Subgroups — C₆₇×#59830 #30739081

Order 17152.

2274 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2734	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2732	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2726	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2579	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2556	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2556	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2549	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2462	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2449	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2449	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2449	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2429	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2364	C₂	1	2	yes	maximal
16	C₆₇×#2360	C₂	1	2	yes	maximal, complemented
17	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
19	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#554×C₆₇	—	2	16	no	—
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
22	C₂×#125×C₆₇	C₂²	1	2	yes	—
23	C₂×#125×C₆₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#399×C₆₇	C₂²	1	2	yes	—
45	#399×C₆₇	C₂²	1	2	yes	—
46	#398×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#398×C₆₇	C₂²	1	2	yes	—
49	#398×C₆₇	C₂²	1	2	yes	—
50	#398×C₆₇	C₂²	1	2	yes	—
51	#398×C₆₇	C₂²	1	2	yes	—
52	#396×C₆₇	C₂²	1	2	yes	—
53	#396×C₆₇	C₂²	1	2	yes	—
54	#396×C₆₇	C₂²	1	2	yes	—
55	#396×C₆₇	C₂²	1	2	yes	—
56	#395×C₆₇	C₂²	1	2	yes	—
57	#395×C₆₇	C₂²	1	2	yes	—
58	#395×C₆₇	C₂²	1	2	yes	—
59	#395×C₆₇	C₂²	1	2	yes	—
60	#391×C₆₇	C₂²	1	2	yes	—
61	#391×C₆₇	C₂²	1	2	yes	—
62	#391×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	2	yes	—
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	1	yes	characteristic
68	#389×C₆₇	C₂²	1	2	yes	—
69	#389×C₆₇	C₂²	1	1	yes	characteristic
70	#389×C₆₇	C₂²	1	2	yes	—
71	#389×C₆₇	C₂²	1	2	yes	—
72	#389×C₆₇	C₂²	1	1	yes	characteristic
73	#389×C₆₇	C₂²	1	1	yes	characteristic
74	#389×C₆₇	C₂²	1	2	yes	—
75	#389×C₆₇	C₂²	1	2	yes	—
76	#388×C₆₇	C₂²	1	2	yes	—
77	#388×C₆₇	C₂²	1	2	yes	—
78	#388×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#387×C₆₇	C₂²	1	2	yes	—
82	#387×C₆₇	C₂²	1	2	yes	—
83	#387×C₆₇	C₂²	1	2	yes	—
84	#387×C₆₇	C₂²	1	2	yes	—
85	#387×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#385×C₆₇	C₂²	1	2	yes	—
96	#385×C₆₇	C₂²	1	2	yes	—
97	#385×C₆₇	C₂²	1	2	yes	—
98	#380×C₆₇	C₂²	1	1	yes	characteristic
99	#380×C₆₇	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
106	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
107	C₂×#95×C₆₇	C₂²	1	2	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₇	—	2	8	no	—
122	#125×C₆₇	—	2	8	no	—
123	#125×C₆₇	—	2	8	no	—
124	C₂²⋊Q₈×C₆₇	—	2	8	no	—
125	C₂²⋊Q₈×C₆₇	—	2	8	no	—
126	C₂²⋊Q₈×C₆₇	—	2	8	no	—
127	C₂²⋊Q₈×C₆₇	—	2	8	no	—
128	C₂²⋊Q₈×C₆₇	—	2	8	no	—
129	C₂²⋊Q₈×C₆₇	—	2	8	no	—
130	C₂²⋊Q₈×C₆₇	—	4	4	no	—
131	C₂²⋊Q₈×C₆₇	D₄	1	8	yes	complemented
132	#121×C₆₇	Q₈	1	8	yes	complemented
133	C₄×Q₈×C₆₇	—	2	8	no	—
134	C₄×Q₈×C₆₇	—	4	2	no	—
135	C₄×D₄×C₆₇	—	2	8	no	—
136	C₄×D₄×C₆₇	—	2	8	no	—
137	C₄×D₄×C₆₇	—	2	8	no	—
138	C₄×D₄×C₆₇	—	4	2	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
140	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
141	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
142	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	—	4	2	no	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
219	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂×Q₈×C₆₇	—	2	4	no	—
221	C₂×Q₈×C₆₇	—	2	4	no	—
222	C₂×Q₈×C₆₇	—	2	4	no	—
223	C₂×Q₈×C₆₇	—	4	1	no	—
224	C₂×Q₈×C₆₇	—	4	2	no	—
225	C₂×Q₈×C₆₇	—	4	1	no	—
226	C₂×Q₈×C₆₇	—	4	2	no	—
227	C₂×Q₈×C₆₇	—	4	2	no	—
228	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	4	no	—
231	C₂×D₄×C₆₇	—	4	1	no	—
232	C₂×D₄×C₆₇	—	4	1	no	—
233	C₂×D₄×C₆₇	C₂×Q₈	1	8	yes	—
234	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	2	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	4	1	no	—
246	C₂²×C₄×C₆₇	—	4	1	no	—
247	C₂²×C₄×C₆₇	—	4	1	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	1	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	2	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
258	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	4	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	4	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	2	4	no	—
293	C₄⋊C₄×C₆₇	—	2	4	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	4	1	no	—
296	C₄⋊C₄×C₆₇	—	4	1	no	—
297	C₄⋊C₄×C₆₇	—	4	1	no	—
298	C₄⋊C₄×C₆₇	—	4	1	no	—
299	C₄⋊C₄×C₆₇	—	4	2	no	—
300	C₄⋊C₄×C₆₇	—	4	2	no	—
301	C₄⋊C₄×C₆₇	—	4	1	no	—
302	C₄⋊C₄×C₆₇	—	4	1	no	—
303	C₄⋊C₄×C₆₇	—	4	2	no	—
304	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
305	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
307	C₄⋊C₄×C₆₇	#41	1	4	yes	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
320	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
321	C₄²×C₆₇	—	2	4	no	—
322	C₄²×C₆₇	—	2	4	no	—
323	C₄²×C₆₇	—	2	4	no	—
324	C₄²×C₆₇	—	2	2	no	—
325	C₄²×C₆₇	—	2	2	no	—
326	C₄²×C₆₇	—	4	1	no	—
327	C₄²×C₆₇	—	4	1	no	—
328	C₄²×C₆₇	—	4	2	no	—
329	C₄²×C₆₇	—	4	2	no	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	—	2	1	no	—
333	C₂³×C₆₇	—	2	1	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	2	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
341	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
342	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
343	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
344	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
345	Q₈×C₆₇	—	4	4	no	—
346	Q₈×C₆₇	—	4	8	no	—
347	Q₈×C₆₇	—	8	4	no	—
348	D₄×C₆₇	—	2	16	no	—
349	D₄×C₆₇	—	4	4	no	—
350	C₂×C₄×C₆₇	—	2	8	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	1	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	4	4	no	—
393	C₂×C₄×C₆₇	—	4	4	no	—
394	C₂×C₄×C₆₇	—	4	8	no	—
395	C₂×C₄×C₆₇	—	4	8	no	—
396	C₂×C₄×C₆₇	—	8	4	no	—
397	C₂×C₄×C₆₇	—	8	4	no	—
398	C₂×C₄×C₆₇	—	8	4	no	—
399	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
401	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
402	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
404	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
405	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
406	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
407	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
408	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	2	2	no	—
412	C₂²×C₆₇	—	2	2	no	—
413	C₂²×C₆₇	—	2	2	no	—
414	C₂²×C₆₇	—	2	2	no	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	4	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	D₄×Q₈	1	4	yes	—
423	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
424	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
425	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂²×C₆₇	#585	1	1	yes	characteristic
429	C₂²×C₆₇	#585	1	1	yes	characteristic
430	C₄×C₆₇	—	2	4	no	—
431	C₄×C₆₇	—	2	4	no	—
432	C₄×C₆₇	—	2	4	no	—
433	C₄×C₆₇	—	2	2	no	—
434	C₄×C₆₇	—	2	2	no	—
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	2	4	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	#59830	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
448	C₂×C₆₇	—	2	4	no	—
449	C₂×C₆₇	—	4	4	no	—
450	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
451	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
452	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
453	C₂×C₆₇	#3492	1	1	yes	characteristic
454	C₂×C₆₇	#3496	1	1	yes	characteristic
455	C₂×C₆₇	#3501	1	1	yes	characteristic
456	C₂×C₆₇	#3553	1	1	yes	characteristic
457	C₂×#554	C₂×C₆₇	1	2	yes	complemented
458	#2734	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#2732	C₂×C₆₇	1	1	yes	characteristic, complemented
460	#2726	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2683	C₂×C₆₇	1	1	yes	characteristic, complemented
462	#2579	C₂×C₆₇	1	2	yes	complemented
463	#2556	C₂×C₆₇	1	2	yes	complemented
464	#2556	C₂×C₆₇	1	2	yes	complemented
465	#2549	C₂×C₆₇	1	2	yes	complemented
466	#2462	C₂×C₆₇	1	2	yes	complemented
467	#2449	C₂×C₆₇	1	2	yes	complemented
468	#2449	C₂×C₆₇	1	2	yes	complemented
469	#2449	C₂×C₆₇	1	2	yes	complemented
470	#2429	C₂×C₆₇	1	2	yes	complemented
471	#2364	C₂×C₆₇	1	2	yes	—
472	#2360	C₂×C₆₇	1	2	yes	complemented
473	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
474	C₄×#121	C₂×C₆₇	1	1	yes	characteristic
475	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
476	C₆₇	#59830	1	1	yes	characteristic, direct product factor, Sylow
477	#554	—	2	16	no	—
478	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
479	C₂×#125	C₂²×C₆₇	1	2	yes	—
480	C₂×#125	C₂²×C₆₇	1	2	yes	—
481	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
482	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
483	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
484	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
486	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
487	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
488	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
491	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
493	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
494	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
495	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
496	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
497	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
498	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
499	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
500	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
501	#399	C₂²×C₆₇	1	2	yes	—
502	#399	C₂²×C₆₇	1	2	yes	—
503	#398	C₂²×C₆₇	1	2	yes	—
504	#398	C₂²×C₆₇	1	2	yes	—
505	#398	C₂²×C₆₇	1	2	yes	—
506	#398	C₂²×C₆₇	1	2	yes	—
507	#398	C₂²×C₆₇	1	2	yes	—
508	#398	C₂²×C₆₇	1	2	yes	—
509	#396	C₂²×C₆₇	1	2	yes	—
510	#396	C₂²×C₆₇	1	2	yes	—
511	#396	C₂²×C₆₇	1	2	yes	—
512	#396	C₂²×C₆₇	1	2	yes	—
513	#395	C₂²×C₆₇	1	2	yes	—
514	#395	C₂²×C₆₇	1	2	yes	—
515	#395	C₂²×C₆₇	1	2	yes	—
516	#395	C₂²×C₆₇	1	2	yes	—
517	#391	C₂²×C₆₇	1	2	yes	—
518	#391	C₂²×C₆₇	1	2	yes	—
519	#391	C₂²×C₆₇	1	1	yes	characteristic
520	#390	C₂²×C₆₇	1	1	yes	characteristic
521	#389	C₂²×C₆₇	1	1	yes	characteristic
522	#389	C₂²×C₆₇	1	2	yes	—
523	#389	C₂²×C₆₇	1	2	yes	—
524	#389	C₂²×C₆₇	1	1	yes	characteristic
525	#389	C₂²×C₆₇	1	1	yes	characteristic
526	#389	C₂²×C₆₇	1	2	yes	—
527	#389	C₂²×C₆₇	1	2	yes	—
528	#389	C₂²×C₆₇	1	2	yes	—
529	#389	C₂²×C₆₇	1	1	yes	characteristic
530	#389	C₂²×C₆₇	1	1	yes	characteristic
531	#389	C₂²×C₆₇	1	1	yes	characteristic
532	#389	C₂²×C₆₇	1	2	yes	—
533	#388	C₂²×C₆₇	1	2	yes	—
534	#388	C₂²×C₆₇	1	2	yes	—
535	#388	C₂²×C₆₇	1	2	yes	—
536	#387	C₂²×C₆₇	1	2	yes	—
537	#387	C₂²×C₆₇	1	2	yes	—
538	#387	C₂²×C₆₇	1	2	yes	—
539	#387	C₂²×C₆₇	1	2	yes	—
540	#387	C₂²×C₆₇	1	2	yes	—
541	#387	C₂²×C₆₇	1	2	yes	—
542	#387	C₂²×C₆₇	1	2	yes	—
543	#386	C₂²×C₆₇	1	2	yes	—
544	#386	C₂²×C₆₇	1	2	yes	—
545	#386	C₂²×C₆₇	1	2	yes	—
546	#386	C₂²×C₆₇	1	2	yes	—
547	#386	C₂²×C₆₇	1	2	yes	—
548	#385	C₂²×C₆₇	1	2	yes	—
549	#385	C₂²×C₆₇	1	2	yes	—
550	#385	C₂²×C₆₇	1	2	yes	—
551	#385	C₂²×C₆₇	1	2	yes	—
552	#385	C₂²×C₆₇	1	2	yes	—
553	#385	C₂²×C₆₇	1	2	yes	—
554	#385	C₂²×C₆₇	1	2	yes	—
555	#380	C₂²×C₆₇	1	1	yes	characteristic
556	#380	C₂²×C₆₇	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
558	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
563	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
564	C₂×#95	C₂²×C₆₇	1	2	yes	—
565	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
566	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
567	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
569	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
572	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
573	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
574	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
576	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₄⋊Q₈	—	2	8	no	—
579	#125	—	2	8	no	—
580	#125	—	2	8	no	—
581	C₂²⋊Q₈	—	2	8	no	—
582	C₂²⋊Q₈	—	2	8	no	—
583	C₂²⋊Q₈	—	2	8	no	—
584	C₂²⋊Q₈	—	2	8	no	—
585	C₂²⋊Q₈	—	2	8	no	—
586	C₂²⋊Q₈	—	2	8	no	—
587	C₂²⋊Q₈	—	4	4	no	—
588	C₂²⋊Q₈	D₄×C₆₇	1	8	yes	complemented
589	#121	Q₈×C₆₇	1	8	yes	complemented
590	C₄×Q₈	—	2	8	no	—
591	C₄×Q₈	—	4	2	no	—
592	C₄×D₄	—	2	8	no	—
593	C₄×D₄	—	2	8	no	—
594	C₄×D₄	—	2	8	no	—
595	C₄×D₄	—	4	2	no	—
596	C₂×C₄⋊C₄	—	2	8	no	—
597	C₂×C₄⋊C₄	—	2	8	no	—
598	C₂×C₄⋊C₄	—	2	4	no	—
599	C₂×C₄⋊C₄	—	4	2	no	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄²	—	4	2	no	—
646	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
649	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
653	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	2	yes	—
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	2	yes	—
673	#95	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	2	yes	—
675	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
676	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	1	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	4	1	no	—
689	C₂×D₄	—	4	1	no	—
690	C₂×D₄	C₂×Q₈×C₆₇	1	8	yes	—
691	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	1	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	1	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
715	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	4	1	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	1	no	—
755	C₄⋊C₄	—	4	1	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
762	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
763	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
764	C₄⋊C₄	#41×C₆₇	1	4	yes	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
777	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	4	no	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	4	1	no	—
784	C₄²	—	4	1	no	—
785	C₄²	—	4	2	no	—
786	C₄²	—	4	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
798	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
799	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
800	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
801	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
802	Q₈	—	4	4	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	8	4	no	—
805	D₄	—	2	16	no	—
806	D₄	—	4	4	no	—
807	C₂×C₄	—	2	8	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	8	4	no	—
854	C₂×C₄	—	8	4	no	—
855	C₂×C₄	—	8	4	no	—
856	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
858	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
859	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
860	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
861	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
862	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
863	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
864	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
865	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	D₄×Q₈×C₆₇	1	4	yes	—
880	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
881	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
882	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
883	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
884	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
885	C₂²	#585×C₆₇	1	1	yes	characteristic
886	C₂²	#585×C₆₇	1	1	yes	characteristic
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₂	—	2	4	no	—
905	C₂	—	4	4	no	—
906	C₂	C₂×D₄×Q₈×C₆₇	1	1	yes	characteristic
907	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
908	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
909	C₂	C₆₇×#3492	1	1	yes	characteristic
910	C₂	C₆₇×#3496	1	1	yes	characteristic
911	C₂	C₆₇×#3501	1	1	yes	characteristic
912	C₂	C₆₇×#3553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#121×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₆₇	C₂	semidirect
2. C₆₇×#2734	C₂	semidirect
3. C₆₇×#2732	C₂	semidirect
4. C₆₇×#2726	C₂	semidirect
5. C₆₇×#2683	C₂	semidirect
6. C₆₇×#2579	C₂	semidirect
7. C₆₇×#2556	C₂	semidirect
8. C₆₇×#2556	C₂	semidirect
9. C₆₇×#2549	C₂	semidirect
10. C₆₇×#2462	C₂	semidirect
11. C₆₇×#2449	C₂	semidirect
12. C₆₇×#2449	C₂	semidirect
13. C₆₇×#2449	C₂	semidirect
14. C₆₇×#2429	C₂	semidirect
16. C₆₇×#2360	C₂	semidirect
17. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
19. C₂×#389×C₆₇	C₂	semidirect
131. C₂²⋊Q₈×C₆₇	D₄	semidirect
132. #121×C₆₇	Q₈	semidirect
447. #59830	C₆₇	direct (N × H)
457. C₂×#554	C₂×C₆₇	semidirect
458. #2734	C₂×C₆₇	semidirect
459. #2732	C₂×C₆₇	semidirect
460. #2726	C₂×C₆₇	semidirect
461. #2683	C₂×C₆₇	semidirect
462. #2579	C₂×C₆₇	semidirect
463. #2556	C₂×C₆₇	semidirect
464. #2556	C₂×C₆₇	semidirect
465. #2549	C₂×C₆₇	semidirect
466. #2462	C₂×C₆₇	semidirect
467. #2449	C₂×C₆₇	semidirect
468. #2449	C₂×C₆₇	semidirect
469. #2449	C₂×C₆₇	semidirect
470. #2429	C₂×C₆₇	semidirect
472. #2360	C₂×C₆₇	semidirect
473. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
475. C₂×#389	C₂×C₆₇	semidirect
476. C₆₇	#59830	direct (N × H)
588. C₂²⋊Q₈	D₄×C₆₇	semidirect
589. #121	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₆₇	2
C₆₇×#2734	2
C₆₇×#2732	2
C₆₇×#2726	2
C₆₇×#2683	2
C₆₇×#2579	2
C₆₇×#2556	2
C₆₇×#2549	2
C₆₇×#2462	2
C₆₇×#2449	2
C₆₇×#2429	2
C₆₇×#2364	2
C₆₇×#2360	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#389×C₆₇	2
#59830	67

Subgroups — C67×#59830 #30739081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59830 #30739081