Subgroups — C₆₇×#34495 #30713746

Order 17152.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2376	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2375	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2333	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2321	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2312	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2311	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2309	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2293	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	#546×C₆₇	C₄	1	16	yes	complemented
27	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	2	yes	—
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
40	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
46	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#390×C₆₇	C₂²	1	1	yes	characteristic
50	#390×C₆₇	C₂²	1	1	yes	characteristic
51	#390×C₆₇	C₂²	1	1	yes	characteristic
52	#390×C₆₇	C₂²	1	1	yes	characteristic
53	#390×C₆₇	C₂²	1	1	yes	characteristic
54	#390×C₆₇	C₂²	1	2	yes	—
55	#390×C₆₇	C₂²	1	1	yes	characteristic
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	2	yes	—
58	#390×C₆₇	C₂²	1	1	yes	characteristic
59	#390×C₆₇	C₂²	1	2	yes	complemented
60	#390×C₆₇	C₂²	1	2	yes	complemented
61	#390×C₆₇	C₂²	1	2	yes	complemented
62	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#389×C₆₇	C₂²	1	2	yes	complemented
67	#388×C₆₇	C₂²	1	1	yes	characteristic
68	#388×C₆₇	C₂²	1	1	yes	characteristic
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	—
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	complemented
75	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#388×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#388×C₆₇	C₂²	1	2	yes	complemented
78	#388×C₆₇	C₂²	1	2	yes	complemented
79	#388×C₆₇	C₂²	1	2	yes	complemented
80	#388×C₆₇	C₂²	1	2	yes	complemented
81	#388×C₆₇	C₂²	1	2	yes	complemented
82	#388×C₆₇	C₂²	1	2	yes	complemented
83	#388×C₆₇	C₂²	1	2	yes	complemented
84	#388×C₆₇	C₂²	1	2	yes	complemented
85	#388×C₆₇	C₂²	1	2	yes	complemented
86	#387×C₆₇	C₂²	1	2	yes	complemented
87	#387×C₆₇	C₂²	1	2	yes	complemented
88	#387×C₆₇	C₂²	1	2	yes	complemented
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	complemented
93	#386×C₆₇	C₂²	1	2	yes	complemented
94	#386×C₆₇	C₂²	1	2	yes	complemented
95	#386×C₆₇	C₂²	1	2	yes	complemented
96	#385×C₆₇	C₂²	1	2	yes	complemented
97	#385×C₆₇	C₂²	1	2	yes	complemented
98	#385×C₆₇	C₂²	1	2	yes	complemented
99	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#381×C₆₇	C₂²	1	2	yes	complemented
101	#380×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	2	yes	complemented
103	#380×C₆₇	C₂²	1	2	yes	complemented
104	#380×C₆₇	C₂²	1	2	yes	complemented
105	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#379×C₆₇	C₂²	1	2	yes	—
107	#379×C₆₇	C₂²	1	2	yes	—
108	#379×C₆₇	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₆₇	C₂³	1	2	yes	—
125	C₂×#41×C₆₇	—	4	2	no	—
126	C₂×#41×C₆₇	—	4	2	no	—
127	C₂×#41×C₆₇	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	—	4	2	no	—
130	C₂²×D₄×C₆₇	—	4	2	no	—
131	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
145	#124×C₆₇	C₂×C₄	1	8	yes	complemented
146	#123×C₆₇	C₂×C₄	1	16	yes	complemented
147	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
148	#121×C₆₇	C₂×C₄	1	8	yes	—
149	#121×C₆₇	C₂×C₄	1	16	yes	complemented
150	#120×C₆₇	C₂×C₄	1	16	yes	complemented
151	C₄×Q₈×C₆₇	—	4	2	no	—
152	C₄×Q₈×C₆₇	—	4	2	no	—
153	C₄×D₄×C₆₇	—	4	2	no	—
154	C₄×D₄×C₆₇	—	4	2	no	—
155	C₄×D₄×C₆₇	—	4	4	no	—
156	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
157	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
158	#117×C₆₇	—	4	2	no	—
159	#117×C₆₇	—	4	2	no	—
160	#117×C₆₇	—	4	4	no	—
161	#117×C₆₇	—	4	2	no	—
162	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
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	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
182	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	1	yes	characteristic
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	1	yes	characteristic
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	1	yes	characteristic
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	C₂⁴×C₆₇	—	4	2	no	—
250	C₂⁴×C₆₇	—	4	2	no	—
251	C₂⁴×C₆₇	—	4	2	no	—
252	C₂⁴×C₆₇	—	4	2	no	—
253	C₂⁴×C₆₇	—	4	2	no	—
254	C₂⁴×C₆₇	—	4	2	no	—
255	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
256	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
258	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
259	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
260	#41×C₆₇	—	4	16	no	—
261	C₂×Q₈×C₆₇	—	2	2	no	—
262	C₂×Q₈×C₆₇	—	2	2	no	—
263	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	2	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	4	16	no	—
269	C₂×D₄×C₆₇	—	4	2	no	—
270	C₂×D₄×C₆₇	—	4	2	no	—
271	C₂×D₄×C₆₇	—	4	2	no	—
272	C₂×D₄×C₆₇	—	4	1	no	—
273	C₂×D₄×C₆₇	—	4	1	no	—
274	C₂×D₄×C₆₇	—	4	2	no	—
275	C₂×D₄×C₆₇	—	4	2	no	—
276	C₂×D₄×C₆₇	—	4	2	no	—
277	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
278	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
279	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
280	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
281	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
282	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	2	no	—
285	C₂²×C₄×C₆₇	—	2	2	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	4	no	—
288	C₂²×C₄×C₆₇	—	4	2	no	—
289	C₂²×C₄×C₆₇	—	4	2	no	—
290	C₂²×C₄×C₆₇	—	4	2	no	—
291	C₂²×C₄×C₆₇	—	4	2	no	—
292	C₂²×C₄×C₆₇	—	4	2	no	—
293	C₂²×C₄×C₆₇	—	4	2	no	—
294	C₂²×C₄×C₆₇	—	4	2	no	—
295	C₂²×C₄×C₆₇	—	4	2	no	—
296	C₂²×C₄×C₆₇	—	4	2	no	—
297	C₂²×C₄×C₆₇	—	4	2	no	—
298	C₂²×C₄×C₆₇	—	4	2	no	—
299	C₂²×C₄×C₆₇	—	4	2	no	—
300	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
301	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
302	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
303	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	4	2	no	—
329	C₄⋊C₄×C₆₇	—	4	1	no	—
330	C₄⋊C₄×C₆₇	—	4	1	no	—
331	C₄⋊C₄×C₆₇	—	4	2	no	—
332	C₄⋊C₄×C₆₇	—	4	1	no	—
333	C₄⋊C₄×C₆₇	—	4	1	no	—
334	C₄⋊C₄×C₆₇	—	4	1	no	—
335	C₄⋊C₄×C₆₇	—	4	1	no	—
336	C₄⋊C₄×C₆₇	—	4	2	no	—
337	C₄⋊C₄×C₆₇	—	4	2	no	—
338	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
339	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
340	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	4	2	no	—
345	C₂²⋊C₄×C₆₇	—	4	2	no	—
346	C₂²⋊C₄×C₆₇	—	4	1	no	—
347	C₂²⋊C₄×C₆₇	—	4	2	no	—
348	C₂²⋊C₄×C₆₇	—	4	2	no	—
349	C₂²⋊C₄×C₆₇	—	4	2	no	—
350	C₂²⋊C₄×C₆₇	—	4	1	no	—
351	C₂²⋊C₄×C₆₇	—	4	2	no	—
352	C₂²⋊C₄×C₆₇	—	4	2	no	—
353	C₂²⋊C₄×C₆₇	—	4	2	no	—
354	C₂²⋊C₄×C₆₇	—	4	2	no	—
355	C₂²⋊C₄×C₆₇	—	4	2	no	—
356	C₂²⋊C₄×C₆₇	—	4	2	no	—
357	C₂²⋊C₄×C₆₇	—	4	1	no	—
358	C₂²⋊C₄×C₆₇	—	4	1	no	—
359	C₂²⋊C₄×C₆₇	—	4	1	no	—
360	C₂²⋊C₄×C₆₇	—	4	1	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₂²⋊C₄×C₆₇	—	4	2	no	—
364	C₂²⋊C₄×C₆₇	—	4	2	no	—
365	C₂²⋊C₄×C₆₇	—	4	2	no	—
366	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
367	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
368	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
369	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
370	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
371	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
372	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
373	C₄²×C₆₇	—	2	2	no	—
374	C₄²×C₆₇	—	2	2	no	—
375	C₄²×C₆₇	—	2	2	no	—
376	C₄²×C₆₇	—	2	2	no	—
377	C₄²×C₆₇	—	2	2	no	—
378	C₄²×C₆₇	—	4	1	no	—
379	C₄²×C₆₇	—	4	1	no	—
380	C₄²×C₆₇	—	4	1	no	—
381	C₄²×C₆₇	—	4	2	no	—
382	C₄²×C₆₇	—	4	2	no	—
383	C₄²×C₆₇	—	4	2	no	—
384	C₄²×C₆₇	—	4	2	no	—
385	C₄²×C₆₇	—	4	2	no	—
386	C₄²×C₆₇	—	4	2	no	—
387	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	1	no	—
392	C₂³×C₆₇	—	2	1	no	—
393	C₂³×C₆₇	—	2	1	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	1	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	2	1	no	—
409	C₂³×C₆₇	—	2	1	no	—
410	C₂³×C₆₇	—	2	1	no	—
411	C₂³×C₆₇	—	2	1	no	—
412	C₂³×C₆₇	—	4	8	no	—
413	C₂³×C₆₇	—	4	8	no	—
414	C₂³×C₆₇	—	4	8	no	—
415	C₂³×C₆₇	—	8	4	no	—
416	C₂³×C₆₇	—	8	4	no	—
417	C₂³×C₆₇	—	8	4	no	—
418	C₂³×C₆₇	—	8	4	no	—
419	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
420	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
421	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
422	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
423	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
424	Q₈×C₆₇	—	2	8	no	—
425	D₄×C₆₇	—	2	8	no	—
426	D₄×C₆₇	—	2	8	no	—
427	D₄×C₆₇	—	4	8	no	—
428	D₄×C₆₇	—	4	4	no	—
429	D₄×C₆₇	—	4	8	no	—
430	D₄×C₆₇	—	4	8	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	8	no	—
446	C₂×C₄×C₆₇	—	2	8	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	2	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	4	8	no	—
481	C₂×C₄×C₆₇	—	4	8	no	—
482	C₂×C₄×C₆₇	—	8	4	no	—
483	C₂×C₄×C₆₇	—	8	4	no	—
484	C₂×C₄×C₆₇	—	8	4	no	—
485	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
486	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
487	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
488	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
489	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
490	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
491	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
492	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
493	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
495	C₂²×C₆₇	—	2	2	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	2	4	no	—
498	C₂²×C₆₇	—	2	4	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	2	no	—
501	C₂²×C₆₇	—	2	4	no	—
502	C₂²×C₆₇	—	2	4	no	—
503	C₂²×C₆₇	—	2	4	no	—
504	C₂²×C₆₇	—	2	2	no	—
505	C₂²×C₆₇	—	2	4	no	—
506	C₂²×C₆₇	—	2	2	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	1	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	1	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	1	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	1	no	—
519	C₂²×C₆₇	—	4	1	no	—
520	C₂²×C₆₇	—	4	2	no	—
521	C₂²×C₆₇	—	4	2	no	—
522	C₂²×C₆₇	—	4	1	no	—
523	C₂²×C₆₇	—	8	16	no	—
524	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
525	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂²×C₆₇	#585	1	1	yes	characteristic
529	C₂²×C₆₇	#585	1	1	yes	characteristic
530	C₂²×C₆₇	#585	1	1	yes	characteristic
531	C₄×C₆₇	—	2	2	no	—
532	C₄×C₆₇	—	2	2	no	—
533	C₄×C₆₇	—	2	4	no	—
534	C₄×C₆₇	—	2	2	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	4	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	—	4	1	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	1	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	2	no	—
546	C₄×C₆₇	—	4	2	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	#518	1	4	yes	—
550	#34495	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
551	C₂×C₆₇	—	4	2	no	—
552	C₂×C₆₇	—	4	4	no	—
553	C₂×C₆₇	—	4	4	no	—
554	C₂×C₆₇	—	4	2	no	—
555	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
556	C₂×C₆₇	#3428	1	1	yes	characteristic
557	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂×C₆₇	#3546	1	1	yes	characteristic
559	C₂×C₆₇	#3551	1	1	yes	characteristic
560	C₂×C₆₇	#3558	1	1	yes	characteristic
561	C₂×C₆₇	#3562	1	1	yes	characteristic
562	C₂×#546	C₂×C₆₇	1	1	yes	characteristic
563	#2376	C₂×C₆₇	1	2	yes	complemented
564	#2375	C₂×C₆₇	1	2	yes	complemented
565	#2367	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#2363	C₂×C₆₇	1	2	yes	complemented
567	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#2357	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#2342	C₂×C₆₇	1	2	yes	complemented
572	#2341	C₂×C₆₇	1	1	yes	characteristic, complemented
573	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#2335	C₂×C₆₇	1	2	yes	complemented
575	#2333	C₂×C₆₇	1	2	yes	complemented
576	#2324	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#2323	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#2321	C₂×C₆₇	1	2	yes	complemented
579	#2312	C₂×C₆₇	1	2	yes	complemented
580	#2311	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#2309	C₂×C₆₇	1	1	yes	characteristic, complemented
582	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
585	C₆₇	#34495	1	1	yes	characteristic, direct product factor, Sylow
586	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
587	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
588	#546	C₄×C₆₇	1	16	yes	complemented
589	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×#123	C₂²×C₆₇	1	2	yes	—
591	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
592	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
593	C₂×#121	C₂²×C₆₇	1	2	yes	—
594	C₂×#120	C₂²×C₆₇	1	2	yes	—
595	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
597	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
599	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
602	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
606	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
607	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
608	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
609	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#390	C₂²×C₆₇	1	1	yes	characteristic
612	#390	C₂²×C₆₇	1	1	yes	characteristic
613	#390	C₂²×C₆₇	1	2	yes	—
614	#390	C₂²×C₆₇	1	1	yes	characteristic
615	#390	C₂²×C₆₇	1	1	yes	characteristic
616	#390	C₂²×C₆₇	1	2	yes	—
617	#390	C₂²×C₆₇	1	1	yes	characteristic
618	#390	C₂²×C₆₇	1	1	yes	characteristic
619	#390	C₂²×C₆₇	1	1	yes	characteristic
620	#390	C₂²×C₆₇	1	1	yes	characteristic
621	#390	C₂²×C₆₇	1	2	yes	complemented
622	#390	C₂²×C₆₇	1	2	yes	complemented
623	#390	C₂²×C₆₇	1	2	yes	complemented
624	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#389	C₂²×C₆₇	1	2	yes	complemented
626	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#388	C₂²×C₆₇	1	1	yes	characteristic
630	#388	C₂²×C₆₇	1	2	yes	—
631	#388	C₂²×C₆₇	1	2	yes	—
632	#388	C₂²×C₆₇	1	2	yes	—
633	#388	C₂²×C₆₇	1	2	yes	—
634	#388	C₂²×C₆₇	1	2	yes	—
635	#388	C₂²×C₆₇	1	1	yes	characteristic
636	#388	C₂²×C₆₇	1	2	yes	complemented
637	#388	C₂²×C₆₇	1	2	yes	complemented
638	#388	C₂²×C₆₇	1	2	yes	complemented
639	#388	C₂²×C₆₇	1	2	yes	complemented
640	#388	C₂²×C₆₇	1	2	yes	complemented
641	#388	C₂²×C₆₇	1	2	yes	complemented
642	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#388	C₂²×C₆₇	1	2	yes	complemented
644	#388	C₂²×C₆₇	1	2	yes	complemented
645	#388	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#388	C₂²×C₆₇	1	2	yes	complemented
647	#388	C₂²×C₆₇	1	2	yes	complemented
648	#387	C₂²×C₆₇	1	2	yes	complemented
649	#387	C₂²×C₆₇	1	2	yes	complemented
650	#387	C₂²×C₆₇	1	2	yes	complemented
651	#386	C₂²×C₆₇	1	2	yes	—
652	#386	C₂²×C₆₇	1	2	yes	—
653	#386	C₂²×C₆₇	1	2	yes	—
654	#386	C₂²×C₆₇	1	2	yes	complemented
655	#386	C₂²×C₆₇	1	2	yes	complemented
656	#386	C₂²×C₆₇	1	2	yes	complemented
657	#386	C₂²×C₆₇	1	2	yes	complemented
658	#385	C₂²×C₆₇	1	2	yes	complemented
659	#385	C₂²×C₆₇	1	2	yes	complemented
660	#385	C₂²×C₆₇	1	2	yes	complemented
661	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#381	C₂²×C₆₇	1	2	yes	complemented
663	#380	C₂²×C₆₇	1	1	yes	characteristic
664	#380	C₂²×C₆₇	1	2	yes	complemented
665	#380	C₂²×C₆₇	1	2	yes	complemented
666	#380	C₂²×C₆₇	1	2	yes	complemented
667	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
668	#379	C₂²×C₆₇	1	2	yes	—
669	#379	C₂²×C₆₇	1	2	yes	—
670	#379	C₂²×C₆₇	1	2	yes	—
671	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
674	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
677	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
678	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
679	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
680	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
681	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
682	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
683	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
685	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	C₂⁵	C₂³×C₆₇	1	2	yes	—
687	C₂×#41	—	4	2	no	—
688	C₂×#41	—	4	2	no	—
689	C₂×#41	C₂×C₄×C₆₇	1	8	yes	complemented
690	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²×D₄	—	4	2	no	—
692	C₂²×D₄	—	4	2	no	—
693	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
694	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
698	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
699	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
700	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
703	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
704	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
705	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
706	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
707	#124	C₂×C₄×C₆₇	1	8	yes	complemented
708	#123	C₂×C₄×C₆₇	1	16	yes	complemented
709	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
710	#121	C₂×C₄×C₆₇	1	8	yes	—
711	#121	C₂×C₄×C₆₇	1	16	yes	complemented
712	#120	C₂×C₄×C₆₇	1	16	yes	complemented
713	C₄×Q₈	—	4	2	no	—
714	C₄×Q₈	—	4	2	no	—
715	C₄×D₄	—	4	2	no	—
716	C₄×D₄	—	4	2	no	—
717	C₄×D₄	—	4	4	no	—
718	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
719	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
720	#117	—	4	2	no	—
721	#117	—	4	2	no	—
722	#117	—	4	4	no	—
723	#117	—	4	2	no	—
724	C₂×C₄⋊C₄	—	4	2	no	—
725	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₂²⋊C₄	—	4	4	no	—
744	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
745	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
777	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
783	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
784	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
785	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
787	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
790	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
791	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
792	#95	C₂³×C₆₇	1	1	yes	characteristic
793	#95	C₂³×C₆₇	1	1	yes	characteristic
794	#95	C₂³×C₆₇	1	2	yes	—
795	#95	C₂³×C₆₇	1	1	yes	characteristic
796	#95	C₂³×C₆₇	1	1	yes	characteristic
797	#95	C₂³×C₆₇	1	1	yes	characteristic
798	#95	C₂³×C₆₇	1	2	yes	—
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	1	yes	characteristic
801	#95	C₂³×C₆₇	1	2	yes	—
802	#95	C₂³×C₆₇	1	2	yes	—
803	#95	C₂³×C₆₇	1	2	yes	—
804	#95	C₂³×C₆₇	1	2	yes	—
805	#95	C₂³×C₆₇	1	2	yes	—
806	#95	C₂³×C₆₇	1	2	yes	—
807	#95	C₂³×C₆₇	1	2	yes	—
808	#95	C₂³×C₆₇	1	2	yes	—
809	#95	C₂³×C₆₇	1	2	yes	—
810	#95	C₂³×C₆₇	1	2	yes	—
811	C₂⁴	—	4	2	no	—
812	C₂⁴	—	4	2	no	—
813	C₂⁴	—	4	2	no	—
814	C₂⁴	—	4	2	no	—
815	C₂⁴	—	4	2	no	—
816	C₂⁴	—	4	2	no	—
817	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
818	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
820	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
821	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
822	#41	—	4	16	no	—
823	C₂×Q₈	—	2	2	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	4	16	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	1	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
840	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
841	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
842	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
843	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
844	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	4	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
863	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
864	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
865	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
866	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	4	2	no	—
891	C₄⋊C₄	—	4	2	no	—
892	C₄⋊C₄	—	4	1	no	—
893	C₄⋊C₄	—	4	1	no	—
894	C₄⋊C₄	—	4	1	no	—
895	C₄⋊C₄	—	4	1	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	1	no	—
899	C₄⋊C₄	—	4	1	no	—
900	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
901	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
902	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	1	no	—
909	C₂²⋊C₄	—	4	1	no	—
910	C₂²⋊C₄	—	4	1	no	—
911	C₂²⋊C₄	—	4	1	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	1	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	1	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
929	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
930	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
931	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
932	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
933	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
934	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	—	2	2	no	—
940	C₄²	—	4	2	no	—
941	C₄²	—	4	2	no	—
942	C₄²	—	4	2	no	—
943	C₄²	—	4	2	no	—
944	C₄²	—	4	2	no	—
945	C₄²	—	4	1	no	—
946	C₄²	—	4	1	no	—
947	C₄²	—	4	1	no	—
948	C₄²	—	4	2	no	—
949	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	4	8	no	—
975	C₂³	—	4	8	no	—
976	C₂³	—	4	8	no	—
977	C₂³	—	8	4	no	—
978	C₂³	—	8	4	no	—
979	C₂³	—	8	4	no	—
980	C₂³	—	8	4	no	—
981	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
982	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
983	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
984	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
985	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
986	Q₈	—	2	8	no	—
987	D₄	—	2	8	no	—
988	D₄	—	2	8	no	—
989	D₄	—	4	8	no	—
990	D₄	—	4	8	no	—
991	D₄	—	4	4	no	—
992	D₄	—	4	8	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	8	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	8	4	no	—
1045	C₂×C₄	—	8	4	no	—
1046	C₂×C₄	—	8	4	no	—
1047	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1048	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1049	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1050	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1051	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1052	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1053	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1054	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1055	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1056	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	4	no	—
1060	C₂²	—	2	4	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	2	4	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	8	16	no	—
1086	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1087	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1088	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1089	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1090	C₂²	#585×C₆₇	1	1	yes	characteristic
1091	C₂²	#585×C₆₇	1	1	yes	characteristic
1092	C₂²	#585×C₆₇	1	1	yes	characteristic
1093	C₄	—	2	2	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	4	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	4	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	#518×C₆₇	1	4	yes	—
1112	C₂	—	4	2	no	—
1113	C₂	—	4	4	no	—
1114	C₂	—	4	4	no	—
1115	C₂	—	4	2	no	—
1116	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
1117	C₂	C₆₇×#3428	1	1	yes	characteristic
1118	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1119	C₂	C₆₇×#3546	1	1	yes	characteristic
1120	C₂	C₆₇×#3551	1	1	yes	characteristic
1121	C₂	C₆₇×#3558	1	1	yes	characteristic
1122	C₂	C₆₇×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#546×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2376	C₂	semidirect
3. C₆₇×#2375	C₂	semidirect
4. C₆₇×#2367	C₂	semidirect
5. C₆₇×#2363	C₂	semidirect
6. C₆₇×#2362	C₂	semidirect
7. C₆₇×#2361	C₂	semidirect
8. C₆₇×#2357	C₂	semidirect
9. C₆₇×#2352	C₂	semidirect
10. C₆₇×#2342	C₂	semidirect
11. C₆₇×#2341	C₂	semidirect
12. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
13. C₆₇×#2335	C₂	semidirect
14. C₆₇×#2333	C₂	semidirect
15. C₆₇×#2324	C₂	semidirect
16. C₆₇×#2323	C₂	semidirect
17. C₆₇×#2321	C₂	semidirect
18. C₆₇×#2312	C₂	semidirect
19. C₆₇×#2311	C₂	semidirect
20. C₆₇×#2309	C₂	semidirect
21. C₄×#124×C₆₇	C₂	semidirect
22. C₆₇×#2293	C₂	semidirect
23. C₆₇×#2293	C₂	semidirect
26. #546×C₆₇	C₄	semidirect
33. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
34. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
42. C₂×#117×C₆₇	C₂²	semidirect
43. C₂×#117×C₆₇	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
47. #391×C₆₇	C₂²	semidirect
48. #391×C₆₇	C₂²	semidirect
59. #390×C₆₇	C₂²	semidirect
60. #390×C₆₇	C₂²	semidirect
61. #390×C₆₇	C₂²	semidirect
62. #389×C₆₇	C₂²	semidirect
63. #389×C₆₇	C₂²	semidirect
64. #389×C₆₇	C₂²	semidirect
65. #389×C₆₇	C₂²	semidirect
66. #389×C₆₇	C₂²	semidirect
74. #388×C₆₇	C₂²	semidirect
75. #388×C₆₇	C₂²	semidirect
76. #388×C₆₇	C₂²	semidirect
77. #388×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #388×C₆₇	C₂²	semidirect
80. #388×C₆₇	C₂²	semidirect
81. #388×C₆₇	C₂²	semidirect
82. #388×C₆₇	C₂²	semidirect
83. #388×C₆₇	C₂²	semidirect
84. #388×C₆₇	C₂²	semidirect
85. #388×C₆₇	C₂²	semidirect
86. #387×C₆₇	C₂²	semidirect
87. #387×C₆₇	C₂²	semidirect
88. #387×C₆₇	C₂²	semidirect
92. #386×C₆₇	C₂²	semidirect
93. #386×C₆₇	C₂²	semidirect
94. #386×C₆₇	C₂²	semidirect
95. #386×C₆₇	C₂²	semidirect
96. #385×C₆₇	C₂²	semidirect
97. #385×C₆₇	C₂²	semidirect
98. #385×C₆₇	C₂²	semidirect
99. #382×C₆₇	C₂²	semidirect
100. #381×C₆₇	C₂²	semidirect
102. #380×C₆₇	C₂²	semidirect
103. #380×C₆₇	C₂²	semidirect
104. #380×C₆₇	C₂²	semidirect
105. #380×C₆₇	C₂²	semidirect
109. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
110. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
111. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
112. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
113. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
115. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
123. C₄³×C₆₇	C₂²	semidirect
127. C₂×#41×C₆₇	C₂×C₄	semidirect
131. C₂²×D₄×C₆₇	C₂×C₄	semidirect
145. #124×C₆₇	C₂×C₄	semidirect
146. #123×C₆₇	C₂×C₄	semidirect
147. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
149. #121×C₆₇	C₂×C₄	semidirect
150. #120×C₆₇	C₂×C₄	semidirect
156. C₄×D₄×C₆₇	C₂×C₄	semidirect
157. C₄×D₄×C₆₇	C₂×C₄	semidirect
182. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
550. #34495	C₆₇	direct (N × H)
563. #2376	C₂×C₆₇	semidirect
564. #2375	C₂×C₆₇	semidirect
565. #2367	C₂×C₆₇	semidirect
566. #2363	C₂×C₆₇	semidirect
567. #2362	C₂×C₆₇	semidirect
568. #2361	C₂×C₆₇	semidirect
569. #2357	C₂×C₆₇	semidirect
570. #2352	C₂×C₆₇	semidirect
571. #2342	C₂×C₆₇	semidirect
572. #2341	C₂×C₆₇	semidirect
573. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
574. #2335	C₂×C₆₇	semidirect
575. #2333	C₂×C₆₇	semidirect
576. #2324	C₂×C₆₇	semidirect
577. #2323	C₂×C₆₇	semidirect
578. #2321	C₂×C₆₇	semidirect
579. #2312	C₂×C₆₇	semidirect
580. #2311	C₂×C₆₇	semidirect
581. #2309	C₂×C₆₇	semidirect
582. C₄×#124	C₂×C₆₇	semidirect
583. #2293	C₂×C₆₇	semidirect
584. #2293	C₂×C₆₇	semidirect
585. C₆₇	#34495	direct (N × H)
588. #546	C₄×C₆₇	semidirect
595. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
596. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
601. C₂×C₄×D₄	C₂²×C₆₇	semidirect
604. C₂×#117	C₂²×C₆₇	semidirect
605. C₂×#117	C₂²×C₆₇	semidirect
606. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
609. #391	C₂²×C₆₇	semidirect
610. #391	C₂²×C₆₇	semidirect
621. #390	C₂²×C₆₇	semidirect
622. #390	C₂²×C₆₇	semidirect
623. #390	C₂²×C₆₇	semidirect
624. #389	C₂²×C₆₇	semidirect
625. #389	C₂²×C₆₇	semidirect
626. #389	C₂²×C₆₇	semidirect
627. #389	C₂²×C₆₇	semidirect
628. #389	C₂²×C₆₇	semidirect
636. #388	C₂²×C₆₇	semidirect
637. #388	C₂²×C₆₇	semidirect
638. #388	C₂²×C₆₇	semidirect
639. #388	C₂²×C₆₇	semidirect
640. #388	C₂²×C₆₇	semidirect
641. #388	C₂²×C₆₇	semidirect
642. #388	C₂²×C₆₇	semidirect
643. #388	C₂²×C₆₇	semidirect
644. #388	C₂²×C₆₇	semidirect
645. #388	C₂²×C₆₇	semidirect
646. #388	C₂²×C₆₇	semidirect
647. #388	C₂²×C₆₇	semidirect
648. #387	C₂²×C₆₇	semidirect
649. #387	C₂²×C₆₇	semidirect
650. #387	C₂²×C₆₇	semidirect
654. #386	C₂²×C₆₇	semidirect
655. #386	C₂²×C₆₇	semidirect
656. #386	C₂²×C₆₇	semidirect
657. #386	C₂²×C₆₇	semidirect
658. #385	C₂²×C₆₇	semidirect
659. #385	C₂²×C₆₇	semidirect
660. #385	C₂²×C₆₇	semidirect
661. #382	C₂²×C₆₇	semidirect
662. #381	C₂²×C₆₇	semidirect
664. #380	C₂²×C₆₇	semidirect
665. #380	C₂²×C₆₇	semidirect
666. #380	C₂²×C₆₇	semidirect
667. #380	C₂²×C₆₇	semidirect
671. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
672. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
673. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
674. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
675. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
677. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
678. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
679. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
680. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
681. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
682. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
683. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
684. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
685. C₄³	C₂²×C₆₇	semidirect
689. C₂×#41	C₂×C₄×C₆₇	semidirect
693. C₂²×D₄	C₂×C₄×C₆₇	semidirect
707. #124	C₂×C₄×C₆₇	semidirect
708. #123	C₂×C₄×C₆₇	semidirect
709. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
711. #121	C₂×C₄×C₆₇	semidirect
712. #120	C₂×C₄×C₆₇	semidirect
718. C₄×D₄	C₂×C₄×C₆₇	semidirect
719. C₄×D₄	C₂×C₄×C₆₇	semidirect
744. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₆₇	2
C₆₇×#2376	2
C₆₇×#2375	2
C₆₇×#2367	2
C₆₇×#2363	2
C₆₇×#2362	2
C₆₇×#2361	2
C₆₇×#2357	2
C₆₇×#2352	2
C₆₇×#2342	2
C₆₇×#2341	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2335	2
C₆₇×#2333	2
C₆₇×#2324	2
C₆₇×#2323	2
C₆₇×#2321	2
C₆₇×#2312	2
C₆₇×#2311	2
C₆₇×#2309	2
C₄×#124×C₆₇	2
C₆₇×#2293	2
#34495	67

Subgroups — C67×#34495 #30713746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34495 #30713746