1	2	yes	complemented
87	#1573	C₂²	1	2	yes	—
88	#1573	C₂²	1	2	yes	—
89	#1573	C₂²	1	2	yes	—
90	#1573	C₂²	1	2	yes	—
91	#1573	C₂²	1	1	yes	characteristic
92	#1573	C₂²	1	1	yes	characteristic
93	#1573	C₂²	1	1	yes	characteristic
94	#1573	C₂²	1	1	yes	characteristic
95	#1573	C₂²	1	2	yes	complemented
96	#1573	C₂²	1	2	yes	complemented
97	#1573	C₂²	1	2	yes	complemented
98	#1573	C₂²	1	2	yes	complemented
99	#1572	C₂²	1	2	yes	complemented
100	#1572	C₂²	1	2	yes	complemented
101	#1572	C₂²	1	2	yes	complemented
102	#1572	C₂²	1	2	yes	complemented
103	#1571	C₂²	1	2	yes	complemented
104	#1571	C₂²	1	2	yes	complemented
105	#1570	C₂²	1	2	yes	complemented
106	#1570	C₂²	1	2	yes	complemented
107	#1569	C₂²	1	2	yes	—
108	#1569	C₂²	1	2	yes	—
109	#1569	C₂²	1	2	yes	complemented
110	#1569	C₂²	1	2	yes	complemented
111	#1569	C₂²	1	2	yes	complemented
112	#1569	C₂²	1	2	yes	complemented
113	#1568	C₂²	1	2	yes	—
114	#1568	C₂²	1	2	yes	—
115	#1568	C₂²	1	2	yes	complemented
116	#1568	C₂²	1	2	yes	complemented
117	#1567	C₂²	1	2	yes	complemented
118	#1566	C₂²	1	2	yes	complemented
119	#1565	C₂²	1	1	yes	characteristic
120	#1565	C₂²	1	1	yes	characteristic
121	#1565	C₂²	1	1	yes	characteristic
122	#1565	C₂²	1	1	yes	characteristic
123	#1565	C₂²	1	2	yes	—
124	#1565	C₂²	1	2	yes	—
125	#1565	C₂²	1	1	yes	characteristic
126	#1565	C₂²	1	1	yes	characteristic
127	#1565	C₂²	1	1	yes	characteristic
128	#1565	C₂²	1	1	yes	characteristic
129	#1565	C₂²	1	2	yes	complemented
130	#1565	C₂²	1	2	yes	complemented
131	#1565	C₂²	1	2	yes	complemented
132	#1565	C₂²	1	2	yes	complemented
133	#1564	C₂²	1	1	yes	characteristic
134	#1564	C₂²	1	1	yes	characteristic
135	#1564	C₂²	1	1	yes	characteristic
136	#1564	C₂²	1	1	yes	characteristic
137	#1564	C₂²	1	2	yes	complemented
138	#1564	C₂²	1	2	yes	complemented
139	C₂×#335	C₂²	1	2	yes	—
140	C₂×#335	C₂²	1	1	yes	characteristic
141	C₂×#335	C₂²	1	1	yes	characteristic
142	C₂×#335	C₂²	1	2	yes	complemented
143	C₂×#334	C₂²	1	2	yes	—
144	C₂×#334	C₂²	1	1	yes	characteristic
145	C₂×#334	C₂²	1	1	yes	characteristic
146	C₂×#334	C₂²	1	2	yes	complemented
147	C₂×#131	—	2	2	no	—
148	C₂×#131	C₂×C₄	1	1	yes	characteristic
149	C₂×#131	C₂×C₄	1	1	yes	characteristic
150	C₂×#131	C₂×C₄	1	1	yes	characteristic
151	C₂×#131	C₂×C₄	1	1	yes	characteristic
152	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
153	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
154	C₂³×C₈	—	2	1	no	—
155	#533	C₂×C₄	1	1	yes	characteristic
156	#533	D₄	1	1	yes	characteristic
157	#533	Q₈	1	1	yes	characteristic
158	#532	C₂×C₄	1	1	yes	characteristic
159	#532	D₄	1	1	yes	characteristic
160	#532	Q₈	1	1	yes	characteristic
161	#529	C₂×C₄	1	2	yes	—
162	#529	C₂×C₄	1	2	yes	—
163	#529	D₄	1	1	yes	characteristic
164	#529	D₄	1	1	yes	characteristic
165	#529	D₄	1	2	yes	—
166	#529	Q₈	1	1	yes	characteristic
167	#529	Q₈	1	1	yes	characteristic
168	#529	Q₈	1	2	yes	—
169	#525	C₂×C₄	1	1	yes	characteristic
170	#525	C₂×C₄	1	1	yes	characteristic
171	#525	D₄	1	2	yes	—
172	#525	Q₈	1	2	yes	—
173	C₄×#41	C₂³	1	1	yes	characteristic
174	C₄×#41	C₂³	1	1	yes	characteristic
175	C₄×#41	C₂³	1	2	yes	—
176	C₄×#41	C₂³	1	2	yes	—
177	C₂²×C₄²	C₂³	1	1	yes	characteristic
178	#446	—	2	1	no	—
179	#446	—	2	1	no	—
180	#446	—	2	2	no	—
181	#446	—	2	2	no	—
182	#446	—	2	1	no	—
183	#446	—	2	1	no	—
184	#446	—	2	2	no	—
185	#446	—	2	2	no	—
186	#446	C₂×C₄	1	2	yes	—
187	#446	C₂×C₄	1	2	yes	—
188	#446	C₂×C₄	1	2	yes	—
189	#446	C₂×C₄	1	2	yes	—
190	#446	C₂×C₄	1	2	yes	—
191	#446	C₂×C₄	1	2	yes	—
192	C₈×Q₈	—	2	1	no	—
193	C₈×Q₈	—	2	1	no	—
194	C₈×Q₈	—	2	1	no	—
195	C₈×Q₈	—	2	1	no	—
196	C₈×Q₈	C₂×C₄	1	2	yes	—
197	C₈×Q₈	C₂×C₄	1	2	yes	—
198	#436	—	2	1	no	—
199	#436	—	2	1	no	—
200	#436	—	2	1	no	—
201	#436	—	2	1	no	—
202	#436	C₂×C₄	1	2	yes	—
203	#436	C₂×C₄	1	2	yes	—
204	#436	C₂×C₄	1	2	yes	—
205	#436	C₂×C₄	1	2	yes	—
206	#436	C₂×C₄	1	2	yes	—
207	#436	C₂×C₄	1	2	yes	—
208	#435	—	2	2	no	—
209	#435	—	2	2	no	—
210	#435	—	2	2	no	—
211	#435	—	2	2	no	—
212	#435	—	2	2	no	—
213	#435	—	2	2	no	—
214	#435	—	2	2	no	—
215	#435	—	2	2	no	—
216	#435	—	2	2	no	—
217	#435	—	2	2	no	—
218	#435	—	2	2	no	—
219	#435	—	2	2	no	—
220	#435	C₂×C₄	1	2	yes	—
221	#435	C₂×C₄	1	2	yes	—
222	#435	C₂×C₄	1	2	yes	—
223	#435	C₂×C₄	1	2	yes	—
224	#435	C₂×C₄	1	2	yes	—
225	#435	C₂×C₄	1	2	yes	—
226	#435	C₂×C₄	1	2	yes	—
227	#435	C₂×C₄	1	2	yes	—
228	#435	C₂×C₄	1	2	yes	—
229	#435	C₂×C₄	1	2	yes	—
230	#435	C₂×C₄	1	2	yes	—
231	#435	C₂×C₄	1	2	yes	—
232	C₈×D₄	—	2	2	no	—
233	C₈×D₄	—	2	2	no	—
234	C₈×D₄	—	2	2	no	—
235	C₈×D₄	—	2	2	no	—
236	C₈×D₄	—	2	1	no	—
237	C₈×D₄	—	2	1	no	—
238	C₈×D₄	—	2	2	no	—
239	C₈×D₄	—	2	2	no	—
240	C₈×D₄	—	2	1	no	—
241	C₈×D₄	—	2	1	no	—
242	C₈×D₄	—	2	2	no	—
243	C₈×D₄	—	2	2	no	—
244	C₈×D₄	C₂×C₄	1	2	yes	—
245	C₈×D₄	C₂×C₄	1	2	yes	—
246	C₈×D₄	C₂×C₄	1	2	yes	—
247	C₈×D₄	C₂×C₄	1	2	yes	—
248	C₈×D₄	C₂×C₄	1	2	yes	—
249	C₈×D₄	C₂×C₄	1	2	yes	—
250	#433	—	2	2	no	—
251	#433	—	2	2	no	—
252	#433	—	2	2	no	—
253	#433	—	2	2	no	—
254	#433	—	2	2	no	—
255	#433	—	2	2	no	—
256	#433	C₂×C₄	1	2	yes	—
257	#433	C₂×C₄	1	2	yes	—
258	#433	C₂×C₄	1	2	yes	—
259	#433	C₂×C₄	1	2	yes	—
260	#432	—	2	1	no	—
261	#432	—	2	1	no	—
262	#432	—	2	1	no	—
263	#432	C₂³	1	2	yes	—
264	#432	C₂³	1	1	yes	characteristic
265	#432	C₂³	1	1	yes	characteristic
266	#432	C₂³	1	2	yes	—
267	#432	C₂³	1	2	yes	—
268	#432	C₂³	1	2	yes	—
269	#432	C₂³	1	2	yes	—
270	#432	C₂³	1	2	yes	—
271	#431	—	2	1	no	—
272	#431	—	2	1	no	—
273	#431	—	2	1	no	—
274	#431	C₂×C₄	1	1	yes	characteristic
275	#431	C₂×C₄	1	1	yes	characteristic
276	#431	C₂×C₄	1	1	yes	characteristic
277	#431	C₂×C₄	1	1	yes	characteristic
278	#431	C₂³	1	1	yes	characteristic
279	#431	C₂³	1	1	yes	characteristic
280	#431	C₂³	1	1	yes	characteristic
281	#431	C₂³	1	1	yes	characteristic
282	#431	C₂³	1	2	yes	—
283	#431	C₂³	1	2	yes	—
284	#431	C₂³	1	2	yes	—
285	#431	C₂³	1	2	yes	—
286	#431	C₂³	1	1	yes	characteristic
287	#431	C₂³	1	1	yes	characteristic
288	#431	C₂³	1	2	yes	—
289	#431	C₂³	1	2	yes	—
290	#431	C₂³	1	1	yes	characteristic
291	#431	C₂³	1	1	yes	characteristic
292	#431	C₂³	1	1	yes	characteristic
293	#431	C₂³	1	1	yes	characteristic
294	#431	C₂³	1	2	yes	—
295	#431	C₂³	1	2	yes	—
296	#424	—	2	2	no	—
297	#424	—	2	2	no	—
298	#424	—	2	2	no	—
299	#424	C₂×C₄	1	1	yes	characteristic
300	#424	C₂×C₄	1	1	yes	characteristic
301	#424	C₂×C₄	1	1	yes	characteristic
302	#424	C₂×C₄	1	1	yes	characteristic
303	#423	C₂³	1	2	yes	—
304	#423	C₂³	1	2	yes	—
305	#423	C₂³	1	2	yes	—
306	#423	C₂³	1	2	yes	—
307	#423	C₂³	1	1	yes	characteristic
308	#423	C₂³	1	1	yes	characteristic
309	C₂×C₄⋊C₈	—	2	1	no	—
310	C₂×C₄⋊C₈	—	2	1	no	—
311	C₂×C₄⋊C₈	—	2	1	no	—
312	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂³	1	2	yes	—
319	C₂×C₄⋊C₈	C₂³	1	2	yes	—
320	C₂×C₄⋊C₈	C₂³	1	2	yes	—
321	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂³	1	2	yes	—
324	C₂×C₄⋊C₈	C₂³	1	2	yes	—
325	C₂×C₄⋊C₈	C₂³	1	2	yes	—
326	#408	—	2	2	no	—
327	#408	—	2	2	no	—
328	#408	—	2	2	no	—
329	#408	C₂×C₄	1	1	yes	characteristic
330	#408	C₂×C₄	1	1	yes	characteristic
331	#408	C₂×C₄	1	1	yes	characteristic
332	#408	C₂×C₄	1	1	yes	characteristic
333	#407	—	2	1	no	—
334	C₂×C₂²⋊C₈	—	2	1	no	—
335	C₂×C₂²⋊C₈	—	2	1	no	—
336	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
338	#405	—	2	2	no	—
339	#405	—	2	2	no	—
340	#405	—	2	2	no	—
341	#405	C₂×C₄	1	1	yes	characteristic
342	#405	C₂×C₄	1	1	yes	characteristic
343	#405	C₂×C₄	1	1	yes	characteristic
344	#405	C₂×C₄	1	1	yes	characteristic
345	#405	C₂×C₄	1	2	yes	—
346	#405	C₂×C₄	1	2	yes	—
347	#405	C₂×C₄	1	2	yes	—
348	#405	C₂×C₄	1	2	yes	—
349	C₄×M₁₆	—	2	1	no	—
350	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
351	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
352	C₄×M₁₆	C₂×C₄	1	2	yes	—
353	C₄×M₁₆	C₂³	1	1	yes	characteristic
354	C₄×M₁₆	C₂³	1	1	yes	characteristic
355	C₄×M₁₆	C₂³	1	2	yes	—
356	C₄×M₁₆	C₂³	1	2	yes	—
357	C₄×M₁₆	C₂³	1	2	yes	—
358	C₂×#97	—	2	1	no	—
359	C₂×#97	C₂×C₄	1	2	yes	—
360	C₂×C₄×C₈	—	2	1	no	—
361	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
362	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
363	C₂×C₄×C₈	C₂³	1	2	yes	—
364	C₂×C₄×C₈	C₂³	1	2	yes	—
365	C₂×C₄×C₈	C₂³	1	2	yes	—
366	#335	C₂³	1	2	yes	—
367	#335	C₂³	1	2	yes	—
368	#335	C₂³	1	2	yes	—
369	#335	C₂³	1	2	yes	—
370	#335	C₂³	1	2	yes	—
371	#335	C₂³	1	2	yes	—
372	#335	C₂³	1	2	yes	—
373	#335	C₂³	1	2	yes	—
374	#335	C₂³	1	1	yes	characteristic
375	#335	C₂³	1	2	yes	—
376	#335	C₂³	1	1	yes	characteristic
377	#335	C₂³	1	1	yes	characteristic
378	#335	C₂³	1	1	yes	characteristic
379	#335	C₂³	1	1	yes	characteristic
380	#335	C₂³	1	1	yes	characteristic
381	#335	C₂³	1	1	yes	characteristic
382	#335	C₂³	1	1	yes	characteristic
383	#335	C₂³	1	2	yes	—
384	#335	C₂³	1	2	yes	—
385	#335	C₂³	1	2	yes	—
386	#334	C₂³	1	2	yes	—
387	#334	C₂³	1	2	yes	—
388	#334	C₂³	1	2	yes	—
389	#334	C₂³	1	2	yes	—
390	#334	C₂³	1	2	yes	—
391	#334	C₂³	1	2	yes	—
392	#334	C₂³	1	2	yes	—
393	#334	C₂³	1	2	yes	—
394	#334	C₂³	1	1	yes	characteristic
395	#334	C₂³	1	2	yes	—
396	#334	C₂³	1	1	yes	characteristic
397	#334	C₂³	1	1	yes	characteristic
398	#334	C₂³	1	1	yes	characteristic
399	#334	C₂³	1	1	yes	characteristic
400	#334	C₂³	1	1	yes	characteristic
401	#334	C₂³	1	1	yes	characteristic
402	#334	C₂³	1	1	yes	characteristic
403	#334	C₂³	1	2	yes	—
404	#334	C₂³	1	2	yes	—
405	#334	C₂³	1	2	yes	—
406	C₂×#41	C₂²×C₄	1	1	yes	characteristic
407	C₂×#41	C₂²×C₄	1	1	yes	characteristic
408	C₂×#41	C₂×D₄	1	2	yes	—
409	C₂×#41	C₂×Q₈	1	2	yes	—
410	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
411	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
412	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
413	#131	—	2	4	no	—
414	#131	—	2	4	no	—
415	#131	—	4	2	no	—
416	#131	—	4	2	no	—
417	#131	—	8	4	no	—
418	C₂×M₁₆	—	2	4	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂×M₁₆	—	2	1	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	2	2	no	—
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	—	4	2	no	—
426	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
427	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
428	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
429	C₂×M₁₆	C₂²×C₄	1	2	yes	—
430	C₂×M₁₆	C₂²×C₄	1	2	yes	—
431	C₂×M₁₆	C₂²×C₄	1	2	yes	—
432	C₂×M₁₆	C₂²×C₄	1	2	yes	—
433	C₂×M₁₆	C₂²×C₄	1	2	yes	—
434	C₂×M₁₆	C₂²×C₄	1	2	yes	—
435	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
436	C₂²×C₈	—	2	2	no	—
437	C₂²×C₈	—	2	1	no	—
438	C₂²×C₈	—	2	2	no	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	—	2	2	no	—
441	C₂²×C₈	—	2	2	no	—
442	C₂²×C₈	—	2	1	no	—
443	C₂²×C₈	—	2	1	no	—
444	C₂²×C₈	—	2	1	no	—
445	C₂²×C₈	—	2	1	no	—
446	C₂²×C₈	—	2	2	no	—
447	C₂²×C₈	—	2	2	no	—
448	C₂²×C₈	—	8	2	no	—
449	C₂²×C₈	C₂²×C₄	1	2	yes	—
450	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
451	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
452	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
453	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
454	C₂²×C₈	C₂²×C₄	1	2	yes	—
455	C₂²×C₈	C₂²×C₄	1	2	yes	—
456	C₂²×C₈	C₂²×C₄	1	2	yes	—
457	C₂²×C₈	C₂²×C₄	1	2	yes	—
458	C₂²×C₈	C₂²×C₄	1	2	yes	—
459	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
460	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
461	C₄⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
462	#127	C₄⋊C₄	1	1	yes	characteristic
463	#126	C₄⋊C₄	1	2	yes	—
464	#126	C₄⋊C₄	1	2	yes	—
465	#126	C₄⋊C₄	1	2	yes	—
466	#126	C₄⋊C₄	1	2	yes	—
467	#125	C₄⋊C₄	1	2	yes	—
468	#125	C₄⋊C₄	1	2	yes	—
469	#125	C₄⋊C₄	1	1	yes	characteristic
470	#125	C₄⋊C₄	1	1	yes	characteristic
471	#124	C₄⋊C₄	1	2	yes	—
472	#124	C₄⋊C₄	1	2	yes	—
473	#124	C₄⋊C₄	1	1	yes	characteristic
474	#124	C₄⋊C₄	1	1	yes	characteristic
475	#123	C₄⋊C₄	1	2	yes	—
476	#123	C₄⋊C₄	1	2	yes	—
477	#123	C₄⋊C₄	1	2	yes	—
478	#123	C₄⋊C₄	1	2	yes	—
479	#123	C₄⋊C₄	1	2	yes	—
480	#123	C₄⋊C₄	1	2	yes	—
481	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
482	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
483	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
484	C₂²⋊Q₈	C₄⋊C₄	1	1	yes	characteristic
485	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
486	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
487	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
488	C₂²⋊Q₈	C₄⋊C₄	1	2	yes	—
489	#121	C₄⋊C₄	1	1	yes	characteristic
490	#121	C₄⋊C₄	1	1	yes	characteristic
491	#121	C₄⋊C₄	1	1	yes	characteristic
492	#121	C₄⋊C₄	1	1	yes	characteristic
493	#121	C₄⋊C₄	1	2	yes	—
494	#121	C₄⋊C₄	1	2	yes	—
495	#121	C₄⋊C₄	1	2	yes	—
496	#121	C₄⋊C₄	1	2	yes	—
497	#120	C₄⋊C₄	1	2	yes	—
498	#120	C₄⋊C₄	1	2	yes	—
499	C₄×Q₈	C₂²×C₄	1	2	yes	—
500	C₄×Q₈	C₂²×C₄	1	2	yes	—
501	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
502	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
503	C₄×Q₈	C₂×D₄	1	2	yes	—
504	C₄×Q₈	C₂×Q₈	1	1	yes	characteristic
505	C₄×Q₈	C₂×Q₈	1	1	yes	characteristic
506	C₄×Q₈	C₂×Q₈	1	2	yes	—
507	C₄×D₄	C₂²×C₄	1	2	yes	—
508	C₄×D₄	C₂²×C₄	1	2	yes	—
509	C₄×D₄	C₂²×C₄	1	2	yes	—
510	C₄×D₄	C₂²×C₄	1	2	yes	—
511	C₄×D₄	C₂²×C₄	1	2	yes	—
512	C₄×D₄	C₂²×C₄	1	2	yes	—
513	C₄×D₄	C₂×D₄	1	2	yes	—
514	C₄×D₄	C₂×D₄	1	2	yes	—
515	C₄×D₄	C₂×D₄	1	2	yes	—
516	C₄×D₄	C₂×D₄	1	2	yes	—
517	C₄×D₄	C₂×D₄	1	1	yes	characteristic
518	C₄×D₄	C₂×D₄	1	1	yes	characteristic
519	C₄×D₄	C₂×D₄	1	2	yes	—
520	C₄×D₄	C₂×Q₈	1	2	yes	—
521	C₄×D₄	C₂×Q₈	1	2	yes	—
522	C₄×D₄	C₂×Q₈	1	2	yes	—
523	C₄×D₄	C₂×Q₈	1	2	yes	—
524	C₄×D₄	C₂×Q₈	1	1	yes	characteristic
525	C₄×D₄	C₂×Q₈	1	1	yes	characteristic
526	C₄×D₄	C₂×Q₈	1	2	yes	—
527	#117	C₂²×C₄	1	1	yes	characteristic
528	#117	C₂²×C₄	1	1	yes	characteristic
529	#117	C₂²×C₄	1	2	yes	—
530	#117	C₂²×C₄	1	2	yes	—
531	#117	C₂×D₄	1	2	yes	—
532	#117	C₂×D₄	1	2	yes	—
533	#117	C₂×D₄	1	2	yes	—
534	#117	C₂×Q₈	1	2	yes	—
535	#117	C₂×Q₈	1	2	yes	—
536	#117	C₂×Q₈	1	2	yes	—
537	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
538	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
539	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
540	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
541	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
542	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
543	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
544	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
545	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
546	C₂×C₄²	C₂⁴	1	2	yes	—
547	C₂×C₄²	C₂⁴	1	2	yes	—
548	C₂×C₄²	C₂⁴	1	1	yes	characteristic
549	C₂×C₄²	C₂⁴	1	1	yes	characteristic
550	C₂×C₄²	C₂⁴	1	1	yes	characteristic
551	C₄⋊C₈	—	2	2	no	—
552	C₄⋊C₈	—	2	1	no	—
553	C₄⋊C₈	—	2	2	no	—
554	C₄⋊C₈	—	2	1	no	—
555	C₄⋊C₈	—	2	2	no	—
556	C₄⋊C₈	—	2	2	no	—
557	C₄⋊C₈	—	2	1	no	—
558	C₄⋊C₈	—	2	1	no	—
559	C₄⋊C₈	—	2	1	no	—
560	C₄⋊C₈	—	2	1	no	—
561	C₄⋊C₈	—	2	2	no	—
562	C₄⋊C₈	—	2	2	no	—
563	C₄⋊C₈	—	2	1	no	—
564	C₄⋊C₈	—	2	2	no	—
565	C₄⋊C₈	—	2	2	no	—
566	C₄⋊C₈	—	2	1	no	—
567	C₄⋊C₈	—	2	2	no	—
568	C₄⋊C₈	—	2	2	no	—
569	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
570	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
571	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
572	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
573	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
574	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
575	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
576	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
577	C₄⋊C₈	C₂²×C₄	1	2	yes	—
578	C₄⋊C₈	C₂²×C₄	1	2	yes	—
579	C₄⋊C₈	C₂²×C₄	1	2	yes	—
580	C₄⋊C₈	C₂²×C₄	1	2	yes	—
581	C₄⋊C₈	C₂²×C₄	1	2	yes	—
582	C₄⋊C₈	C₂²×C₄	1	2	yes	—
583	C₄⋊C₈	C₂²×C₄	1	2	yes	—
584	C₄⋊C₈	C₂²×C₄	1	2	yes	—
585	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
586	C₄⋊C₈	C₂⁴	1	2	yes	—
587	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
588	C₄⋊C₈	C₂⁴	1	2	yes	—
589	C₄⋊C₈	C₂⁴	1	2	yes	—
590	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
591	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
592	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
593	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
594	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
595	C₄⋊C₈	C₂⁴	1	2	yes	—
596	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
597	C₂²⋊C₈	—	2	1	no	—
598	C₂²⋊C₈	—	2	1	no	—
599	C₂²⋊C₈	—	2	2	no	—
600	C₂²⋊C₈	—	2	1	no	—
601	C₂²⋊C₈	—	2	1	no	—
602	C₂²⋊C₈	—	2	2	no	—
603	C₂²⋊C₈	—	2	1	no	—
604	C₂²⋊C₈	—	2	1	no	—
605	C₂²⋊C₈	—	2	1	no	—
606	C₂²⋊C₈	—	2	1	no	—
607	C₂²⋊C₈	—	2	2	no	—
608	C₂²⋊C₈	—	2	2	no	—
609	C₂²⋊C₈	—	2	2	no	—
610	C₂²⋊C₈	—	2	2	no	—
611	C₂²⋊C₈	—	2	2	no	—
612	C₂²⋊C₈	—	2	2	no	—
613	C₂²⋊C₈	—	2	2	no	—
614	C₂²⋊C₈	—	2	2	no	—
615	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
616	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
617	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
618	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
619	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
620	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
621	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
622	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
623	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
624	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
625	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
626	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
627	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
628	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
629	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
630	C₂²⋊C₈	C₂²×C₄	1	2	yes	—
631	#97	—	2	2	no	—
632	#97	—	2	2	no	—
633	#97	—	2	1	no	—
634	#97	—	2	1	no	—
635	#97	—	2	2	no	—
636	#97	—	2	2	no	—
637	#97	—	2	2	no	—
638	#97	—	2	2	no	—
639	#97	C₂²×C₄	1	2	yes	—
640	#97	C₂²×C₄	1	2	yes	—
641	#97	C₂²×C₄	1	2	yes	—
642	#97	C₂²×C₄	1	2	yes	—
643	#97	C₂²×C₄	1	2	yes	—
644	#97	C₂²×C₄	1	2	yes	—
645	#97	C₂²×C₄	1	2	yes	—
646	#97	C₂²×C₄	1	2	yes	—
647	C₄×C₈	—	2	1	no	—
648	C₄×C₈	—	2	1	no	—
649	C₄×C₈	—	2	1	no	—
650	C₄×C₈	—	2	1	no	—
651	C₄×C₈	—	2	1	no	—
652	C₄×C₈	—	2	1	no	—
653	C₄×C₈	—	2	2	no	—
654	C₄×C₈	—	2	2	no	—
655	C₄×C₈	—	2	2	no	—
656	C₄×C₈	—	2	2	no	—
657	C₄×C₈	C₂²×C₄	1	2	yes	—
658	C₄×C₈	C₂²×C₄	1	2	yes	—
659	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
660	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
661	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
662	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
663	C₄×C₈	C₂²×C₄	1	2	yes	—
664	C₄×C₈	C₂²×C₄	1	2	yes	—
665	C₄×C₈	C₂²×C₄	1	2	yes	—
666	C₄×C₈	C₂²×C₄	1	2	yes	—
667	C₄×C₈	C₂⁴	1	2	yes	—
668	C₄×C₈	C₂⁴	1	1	yes	characteristic
669	C₄×C₈	C₂⁴	1	1	yes	characteristic
670	C₄×C₈	C₂⁴	1	2	yes	—
671	C₄×C₈	C₂⁴	1	1	yes	characteristic
672	C₄×C₈	C₂⁴	1	1	yes	characteristic
673	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
674	#41	—	2	2	no	—
675	#41	—	2	2	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	2	no	—
680	#41	—	4	4	no	—
681	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
682	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
683	C₂×Q₈	C₂×C₄⋊C₄	1	2	yes	—
684	C₂×Q₈	C₂×C₄⋊C₄	1	2	yes	—
685	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
686	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
687	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
688	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
689	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
690	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
691	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
692	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
693	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
694	C₂×D₄	C₂×C₄⋊C₄	1	2	yes	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	4	1	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
701	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
702	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
703	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
709	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
710	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
711	C₂²×C₄	C₂³×C₄	1	2	yes	—
712	C₂²×C₄	C₂³×C₄	1	2	yes	—
713	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
714	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
715	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₄	1	2	yes	—
718	C₂²×C₄	C₂²×D₄	1	2	yes	—
719	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
720	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
721	C₂²×C₄	C₂²×Q₈	1	1	yes	characteristic
722	C₂²×C₄	C₂²×Q₈	1	2	yes	—
723	C₂²×C₄	C₂²×Q₈	1	2	yes	—
724	M₁₆	—	2	2	no	—
725	M₁₆	—	2	2	no	—
726	M₁₆	—	2	2	no	—
727	M₁₆	—	2	4	no	—
728	M₁₆	—	2	4	no	—
729	M₁₆	—	2	4	no	—
730	M₁₆	—	4	2	no	—
731	M₁₆	—	4	2	no	—
732	M₁₆	—	4	2	no	—
733	M₁₆	—	4	2	no	—
734	M₁₆	—	4	2	no	—
735	M₁₆	—	8	2	no	—
736	M₁₆	—	8	2	no	—
737	M₁₆	—	8	2	no	—
738	M₁₆	—	8	2	no	—
739	M₁₆	#131	1	4	yes	complemented
740	C₂×C₈	—	2	2	no	—
741	C₂×C₈	—	2	2	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	4	no	—
745	C₂×C₈	—	2	4	no	—
746	C₂×C₈	—	2	4	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	—	2	1	no	—
750	C₂×C₈	—	2	1	no	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	2	no	—
754	C₂×C₈	—	2	2	no	—
755	C₂×C₈	—	2	2	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	2	no	—
759	C₂×C₈	—	4	2	no	—
760	C₂×C₈	—	4	2	no	—
761	C₂×C₈	—	4	2	no	—
762	C₂×C₈	—	4	4	no	—
763	C₂×C₈	—	8	2	no	—
764	C₂×C₈	—	8	1	no	—
765	C₂×C₈	—	8	1	no	—
766	C₂×C₈	—	8	2	no	—
767	C₂×C₈	—	8	1	no	—
768	C₂×C₈	—	8	1	no	—
769	C₂×C₈	—	8	1	no	—
770	C₂×C₈	—	8	2	no	—
771	C₂×C₈	—	8	1	no	—
772	C₂×C₈	—	8	2	no	—
773	C₂×C₈	—	8	2	no	—
774	C₂×C₈	C₂³×C₄	1	2	yes	—
775	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
776	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
777	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
778	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
779	C₂×C₈	C₂³×C₄	1	2	yes	—
780	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
781	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
782	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
783	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
784	C₂×C₈	C₂³×C₄	1	2	yes	—
785	C₂×C₈	C₂³×C₄	1	2	yes	—
786	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
787	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
788	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
789	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
790	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
791	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
792	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
793	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
794	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
795	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
796	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
797	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
798	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
799	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
800	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
801	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
802	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
803	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
804	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
805	C₄⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
806	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
807	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
808	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
809	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
810	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
811	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
812	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
813	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
814	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
815	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
816	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
817	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
818	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
819	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
820	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
821	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
822	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
823	C₂²⋊C₄	C₂×C₄⋊C₄	1	2	yes	—
824	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
825	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
826	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
827	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
828	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
829	C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
830	C₄²	C₂³×C₄	1	1	yes	characteristic
831	C₄²	C₂³×C₄	1	1	yes	characteristic
832	C₄²	C₂³×C₄	1	2	yes	—
833	C₄²	C₂³×C₄	1	2	yes	—
834	C₄²	C₂³×C₄	1	1	yes	characteristic
835	C₄²	C₂²×D₄	1	1	yes	characteristic
836	C₄²	C₂²×D₄	1	1	yes	characteristic
837	C₄²	C₂²×D₄	1	2	yes	—
838	C₄²	C₂²×D₄	1	2	yes	—
839	C₄²	C₂²×D₄	1	1	yes	characteristic
840	C₄²	C₂²×Q₈	1	1	yes	characteristic
841	C₄²	C₂²×Q₈	1	1	yes	characteristic
842	C₄²	C₂²×Q₈	1	1	yes	characteristic
843	C₄²	C₂²×Q₈	1	2	yes	—
844	C₄²	C₂²×Q₈	1	2	yes	—
845	C₄²	C₂⁵	1	1	yes	characteristic
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	1	no	—
849	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
850	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
851	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
852	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
853	C₂³	C₂²×C₄⋊C₄	1	1	yes	characteristic
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	4	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	2	4	no	—
860	D₄	—	2	4	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	2	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	1	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
901	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
902	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
903	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
904	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
905	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
906	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
907	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
908	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
909	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
910	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
911	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
912	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
913	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
914	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
915	C₂×C₄	C₂×#131	1	2	yes	—
916	C₂×C₄	#568	1	2	yes	—
917	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
919	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₈	—	2	1	no	—
923	C₈	—	2	1	no	—
924	C₈	—	2	2	no	—
925	C₈	—	2	1	no	—
926	C₈	—	2	1	no	—
927	C₈	—	2	1	no	—
928	C₈	—	2	1	no	—
929	C₈	—	2	2	no	—
930	C₈	—	2	2	no	—
931	C₈	—	4	2	no	—
932	C₈	—	4	2	no	—
933	C₈	—	4	1	no	—
934	C₈	—	4	1	no	—
935	C₈	—	4	1	no	—
936	C₈	—	4	2	no	—
937	C₈	—	4	1	no	—
938	C₈	—	4	1	no	—
939	C₈	—	4	2	no	—
940	C₈	—	4	1	no	—
941	C₈	—	4	1	no	—
942	C₈	—	4	1	no	—
943	C₈	C₂×#131	1	4	yes	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	4	4	no	—
958	C₂²	#2906	1	2	yes	—
959	C₂²	#2916	1	2	yes	—
960	C₂²	C₂³×C₄⋊C₄	1	1	yes	characteristic
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	1	no	—
973	C₄	—	2	1	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	#2906	1	2	yes	—
977	C₄	C₂²×#131	1	1	yes	characteristic
978	C₄	C₂×#568	1	1	yes	characteristic
979	C₄	#3585	1	1	yes	characteristic
980	C₄	#3586	1	1	yes	characteristic
981	C₂	—	2	2	no	—
982	C₂	—	2	2	no	—
983	C₂	—	4	2	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	1	no	—
986	C₂	C₂×#2906	1	1	yes	characteristic
987	C₂	#60109	1	1	yes	characteristic
988	C₂	C₂×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂³×C₄⋊C₄
prime radical	#3444	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #3444 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #17840	C₂	semidirect
5. #17838	C₂	semidirect
6. #17836	C₂	semidirect
7. #17834	C₂	semidirect
8. #17833	C₂	semidirect
9. #17832	C₂	semidirect
10. #17831	C₂	semidirect
11. #17830	C₂	semidirect
12. #17812	C₂	semidirect
13. #17812	C₂	semidirect
14. #17811	C₂	semidirect
15. #17811	C₂	semidirect
16. #17806	C₂	semidirect
17. C₂×#1573	C₂	semidirect
18. #17799	C₂	semidirect
19. #17798	C₂	semidirect
20. #17797	C₂	semidirect
21. #17789	C₂	semidirect
22. #17788	C₂	semidirect
23. C₂×#1565	C₂	semidirect
83. #1574	C₂²	semidirect
84. #1574	C₂²	semidirect
85. #1574	C₂²	semidirect
86. #1574	C₂²	semidirect
95. #1573	C₂²	semidirect
96. #1573	C₂²	semidirect
97. #1573	C₂²	semidirect
98. #1573	C₂²	semidirect
99. #1572	C₂²	semidirect
100. #1572	C₂²	semidirect
101. #1572	C₂²	semidirect
102. #1572	C₂²	semidirect
103. #1571	C₂²	semidirect
104. #1571	C₂²	semidirect
105. #1570	C₂²	semidirect
106. #1570	C₂²	semidirect
109. #1569	C₂²	semidirect
110. #1569	C₂²	semidirect
111. #1569	C₂²	semidirect
112. #1569	C₂²	semidirect
115. #1568	C₂²	semidirect
116. #1568	C₂²	semidirect
117. #1567	C₂²	semidirect
118. #1566	C₂²	semidirect
129. #1565	C₂²	semidirect
130. #1565	C₂²	semidirect
131. #1565	C₂²	semidirect
132. #1565	C₂²	semidirect
137. #1564	C₂²	semidirect
138. #1564	C₂²	semidirect
142. C₂×#335	C₂²	semidirect
146. C₂×#334	C₂²	semidirect
739. M₁₆	#131	semidirect

Maximal subgroups

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

subgroup	index
#60294	2
#60265	2
#60210	2
#17840	2
#17838	2
#17836	2
#17834	2
#17833	2
#17832	2
#17831	2
#17830	2
#17812	2
#17811	2
#17806	2
C₂×#1573	2
#17799	2
#17798	2
#17797	2
#17789	2
#17788	2
C₂×#1565	2