Subgroups — C₆₇×#59807 #30739058

Order 17152.

2698 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2714	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2694	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2554	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2539	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2490	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2486	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2414	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2412	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2411	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2408	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2341	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	#552×C₆₇	—	2	8	no	—
27	#546×C₆₇	—	2	8	no	—
28	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×#123×C₆₇	C₂²	1	2	yes	—
34	C₂×#123×C₆₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#121×C₆₇	C₂²	1	2	yes	—
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#120×C₆₇	C₂²	1	2	yes	—
43	C₂×#120×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×#117×C₆₇	C₂²	1	2	yes	—
51	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
54	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
55	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
56	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
57	#399×C₆₇	C₂²	1	2	yes	complemented
58	#399×C₆₇	C₂²	1	2	yes	complemented
59	#398×C₆₇	C₂²	1	2	yes	complemented
60	#397×C₆₇	C₂²	1	2	yes	complemented
61	#397×C₆₇	C₂²	1	2	yes	complemented
62	#397×C₆₇	C₂²	1	2	yes	complemented
63	#396×C₆₇	C₂²	1	2	yes	complemented
64	#396×C₆₇	C₂²	1	2	yes	complemented
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	complemented
67	#394×C₆₇	C₂²	1	2	yes	complemented
68	#394×C₆₇	C₂²	1	2	yes	complemented
69	#394×C₆₇	C₂²	1	2	yes	complemented
70	#392×C₆₇	C₂²	1	2	yes	—
71	#392×C₆₇	C₂²	1	2	yes	complemented
72	#392×C₆₇	C₂²	1	2	yes	complemented
73	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#390×C₆₇	C₂²	1	2	yes	—
75	#390×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	1	yes	characteristic
77	#390×C₆₇	C₂²	1	1	yes	characteristic
78	#390×C₆₇	C₂²	1	1	yes	characteristic
79	#390×C₆₇	C₂²	1	2	yes	—
80	#390×C₆₇	C₂²	1	1	yes	characteristic
81	#390×C₆₇	C₂²	1	1	yes	characteristic
82	#390×C₆₇	C₂²	1	2	yes	complemented
83	#390×C₆₇	C₂²	1	2	yes	complemented
84	#390×C₆₇	C₂²	1	2	yes	complemented
85	#390×C₆₇	C₂²	1	2	yes	complemented
86	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#390×C₆₇	C₂²	1	2	yes	complemented
88	#390×C₆₇	C₂²	1	2	yes	complemented
89	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#388×C₆₇	C₂²	1	2	yes	complemented
95	#388×C₆₇	C₂²	1	2	yes	complemented
96	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#388×C₆₇	C₂²	1	2	yes	complemented
98	#388×C₆₇	C₂²	1	2	yes	complemented
99	#388×C₆₇	C₂²	1	2	yes	complemented
100	#388×C₆₇	C₂²	1	2	yes	complemented
101	#387×C₆₇	C₂²	1	2	yes	complemented
102	#386×C₆₇	C₂²	1	1	yes	characteristic
103	#386×C₆₇	C₂²	1	1	yes	characteristic
104	#386×C₆₇	C₂²	1	2	yes	complemented
105	#386×C₆₇	C₂²	1	2	yes	complemented
106	#385×C₆₇	C₂²	1	2	yes	—
107	#385×C₆₇	C₂²	1	2	yes	complemented
108	#385×C₆₇	C₂²	1	2	yes	complemented
109	#381×C₆₇	C₂²	1	2	yes	—
110	#380×C₆₇	C₂²	1	1	yes	characteristic
111	#380×C₆₇	C₂²	1	1	yes	characteristic
112	#380×C₆₇	C₂²	1	2	yes	complemented
113	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#380×C₆₇	C₂²	1	2	yes	complemented
116	#379×C₆₇	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
125	C₂⁵×C₆₇	C₂³	1	2	yes	—
126	C₂×#41×C₆₇	—	2	4	no	—
127	C₂×#41×C₆₇	—	2	4	no	—
128	C₂×#41×C₆₇	—	4	2	no	—
129	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	—	2	4	no	—
131	C₂²×D₄×C₆₇	—	2	4	no	—
132	C₂²×D₄×C₆₇	—	4	2	no	—
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
142	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	#126×C₆₇	—	2	8	no	—
152	#125×C₆₇	—	2	8	no	—
153	#125×C₆₇	—	2	4	no	—
154	#124×C₆₇	—	2	4	no	—
155	#123×C₆₇	—	2	8	no	—
156	#123×C₆₇	—	2	8	no	—
157	#123×C₆₇	—	4	4	no	—
158	C₂²⋊Q₈×C₆₇	—	2	4	no	—
159	C₂²⋊Q₈×C₆₇	D₄	1	8	yes	complemented
160	#121×C₆₇	—	2	4	no	—
161	#121×C₆₇	—	2	4	no	—
162	#121×C₆₇	—	2	4	no	—
163	#121×C₆₇	—	2	8	no	—
164	#121×C₆₇	—	4	2	no	—
165	#120×C₆₇	—	2	8	no	—
166	#120×C₆₇	—	4	4	no	—
167	C₄×Q₈×C₆₇	—	2	4	no	—
168	C₄×Q₈×C₆₇	—	4	2	no	—
169	C₄×D₄×C₆₇	—	2	4	no	—
170	C₄×D₄×C₆₇	—	2	4	no	—
171	C₄×D₄×C₆₇	—	2	4	no	—
172	C₄×D₄×C₆₇	—	4	2	no	—
173	#117×C₆₇	—	2	4	no	—
174	#117×C₆₇	—	2	8	no	—
175	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
197	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
198	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	—	4	2	no	—
234	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
237	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
238	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
243	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	1	yes	characteristic
247	#95×C₆₇	C₂³	1	1	yes	characteristic
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	1	yes	characteristic
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	1	yes	characteristic
252	#95×C₆₇	C₂³	1	2	yes	—
253	#95×C₆₇	C₂³	1	1	yes	characteristic
254	#95×C₆₇	C₂³	1	2	yes	—
255	#95×C₆₇	C₂³	1	2	yes	—
256	#95×C₆₇	C₂³	1	1	yes	characteristic
257	#95×C₆₇	C₂³	1	2	yes	—
258	#95×C₆₇	C₂³	1	2	yes	—
259	C₂⁴×C₆₇	—	2	4	no	—
260	C₂⁴×C₆₇	—	2	4	no	—
261	C₂⁴×C₆₇	—	2	4	no	—
262	C₂⁴×C₆₇	—	2	4	no	—
263	C₂⁴×C₆₇	—	4	2	no	—
264	C₂⁴×C₆₇	—	4	2	no	—
265	C₂⁴×C₆₇	—	4	2	no	—
266	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
267	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
270	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
271	#41×C₆₇	—	4	16	no	—
272	C₂×Q₈×C₆₇	—	2	2	no	—
273	C₂×Q₈×C₆₇	—	2	2	no	—
274	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	4	no	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	4	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	2	4	no	—
286	C₂×D₄×C₆₇	—	2	4	no	—
287	C₂×D₄×C₆₇	—	2	2	no	—
288	C₂×D₄×C₆₇	—	2	4	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	2	2	no	—
291	C₂×D₄×C₆₇	—	2	2	no	—
292	C₂×D₄×C₆₇	—	2	2	no	—
293	C₂×D₄×C₆₇	—	4	16	no	—
294	C₂×D₄×C₆₇	—	4	1	no	—
295	C₂×D₄×C₆₇	—	4	2	no	—
296	C₂×D₄×C₆₇	—	4	1	no	—
297	C₂×D₄×C₆₇	—	4	2	no	—
298	C₂×D₄×C₆₇	—	4	2	no	—
299	C₂×D₄×C₆₇	—	4	2	no	—
300	C₂×D₄×C₆₇	—	4	2	no	—
301	C₂×D₄×C₆₇	—	4	2	no	—
302	C₂×D₄×C₆₇	—	4	2	no	—
303	C₂×D₄×C₆₇	—	4	2	no	—
304	C₂×D₄×C₆₇	—	4	2	no	—
305	C₂×D₄×C₆₇	#41	1	4	yes	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	2	2	no	—
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	2	no	—
312	C₂²×C₄×C₆₇	—	2	4	no	—
313	C₂²×C₄×C₆₇	—	2	4	no	—
314	C₂²×C₄×C₆₇	—	2	2	no	—
315	C₂²×C₄×C₆₇	—	2	2	no	—
316	C₂²×C₄×C₆₇	—	2	2	no	—
317	C₂²×C₄×C₆₇	—	2	2	no	—
318	C₂²×C₄×C₆₇	—	2	2	no	—
319	C₂²×C₄×C₆₇	—	2	2	no	—
320	C₂²×C₄×C₆₇	—	2	4	no	—
321	C₂²×C₄×C₆₇	—	4	1	no	—
322	C₂²×C₄×C₆₇	—	4	1	no	—
323	C₂²×C₄×C₆₇	—	4	1	no	—
324	C₂²×C₄×C₆₇	—	4	1	no	—
325	C₂²×C₄×C₆₇	—	4	2	no	—
326	C₂²×C₄×C₆₇	—	4	2	no	—
327	C₂²×C₄×C₆₇	—	4	2	no	—
328	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
329	C₂²×C₄×C₆₇	#41	1	4	yes	complemented
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	2	no	—
350	C₄⋊C₄×C₆₇	—	2	4	no	—
351	C₄⋊C₄×C₆₇	—	2	4	no	—
352	C₄⋊C₄×C₆₇	—	2	4	no	—
353	C₄⋊C₄×C₆₇	—	2	2	no	—
354	C₄⋊C₄×C₆₇	—	2	2	no	—
355	C₄⋊C₄×C₆₇	—	2	4	no	—
356	C₄⋊C₄×C₆₇	—	2	4	no	—
357	C₄⋊C₄×C₆₇	—	2	2	no	—
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	4	1	no	—
361	C₄⋊C₄×C₆₇	—	4	2	no	—
362	C₄⋊C₄×C₆₇	—	4	1	no	—
363	C₄⋊C₄×C₆₇	—	4	2	no	—
364	C₄⋊C₄×C₆₇	—	4	2	no	—
365	C₄⋊C₄×C₆₇	—	4	2	no	—
366	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
367	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
368	C₂²⋊C₄×C₆₇	—	2	2	no	—
369	C₂²⋊C₄×C₆₇	—	2	2	no	—
370	C₂²⋊C₄×C₆₇	—	2	4	no	—
371	C₂²⋊C₄×C₆₇	—	2	4	no	—
372	C₂²⋊C₄×C₆₇	—	2	4	no	—
373	C₂²⋊C₄×C₆₇	—	2	4	no	—
374	C₂²⋊C₄×C₆₇	—	2	4	no	—
375	C₂²⋊C₄×C₆₇	—	2	4	no	—
376	C₂²⋊C₄×C₆₇	—	2	2	no	—
377	C₂²⋊C₄×C₆₇	—	2	2	no	—
378	C₂²⋊C₄×C₆₇	—	2	4	no	—
379	C₂²⋊C₄×C₆₇	—	2	4	no	—
380	C₂²⋊C₄×C₆₇	—	2	4	no	—
381	C₂²⋊C₄×C₆₇	—	2	4	no	—
382	C₂²⋊C₄×C₆₇	—	2	4	no	—
383	C₂²⋊C₄×C₆₇	—	2	4	no	—
384	C₂²⋊C₄×C₆₇	—	2	2	no	—
385	C₂²⋊C₄×C₆₇	—	2	2	no	—
386	C₂²⋊C₄×C₆₇	—	4	2	no	—
387	C₂²⋊C₄×C₆₇	—	4	2	no	—
388	C₂²⋊C₄×C₆₇	—	4	2	no	—
389	C₂²⋊C₄×C₆₇	—	4	2	no	—
390	C₂²⋊C₄×C₆₇	—	4	2	no	—
391	C₂²⋊C₄×C₆₇	—	4	1	no	—
392	C₂²⋊C₄×C₆₇	—	4	2	no	—
393	C₂²⋊C₄×C₆₇	—	4	1	no	—
394	C₂²⋊C₄×C₆₇	—	4	1	no	—
395	C₂²⋊C₄×C₆₇	—	4	1	no	—
396	C₂²⋊C₄×C₆₇	—	4	2	no	—
397	C₂²⋊C₄×C₆₇	—	4	2	no	—
398	C₂²⋊C₄×C₆₇	—	4	2	no	—
399	C₂²⋊C₄×C₆₇	—	4	2	no	—
400	C₂²⋊C₄×C₆₇	—	4	2	no	—
401	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
402	C₄²×C₆₇	—	2	4	no	—
403	C₄²×C₆₇	—	2	4	no	—
404	C₄²×C₆₇	—	2	2	no	—
405	C₄²×C₆₇	—	2	2	no	—
406	C₄²×C₆₇	—	2	2	no	—
407	C₄²×C₆₇	—	2	2	no	—
408	C₄²×C₆₇	—	4	1	no	—
409	C₄²×C₆₇	—	4	1	no	—
410	C₄²×C₆₇	—	4	2	no	—
411	C₄²×C₆₇	—	4	2	no	—
412	C₂³×C₆₇	—	2	1	no	—
413	C₂³×C₆₇	—	2	1	no	—
414	C₂³×C₆₇	—	2	1	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	2	no	—
417	C₂³×C₆₇	—	2	2	no	—
418	C₂³×C₆₇	—	2	2	no	—
419	C₂³×C₆₇	—	2	2	no	—
420	C₂³×C₆₇	—	2	2	no	—
421	C₂³×C₆₇	—	2	2	no	—
422	C₂³×C₆₇	—	2	1	no	—
423	C₂³×C₆₇	—	2	2	no	—
424	C₂³×C₆₇	—	2	1	no	—
425	C₂³×C₆₇	—	2	2	no	—
426	C₂³×C₆₇	—	2	1	no	—
427	C₂³×C₆₇	—	2	1	no	—
428	C₂³×C₆₇	—	2	1	no	—
429	C₂³×C₆₇	—	2	1	no	—
430	C₂³×C₆₇	—	2	2	no	—
431	C₂³×C₆₇	—	2	1	no	—
432	C₂³×C₆₇	—	2	2	no	—
433	C₂³×C₆₇	—	2	1	no	—
434	C₂³×C₆₇	—	2	1	no	—
435	C₂³×C₆₇	—	2	2	no	—
436	C₂³×C₆₇	—	2	1	no	—
437	C₂³×C₆₇	—	2	1	no	—
438	C₂³×C₆₇	—	2	1	no	—
439	C₂³×C₆₇	—	2	2	no	—
440	C₂³×C₆₇	—	2	1	no	—
441	C₂³×C₆₇	—	2	1	no	—
442	C₂³×C₆₇	—	2	2	no	—
443	C₂³×C₆₇	—	4	8	no	—
444	C₂³×C₆₇	—	4	8	no	—
445	C₂³×C₆₇	—	4	8	no	—
446	C₂³×C₆₇	—	4	8	no	—
447	C₂³×C₆₇	—	8	4	no	—
448	C₂³×C₆₇	—	8	4	no	—
449	C₂³×C₆₇	—	8	4	no	—
450	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
451	C₂³×C₆₇	C₂×#41	1	4	yes	—
452	C₂³×C₆₇	C₂×#41	1	2	yes	—
453	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
454	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
455	Q₈×C₆₇	—	2	8	no	—
456	D₄×C₆₇	—	2	8	no	—
457	D₄×C₆₇	—	4	8	no	—
458	D₄×C₆₇	—	4	8	no	—
459	D₄×C₆₇	—	4	4	no	—
460	D₄×C₆₇	—	4	4	no	—
461	D₄×C₆₇	—	4	4	no	—
462	D₄×C₆₇	—	4	4	no	—
463	D₄×C₆₇	—	8	4	no	—
464	D₄×C₆₇	—	8	4	no	—
465	D₄×C₆₇	—	8	4	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	2	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	8	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	2	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	1	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	4	4	no	—
514	C₂×C₄×C₆₇	—	4	8	no	—
515	C₂×C₄×C₆₇	—	4	4	no	—
516	C₂×C₄×C₆₇	—	4	8	no	—
517	C₂×C₄×C₆₇	—	4	4	no	—
518	C₂×C₄×C₆₇	—	4	4	no	—
519	C₂×C₄×C₆₇	—	8	4	no	—
520	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
521	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
522	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
525	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
526	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
527	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
528	C₂²×C₆₇	—	2	2	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	2	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	2	4	no	—
535	C₂²×C₆₇	—	2	4	no	—
536	C₂²×C₆₇	—	2	4	no	—
537	C₂²×C₆₇	—	4	2	no	—
538	C₂²×C₆₇	—	4	2	no	—
539	C₂²×C₆₇	—	4	2	no	—
540	C₂²×C₆₇	—	4	2	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	2	no	—
544	C₂²×C₆₇	—	4	1	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	2	no	—
547	C₂²×C₆₇	—	4	1	no	—
548	C₂²×C₆₇	—	4	1	no	—
549	C₂²×C₆₇	—	4	2	no	—
550	C₂²×C₆₇	—	4	1	no	—
551	C₂²×C₆₇	—	4	2	no	—
552	C₂²×C₆₇	—	4	1	no	—
553	C₂²×C₆₇	—	4	1	no	—
554	C₂²×C₆₇	—	4	1	no	—
555	C₂²×C₆₇	—	4	2	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	2	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	4	2	no	—
561	C₂²×C₆₇	—	4	1	no	—
562	C₂²×C₆₇	—	8	16	no	—
563	C₂²×C₆₇	#550	1	4	yes	—
564	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
565	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
566	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
567	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂²×C₆₇	#585	1	1	yes	characteristic
570	C₂²×C₆₇	#585	1	1	yes	characteristic
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	4	no	—
573	C₄×C₆₇	—	2	4	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	2	2	no	—
576	C₄×C₆₇	—	4	1	no	—
577	C₄×C₆₇	—	4	1	no	—
578	C₄×C₆₇	—	4	2	no	—
579	C₄×C₆₇	—	4	2	no	—
580	C₄×C₆₇	—	4	1	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	1	no	—
584	C₄×C₆₇	—	4	2	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	—	4	1	no	—
587	C₄×C₆₇	—	4	2	no	—
588	C₄×C₆₇	#546	1	4	yes	—
589	#59807	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
590	C₂×C₆₇	—	2	4	no	—
591	C₂×C₆₇	—	4	4	no	—
592	C₂×C₆₇	—	8	1	no	—
593	C₂×C₆₇	—	8	1	no	—
594	C₂×C₆₇	—	8	2	no	—
595	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
596	C₂×C₆₇	C₂×#550	1	1	yes	characteristic
597	C₂×C₆₇	#3475	1	1	yes	characteristic
598	C₂×C₆₇	#3500	1	1	yes	characteristic
599	C₂×C₆₇	#3505	1	1	yes	characteristic
600	C₂×C₆₇	#3513	1	1	yes	characteristic
601	C₂×C₆₇	#3542	1	1	yes	characteristic
602	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
603	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#2714	C₂×C₆₇	1	2	yes	complemented
605	#2694	C₂×C₆₇	1	2	yes	complemented
606	#2554	C₂×C₆₇	1	2	yes	complemented
607	#2539	C₂×C₆₇	1	2	yes	complemented
608	#2490	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#2490	C₂×C₆₇	1	2	yes	complemented
610	#2486	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#2448	C₂×C₆₇	1	1	yes	characteristic, complemented
613	#2426	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#2414	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#2412	C₂×C₆₇	1	2	yes	complemented
616	#2411	C₂×C₆₇	1	2	yes	complemented
617	#2408	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#2363	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#2342	C₂×C₆₇	1	2	yes	complemented
621	#2341	C₂×C₆₇	1	1	yes	characteristic, complemented
622	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
623	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
624	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
625	C₆₇	#59807	1	1	yes	characteristic, direct product factor, Sylow
626	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
627	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
628	#552	—	2	8	no	—
629	#546	—	2	8	no	—
630	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
631	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
632	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×#123	C₂²×C₆₇	1	2	yes	—
635	C₂×#123	C₂²×C₆₇	1	2	yes	—
636	C₂×#123	C₂²×C₆₇	1	2	yes	—
637	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
641	C₂×#121	C₂²×C₆₇	1	2	yes	—
642	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
643	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×#120	C₂²×C₆₇	1	2	yes	—
645	C₂×#120	C₂²×C₆₇	1	2	yes	—
646	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
649	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
650	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
651	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
652	C₂×#117	C₂²×C₆₇	1	2	yes	—
653	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
655	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
656	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
657	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
658	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
659	#399	C₂²×C₆₇	1	2	yes	complemented
660	#399	C₂²×C₆₇	1	2	yes	complemented
661	#398	C₂²×C₆₇	1	2	yes	complemented
662	#397	C₂²×C₆₇	1	2	yes	complemented
663	#397	C₂²×C₆₇	1	2	yes	complemented
664	#397	C₂²×C₆₇	1	2	yes	complemented
665	#396	C₂²×C₆₇	1	2	yes	complemented
666	#396	C₂²×C₆₇	1	2	yes	complemented
667	#394	C₂²×C₆₇	1	2	yes	—
668	#394	C₂²×C₆₇	1	2	yes	complemented
669	#394	C₂²×C₆₇	1	2	yes	complemented
670	#394	C₂²×C₆₇	1	2	yes	complemented
671	#394	C₂²×C₆₇	1	2	yes	complemented
672	#392	C₂²×C₆₇	1	2	yes	—
673	#392	C₂²×C₆₇	1	2	yes	complemented
674	#392	C₂²×C₆₇	1	2	yes	complemented
675	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#390	C₂²×C₆₇	1	1	yes	characteristic
677	#390	C₂²×C₆₇	1	1	yes	characteristic
678	#390	C₂²×C₆₇	1	1	yes	characteristic
679	#390	C₂²×C₆₇	1	1	yes	characteristic
680	#390	C₂²×C₆₇	1	1	yes	characteristic
681	#390	C₂²×C₆₇	1	1	yes	characteristic
682	#390	C₂²×C₆₇	1	2	yes	—
683	#390	C₂²×C₆₇	1	2	yes	—
684	#390	C₂²×C₆₇	1	2	yes	complemented
685	#390	C₂²×C₆₇	1	2	yes	complemented
686	#390	C₂²×C₆₇	1	2	yes	complemented
687	#390	C₂²×C₆₇	1	2	yes	complemented
688	#390	C₂²×C₆₇	1	2	yes	complemented
689	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#390	C₂²×C₆₇	1	2	yes	complemented
691	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	#388	C₂²×C₆₇	1	2	yes	complemented
696	#388	C₂²×C₆₇	1	2	yes	complemented
697	#388	C₂²×C₆₇	1	2	yes	complemented
698	#388	C₂²×C₆₇	1	2	yes	complemented
699	#388	C₂²×C₆₇	1	2	yes	complemented
700	#388	C₂²×C₆₇	1	2	yes	complemented
701	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#387	C₂²×C₆₇	1	2	yes	complemented
704	#386	C₂²×C₆₇	1	1	yes	characteristic
705	#386	C₂²×C₆₇	1	1	yes	characteristic
706	#386	C₂²×C₆₇	1	2	yes	complemented
707	#386	C₂²×C₆₇	1	2	yes	complemented
708	#385	C₂²×C₆₇	1	2	yes	—
709	#385	C₂²×C₆₇	1	2	yes	complemented
710	#385	C₂²×C₆₇	1	2	yes	complemented
711	#381	C₂²×C₆₇	1	2	yes	—
712	#380	C₂²×C₆₇	1	1	yes	characteristic
713	#380	C₂²×C₆₇	1	1	yes	characteristic
714	#380	C₂²×C₆₇	1	2	yes	complemented
715	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	#380	C₂²×C₆₇	1	2	yes	complemented
718	#379	C₂²×C₆₇	1	2	yes	—
719	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
722	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
723	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
724	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
726	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₂⁵	C₂³×C₆₇	1	2	yes	—
728	C₂×#41	—	2	4	no	—
729	C₂×#41	—	2	4	no	—
730	C₂×#41	—	4	2	no	—
731	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
732	C₂²×D₄	—	2	4	no	—
733	C₂²×D₄	—	2	4	no	—
734	C₂²×D₄	—	4	2	no	—
735	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
739	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
740	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
743	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
744	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
745	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
746	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
748	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
749	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
750	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
751	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
752	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
753	#126	—	2	8	no	—
754	#125	—	2	8	no	—
755	#125	—	2	4	no	—
756	#124	—	2	4	no	—
757	#123	—	2	8	no	—
758	#123	—	2	8	no	—
759	#123	—	4	4	no	—
760	C₂²⋊Q₈	—	2	4	no	—
761	C₂²⋊Q₈	D₄×C₆₇	1	8	yes	complemented
762	#121	—	2	4	no	—
763	#121	—	2	4	no	—
764	#121	—	2	4	no	—
765	#121	—	2	8	no	—
766	#121	—	4	2	no	—
767	#120	—	2	8	no	—
768	#120	—	4	4	no	—
769	C₄×Q₈	—	2	4	no	—
770	C₄×Q₈	—	4	2	no	—
771	C₄×D₄	—	2	4	no	—
772	C₄×D₄	—	2	4	no	—
773	C₄×D₄	—	2	4	no	—
774	C₄×D₄	—	4	2	no	—
775	#117	—	2	4	no	—
776	#117	—	2	8	no	—
777	C₂×C₄⋊C₄	—	2	4	no	—
778	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
787	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
790	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
798	C₂×C₂²⋊C₄	—	2	8	no	—
799	C₂×C₂²⋊C₄	—	2	8	no	—
800	C₂×C₂²⋊C₄	—	4	4	no	—
801	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
809	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
812	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
824	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
830	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
831	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
832	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
834	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
835	C₂×C₄²	—	4	2	no	—
836	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
837	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
838	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
842	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
843	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
844	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
846	#95	C₂³×C₆₇	1	2	yes	—
847	#95	C₂³×C₆₇	1	2	yes	—
848	#95	C₂³×C₆₇	1	1	yes	characteristic
849	#95	C₂³×C₆₇	1	1	yes	characteristic
850	#95	C₂³×C₆₇	1	2	yes	—
851	#95	C₂³×C₆₇	1	1	yes	characteristic
852	#95	C₂³×C₆₇	1	2	yes	—
853	#95	C₂³×C₆₇	1	1	yes	characteristic
854	#95	C₂³×C₆₇	1	2	yes	—
855	#95	C₂³×C₆₇	1	1	yes	characteristic
856	#95	C₂³×C₆₇	1	2	yes	—
857	#95	C₂³×C₆₇	1	2	yes	—
858	#95	C₂³×C₆₇	1	1	yes	characteristic
859	#95	C₂³×C₆₇	1	2	yes	—
860	#95	C₂³×C₆₇	1	2	yes	—
861	C₂⁴	—	2	4	no	—
862	C₂⁴	—	2	4	no	—
863	C₂⁴	—	2	4	no	—
864	C₂⁴	—	2	4	no	—
865	C₂⁴	—	4	2	no	—
866	C₂⁴	—	4	2	no	—
867	C₂⁴	—	4	2	no	—
868	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
869	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
870	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
871	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
872	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
873	#41	—	4	16	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	4	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	4	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	4	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	4	16	no	—
896	C₂×D₄	—	4	1	no	—
897	C₂×D₄	—	4	2	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	1	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	#41×C₆₇	1	4	yes	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	4	no	—
911	C₂²×C₄	—	2	4	no	—
912	C₂²×C₄	—	2	4	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	4	no	—
915	C₂²×C₄	—	2	4	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	4	no	—
923	C₂²×C₄	—	4	1	no	—
924	C₂²×C₄	—	4	1	no	—
925	C₂²×C₄	—	4	2	no	—
926	C₂²×C₄	—	4	1	no	—
927	C₂²×C₄	—	4	1	no	—
928	C₂²×C₄	—	4	2	no	—
929	C₂²×C₄	—	4	2	no	—
930	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
931	C₂²×C₄	#41×C₆₇	1	4	yes	complemented
932	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	4	no	—
953	C₄⋊C₄	—	2	4	no	—
954	C₄⋊C₄	—	2	4	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	4	no	—
958	C₄⋊C₄	—	2	4	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	4	1	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	1	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
969	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	4	no	—
974	C₂²⋊C₄	—	2	4	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	4	no	—
977	C₂²⋊C₄	—	2	4	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	1	no	—
993	C₂²⋊C₄	—	4	1	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	1	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	1	no	—
1003	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
1004	C₄²	—	2	4	no	—
1005	C₄²	—	2	4	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	4	1	no	—
1011	C₄²	—	4	1	no	—
1012	C₄²	—	4	2	no	—
1013	C₄²	—	4	2	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	4	8	no	—
1046	C₂³	—	4	8	no	—
1047	C₂³	—	4	8	no	—
1048	C₂³	—	4	8	no	—
1049	C₂³	—	8	4	no	—
1050	C₂³	—	8	4	no	—
1051	C₂³	—	8	4	no	—
1052	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1053	C₂³	C₂×#41×C₆₇	1	4	yes	—
1054	C₂³	C₂×#41×C₆₇	1	2	yes	—
1055	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
1056	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1057	Q₈	—	2	8	no	—
1058	D₄	—	2	8	no	—
1059	D₄	—	4	8	no	—
1060	D₄	—	4	8	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	8	4	no	—
1066	D₄	—	8	4	no	—
1067	D₄	—	8	4	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	8	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	8	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	4	8	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	4	no	—
1121	C₂×C₄	—	8	4	no	—
1122	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1123	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1124	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1126	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1127	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1128	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1129	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	4	no	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	2	4	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	8	16	no	—
1165	C₂²	#550×C₆₇	1	4	yes	—
1166	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1167	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1168	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1169	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1170	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1171	C₂²	#585×C₆₇	1	1	yes	characteristic
1172	C₂²	#585×C₆₇	1	1	yes	characteristic
1173	C₄	—	2	2	no	—
1174	C₄	—	2	4	no	—
1175	C₄	—	2	4	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	#546×C₆₇	1	4	yes	—
1191	C₂	—	2	4	no	—
1192	C₂	—	4	4	no	—
1193	C₂	—	8	2	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	1	no	—
1196	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1197	C₂	C₂×#550×C₆₇	1	1	yes	characteristic
1198	C₂	C₆₇×#3475	1	1	yes	characteristic
1199	C₂	C₆₇×#3500	1	1	yes	characteristic
1200	C₂	C₆₇×#3505	1	1	yes	characteristic
1201	C₂	C₆₇×#3513	1	1	yes	characteristic
1202	C₂	C₆₇×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
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×#552×C₆₇	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#2714	C₂	semidirect
4. C₆₇×#2694	C₂	semidirect
5. C₆₇×#2554	C₂	semidirect
6. C₆₇×#2539	C₂	semidirect
7. C₆₇×#2490	C₂	semidirect
8. C₆₇×#2490	C₂	semidirect
9. C₆₇×#2486	C₂	semidirect
10. C₆₇×#2454	C₂	semidirect
11. C₆₇×#2448	C₂	semidirect
12. C₆₇×#2426	C₂	semidirect
13. C₆₇×#2414	C₂	semidirect
14. C₆₇×#2412	C₂	semidirect
15. C₆₇×#2411	C₂	semidirect
16. C₆₇×#2408	C₂	semidirect
17. C₆₇×#2407	C₂	semidirect
18. C₆₇×#2363	C₂	semidirect
19. C₆₇×#2342	C₂	semidirect
20. C₆₇×#2341	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#390×C₆₇	C₂	semidirect
28. C₂×#126×C₆₇	C₂²	semidirect
29. C₂×#125×C₆₇	C₂²	semidirect
30. C₂×#125×C₆₇	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
44. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
45. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
49. C₂×C₄×D₄×C₆₇	C₂²	semidirect
51. C₂×#117×C₆₇	C₂²	semidirect
57. #399×C₆₇	C₂²	semidirect
58. #399×C₆₇	C₂²	semidirect
59. #398×C₆₇	C₂²	semidirect
60. #397×C₆₇	C₂²	semidirect
61. #397×C₆₇	C₂²	semidirect
62. #397×C₆₇	C₂²	semidirect
63. #396×C₆₇	C₂²	semidirect
64. #396×C₆₇	C₂²	semidirect
66. #394×C₆₇	C₂²	semidirect
67. #394×C₆₇	C₂²	semidirect
68. #394×C₆₇	C₂²	semidirect
69. #394×C₆₇	C₂²	semidirect
71. #392×C₆₇	C₂²	semidirect
72. #392×C₆₇	C₂²	semidirect
73. #391×C₆₇	C₂²	semidirect
82. #390×C₆₇	C₂²	semidirect
83. #390×C₆₇	C₂²	semidirect
84. #390×C₆₇	C₂²	semidirect
85. #390×C₆₇	C₂²	semidirect
86. #390×C₆₇	C₂²	semidirect
87. #390×C₆₇	C₂²	semidirect
88. #390×C₆₇	C₂²	semidirect
89. #389×C₆₇	C₂²	semidirect
90. #389×C₆₇	C₂²	semidirect
91. #389×C₆₇	C₂²	semidirect
92. #389×C₆₇	C₂²	semidirect
93. #388×C₆₇	C₂²	semidirect
94. #388×C₆₇	C₂²	semidirect
95. #388×C₆₇	C₂²	semidirect
96. #388×C₆₇	C₂²	semidirect
97. #388×C₆₇	C₂²	semidirect
98. #388×C₆₇	C₂²	semidirect
99. #388×C₆₇	C₂²	semidirect
100. #388×C₆₇	C₂²	semidirect
101. #387×C₆₇	C₂²	semidirect
104. #386×C₆₇	C₂²	semidirect
105. #386×C₆₇	C₂²	semidirect
107. #385×C₆₇	C₂²	semidirect
108. #385×C₆₇	C₂²	semidirect
112. #380×C₆₇	C₂²	semidirect
113. #380×C₆₇	C₂²	semidirect
114. #380×C₆₇	C₂²	semidirect
115. #380×C₆₇	C₂²	semidirect
117. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
118. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
119. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
159. C₂²⋊Q₈×C₆₇	D₄	semidirect
329. C₂²×C₄×C₆₇	#41	semidirect
589. #59807	C₆₇	direct (N × H)
602. C₂×#552	C₂×C₆₇	semidirect
603. C₂×#546	C₂×C₆₇	semidirect
604. #2714	C₂×C₆₇	semidirect
605. #2694	C₂×C₆₇	semidirect
606. #2554	C₂×C₆₇	semidirect
607. #2539	C₂×C₆₇	semidirect
608. #2490	C₂×C₆₇	semidirect
609. #2490	C₂×C₆₇	semidirect
610. #2486	C₂×C₆₇	semidirect
611. #2454	C₂×C₆₇	semidirect
612. #2448	C₂×C₆₇	semidirect
613. #2426	C₂×C₆₇	semidirect
614. #2414	C₂×C₆₇	semidirect
615. #2412	C₂×C₆₇	semidirect
616. #2411	C₂×C₆₇	semidirect
617. #2408	C₂×C₆₇	semidirect
618. #2407	C₂×C₆₇	semidirect
619. #2363	C₂×C₆₇	semidirect
620. #2342	C₂×C₆₇	semidirect
621. #2341	C₂×C₆₇	semidirect
622. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
623. C₄×#121	C₂×C₆₇	semidirect
624. C₂×#390	C₂×C₆₇	semidirect
625. C₆₇	#59807	direct (N × H)
630. C₂×#126	C₂²×C₆₇	semidirect
631. C₂×#125	C₂²×C₆₇	semidirect
632. C₂×#125	C₂²×C₆₇	semidirect
638. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
646. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
647. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
651. C₂×C₄×D₄	C₂²×C₆₇	semidirect
653. C₂×#117	C₂²×C₆₇	semidirect
659. #399	C₂²×C₆₇	semidirect
660. #399	C₂²×C₆₇	semidirect
661. #398	C₂²×C₆₇	semidirect
662. #397	C₂²×C₆₇	semidirect
663. #397	C₂²×C₆₇	semidirect
664. #397	C₂²×C₆₇	semidirect
665. #396	C₂²×C₆₇	semidirect
666. #396	C₂²×C₆₇	semidirect
668. #394	C₂²×C₆₇	semidirect
669. #394	C₂²×C₆₇	semidirect
670. #394	C₂²×C₆₇	semidirect
671. #394	C₂²×C₆₇	semidirect
673. #392	C₂²×C₆₇	semidirect
674. #392	C₂²×C₆₇	semidirect
675. #391	C₂²×C₆₇	semidirect
684. #390	C₂²×C₆₇	semidirect
685. #390	C₂²×C₆₇	semidirect
686. #390	C₂²×C₆₇	semidirect
687. #390	C₂²×C₆₇	semidirect
688. #390	C₂²×C₆₇	semidirect
689. #390	C₂²×C₆₇	semidirect
690. #390	C₂²×C₆₇	semidirect
691. #389	C₂²×C₆₇	semidirect
692. #389	C₂²×C₆₇	semidirect
693. #389	C₂²×C₆₇	semidirect
694. #389	C₂²×C₆₇	semidirect
695. #388	C₂²×C₆₇	semidirect
696. #388	C₂²×C₆₇	semidirect
697. #388	C₂²×C₆₇	semidirect
698. #388	C₂²×C₆₇	semidirect
699. #388	C₂²×C₆₇	semidirect
700. #388	C₂²×C₆₇	semidirect
701. #388	C₂²×C₆₇	semidirect
702. #388	C₂²×C₆₇	semidirect
703. #387	C₂²×C₆₇	semidirect
706. #386	C₂²×C₆₇	semidirect
707. #386	C₂²×C₆₇	semidirect
709. #385	C₂²×C₆₇	semidirect
710. #385	C₂²×C₆₇	semidirect
714. #380	C₂²×C₆₇	semidirect
715. #380	C₂²×C₆₇	semidirect
716. #380	C₂²×C₆₇	semidirect
717. #380	C₂²×C₆₇	semidirect
719. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
720. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
721. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
723. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
724. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
725. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
726. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
761. C₂²⋊Q₈	D₄×C₆₇	semidirect
931. C₂²×C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₆₇	2
C₂×#546×C₆₇	2
C₆₇×#2714	2
C₆₇×#2694	2
C₆₇×#2554	2
C₆₇×#2539	2
C₆₇×#2490	2
C₆₇×#2486	2
C₆₇×#2454	2
C₆₇×#2448	2
C₆₇×#2426	2
C₆₇×#2414	2
C₆₇×#2412	2
C₆₇×#2411	2
C₆₇×#2408	2
C₆₇×#2407	2
C₆₇×#2363	2
C₆₇×#2342	2
C₆₇×#2341	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#390×C₆₇	2
#59807	67

Subgroups — C67×#59807 #30739058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59807 #30739058